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Document : 97

Title: The Connexion of the Physical Science

Author(s): Somerville, Mary

ON
THE CONNEXION
OF
THE PHYSICAL SCIENCES.
BYMRS. SOMERVILLE.
LONDON:
JOHN MURRAY, ALBEMARLE STREET.
MDCCCXXXIV.
To the Queen.
MADAM,
IF I HAVE SUCCEEDED IN MY ENDEAVOUR
TO MAKE THE LAWS BY WHICH THE MATERIAL
WORLD IS GOVERNED MORE FAMILIAR TO MY
COUNTRYWOMEN, I SHALL HAVE THE GRATIFICATION
OF THINKING, THAT THE GRACIOUS PERMISSION
TO DEDICATE MY BOOK TO YOUR MAJESTY
HAS NOT BEEN MISPLACED.
I AM,
WITH THE GREATEST RESPECT,
YOUR MAJESTY'S
OBEDIENT AND HUMBLE SERVANT,
MARY SOMERVILLE.
Royal Hospital, Chelsea,
1 Jan. 1834.

PREFACE.
THE progress of modern science, especially within
the last five years, has been remarkable for a tendency
to simplify the laws of nature, and to unite
detached branches by general principles. In
some cases identity has been proved where there
appeared to be nothing in common, as in the electric
and magnetic influences; in others, as that of
light and heat, such analogies have been pointed
out as to justify the expectation, that they will
ultimately be referred to the same agent: and in
all there exists such a bond of union, that proficiency
cannot be attained in any one without a
knowledge of others.
Although well aware that a far more extensive
illustration of these views might have been given,
the author hopes that enough has been done to
show the connexion of the physical sciences.

ERRATA.
Page
46,	line 5, for "13th," read "30th."
56, 	line 6 from bottom, for "discrepancies," read "discrepances."
57, 	for lines 3d and 4th, read "gives 1/298.33 for the compression
deduced from arcs of the meridian."
59,	Note. — The effect of local attraction on the pendulum is so great,
that it has rendered the experiments made with that instrument
for the purpose of ascertaining the compression of the earth very
uncertain. Mr. Bally, President of the Astronomical Society, has
devoted much attention to the investigation of this subject. He
finds that the experiments of Captain Foster, whose early loss is
so justly lamented, give a compression of those of Captain
Sabine give 1/288.40; the mean of the French and Russian
experiments give 1/267.23; from the mean of the whole Mr.
Bally deduces the compression to be 1/285.26; but even this is
not conclusive.
64,	line 7, for "92246700," read "95296400." — Line 8, for "ninety--
two," read "ninety-five."
Note. — If the computation be made with the more accurate parallax
8".5776, the sun's distance is 95070500 miles.
67, 	line 8, the quantity 1/1053.924, representing the compression
of Jupiter, was not deduced from Encke's comet, but from the
perturbations of Juno.
Note. — Professor Airy has recently determined the most accurate
estimation of the value of the mass of Jupiter to be 1/1048.69
deduced from the elongation of the fourth satellite: he has also
found that the mass of the whole Jovial system is 1/1048.70
showing how small a proportion the mass of the satellites bears to
that of the planet.
68, 	line 8, for "886860," read "886952."
88,	lines 7 and 8 from bottom, for "radius," read "diameter."
99,	line 7, for "poles," read "pole."
128, 	lines 1 and 2 from bottom, for "volume," and "volumes," read
"atom" and "atoms."
129, 	lines 1 and 3, for "volumes" and "volume," read "atoms"
and "atom."
132,	line 9, for "freezing," read "zero."
144,	line 11, for "1090," read "1123."
220,	line 3 from bottom, for "rays," read "images."

SECTION I.
ALL the knowledge we possess of external objects
is founded upon experience, which furnishes
facts; and the comparison of these facts establishes
relations, from which induction, the intuitive
belief that like causes will produce like
effects, leads to general laws. Thus; experience
teaches that bodies fall at the surface of the
earth with an accelerated velocity, and with a
force proportional to their masses. By comparison,
Newton proved that the force which occasions the
fall of bodies at the earth's surface, is identical
with that which retains the moon in her orbit;
and induction led him to conclude that, as the
moon is kept in her orbit by the attraction of the
earth, so the planets might be retained in their
orbits by the attraction of the sun. By such steps
he was led to the discovery of one of those powers
with which the Creator has ordained that matter
should reciprocally act upon matter.
Physical astronomy is the science which compares
and identifies the laws of motion observed on
earth with the motions that take place in the
heavens; and which traces, by an uninterrupted
chain of deduction from the great principle that
governs the universe, the revolutions and rotations
of the planets, and the oscillations of the fluids at
their surfaces; and which estimates the changes the
system has hitherto undergone, or may hereafter
experience — changes which require millions of
years for their accomplishment.
The accumulated efforts of astronomers, from
the earliest dawn of civilization, have been necessary
to establish the mechanical theory of astronomy.
The courses of the planets have been observed
for ages with a degree of perseverance that
is astonishing, if we consider the imperfection and
even the want of instruments. The real motions
of the earth have been separated from the apparent
motions of the planets; the laws of the planetary
revolutions have been discovered; and the discovery
of these laws has led to the knowledge of the
gravitation of matter. On the other hand, descending
from the principle of gravitation, every
motion in the solar system has been so completely
explained, that the account of no astronomical
phenomenon can now be transmitted to posterity
of which the laws have not been determined.
Science, regarded as the pursuit of truth, which
can only be attained by patient and unprejudiced
investigation, wherein nothing is too great to be
attempted, nothing so minute as to be justly disregarded,
must ever afford occupation of consummate
interest and subject of elevated meditation. The
contemplation of the works of creation elevates the
mind to the admiration of whatever is great and noble;
accomplishing the object of all study, — which,
in the elegant language of Sir James Mackintosh,
'is to inspire the love of truth, of wisdom, of beauty,
especially of goodness, the highest beauty, and of
that supreme and eternal Mind, which contains all
truth and wisdom, all beauty and goodness. By
the love or delightful contemplation and pursuit
of these transcendent aims, for their own sake only,
the mind of man is raised from low and perishable
objects, and prepared for those high destinies which
are appointed for all those who are capable of
them.'
The heavens afford the most sublime subject of
study which can be derived from science. The
magnitude and splendour of the objects, the inconceivable
rapidity with which they move, and
the enormous distances between them, impress the
mind with some notion of the energy that maintains
them in their motions with a durability to
which we can see no limit. Equally conspicuous
is the goodness of the great First Cause, in having
endowed man with faculties by which he can not
only appreciate the magnificence of His works,
but trace, with precision, the operation of his laws;
use the globe he inhabits as a base wherewith to
measure the magnitude and distance' of the sun
and planets, and make the diameter of the earth's
orbit the first step of a scale by which he may ascend
to the starry firmament. Such pursuits, while
they ennoble the mind, at the same time inculcate
humility, by showing that there is a barrier which
no energy, mental or physical, can ever enable us
to pass: that however profoundly we may penetrate
the depths of space, there still remain innumerable
systems, compared with which those apparently
so vast roust dwindle into insignificance,
or even become invisible; and that not only man,
but the globe he inhabits, — nay, the whole system
of which it forms so small a part, — might be annihilated,
and its extinction be unperceived in the
immensity of creation.
Although it must be acknowledged that a complete
acquaintance with physical astronomy can be
attained by those only who are well versed in the
higher branches of mathematical and mechanical
science, and that they alone can appreciate the extreme
beauty of the results, and of the means by
which these results are obtained, it is nevertheless
true that a sufficient skill in analysis to follow the
general outline, — to see the mutual dependence of
the different parts of the system, and to comprehend
by what means some of the most extraordinary
conclusions have been arrived at, — is within
the reach of many who shrink from the task, appalled
by difficulties, which, perhaps, are not more
formidable than those incident to the study of the
elements of every branch of knowledge ; and who
possibly overrate them from disregarding the distinction
between the degree of mathematical acquirement
necessary for making discoveries; and
that which is requisite for understanding what
others have done. That the study of mathematics,
and their application to astronomy, are full of interest,
will be allowed by all who have devoted their
time and attention to these pursuits; and they
only can estimate the delight of arriving at the
truths they disclose, whether,it be in the discovery
of a world or of a new property of numbers.
SECTION II.
It has been proved by Newton, that a particle
of matter, placed without the surface of a hollow
sphere, is attracted by it in the same manner as if
the mass of the hollow sphere, or the whole matter
it contains, were collected in its centre. The same
is, therefore, true of a solid sphere, which may be
supposed to consist of an infinite number of concentric
hollow spheres. This, however, is not the
case with a spheroid; but the celestial bodies are so
nearly spherical, and at such remote distances from
one another, that they attract and are attracted as
if each were a dense point situate in its centre of
gravity, — a circumstance which greatly facilitates
the investigation of their motions.
The attraction of the earth on bodies at its surface
in that latitude the square of whose sine is 1/3,
is the same as if it were a sphere; and experience
shows that bodies there fall through 16.0697 feet
in a second. The mean distance of the moon from
the earth is about sixty times the mean radius of
the earth. When the number 16.0697 is diminished
in the ratio of 1 to 3600, which is the
square of the moon's distance from the earth's
centre, it is found to be exactly the space the moon
would fall through in the first second of her descent
to the earth, were she not prevented by the
centrifugal force arising from the velocity with
which she moves in her orbit; so that the moon is
retained in her orbit by a force having the same
origin, and regulated by the same law, with that
which causes a stone to fall at the earth's surface.
The earth may, therefore, be regarded as the centre
of a force which extends to the moon; and, as experience
shows that the action and re-action of
matter are equal and contrary, the moon must attract
the earth with an equal and contrary force.
Newton proved that a body projected in space
will move in a conic section, if it be attracted by
a force directed towards a fixed point, and having
an intensity inversely as the square of the distance ;
but that any deviation from that law will cause it
to move in a curve of a different nature. Kepler
ascertained, by direct observation, that the planets
describe ellipses round the sun; and later observations
show that comets also move in conic sections:
it consequently follows that the sun attracts
all the planets and comets inversely as the square
of their distances from his centre; the sun, therefore,
is the centre of a force extending indefinitely
in space, and including all the bodies of the system
in its action.
Kepler also deduced from observation, that the
squares of the periodic times of the planets, or the
times of their revolutions round the sun, are proportional
to the cubes of their mean distances from
his centre: whence it follows that the intensity
of gravitation of all the bodies towards the sun is
the same at equal distances; consequently gravitation
is proportional to the masses, for, if the
planets and comets were at equal distances from
the sun, and left to the effects of gravity, they would
arrive at his surface at the same time. The satellites
also gravitate to their primaries according
to the same law that their primaries do to the sun.
Hence, by the law of action and re-action, each
body is itself the centre of an attractive force extending
indefinitely in space, whence proceed all
the mutual disturbances which render the celestial
motions so complicated, and their investigation so
difficult.
The gravitation of matter, directed to a centre,
and attracting directly as the mass and, inversely
as the square of the distance, does not belong to
it when considered in mass only; particle acts on
particle according to the same law when at sensible
distances from each other. If the sun acted on the
centre of the earth without attracting each of its
particles, the tides would be very much greater
than they now are; and would also, in other respects,
be very different. The gravitation of the
earth to the sun results from the gravitation of
all its particles, which, in their turn, attract the
sun in the ratio of their respective masses. There
is a reciprocal action likewise between the earth
and every particle at its surface; were this not
the case, and were any portion of the earth, however
small, to attract another portion, and not be
itself attracted, the centre of gravity of the earth
would be moved in space by this action, which is
impossible.
The forms of the planets result from the reciprocal
attraction of their component particles. A
detached fluid mass, if at rest, would assume the
form of a sphere, from the reciprocal attraction of
its particles; but if the mass revolves about an
axis, it becomes flattened at the poles, and bulges
at the equator, in consequence of the centrifugal
force arising from the velocity of rotation, — for
the centrifugal force diminishes the gravity of the
particles at the equator, and equilibrium can only
exist where these two forces are balanced by an
increase of gravity; therefore, as the attractive
force is the same in all particles at equal distances
from the centre of a sphere, the equatorial particles
would recede from the centre, till their increase in
number balanced the centrifugal force by their
attraction: consequently, the sphere would become
an oblate spheroid; and a fluid partially or entirely
covering a solid, as the ocean and atmosphere cover
the earth, must assume that form in order to remain
in equilibrio. The surface of the sea is therefore
spheroidal, and the surface of the earth only
deviates from that figure where it rises above, or
sinks below, the level of the sea; but the deviation
is so small that it is unimportant when compared
with the magnitude of the earth — for the mighty
chain of the Andes, and the yet more lofty Himalaya,
bear about the same proportion to the earth
that a grain of sand does to a globe three feet in
diameter. Such is the form of the earth and
planets; but the compression or flattening at their
poles is so small, that even Jupiter, whose rotation
is the most rapid, and therefore the most elliptical
of the planets, may, from his great distance, be
regarded as spherical. Although the planets attract
each other as if they were spheres, on account of
their distances, yet the satellites are near enough
to be sensibly affected in their motions by the
forms of their primaries. The moon, for example,
is so near the earth, that the reciprocal attraction
between each of her particles, and each of the particles
in the prominent mass at the terrestrial equator,
occasions considerable disturbances in the motions
of both bodies: for the action of the moon,
on the matter at the earth's equator, produces a
mutation in the axis of rotation, and the reaction
of that matter on the moon is the cause of a corresponding
nutation in the lunar orbit.
If a sphere, at rest in space, receive an impulse
passing through its centre of gravity, all its parts
will move with an equal velocity in a straight line;
but if the impulse does not pass through the centre
of gravity, its particles, having unequal velocities,
will have a rotatory motion at the same time that
it is translated in space. These motions are independent
of one another; so that a contrary impulse,
passing through its centre of gravity, will impede
its progress, without interfering with its rotation.
As the sun rotates about an axis, it seems probable,
if an impulse in a contrary direction has not been
given to his centre of gravity, that he moves in
space, accompanied by all those bodies which compose
the solar system — a circumstance which would
in no way interfere with their relative motions;
for, in consequence of the principle that force is
proportional to velocity, the reciprocal attractions
of a system remain the same, whether its centre of
gravity be at rest, or moving uniformly in space.
It is computed that had the earth received its motion
from a single impulse, such impulse must have
passed through a point about twenty-five miles
from its centre.
Since the motions of rotation and translation of
the planets are independent of each other, though
probably communicated by the same impulse, they
form separate subjects of investigation.
SECTION III.
A planet moves in its elliptical orbit with a velocity
varying every instant, in consequence of two
forces, one tending to the centre of the sun, and
the other in the direction of a tangent to its orbit,
arising from the primitive impulse given at the
time when it was launched into space: should the
force in the tangent cease, the planet would fall to
the sun: by its gravity; were the sun not to attract
it, the planet would fly off in the tangent. Thus,
when the planet is in aphelion, or at the point
where the orbit is farthest from the sun, his action
overcomes the planet's velocity, and brings it towards
him with such an accelerated motion, that,
at last, it overcomes the sun's attraction, and,
shooting past him, gradually decreases in velocity,
until it arrives at the aphelion where the sun's attraction
again prevails. In this motion the radii
vectores, or imaginary lines joining the centres of
the sun and the planets, pass over equal areas in
equal times.
If the planets were attracted by the sun only,
this would ever be their course; and because his
action is proportional to his mass, which is much
larger than that of all the planets put together, the
elliptical is the nearest approximation to their true
motions, which are extremely complicated, in consequence
of their mutual attraction, so that they do
not move in any known or symmetrical curve, but
in paths now approaching to, now receding from,
the elliptical form; and their radii vectores do not
describe areas exactly proportional to the time.
Thus the areas become a test of disturbing forces.
To deterinine the motion of each body, when
disturbed by all the rest, is beyond the power of
analysis; it is, therefore, necessary to estimate the
disturbing action of one planet at a time, whence
the celebrated problem of the three bodies, originally
applied to the moon, the earth, and the sun,
— namely, the masses being given of three bodies
projected from three given points, with velocities
given both in quantity and direction; and, supposing
the bodies to gravitate to one another with
forces that are directly as their masses and inversely
as the squares of the distances, to find the lines
described by these bodies, and their positions at any
given instant.
By this problem the motions of translation of all
the celestial bodies are determined. It is an extremely
difficult one, and would be infinitely more
so, if the disturbing action were not very small
when compared with the central force. As the disturbing
influence of each body may be found separately,
it is assumed that the action of the whole
system, in disturbing any one planet, is equal to
the sum of all the particular disturbances it experiences,
on the general mechanical principle, that
the sum of any number of small oscillations is
nearly equal to their simultaneous and joint effect.
On account of the reciprocal action of matter, the
stability of the system depends upon the intensity
of the primitive momentum of the planets, and the
ratio of their masses to that of the sun — for the
nature of the conic sections in which the celestial
bodies move, depends upon the velocity with which
they were first propelled in space: had that velocity
been such as to make the planets move in
orbits of unstable equilibrium, their mutual attractions
might have changed them into parabolas, or
even hyperbolas, so that the earth and planets
might, ages ago, have been sweeping far from our
sun through the abyss of space: but as the orbits
differ very little from circles, the momentum of
the planets, when projected, must have been exactly
sufficient to ensure the permanency and stability of
the system. Besides, the mass of the sun is vastly
greater than that of any planet; and as their inequalities
hear the same ratio to their elliptical motions
as their masses do to that of the sun, their
mutual disturbances only increase or diminish the
eccentricities of their orbits by very minute quantities;
consequently, the magnitude of the sun's mass
is the principal cause of the stability of the system.
There is not in the physical world a more splendid
example of the adaptation of means to the accomplishment
of the end, than is exhibited in the nice
adjustment of these forces, at once the cause of
the variety and of the order of Nature.
The mean distance of a planet from the sun is
equal to half the major axis of its orbit: if, therefore,
the planet described a circle round the sun at
its mean distance, the motion would be uniform,
and the periodic time unaltered, because the planet
would arrive at the apsides or extremities of the
major axis at the same instant, and would have the
same velocity, whether it moved in the circular or
elliptical orbit, since the curves coincide in these
points; but, in every other part, the elliptical motion
would either be faster or slower than the circular
or mean motion. The difference between the
two is called the equation of the centre, which consequently
vanishes at the apsides, and is at its
maximum ninety degrees distant from these points,
or in quadratures, where it measures the eccentricity
of the orbit, so that the place of a planet in its
elliptical orbit is obtained by adding or subtracting
the equation of the centre to or from its mean
motion.
The orbits of the planets have a very small inclination
to the plane of the ecliptic in which the
earth moves; and, on that account, astronomers refer
their motions to this plane at a given epoch as a
known and fixed position. The paths of the planets,
when their mutual disturbances are omitted, are
ellipses, nearly approaching to circles, whose planes,
slightly inclined to the ecliptic, cut it in straight
lines passing through the centre of the sun; the
points where an orbit intersects the plane of the
ecliptic are its nodes. The ascending node of the
lunar orbit, for example, is the point in which the
moon rises above the plane of the ecliptic in going
towards the north; and her descending node is that
in which she sinks below the same plane in moving
towards the south. The orbits of the recently
discovered planets deviate more from the ecliptic
than those of the ancient planets: that of Pallas,
for instance, has an inclination of 35° to it; on
which account it is more difficult to determine
their motions. These little planets have no sensible
effect in disturbing the rest, though their
own motions are rendered very irregular by the
proximity of Jupiter and Saturn.
SECTION IV.
The planets are subject to disturbances of two
kinds, both resulting from the constant operation
of their reciprocal attraction; one kind, depending
upon their positions with regard to each other,
begins from zero, increases to a maximum, decreases
and becomes zero again, when the planets
return to the same relative positions. In consequence
of these, the disturbed planet is sometimes
drawn away from the sun, sometimes brought nearer
to him; at one time it is drawn above the plane of
its orbit, at another time below it, according to the
position of the disturbing body. All such changes,
being accomplished in short periods, some in a few
months, others in years, or in hundreds of years,
are denominated Periodic Inequalities.
The inequalities of the other kind, though occasioned
likewise by the disturbing energy of the
planets, are entirely independent of their relative
positions: they depend upon the relative positions of
the orbits alone, whose forms and places in space
are altered by very minute quantities in immense
periods of time, and are, therefore, called Secular
Inequalities.
In consequence of the latter kind of disturbances,
the apsides, or extremities of the major axes of all
the orbits, have a direct but variable motion in
space, excepting those of the orbit of Venus, which
are retrograde; and the lines of the nodes move
with a variable velocity in a contrary direction. The
motions of both are extremely slow; it requires more
than 114755 years for the major axis of the earth's
orbit to accomplish a sidereal revolution, that is, to
return to the same stars; and 21067 years to
complete its tropical motion, or to return to the
same equinox. The major axis of Jupiter's orbit
requires no less than 200610 years to perform its
sidereal revolution, and 22748 years to accomplish
its tropical revolution, from the disturbing action
of Saturn alone. The periods in which the nodes
revolve are also very great. Besides these, the
inclination and eccentricity of every orbit are in a
state of perpetual but slow change. At the present
time the inclinations of all the orbits are decreasing,
but so slowly that the inclination of Jupiter's
orbit is only about six minutes less now than it
was in the age of Ptolemy. The terrestrial eccentricity
is decreasing at the rate of about 41.44
miles annually; and, if it were to decrease equably,
it would be 37527 years before the earth's
orbit became a circle. But, in the midst of all
these vicissitudes, the major axes and mean motions
of the planets remain permanently independent of
secular changes; they are so connected by Kepler's
law of the squares of the periodic times being proportional
to the cubes of the mean distances of the
planets from the sun, that one cannot vary without
affecting the other.
With the exception of these two elements, it
appears that all the bodies are in motion, and
every orbit in a state of perpetual change. Minute
as these changes are, they might be supposed
to accumulate in the course of ages sufficiently to
derange the whole order of nature, to alter the relative
positions of the planets, to put an end to the
vicissitudes of the seasons, and to bring about
collisions which would involve our whole system,
now so harmonious, in chaotic confusion. It is
natural to inquire what proof exists that nature will
be preserved from such a catastrophe? Nothing
can be known from observation, since the existence
of the human race has occupied comparatively but
a point in duration, while these vicissitudes embrace
myriads of ages. The proof is simple and convincing.
All the variations of the solar system, secular
as well as periodic, are expressed analytically by the
sines and cosines of circular arcs, which increase
with the time; and, as a sine or cosine can never
exceed the radius, but must oscillate between zero
and unity, however much the time may increase,
it follows that when the variations have, by slow
changes, accumulated, in however long a time, to
a maximum, they decrease, by the same slow
degrees, till they arrive at their smallest value, and
again begin a new course, this for ever oscillating
about a mean value. This, however, would not
be the core if the planets moved in a resisting
medium, for then both the eccentricity and the
major axes of the orbits would vary with the time,
so that the stability of the system would be ultimately
destroyed. The existence of such a fluid
is now clearly proved; and although it is so extremely
rare that hitherto its effects on the motions
of the planets have been altogether insensible,
there can be no doubt that, in the immensity of
time, it will modify the forms of the planetary
orbits, and may at last even cause the destruction
of our system, which in itself contains no principle
of decay.
Three circumstances have generally been supposed
necessary to prove the stability of the system:
the small eccentricities of the planetary orbits,
their small inclinations, and the revolutions of all
the bodies, as well planets as satellites, in the
same direction. These, however, though sufficient,
are not necessary conditions; the periodicity of the
terms in which the inequalities are expressed is
enough to assure us that, though we do not know
the extent of the limits, nor the period of that grand
cycle which probably embraces millions of years,
yet they never will exceed what is requisite for the
stability and harmony of the whole, for the preservation
of which every circumstance is so beautifully
and wonderfully adapted.
The plane of the ecliptic itself, though assumed
to be fixed at a given epoch for the convenience of
astronomical computation, is subject to a minute
secular variation of 45".7, occasioned by the reciprocal
action of the planets; but, as this is also
periodical, and cannot exceed 3°, the terrestrial
equator, which is inclined to it at an angle of about
23° 27' 34".5, will never coincide with the plane
of the ecliptic: so there never can be perpetual
spring. The rotation of the earth is uniform;
therefore day and night, summer and winter, will
continue their vicissitudes while the system endures,
or is undisturbed by foreign causes.
Yonder starry sphere
Of planets, and of fixed, in all her wheels
Resembles nearest mazes intricate,
Eccentric, intervolved, yet regular,
Then most, when most irregular they seem.
The stability of our system was established by
La Grange : 'a discovery,' says Professor Playfair,
that must render the name for ever memorable
in science, and revered by those who delight
in the contemplation of whatever is excellent and
sublime.' After Newton's discovery of the mechanical
laws of the elliptical orbits of the planets,
La Grange's discovery of their periodical inequalities
is, without doubt, the noblest truth in physical
astronomy; and, in respect of the doctrine of final
causes, it may be regarded as the greatest of all.
Notwithstanding the permanency of our system,
the secular variations in the planetary orbits would
have been extremely embarrassing to astronomers
when it became necessary to compare observations
separated by long periods. The difficulty was in
part obviated, and the principle for accomplishing
it established, by La Place; but it has since
been extended by M. Poinsot; it appears that
there exists an invariable plane passing through
the centre of gravity of the system, about which
the whole oscillates within very narrow limits, and
that this plane will always remain parallel to itself,
whatever changes time may induce in the orbits of
the planets, in the plane of the ecliptic, or even in
the law of gravitation; provided only that our system
remains unconnected with any other. The
position of the plane is determined by this property
- that if each particle in the system be multiplied
by the area described upon this plane in a given
time, by the projection of its radius vector about
the common centre of gravity of the whole, the
sum of all these products will be a maximum. La
Place found that the plane in question is inclined
to the ecliptic at an angle of nearly 1° 35' 31",
and that, in passing through the sun, and about
midway between the orbits of Jupiter and Saturn,
it may be regarded as the equator of the solar
system, dividing it into two parts, which balance
one another in all their motions. This plane of
greatest inertia, by no means peculiar to the solar
system, but existing in every system of bodies submitted
to their mutual attractions only, always
maintains a fixed position, whence the oscillations
of the system may be estimated through
unlimited time. Future astronomers will know,
from its immutability or variation, whether the
sun and his attendants are connected or not with
the other systems of the universe. Should there
be no link between them, it may be inferred, from
the rotation of the sun, that the centre of gravity
of the system situate within his mass describes a
straight line in this invariable plane or great
equator of the solar system, which, unaffected by
the changes of time, will maintain its stability
through endless ages. But if the fixed stars,
comets, or any unknown and unseen bodies, affect
our sun and planets, the nodes of this plane will
slowly recede on the plane of that immense orbit
which the sun may describe about some most distant
centre, in a period which it transcends the
powers of man to determine. There is every reason
to believe that this is the case; for it is more
than probable that, remote as the fixed stars are,
they in some degree influence our system, and
that even the invariability of this plane is relative,
only appearing fixed to creatures incapable of estimating
its minute and slow changes during the
small extent of time and space granted to the
human race. 'The development of such changes,'
as M. Poinsot justly observes, 'is similar to an
enormous curve, of which we see so small an arc
that we imagine it to be a straight line.' If we
raise our views to the whole extent of the universe,
and consider the stars, together with the sun, to
be wandering bodies, revolving about the common
centre of creation, we may then recognise in the
equatorial plane passing through the centre of
gravity of the universe, the only instance of absolute
and eternal repose.
All the periodic and secular inequalities deduced
from the law of gravitation are so perfectly confirmed
by observation, that analysis has become one
of the most certain means of discovering the planetary
irregularities, either when they are too small,
or too long in their periods, to be detected by other
methods. Jupiter and Saturn, however, exhibit
inequalities which for a long time seemed discordant
with that law. All observations, from those of the
Chinese and Arabs down to the present day, prove
that for ages the mean motions of Jupiter and
Saturn have been affected by a great inequality of
a very long period, forming an apparent anomaly
in the theory of the planets. It was long known
by observation that five times the mean motion of
Saturn is nearly equal to twice that of Jupiter; a
relation which the sagacity of La Place perceived
to be the cause of a periodic irregularity in the
mean motion of each of these planets, which completes
its period in nearly 929 years, the one being
retarded while the other is accelerated; but both
the magnitude and period of these quantities vary,
in consequence of the secular variations in the elements
of the orbits. These inequalities are strictly
periodical, since they depend upon the configuration
of the two planets; and the theory is perfectly
confirmed by observation, which shows that, in the
course of twenty centuries, Jupiter's mean motion
has been accelerated by about 3° 23', and Saturn's
retarded by 5° 13'.
It might be imagined that the reciprocal action
of such planets as have satellites would be
different from the influence of those that have
none; but the distances of the satellites from their
primaries are incomparably less than the distances
of the planets from the sun, and from one another;
so that the system of a planet and its satellites
moves nearly as if all these bodies were united in
their common centre of gravity: the action of the
sun, however, in some degree disturbs the motion
of the satellites about their primary.
SECTION V.
The changes which take place in the planetary
system are exhibited on a smaller scale by Jupiter
and his satellites: and, as the period requisite for
the development of the inequalities of these little
moons only extends to a few centuries, it may be
regarded as an epitome of that grand cycle which
will not be accomplished by the planets in myriads
of ages. The revolutions of the satellites about
Jupiter are precisely similar to those of the planets
about the sun: it is true they are disturbed by the
sun, but his distance is so great, that their motions
are nearly the same as if they were not under his
influence. The satellites, like the planets, were
probably projected in elliptical orbits, but the compression
of Jupiter's spheroid is very great in consequence
of his rapid rotation; and as the masses
of the satellites are nearly 100000 times less than
that of Jupiter, the immense quantity of prominent
matter at his equator must soon have given the
circular form observed in the orbits of the first and
second satellites, which its superior attraction will
always maintain. The third and fourth satellites
being farther removed from its influence, move in
orbits with a very small eccentricity. The same
cause occasions the orbits of the satellites to remain
nearly in the plane of Jupiter's equator, on account
of which they are always seen nearly in the same
line; and the powerful action of that quantity of
prominent matter is the reason why the motions of
the nodes of these small bodies is so much more
rapid than those of the planet. The nodes of the
fourth satellite accomplish a tropical revolution in
531 years, while those of Jupiter's orbit require no
less than 36261 years, — a proof of the reciprocal,
attraction between each particle of Jupiter's equator
and of the satellites. Although the two first
satellites sensibly move in circles, they acquire a
small ellipticity from the disturbances they experience.

The orbits of the satellites do not retain a permanent
inclination either to the plane of Jupiter's
equator or to that of his orbit, but to certain planes
passing between the two, and through their intersection;
these have a greater inclination to his
equator the farther the satellite is removed, owing
to the influence of Jupiter's compression, and they
have a slow motion corresponding to secular variations
in the planes of Jupiter's orbit and equator.
The satellites are not only subject to periodic and
secular inequalities from their mutual attraction,
similar to those which affect the motions and orbits
of the planets, but also to others peculiar to themselves.
Of the periodic inequalities arising from
their mutual attraction the most remarkable take
place in the angular motions of the three nearest
to Jupiter, the second of which receives from the
first a perturbation similar to that which it produces
in the third; and it experiences from the
third a perturbation similar to that which it communicates
to the first. In the eclipses these two
inequalities are combined into one, whose period
is 431.659 days. The variations peculiar to the
satellites arise from the secular inequalities occasioned
by the action of the planets in the form and
position of Jupiter's orbit, and from the displacement
of his equator. It is obvious that whatever
alters the relative positions of the sun, Jupiter, and
his satellites, must occasion a change in the directions
and intensities of the forces, which will
affect the motions and orbits of the satellites. For
this reason the secular variations in the eccentricity
of Jupiter's orbit, occasion secular inequalities in
the mean motions of the satellites, and in the motions
of the nodes and apsides of their orbits. The
displacement of the orbit of Jupiter, and the variation
in the position of his equator, also affect these
small bodies. The plane of Jupiter's equator is
inclined to the plane of his orbit, so that the action
of the sun and of the satellites themselves produces
mutation and precession in his equator, precisely
similar to that which takes place in the rotation of
the earth, from the action of the sun and moon,
whence the protuberant matter at Jupiter's equator
is continually changing its position with regard to
the satellites, and produces corresponding mutations
in their motions; and, as the cause must be
proportional to the effect, these inequalities afford
the means, not only of ascertaining the compression
of Jupiter's spheroid, but they prove that his mass
is not homogeneous. Although the apparent diameters
of the satellites are too small to be measured,
yet their perturbations give the values of
their masses with considerable accuracy, — a striking
proof of the power of analysis.
A singular law obtains among the mean motions
and mean longitudes of the three first satellites.
It appears from observation that the mean motion
of the first satellite, plus twice that of the third, is
equal to three times that of the second; and that
the mean longitude of the first satellite, minus three
times that of the second, plus twice that of the
third, is always equal to two right angles. It is
proved by theory, that if these relations had only
been approximate when the satellites were first
launched into space, their mutual attractions would
have established and maintained them, notwithstanding
the secular inequalities to which they are
liable. They extend to the synodic motions of the
satellites, consequently they affect their eclipses,
and have a very great influence on their whole
theory. The satellites move so nearly in the plane
of Jupiter's equator, which has a very small inclination
to his orbit, that they are frequently eclipsed
by the shadow of the planet. The eclipses take
place close to the disc of Jupiter when he is near
opposition; but at times the shadow is so projected
with regard to the earth, that the third and fourth
satellites vanish and reappear on the same side of
the disc. These eclipses are in all respects similar
to those of the moon ; but, occasionally, the satellites
eclipse Jupiter, passing like black spots
across his surface, and resemble annular eclipses of
the sun. The instant of the beginning or end of
an eclipse of a satellite marks the same instant of
absolute time to all the inhabitants of the earth;
therefore, the time of these eclipses observed by a
traveller, when compared with the time of the
eclipse computed for Greenwich, or any other fixed
meridian, gives the difference of the meridians in
time, and consequently the longitude of the place
of observation. It has required all the refinements
of modern instruments to render the eclipses of
these remote moons available to the mariner; now,
however, that system of bodies invisible to the
naked eye, known to man by the aid of science
alone, enables him to traverse the ocean, spreading
the light of knowledge and the blessings of civilization
over the most remote regions, and to return
loaded with the productions of another hemisphere.
Nor is this all : the eclipses of Jupiter's
satellites have been the means of a discovery which,
though not so immediately applicable to the wants
of man, unfolds one of the properties of light, — that
medium without whose cheering influence all the
beauties of the creation would have been to us a
blank. It is observed, that those eclipses of the
first satellite, which happen when Jupiter is near
conjunction, are later by 16m 26s than those which
take place when the planet is in opposition. But,
as Jupiter is nearer to us when in opposition by
the whole breadth of the earth's orbit than when
in conjunction, this circumstance was attributed to
the time employed by the rays of light in crossing
the earth's orbit, a distance of about 190 millions
of miles ; whence it is estimated that light travels
at the rate of 190000 miles in one second. Such
is its velocity, that the earth, moving at the rate
of 19 miles in a second, would take two months
to pass through a distance which a ray of light
would dart over in eight minutes. The subsequent
discovery of the aberration of light confirmed this
astonishing result.
Objects appear to be situate in the direction of
the rays which proceed from them. Were light
propagated instantaneously, every object, whether
at rest or in motion, would appear in the direction
of these rays; but as light takes some time to travel,
we see Jupiter in conjunction, by means of
rays that left him 16m26s before; but, during that
time, we have changed our position, in consequence
of the motion of the earth in its orbit ; consequently
we refer Jupiter to a place in which he is not.
His true position is in the diagonal of the parallelogram,
whose sides are in the ratio of the velocity
of light to the velocity of the earth in its orbit,
which is as ] 90000 to 19. In consequence of the
aberration of light, the heavenly bodies seem to he
in places in which they are not. In fact, if the
earth were at rest, rays from a star would pass
along the axis of a telescope directed to it : but if
the earth were to begin to move in its orbit, with
its usual velocity, these rays would strike against
the side of the tube ; it would, therefore, he necessary
to incline the telescope a little, in order to see
the star. The angle contained between the axis
of the telescope and a line drawn to the true place
of the star, is its aberration, which varies in
quantity and direction in different parts of the
earth's orbit; but as it is only 20".37, or 20".5,
it is insensible in ordinary cases.
The velocity of light deduced from the observed
aberration of the fixed stars, perfectly corresponds
with that given by the eclipses of the first satellite.
The same result, obtained from sources so different,
leaves not a doubt of its truth. Many such beautiful
coincidences, derived from circumstances apparently
the most unpromising and dissimilar, occur
in the rest of physical astronomy, and prove dependences
which we might otherwise be unable to trace.
The identity of the velocity of light, at the distance
of Jupiter, and on the earth's surface, shows that
its velocity is uniform; and if light consists in the
vibrations of an elastic fluid or ether filling space,
an hypothesis which accords best with observed phenomena,
the uniformity of its velocity shows that
the density of the fluid throughout the whole extent
of the solar system must be proportional to its elasticity.
Among the fortunate conjectures which have
been confirmed by subsequent experience, that of
Bacon is not the least remarkable. 'It produces in
me,' says the restorer of true philosophy, 'a doubt
whether the face of the serene and starry heavens
be seen at the instant it really exists, or not till
some time later; and whether there be not, with
respect to the heavenly bodies, a true time and an
apparent time, no less than a true place and an
apparent place, as astronomers say, on account of
parallax. For it seems incredible that the species
or rays of the celestial bodies can pass through the
immense interval between them and us in an instant,
or that they do not even require some considerable
portion of time.'
As great discoveries generally lead to a variety
of conclusions, the aberration of light affords a
direct proof of the motion of the earth in its orbit;
and its rotation is proved by the theory of falling
bodies, since the centrifugal force it induces retards
the oscillations of the pendulum in going from the
pole to the equator. Thus a high degree of scientific
knowledge has been requisite to dispel the
errors of the senses.
The little that is known of the theories of the
satellites of Saturn and Uranus is, in all respects,
similar to that of Jupiter. The great compression
of Saturn occasions its satellites to move nearly in
the plane of its equator. Of the situation of the
equator of Uranus we know nothing, nor of his
compression; but the orbits of his satellites are
nearly perpendicular to the plane of the ecliptic,
and by analogy they ought to be in the plane of his
equator.
SECTION VI.
Our constant companion, the moon, next claims
our attention. Several circumstances concur to
render her motions the most interesting, and at the
same time the most difficult to investigate of all the
bodies of our system. In the solar system planet
troubles planet, but in the lunar theory the sun is
the great disturbing cause; his vast distance being
compensated by his enormous magnitude, so that
the motions of the moon are more irregular than
those of the planets; and, on account of the great
ellipticity of her orbit, and the size of the sun, the
approximations to her motions are tedious and difficult
beyond what those unaccustomed to such
investigations could imagine. Among the innumerable
periodic inequalities to which the moon's motion
in longitude is liable, the most remarkable are
the Evection, the Variation, and the Annual Equation.
The forces producing the evection diminish
the excentricity of the lunar orbit in conjunction and
opposition, and augment it in quadrature. The
period of this inequality is less than thirty-two days.
Were the increase and diminution always the same,
the evection would only depend upon the distance
of the moon from the sun ; but its absolute value
also varies with her distance from the perigee of
her orbit. Ancient astronomers, who observed the
moon solely with a view to the prediction of eclipses,
which can only happen in conjunction and opposition,
where the excentricity is diminished by the
evection, assigned too small a value to the ellipticity
of her orbit. The variation, which is at its maximum
when the moon is 45° distant from the sun,
vanishes when that distance amounts to a quadrant,
and also when the moon is in conjunction and opposition;
consequently, that inequality never could
have been discovered from the eclipses: its period is
half a lunar month. The annual equation arises from
the moon's motion being accelerated when that
of the earth is retarded, and vice versa — for, when
the earth is in its perihelion, the lunar orbit is
enlarged by the action of the sun; therefore,
the moon requires more time to perform her
revolution. But, as the earth approaches its aphelion,
the moon's orbit contracts, and less time is
necessary to accomplish her motion, — its period,
consequently, depends upon the time of the year.
In the eclipses the annual equation combines with
the equation of the centre of the terrestrial orbit,
so that ancient astronomers imagined the earth's
orbit to have a greater excentricity than modern
astronomers assign to it.
The planets disturb the motion of the moon
both directly and indirectly; because their action
on the earth alters its relative position with regard
to the sun and moon, and occasions inequalities in
the moon's motion, which are more considerable
than those arising from their direct action: for the
same reason the moon, by disturbing the earth, indirectly
disturbs her own motion. Neither the
excentricity of the lunar orbit, nor its mean inclination
to the plane of the ecliptic, have experienced
any changes from secular inequalities; for, although
the mean action of the sun on the moon depends
upon the inclination of the lunar orbit to the
ecliptic, and that the position of the ecliptic is subject
to a secular inequality, yet analysis shows that
it does not occasion a secular variation in the inclination
of the lunar orbit, because the action of the
sun constantly brings the moon's orbit to the same
inclination on the ecliptic. The mean motion,
the nodes, and the perigee, however, are subject to
very remarkable variations.
From an eclipse observed by the Chaldeans at
Babylon, on the 19th of March, seven hundred
and twenty-one years before the Christian era, the
place of the moon is known from that of the sun
at the instant of opposition, whence her mean
longitude may be found; but the comparison of
this mean longitude with another mean longitude,
computed hack for the instant of the eclipse from
modern observations, shows that the moon performs
her revolution round the earth more rapidly
and in a shorter time now, than she did formerly;
and that the acceleration in her mean motion has
been increasing from age to age as the square of
the time: all ancient and intermediate eclipses
confirm this result. As the mean motions of the
planets have no secular inequalities, this seemed
to be an unaccountable anomaly. It was at one
time attributed to the resistance of an etherial
medium pervading space, and at another to the
successive transmission of the gravitating force;
but as La Place proved that neither of these causes,
even if they exist, have any influence on the
motions of the lunar perigee or nodes, they could
not affect the mean motion; a variation in the
mean motion from such causes being inseparably
connected with variations in the motions of the
perigee and nodes. That great mathematician, in
studying the theory of Jupiter's satellites, perceived
that the secular variation in the elements of Jupiter's
orbit, from the action of the planets, occasions
corresponding changes in the motions of the
satellites, which led him to suspect that the acceleration
in the mean motion of the moon might be
connected with the secular variation in the excentricity
of the terrestrial orbit; and analysis has
proved that he assigned the true cause of the acceleration.

If the excentricity of the earth's orbit were
invariable, the moon would be exposed to a variable
disturbance from the action of the sun, in consequence
of the earth's annual revolution; it would
however be periodic, since it would be the same
as often as the sun, the earth, and the moon returned
to the same relative positions: but on
account of the slow and incessant diminution in
the excentricity of the terrestrial orbit, the revolution
of our planet is performed at different
distances from the sun every year. The position
of the moon with regard to the sun undergoes a
corresponding change; so that the mean action
of the sun on the moon varies from one century
to another, and occasions the secular increase in
the moon's velocity called the Acceleration, a
name peculiarly appropriate in the present age,
and which will continue to be so for a vast number
of ages to come; because, as long as the earth's
excentricity diminishes, the moon's mean motion
will be accelerated, but when the excentricity has
passed its minimum, and begins to increase, the
mean motion will be retarded from age to age.
At present the secular acceleration is about
11". 209, but its effect on the moon's place increases
as the square of the time. It is remarkable
that the action of the planets thus reflected
by the sun to the moon is much more sensible
than their direct action, either on the earth or
moon. The secular diminution in the excentricity,
which has not altered the equation of the centre
of the sun by eight minutes since the earliest
recorded eclipses, has produced a variation of
about 1°48' in the moon's longitude, and of 7°12'
in her mean anomaly.
The action of the sun occasions a rapid but
variable motion in the nodes and perigee of the
lunar orbit. Though the nodes recede during the
greater part of the moon's revolution, and advance
during the smaller, they perform their sidereal
revolution in 6793.37953 days; and the perigee
accomplishes a revolution in 3232.56'731 days, or
a little more than nine years, notwithstanding its
motion is sometimes retrograde and sometimes
direct; but such is the difference between the
disturbing energy of the sun and that of all the
planets put together, that it requires no less than
114755 years for the greater axis of the terrestrial
orbit to do the same. It is evident that the same
secular variation which changes the sun's distance
from the earth, and occasions the acceleration in
the moon's mean motion, must affect the nodes
and perigee; and it consequently appears, from
theory as well as observation, that both these
elements are subject to a secular inequality arising
from the variation in the excentricity of the earth's
orbit, which connects them with the Acceleration,
so that both are retarded when the mean motion
is anticipated. The secular variations in these
three elements are in the ratio of the numbers 3,
0.735, and 1; whence the three motions of the
moon, with regard to the sun, to her perigee, and
to her nodes, are continually accelerated, and their
secular equations are as the numbers 1, 4, and
0.265, or, according to the most recent investigations,
as 1, 4.6776, and 0.391. A comparison of
ancient eclipses observed by the Arabs, Greeks,
and Chaldeans, imperfect as they are, with modern
observations, perfectly confirms these results of
analysis. Future ages will develop these great
inequalities, which at some most distant period
will amount to many circumferences. They are
indeed periodic; but who shall tell their period?
Millions of years must elapse before that great
cycle is accomplished; but such changes, though
rare in time, are frequent in eternity.'
The moon is so near, that the excess of matter
at the earth's equator occasions periodic variations
in her longitude, and also that remarkable inequality
in her latitude already mentioned as a nutation
in the lunar orbit, which diminishes its
inclination to the ecliptic when the moon's ascending
node coincides with the equinox of spring,
and augments it when that node coincides with
the equinox of autumn. As the cause must be
proportional to the effect, a comparison of these
inequalities, computed from theory, with the same
given by observation, shows that the compression
of the terrestrial spheroid, or the ratio of the difference
between the polar and equatorial diameters,
to the diameter of the equator, is It is
proved analytically that, if a fluid mass of homogeneous
matter, whose particles attract each other
inversely as the square of the distance, were to
revolve about an axis as the earth does, it would
assume the form of a spheroid whose compression
is 1/230, whence it appears that the earth is not
homogeneous, hut decreases in density from its
centre to its circumference. Thus the moon's
eclipses show the earth to be round, and her inequalities
not only determine the form, but the
internal structure of our planet; results of analysis
which could not have been anticipated.
Similar inequalities in the motions of Jupiter's
satellites prove that his mass is not homogeneous,
and that his compression is 1/13.8. His equatorial
diameter exceeds his polar diameter by about 6230
miles.
The phases of the moon, which vary from a
slender silvery crescent soon after conjunction to
a complete circle of light in opposition, decrease
by the same degrees till the moon is again enveloped
in the morning beams of the sun. These
changes regulate the returns of the eclipses; those
of the sun can only happen in conjunction, when
the moon, coming between the earth and the sun,
intercepts his light; and those of the moon are
occasioned by the earth intervening between the
sun and moon when in opposition. As the earth is
opaque and nearly spherical, it throws a conical
shadow on the side of the moon opposite to the
sun, the axis of which passes through the centres
of the sun and earth. The length of the shadow
terminates at the point where the apparent diameters
of the sun and earth would be the same.
When the moon is in opposition, and at her mean
distance, the diameter of the sun would be seen
from her centre under an angle of 1918".1; and
that of the earth would appear under an angle of
6908'.3; so that the length of the shadow is at
least three times and a half greater than the distance
of the moon from the earth, and the breadth
of the shadow, where it is traversed by the moon,
is about eight-thirds of the lunar diameter. Hence
the moon would be eclipsed every opposition, were
it not for the inclination of her orbit to the plane
of the ecliptic, in consequence of which the moon
in opposition is either above or below the cone of
the earth's shadow, except when in or near her
nodes; her position with regard to them occasions
all the varieties in the lunar eclipses. Every point
of the moon's surface successively loses the light
of different parts of the sun's disc before being
eclipsed. Her brightness therefore gradually diminishes
before she plunges into the earth's shadow.
The breadth of the space occupied by
the penumbra is equal to the apparent diameter
of the sun, as seen from the centre
of the moon. The mean duration of a revolution
of the sun, with regard to the node of the
lunar orbit, is to the duration of a synodic revolution
of the moon as 223 to 19; so that, after a
period of 223 lunar months, the sun and moon
would return to the same relative position to the
node of the moon's orbit, and therefore the eclipses
would recur in the same order, were not the
periods altered by irregularities in the motions, of
the sun and moon. In lunar eclipses, our atmosphere
refracts the sun's rays which pass through
it, and bends them all round into the cone of the
earth's shadow; and as the horizontal refraction
surpasses half the sum of the solar and lunar
parallaxes, that is, half the sum of the semidiameters
of the sun and moon, divided by their
mutual distance, the centre of the lunar disc,
supposed to be in the axis of the shadow, would
receive the rays from the same point of the sun,
round all sides of the earth, so that it would be
more illuminated than in full moon, if the greater
portion of the light were not absorbed by the
atmosphere. Instances are recorded where this
feeble light has been entirely absorbed, so that the
moon has altogether disappeared in her eclipses.
The sun is eclipsed when the moon intercepts
his rays. The moon, though incomparably smaller
than the sun, is so much nearer the earth, that
her apparent diameter differs but little from his,
but both are liable to such variations, that they
alternately surpass one another. Were the eye of
a spectator in the same straight line with the
centres of the sun and moon, he would see the sun
eclipsed. If the apparent diameter of the moon
surpassed that of the sun, the eclipse would be
total ; if it were less, the observer would see a ring
of light round the disc of the moon, and the eclipse
would be annular. If the centre of the moon
should not be in the straight line joining the
centres of the sun and the eye of the observer, the
moon might only eclipse a part of the sun. The
variation, therefore, in the distances of the sun and
moon from the centre of the earth, and of the
moon from her node at the instant of conjunction,
occasions great varieties in the solar eclipses.
Besides, the height of the moon above the horizon
changes her apparent diameter, and may augment
or diminish the apparent distances of the centres
of the sun and moon, so that an eclipse of the sun
may occur to the inhabitants of one country, and
not to those of another. In this respect the solar
eclipses differ from the lunar, which are the same
for every part of the earth where the sun and
moon are above the horizon. In solar eclipses,
the light reflected by the atmosphere diminishes
the obscurity they produce ; even in total eclipses
the higher part of the atmosphere is enlightened
by a part of the sun's disc, and reflects its rays to
the earth. The whole disc of the new moon is frequently
visible from atmospheric reflection.
Planets sometimes eclipse one another. On the
17th of May, 1737, Mercury was eclipsed by Venus
near their inferior conjunction: Mars passed
over Jupiter on the 9th of January, 1591, and on
the 13th of October, 1825, the moon eclipsed Saturn.
These phenomena, however, happen very
seldom, because all the planets, or even a part of
them, are very rarely seen in conjunction at once;
that is, in the same part of the heavens at the same
time. More than 2500 years before our era, the
five great planets were in conjunction. On the 15th
of September, 1186, a similar assemblage took
place between the constellations of Virgo and Libra;
and in 1801, the Moon, Jupiter, Saturn, and
Venus were united in the heart of the Lion. These
conjunctions are so rare, that Lalande has computed
that more than seventeen millions of millions
of years separate the epochs of the contemporaneous
conjunctions of the six great planets.
The motions of the moon have now become of
more importance to the navigator and geographer
than those of any other heavenly body, from the
precision with which the longitude is determined
by the occultations of stars and lunar distances.
The occultation of a star by the moon is a phenomenon
of frequent occurrence : the moon seems
to pass over the star, which almost instantaneously
vanishes at one side of her disc, and
after a short time as suddenly reappears on the
other; and a lunar distance is the observed distance
of the moon from the sun, or from a particular
star or planet, at any instant. The lunar
theory is brought to such perfection, that the times
of these phenomena, observed under any meridian,
when compared with those computed for Greenwich
in the Nautical Almanac, give the longitude of
the observer within a few miles. The accuracy of
that work is obviously of extreme importance to a
maritime nation: we have reason to hope that the
new Ephemeris, now in preparation, will be by far
the most perfect work of the kind that ever has
been published.
From the lunar theory, the mean distance of
the sun from the earth, and thence the whole
dimensions of the solar system, are known; for
the forces which retain the earth and moon in
their orbits are respectively proportional to the
radii vectores of the earth and moon, each being
divided by the square of its periodic time; and as
the lunar theory gives the ratio of the forces, the
ratio of the distances of the sun and moon from
the earth is obtained; whence it appears that the
sun's mean distance from the earth is nearly 396
times greater than that of the moon. The method,
however, of finding the absolute distances of the
celestial bodies in miles, is in fact the same with
that employed in measuring the distances of terrestrial
objects. From the extremities of a known
base, the angles which the visual rays from the
object form with it are measured; their sum subtracted
from two right angles gives the angle
opposite the base ; therefore, by trigonometry, all
the angles and sides of the triangle may be computed
— consequently the distance of the object is
found. The angle under which the base of the
triangle is seen from the object is the parallax of
that object; it evidently increases and decreases
with the distance ; therefore the base must he
very great indeed to be visible at all from the
celestial bodies. The globe itself, whose dimensions
are obtained by actual admeasurement, furnishes
a standard of measures, with which we
compare the distances, masses, densities, and volumes
of the sun and planets.
SECTION VII.
THE theoretical investigation of the figure of the
earth and planets is so complicated, that neither
the geometry of Newton nor the refined analyses
of La Place have attained more than an approximation:
it is only within a few years that a complete
and finite solution of that difficult problem
has been accomplished by our distinguished countryman
Mr. Ivory. The investigation has been
conducted by successive steps, beginning with a
simple case, and then proceeding to the more
difficult; but in all, the forces which occasion the
revolutions of the earth and planets are omitted,
because, by acting equally upon all the particles,
they do not disturb their mutual relations. A fluid
mass of uniform density, whose particles mutually
gravitate to each other, will assume the form of a
sphere when at rest; but if the sphere begins to
revolve, every particle will describe a circle, having
its centre in the axis of revolution; the planes of
all these circles will be parallel to one another,
and perpendicular to the axis, and the particles
will have a tendency to fly from that axis in consequence
of the centrifugal force arising from the
velocity of rotation. The force of gravity is everywhere
perpendicular to the surface, and tends to
the interior of the fluid mass, whereas the centrifugal
force acts perpendicularly to the axis of rotation,
and is directed to the exterior; and as its
intensity diminishes with the distance from the
axis of rotation, it decreases from the equator to
the poles, where it ceases. Now it is clear that
these two forces are in direct opposition to each
other in the equator alone, and that gravity is
there diminished by the whole effect of the centrifugal
force, whereas, in every other part of the
fluid, the centrifugal force is resolved into two
parts, one of which, being perpendicular to the
surface, diminishes the force of gravity; but the
other, being at a tangent to the surface, urges the
particles towards the equator, where they accumulate
till their numbers compensate the diminution
of gravity, which makes the mass bulge at the
equator and become flattened at the poles. It
appears, then, that the influence of the centrifugal
force is most powerful at the equator, not only
because it is actually greater there than elsewhere,
but because its whole effect is employed in diminishing
gravity, whereas, in every other point of
the fluid mass, it is only a resolved part that is so
employed. For both these reasons it gradually
decreases towards the poles, where it ceases. On
the contrary, gravity is least at the equator, because
the particles are farther from the centre of
the mass, and increases towards the poles, where
it is greatest. It is evident, therefore, that, as the
centrifugal force is much less than the force of gravity,
— gravitation, which is the difference between
the two, is least at the equator, and continually
increases towards the poles, where it is a maximum.
On these principles Sir Isaac Newton
proved that a homogeneous fluid mass in rotation
assumes the form of an ellipsoid of revolution,
whose compression is Such, however, cannot
be the form of the earth, because the strata
increase in density towards the centre. The lunar
inequalities also prove the earth to be so constructed;
it was requisite, therefore, to consider
the fluid mass to be of variable density. Including
this condition, it has been found that the mass,
when in rotation, would still assume the form of
an ellipsoid of revolution; that the particles of
equal density would arrange themselves in concentric
elliptical strata, the most dense being in the
centre; but that the compression would be less
than in the case of the homogeneous fluid. The
compression is still less when the mass is considered
to be, as it actually is, a solid nucleus, decreasing
regularly in density from the centre to
the surface, and partially covered by the ocean,
because the solid parts, by their cohesion, nearly
destroy that part of the centrifugal force which
gives the particles a tendency to accumulate at the
equator, though not altogether; otherwise the sea,
by the superior mobility of its particles, would
flow towards the equator and leave the poles dry:
besides, it is well known that the continents at
the equator are more elevated than they are
higher latitudes. It is also necessary for the equilibrium
of the ocean, that its density should be
less than the mean density of the earth, otherwise
the continents would be perpetually liable to inundations
from storms and other causes. On the
whole, it appears from theory that a horizontal
line passing round the earth, through both poles,
must be nearly an ellipse, having its major axis in
the plane of the equator, and its minor axis coinciding
with the axis of the earth's rotation. The
intensity of the centrifugal force is measured by the
deflection of any point from the tangent in a second,
and is determined from the known velocity of the
earth's rotation : the force of gravitation at any
place is measured by the descent of a heavy body in
the first second of its fall. At the equator the centrifugal
force is equal to the 289th part of gravity,
and diminishes towards the poles as the cosine of
the latitude, for the angle between the directions
of these two forces, at any point of the surface, is
equal to its latitude. But whatever the constitution
of the earth and planets may be, analysis
proves that, if the intensity of gravitation at the
equator be taken equal to unity, the sum of the
compression of the ellipsoid and the whole increase
of gravitation, from the equator to the pole,
is equal to five-halves of the ratio of the centrifugal
force to gravitation at the equator. This quantity,
with regard to the earth, is 5/2 of 1/289, or 1/115.2
consequently the compression of the earth is equal
to 1/115.2, diminished by the whole increase of
gravitation, so that its form will be known, if the
whole increase of gravitation, from the equator to
the pole, can be determined by experiment. But
there is another method of ascertaining the figure
of our planet. It is easy to show, in a spheroid
whose strata are elliptical, that the increase in the
length of the radii, the decrease of gravitation,
and the increase in the lengths of the arcs of the
meridian, corresponding to angles of one degree,
from the pole to the equator, are proportional to
the square of the cosine of the latitude. These
quantities are so connected with the ellipticity of
the spheroid, that the total increase in the length
of the radii is equal to the compression, and the
total diminution in the length of the arcs is equal
to the compression multiplied by three times the
length of an arc of one degree at the equator.
Hence, by measuring the meridian curvature of
the earth, the compression, and consequently its
figure, become known. This, indeed, is assuming
the earth to be an ellipsoid of revolution, but the
actual measurement of the globe will show how
far it corresponds with that solid in figure and constitution.

The courses of the great rivers, which are in
general navigable to a considerable extent, prove
that the curvature of the land differs but little
from that of the ocean; and as the heights of the
mountains and continents are inconsiderable when
compared with the magnitude of the earth, its
figure is understood to be determined by a surface
at every point perpendicular to the direction of
gravitation, or of the plumb-line, and is the same
which the sea would have if it were continued all
round the earth beneath the continents. Such is
the figure that has been measured in the following
manner: -
A terrestrial meridian is a line passing through
both poles, all the points of which have their
noon contemporaneously. Were the lengths and
curvatures of different meridians known, the
figure of the earth might be determined; but the
length of one degree is sufficient to give the figure
of the earth, if it be measured on different meridians,
and in a variety of latitudes; for if the earth
were a sphere, all degrees would be of the same
length, but if not, the lengths of the degrees will
be greatest where the curvature is least, and will be
greater exactly in proportion as the curvature is
less; a comparison of the lengths of the degree
in different parts of the earth's surface will therefore
determine its size and form.
An are of the meridian may be measured by
observing the latitude of its extreme points, and
then measuring the distance between them in feet
or fathoms: the distance thus determined on the
surface of the earth, divided by the degrees and
parts of a degree contained in the difference of the
latitudes, will give the exact length of one degree,
the difference of the latitudes being the angle contained
between the verticals at the extremities of
the arc. This would be easily accomplished were
the distance unobstructed, and on a level with the
sea ; but on account of the innumerable obstacles
on the surface of the earth, it is necessary to connect
the extreme points of the arc by a series of
triangles, the sides and angles of which are either
measured or computed, so that the length of the
arc is ascertained with much laborious computation.
In consequence of the irregularities of the surface,
each triangle is in a different plane; they must
therefore be reduced by computation to what they
would have been, had they been measured on the
surface of the sea; and as the earth may in this
case be esteemed spherical, they require a correction
to reduce them to spherical triangles.
Arcs of the meridian have been measured in a
variety of latitudes north and south, as well as arcs
perpendicular to the meridian. From these measurements
it appears that the lengths of the degrees
increase from the equator to the poles, nearly in
proportion to the square of the sine of the latitude;
consequently the convexity of the earth diminishes
from the equator to the poles.
Were the earth an ellipsoid of revolution, the
meridians would be ellipses whose lesser axes
would coincide with the axis of rotation, and all
the degrees measured between the pole and the
equator would give the same compression when
combined two and two. That, however, is far
from being the case. Scarcely any of the measurements
give exactly the same results, chiefly on
account of local attractions, which cause the plumbline
to deviate from the vertical. The vicinity of
mountains has that effect; but one of the most
remarkable, though not unprecedented, anomalies
takes place in the plains in the north of Italy,
where the action of some dense subterraneous
matter causes the plumb-line to deviate seven or
eight times more than it did from the attraction of
Chimborazo during the experiments of Bouguer,
while measuring a degree of the meridian at the
equator. In consequence of this local attraction,
the degrees of the meridian in that part of Italy,
seem to increase towards the equator through a small
space, instead of decreasing, as if the earth was
drawn out at the poles, instead of being flattened.
Many other discrepancies occur, but from the
mean of the five principal measurements of arcs
in Peru, India, France, England, and Lapland,
Mr. Ivory has deduced that the figure which most
nearly follows this law is an ellipsoid of revolution
whose equatorial radius is 3962.824 miles, and
the polar radius 3949.585 miles; the difference,
or 13.239 miles, divided by the equatorial radius,
is 1/298.33 fro, arcs of the meridian, 1/262.90 from
the-pendulnini and the true compression is 1/290.615,
this fraction is called the compression of the earth,
because, according as it is greater or less, the
terrestrial ellipsoid is more or less flattened at the
poles; it does not differ much from that given by
the lunar inequalities. If we assume the earth to
be a sphere, the length of a degree of the meridian
is 69 1/2 British miles; therefore 360 degrees, or
the whole circumference of the globe, is 24856
miles, and the diameter, which is something less
than a third of the circumference, is about 7912 or
8000 miles nearly. Eratosthenes, who died 194
years before the Christian era, was the first to give
an approximate value of the earth's circumference,
by the measurement of an arc between Alexandria
and Syene.
The other method of finding the figure of the
earth is totally independent of either of the preceding.
If the earth were a homogeneous sphere
without rotation, its attraction on bodies at its
surface would be everywhere the same; if it be
elliptical and of variable density, the force of
gravity, theoretically, ought to increase from the
equator to the pole, as unity plus a constant
quantity multiplied into the square of the sine
of the latitude; but for a spheroid in rotation, the
centrifugal force varies, by the laws of mechanics,
as the square of the sine of the latitude, from the
equator, where it is greatest, to the pole, where it
vanishes; and as it tends to make bodies fly off
the surface, it diminishes the force of gravity by a
small quantity. Hence, by gravitation, which is
the difference of these two forces, the fall of bodies
ought to be accelerated from the equator to the
poles, proportionably to the square of the sine of
the latitude; and the weight of the same body
ought to increase in that ratio. This is directly
proved by the oscillations of the pendulum; for if
the fall of bodies be accelerated, the oscillations
will be more rapid; and in order that they may
always be performed in the same time, the length
of the pendulum must be altered. By numerous
and careful experiments, it is proved that a pendulum
which oscillates 86400 times in a mean day
at the equator will do the same at every point of
the earth's surface, if its length be increased progressively
to the pole, as the square of the sine of
the latitude.
From the mean of these it appears that the
whole decrease of gravitation from the poles to the
equator is 0.001451, which, subtracted from 1/115.2
shows that the compression of the terrestrial spheroid
is about 1/282.90, which does not differ much
from that given by the lunar inequalities, and from
the arcs in the direction of the meridian, as well
as those perpendicular to it. The near coincidence
of these three values, deduced by methods
so entirely independent of each other, shows that
the mutual tendencies of the centres of the celestial
bodies to one another, and the attraction of the
earth for bodies at its surface, result from the reciprocal
attraction of all their particles. Another
proof may be added: the natation of the earth's
axis, and the precession of the equinoxes, are
occasioned by the action of the sun and moon on
the protuberant matter at the earth's equator;
and although these inequalities do not give the
absolute value of the terrestrial compression, they
show that the fraction expressing it is comprised
between the limits 1.279 and 1/573.
It might be expected that the same compression
should result from each, if the different methods of
observation could be made without error. This,
however, is not the case; for, after allowance has
been made for every cause of error, such discrepances
are found, both in the degrees of the
meridian and in the length of the pendulum,
as show that the figure of the earth is very complicated;
but they are so small, when compared
with the general results, that they may be disregarded.
The compression deduced from the mean
of the whole appears to be about 1/290.615; that given
by the lunar theory has the advantage of being
independent of the irregularities of the earth's
surface and of local attractions. The regularity
with which the observed variation in the length of
the pendulum follows the law of the square of the
sine of the latitude proves the strata to be elliptical
and symmetrically disposed round the centre of
gravity of the earth, which affords a strong presumption
in favour of its original fluidity. It is
remarkable how little influence the sea has on the
variation of the lengths of the arcs of the meridian
or on gravitation, neither does it much affect the
lunar inequalities, from its density being only
about a fifth of the mean density of the earth.
For, if the earth were to become fluid after being
stripped of the ocean, it would assume the form of
an ellipsoid of revolution whose compression is
1/304.8, which differs very little from that determined
by observation, and proves, not only that
the density of the ocean is inconsiderable, but that
its mean depth is very small. There may be profound
cavities in the bottom of the sea, but its mean
depth probably does not much exceed the mean
height of the continents and islands above its level.
On this account, immense tracts of land may be
deserted or overwhelmed by the ocean, as appears
really to have been the case, without any great
change in the form of the terrestrial spheroid. The
variation in the length of the pendulum was first
remarked by Richter in 1672, while observing
transits of the fixed stars across the meridian at
Cayenne, about five degrees north of the equator.
He found that his clock lost at the rate of 2m. 28s
daily, which induced him to determine the length
of a pendulum beating seconds in that latitude;
and repeating the experiments on his return to
Europe, he found the seconds pendulum at Paris
to be more than the twelfth of an inch longer than
that at Cayenne. The form and size of the earth
being determined, it furnishes a standard of. measure
with which the dimensions of the solar system
may be compared.
SECTION VIII.
THE parallax of a celestial body is the angle
under which the radius of the earth would be
seen if viewed from the centre of that body; it
affords the means of ascertaining the distances of
the sun, moon, and planets. Suppose, when the
moon is in the horizon at the instant of rising or
setting, lines to be drawn from her centre to the
spectator and to the centre of the earth; these
would form a right-angled triangle with the terrestrial
radius, which is of a known length; and
as the parallax or angle at the moon can be
measured, all the angles and one side are given;
whence the distance of the moon from the centre
of the earth may be computed. The parallax of
an object may be found, if two observers under
the same meridian, but at a very great distance
from one another, observe its zenith distance on
the same day at the time of its passage over the
meridian. By such contemporaneous observations
at the Cape of Good Hope and at Berlin, the mean
horizontal parallax of the moon was found to be
3459", whence the mean distance of the moon is
about sixty times the mean terrestrial radius, or
237360 miles nearly. Since the parallax is equal
to the radius of the earth divided by the distance
of the moon, it varies with the distance of the
moon from the earth under the same parallel of
latitude, and proves the ellipticity of the lunar
orbit; when the moon is at her mean distance, it
varies with the terrestrial radii, thus showing that
the earth is not a sphere.
Although the method described is sufficiently
accurate for finding the parallax of an object as
near as the moon, it will not answer for the sun,
which is so remote that the smallest error in
observation would lead to a false result; but that
difficulty is obviated by the transits of Venus.
When that planet is in her nodes, or within 1 1/4°
of them, that is, in, or nearly in, the plane of the
ecliptic, she is occasionally seen to pass over the
sun like a black spot. If we could imagine that
the sun and Venus had no parallax, the line
described by the planet on his disc and the
duration of the transit would be the same to all
the inhabitants of the earth; but as the semi--
diameter of the earth has a sensible magnitude
when viewed from the centre of the sun, the line
described by the planet in its passage over his disc
appears to be nearer to his centre, or farther from
it, according to the position of the observer ; so
that the duration of the transit varies with the
different points of the earth's surface at which it is
observed. This difference of time, being entirely
the effect of parallax, furnishes the means of computing
it from the known motions of the earth
and Venus, by the same method as for the eclipses
of the sun. In fact, the ratio of the distances of
Venus and the sun from the earth at the time of
the transit are known from the theory of their elliptical
motion, consequently the ratio of the parallaxes
of these two bodies, being inversely as their
distances, is given; and as the transit gives the
difference of the parallaxes, that of the sun is
obtained. In 1769, the parallax of the sun was
determined by observations of a transit of Venus
made at Wardhus in Lapland, and at Otaheite
in the South Sea; the latter observation was the
object of Cook's first voyage. The transit lasted
about six hours at Otaheite, and the difference in
duration at these two stations was eight minutes;
whence the sun's horizontal parallax was found to
be 8".72: but by other considerations it has been
reduced to 8".577; from which the mean distance
of the sun appears to be about 92246700
miles, or ninety-two millions of miles nearly.
This is confirmed by an inequality in the motion
of the moon, which depends upon the parallax of
the sun, and which, when compared with observation,
gives 8".6 for the sun's parallax.
The parallax of Venus is determined by her
transits, that of Mars by direct observation, and it
is found to be nearly double that of the sun when
the planet is in opposition. The distances of
these two planets from the earth are therefore
known in terrestrial radii; consequently their
mean distances from the sun may be computed;
and as the ratios of the distances of the planets
from the sun are known by Kepler's law, their
absolute distances in miles are easily found.
Far as the earth seems to be from the sun, it is
near to him when compared with Uranus ; that
planet is no less than 1843000000 of miles
from the luminary that warms and enlivens the
world; situate on the verge of the system, the sun
must appear to it not much larger than Venus
does to us. The earth cannot even be visible as a
telescopic object to a body so remote; yet man,
the inhabitant of the earth, soars beyond the vast
dimensions of the system to which his planet
belongs, and assumes the diameter of its orbit as
the base of a triangle, whose apex extends to the
stars.
Sublime as the idea is, this assumption proves
ineffectual, for the apparent places of the fixed
stars are not sensibly changed by the earth's annual
revolution ; and with the aid derived from the
refinements of modern astronomy, and of the most
perfect of instruments, it is still a matter of doubt
whether 'a sensible parallax has been detected even
in the nearest of these remote suns. If a fixed
star had the parallax of one second, its distance
from the sun would be 20500000000000 of
miles. At such a distance not only the terrestrial
orbit shrinks to a point, but the whole solar
system seen in the focus of the most powerful
telescope, might be covered by the thickness of a
spider's thread. Light flying at the rate of
200000 miles in a second, would take three years
and seven days to travel over that space; one of
the nearest stars may therefore have been kindled
or extinguished more than three years before we
could have been aware of so mighty an event.
But this distance must be small when compared
with that of the most remote of the bodies which
are visible in the heavens. The fixed stars are
undoubtedly luminous like the sun; it is therefore
probable that they are not nearer to one another
than the sun is to the nearest of them. In the
milky way and the other starry nebulæ, some
of the stars that seem to us to be close to others,
may be far behind them in the boundless depth of
space; nay, may be rationally supposed to he
situate many thousand times farther off; light
would therefore require thousands of years to come
to the earth from those myriads of suns, of which
our own is but 'the dim and remote companion.'
SECTION IX.
THE masses of such planets as have no satellites
are known by comparing the inequalities they
produce in the motions of the earth and of each
other, determined theoretically, with the same
inequalities given by observation, for the disturbing
cause must necessarily be proportional to the
effect it produces. But as the quantities of matter
in any two primary planets are directly as the
cubes of the mean distances at which their satellites
revolve, and inversely as the squares of their
periodic times, the mass of the sun and of any
planets which have satellites may be compared
with the mass of the earth. In this manner it is
computed that the mass of the sun is 354936
times that of the earth; whence the great perturbations
of the moon, and the rapid motion of the
perigee and nodes of her orbit. Even Jupiter, the
largest of the planets, is 1050 times less than the
sun;or, as was recently determined by the perturbations
of Encke's comet, appears the 1053.924th
part of the sun. The mass of the moon is determined
from several sources, — from her action on
the terrestrial equator, which occasions the nutation
in the axis of rotation; from her horizontal
parallax; from an inequality she produces in the
sun's longitude, and from her action on the tides.
The three first quantities, computed from theory and
compared with their observed values, give her
mass respectively equal to the 1/71, 1/74.2, and 1/69.2
part of that of the earth, which do not differ much
from each other. Dr. Brinkley, Bishop of Cloyne,
has found it to be a from the constant of lunar
nutation; but from the moon's action in raising the
tides, her mass appears to be about the seventy--
fifth part of that of the earth, a value that cannot
differ much from the truth.
The apparent diameters of the sun, moon, and
planets are determined by measurement; therefore
their real diameters may be compared with that of
the earth; for the real diarineter of a planet is to
the real diameter of the earth, or 7912 miles, as
the apparent diameter of the planet to the apparent
diameter of the earth as seen from the planet,
that is, to twice the parallax of the planet.
The mean apparent diameter of the sun is 1922".8,
and with the solar parallax 8".577, it will be
found that the diameter of the sun is about
886860 miles; therefore if the centre of the sun
were to coincide with the centre of the earth, his
volume would not only include the orbit of the
moon, but would extend nearly as far again, for
the moon's mean distance from the earth is about
sixty times the earth's mean radius, or 237360
miles: so that twice the distance of the moon is
414960 miles, which differs but little from the
solar radius; his equatorial radius is probably not
much less than the major axis of the lunar orbit.
The diameter of the moon is only 2160 miles;
and Jupiter's diameter of 91509 miles is very
much less than that of the sun; the diameter of
Pallas does not much exceed 79 miles, so that an
inhabitant of that planet, in one of our steam-carriages,
might go round his world in a few hours.
Before entering on the theory of rotation, it
may not be thought foreign to the subject to give
some idea of the methods of computing the places
of the planets, and of forming astronomical tables.
Astronomy is now divided into the three distinct
departments of theory, observation, and computation.
Since the problem of the three bodies can
only be solved by approximation, the analytical
astronomer determines the position of a planet in
space by a series of corrections. Its place in its
circular orbit is first found, then the addition or
subtraction of the equation of the centre to or
from its mean place, gives its position in the
ellipse; this again is corrected by the application;
of the principal periodic inequalities; but as these
are determined for some particular position of the
three bodies, they require to be corrected to suit
other relative positions. This process is continued.
till the corrections become less than the errors of
observation, when it is obviously unnecessary to.
carry the approximation further. By a similar
method, the true latitude and distance of the planet
from the sun are obtained.
All these quantities are given in terms of the time
by general analytical formulæ; they will consequently
give the exact place of the body in the
heavens, for any time assumed at pleasure, provided
they can be reduced to numbers; but before
the calculator begins his task, the observer must
furnish the necessary data. These are obviously
the forms of the orbits, and their positions with
regard to the plane of the ecliptic. It is therefore
necessary to determine by observation for each
planet, the length of the major axis of its orbit,
the excentricity, the inclination of the orbit to the
plane of the ecliptic, the longitudes of its perihelion
and ascending node at a given time, the periodic
time of the planet, and its longitude at any instant,
arbitrarily assumed as an origin from whence
all its subsequent and antecedent longitudes are estimated.
Each of these quantities is determined from
that position of the planet on which it has most influence.
For example, the sum of the greatest and
least distances of the planet from the sun is equal
to the major axis of the orbit, and their difference
is equal to the eccentricity; the longitude of the
planet, when at its least distance from the sun, is
the same with the longitude of the perihelion; the
greatest latitude of the planet is equal to the inclination
of the orbit; and the longitude of the
planet, when in the plane of the ecliptic in passing
towards the north, is the longitude of the ascending
node. But, notwithstanding the excellence of
instruments and the accuracy of modern observers,
the unavoidable errors of observation can only be
compensated by finding the value of each element
from the mean of perhaps a thousand, or even many
thousands of observations: for as it is probable that
the errors are not all in one direction, but that some
are in excess and others in defect, they will compensate
each other when combined.
However, the values of the elements determined
separately can only be regarded as approximate,
because they are so connected that
the estimation of any one independently will
induce errors in the others, for the excentricity
depends upon the longitude of the perihelion, the
mean motion depends upon the major axis, the
longitude of the node upon the inclination of the
orbit, and vice versâ, consequently the place of a
planet computed with the approximate data, will
differ from its observed place: then the difficulty is
to ascertain what elements are most in fault, since
the difference in question is the error of all, but
that is obviated by finding the errors of some
thousands of observations, and combining them
so as to correct the elements simultaneously, and
to make the sum of the squares of the errors
a minimum with regard to each element. The
method of accomplishing this depends upon the
Theory of Probabilities, a subject fertile in most
important results in the various departments of
science and of civil life, and quite indispensable in
the determination of astronomical data. A series
of observations continued for some years will give
approximate values of the secular and periodic
inequalities, which must be corrected from time to
time till theory and observation agree; and when
all these quantities are determined in numbers,
the longitude, latitude, and distances of the planet
from the sun are computed for stated intervals,
and formed into tables, arranged according to the
time estimated from a given epoch, so that the
place of the body may be determined from them
by inspection alone, at any instant, for perhaps a
thousand years before and after that epoch. By
this tedious process, tables have been computed
for eleven planets, besides the moon and the satellites
of Jupiter. Those of the four new planets are
astonishingly perfect, considering that these bodies
have not been discovered more than thirty years,
and a much longer time is requisite to develop
their inequalities.
SECTION X.
THE oblate form of several of the planets indicates
rotatory motion; this has been confirmed, in most
cases, by tracing spots on their surface, by which
their poles and times of rotation have been determined.
The rotation of Mercury is unknown, on account
of his proximity to the sun; and that of the
new planets has not yet been ascertained. The sun
revolves in twenty-five days and ten hours about
an axis which is directed towards a point half-way
between the pole-star and Lyra, the plane of rotation
being inclined by 7° 20', or a little more than
seven degrees, to the plane of the ecliptic. From
the rotation of the sun, there is every reason to
believe that he has a progressive motion in space,
although the direction to which he tends is unknown:
but in consequence of the reaction of the
planets, he describes a small irregular orbit about
the centre of inertia of the system, never deviating
from his position by more than twice his own
diameter, or a little more than seven times the
distance of the moon from the earth. The sun and
all his attendants rotate from west to east, on axes
that remain nearly parallel to themselves in every
point of their orbit, and with angular velocities
that are sensibly uniform. Although the uniformity
in the direction of their rotation is a circumstance
hitherto unaccounted for in the economy of
nature, yet from the design and adaptation of
every other part to the perfection of the whole, a
coincidence so remarkable cannot be accidental;
and as the revolutions of the planets and satellites
are also from west to east, it is evident
that both must have arisen fron the primitive cause
which has determined the planetary motions.
Indeed, La Place has computed the probability to
he as four millions to one, that all the motions of
the planets, both of rotation and revolution, were
at once imparted by an original common cause, but
of which we know neither the nature nor the epoch.
The larger planets rotate in shorter periods
than the smaller planets and the earth, their campression
is consequently greater, and the action
of the sun and of their satellites occasions a
notation in their axes, and a precession of their
equinoxes similar to that which obtains in the
terrestrial spheroid, from the attraction of the sun
and moon on the prominent matter at the equator.
It is an evident consequence of Kepler's law of
the squares of the periodic times of the planets
being as the cubes of the major axes of their
orbits, that the heavenly bodies move slower the
farther they are from the sun. In comparing the
periods of the revolutions of Jupiter and Saturn
with the times of their rotation, it appears that a
year of Jupiter contains nearly ten thousand of his
days, and that of Saturn about thirty thousand
Saturnian days.
The appearance of Saturn is unparalleled in the
system of the world; he is a spheroid about 900
times larger than the earth, surrounded by a ring
even brighter than himself, which always remains
suspended in the plane of his equator, and viewed
with a very good telescope, it is found to consist of
two concentric rings, divided by a dark band. The
mean distance of the interior part of this double
ring from the surface of the planet is about 22240
miles, it is no less than 33360 miles broad, but,
by estimation, its thickness does not much exceed
274 miles, so that it appears like a plane. By
the laws of mechanics, it is impossible that this
body can retain its position by the adhesion of its
particles alone; it must necessarily revolve with a
velocity that will generate a centrifugal force
sufficient to balance the attraction of Saturn.
Observation confirms the truth of these principles,
showing that the rings rotate about the planet in
ten hours and a half, which is considerably less
than the time a satellite would take to revolve
about Saturn at the same distance. Their plane
is inclined to the ecliptic, at an angle of 28° 39'
45"; and, in consequence of this obliquity of position,
they always appear elliptical to us, but with
an excentricity so variable as even to be occasionally
like a straight line drawn across the planet.
In the beginning of October, 1832, the plane of
the rings passed through the centre of the earth;
in that position they are only visible with very
superior instruments, and appear like a fine line
across the disc of Saturn. About the middle of
December, in the same year, the rings became
invisible, with ordinary instruments, on account
of their plane passing through the sun. In the
end of April, 1833, the rings vanished a second
time, and reappeared in June of that year.
It is a singular result of theory, that the rings
could not maintain their stability of rotation
if they were every where of uniform thickness;
for the smallest disturbance would destroy the
equilibrium, which would become more and more
deranged till, at last, they would be precipitated
on the surface of the planet. The rings of Saturn
must therefore be irregular solids of unequal
breadth in different parts of the circumference,
so that their centres of gravity do not coincide
with the centres of their figures. Professor Struve
has also discovered that the centre of the ring is
not concentric with the centre of Saturn; the
interval between the outer edge of the globe of
the planet, and the outer edge of the ring on one
side, is 11".073, and, on the other side, the
interval is 11".288, consequently there is an
excentricity of the globe in the ring of 0".215.
If the rings obeyed different forces, they would not
remain in the same plane, but the powerful attraction
of Saturn always maintains them and his
satellites in the plane of his equator. The rings,
by their mutual action, and that of the sun and
satellites, must oscillate about the centre of
Saturn, and produce phenomena of light and
shadow whose periods extend to many years.
The periods of rotation of the moon and the
other satellites are equal to the times of their
revolutions, consequently these bodies always turn
the same face to their primaries: however, as the
mean motion of the moon is subject to a secular
inequality, which will ultimately amount to many
circumferences, if the rotation of the moon
were perfectly uniform, and not affected by the
same inequalities, it would cease exactly to counterbalance
the motion of revolution; and the
moon, in the course of ages, would successively
and gradually discover every point of her surface
to the earth. But theory proves that this never
can happen; for the rotation of the moon,
though it does not partake of the periodic inequalities
of her revolution, is affected by the same
secular variations, so that her motions of rotation
and revolution round the earth will always balance
each other, and remain equal. This circumstance
arises from the form of the lunar spheroid, which
has three principal axes of different lengths at
right angles to each other.
The moon is flattened at her poles from her centrifugal
force, therefore her polar axis is the least;
the other two are in the plane of her equator, but
that directed towards the earth is the greatest.
The attraction of the earth, as if it had drawn out
that part of the moon's equator, constantly brings
the greatest axis, and consequently the same hemisphere,
towards us, which makes her rotation participate
in the secular variations in her mean motion
Of revolution. Even if the angular velocities of rotation
and revolution had not been nicely balanced
in the beginning of the moon's motion, the attraction
of the earth would have recalled the greatest axis
to the direction of the line joining the centres of the
moon and earth; so that it would have vibrated
on each side of that line in the same manner as
a pendulum oscillates on each side of the vertical
from the influence of gravitation. No such libration
is perceptible; and as the smallest disturbance
would make it evident, it is clear that if
the moon has ever been touched by a comet, the
mass of the latter must have been extremely small;
for if it had been only the hundred thousandth part
of that of the earth, it would have rendered the
libration sensible. According to analysis, a similar
libration exists in the motions of Jupiter's satellites,
which still remains insensible to observation.
It is true the moon is liable to librations depending
upon the position of the spectator; at
her rising, part of the western edge of her disc is
visible, which is invisible at her setting, and the
contrary takes place with regard to her eastern
edge. There are also librations arising from the
relative positions of the earth and moon in their
respective orbits, but as they are only optical appearances,
one hemisphere will be eternally concealed
from the earth. For the same reason, the
earth, which must be so splendid. an object to one
lunar hemisphere, will be for ever veiled from the
other. On account of these circumstances, the
remoter hemisphere of the moon has its day a
fortnight long, and a night of the same duration,
not even enlightened by a moon, while the favoured
side is illuminated by the reflection of the earth
during its long night. A planet exhibiting a surface
thirteen times larger than that of the moon,
with all the varieties of clouds, land, and water
coming successively into view, would be a splendid
object to a lunar traveller in a journey to his antipodes.
The great height of the lunar mountains
probably has a considerable influence on the phenomena
of her motion, the more so as her compression
is small, and her mass considerable. In
the curve passing through the poles, and that
diameter of the moon which always points to the
earth, nature has furnished a permanent meridian,
to which the different spots on her surface have
been referred, and their positions determined with
as much accuracy as those of many of the most
remarkable places on the surface of our globe.
The distance and minuteness of Jupiter's satellites
render it extremely difficult to ascertain their
rotation. It was, however, accomplished by Sir
William Herschel from their relative brightness.
He observed that they alternately exceed each
other in brilliancy, and, by comparing the maxima
and minima of their illumination with their positions
relatively to the sun and to their primary, lie
found that, like the moon, the time of their rotation
is equal to the period of their revolution about
Jupiter. Miraldi was led to the same conclusion
with regard to the fourth satellite, from the motion
of a spot on its surface.
SECTION XI.
THE rotation of the earth, which determines the
length of the day, may be regarded as one of the
most important elements in the system of the
world. It serves as a measure of time, and forms
the standard of comparison for the revolutions of
the celestial bodies, which, by their proportional
increase or decrease, would soon disclose any
changes it might sustain. Theory and observation
concur in proving that, among the innumerable
vicissitudes which prevail throughout creation,
the period of the earth's diurnal rotation is
immutable. A fluid, falling from a higher to a
lower level, carries with it the velocity due to its
revolution with the earth at a greater distance
from the centre; it will therefore accelerate,
although to an almost infinitesimal extent, the
earth's daily rotation. The sum of all these increments
of velocity, arising from the descent of
all the rivers on the earth's surface, would in time
become perceptible, did not nature, by the process
of evaporation, raise the waters back to their
sources; and thus, by again removing matter to
a greater distance from the centre, destroy the
velocity generated by its previous approach; so
that the descent of rivers does not affect the
earth's rotation. Enormous masses projected by
volcanos from the equator to the poles, and the
contrary, would indeed aflect it, but there is no
evidence of such convulsions. The disturbing
action of the moon and planets, which has so
powerful an effect on the revolution of the earth,
in no way influences its rotation; the constant
friction of the trade-winds on the mountains and
continents between the tropics does not impede its
velocity, which theory even proves to be the same
as if the sea, together with the earth, formed one
solid mass. But although these circumstances be
inefficient, a variation in the mean temperature
would certainly occasion a corresponding change
in the velocity of rotation; for, in the science of
dynamics, it is a principle in a system of bodies,
or of particles revolving about a fixed centre, that
the momentum, or sum of the products of the
mass of each, into its angular velocity and distance
from the centre, is a constant quantity, if the
system be not deranged by a foreign cause. Now,
since the number of particles in the system is the
same, whatever its temperature may be, when
their distances from the centre are diminished,
their angular velocity must be increased, in order
that the preceding quantity may still remain constant.
It follows then, that, as the primitive
momentum of rotation with which the earth was
projected into space must necessarily remain the
same, the smallest decrease in heat, by contracting
the terrestrial spheroid, would accelerate its rotation,
and consequently diminish the length of the
day. Notwithstanding the constant accession of
heat from the sun's rays, geologists have been
induced to believe, from the fossil remains, that
the mean temperature of the globe is decreasing.
The high temperature of mines, hot springs,
and, above all, the internal fires which have produced
and do still occasion such devastation on
our planet, indicate an augmentation of heat
towards its centre; the increase of density, corresponding
to the depth and the form of the spheroid,
being what theory assigns to a fluid mass in rotation,
concur to induce the idea that the temperature
of the earth was originally so high as to
reduce all the substances of which it is composed
to a state of fusion, or of vapour, and that, in the
course of ages, it has cooled down to its present
state; that it is still becoming colder, and that it
will continue to do so till the whole mass arrives at
the temperature of the medium in which it is
placed, or rather at a state of equilibrium between
this temperature, the cooling power of its own radiation,
and the heating effect of the sun's rays.
Previous to the formation of ice at the poles,
the ancient lands of our northern latitudes, long
since obliterated, might, no doubt, have been
capable of producing those tropical plants whose
debris, swept into the deep at these remote periods,
are preserved in the coal measures which must
have been formed in the abysses of the ocean prior
to the elevation of the modern continents and
islands above its surface. But, even if the decreasing
temperature of the earth be sufficient to
produce the observed efiects, it must be extremely
slow in its operation; for, in consequence of the
rotation of the earth being a measure of the periods
of the celestial motions, it has been proved that,
if the length of the day had decreased by the three--
thousandth part of a second since the observations
of Hipparchus, two thousand years ago, it would
have diminished the secular equation of the moon
by 4".4. It is therefore beyond a doubt that the
mean temperature of the earth cannot have sensibly
varied during that time; if, then, the appearances
exhibited by the strata are really owing to a decrease
of internal temperature, it either shows the
immense periods requisite to produce geological
changes, to which two thousand years are as
nothing, or that the mean temperature of the earth
had arrived at a state of equilibrium before these
observations.
However strong the indications of the primitive
fluidity of the earth, as there is no direct
proof of it, the hypothesis can only be regarded
as very probable; but one of the most profound
philosophers and elegant writers of modern times
has found in the secular variation in the excentricity
of the terrestrial orbit an evident cause
of decreasing temperature. That accomplished
author, in pointing out the mutual dependences of
phenomena, says, It is evident that the mean
temperature of the whole surface of the globe, in
so far as it is maintained by the action of the sun
at a higher degree than it would have were the
sun extinguished, roust depend on the mean quantity
of the sun's rays which it receives, or — which
comes to the same thing — on the total quantity
received in a given invariable time; and the length
of the year being unchangeable in all the fluctuations
of the planetary system, it follows that the
total amount of solar radiation will determine,
cæteris paribus, the general climate of the earth.
Now, it is not difficult to show that this amount
is inversely proportional to the minor axis of the
ellipse described by the earth about the sun, regarded
as slowly variable ; and that, therefore, the
major axis remaining, as we know it to be, constant,
and the orbit being actually in a state of
approach to a circle, and consequently the minor
axis being on the increase, the mean annual
amount of solar radiation received by the whole
earth must be actually on the decrease. We have
therefore an evident real cause to account for the
phenomenon.' The limits of the variation in the
excentricity of the earth's orbit are unknown;
but if its ellipticity has ever been as great as that
of the orbit of Mercury or Pallas, the mean temperature
of the earth must have been sensibly
higher than it is at present; whether it was great
enough to render our northern climates fit for the
production of tropical plants, and for the residence
of the elephant and other animals now inhabitants
of the torrid zone, it is impossible to say.
The relative quantity of heat received by the
earth at different moments during a single revolution
varies with the position of the perigee, which
accomplishes a tropical revolution in 21067 years.
in the year 1245 of our era, and 19822 years
before it, the perigee coincided with the winter
solstice; at both these periods the earth was
nearer the sun during the summer, and farther
from him in the winter, than in any other position
of the apsides; the extremes of temperature must
therefore have been greater than at present; but
as the terrestrial orbit was probably more elliptical
at the distant epoch, the heat of the summers must
have been very great, though possibly compensated
by the rigour of the winters; at all events, none
of these changes affect the length of the day.
It appears, from the marine shells found on the
tops of the highest mountains, and in almost every
part of the globe, that immense continents have
been elevated above the ocean, which must have
engulphed others. Such a catastrophe would be
occasioned by a variation in the position of the
axis of rotation on the surface of the earth; for
the seas, tending to a new equator, would leave
some portions of the globe and overwhelm others.
Now, it is found by the laws of mechanics that,
in every body, be its form or density what it may,
there arc at least three axes at right angles to each
other, round any one of which, if the solid begins
to rotate, it will continue to revolve for ever, provided
it be not disturbed by a foreign cause, but
that the rotation about any other axis will only
be permanent for an instant; consequently the
poles or extremities of the instantaneous axis of
rotation would perpetually change their position
on the surface of the body. In an ellipsoid of
revolution, the polar diameter, and every diameter
in the plane of the equator, are the only permanent
axes of rotation; consequently, if the ellipsoid were
to begin to revolve about any diameter between the
pole and the equator, the motion would be so
unstable, that the axis of rotation and the position
of the poles would change every instant. Hence,
as the earth does not differ much from this figure,
if it did not turn round one of its principal axes,
the position of the poles would change daily ; the
equator, which is 90° distant, would undergo corresponding
variations; and the geographical latitudes
of all places, being estimated from the equator,
assumed to be fixed, would be perpetually
changing.
A displacement in the position of the poles of
only two hundred miles would be sufficient to produce
these effects, and would immediately be detected;
but as the latitudes are found to be invariable,
it may be concluded that the terrestrial
spheroid must have revolved about the same axis
for ages. The earth and planets differ so little
from ellipsoids of revolution, that, in all probability,
any libration from one axis to another, produced
by the primitive impulse which put them in
motion, must have ceased soon after their creation
from the friction of the fluids at their surfaces.
Theory also proves that neither nutation, precession,
nor any of the disturbing forces that affect
the system, have the smallest influence on the axis
of rotation, which maintains a permanent position
on the surface, if the earth be not disturbed in its
rotation by a foreign cause, as the collision of a
comet, which might have happened in the immensity
of time. But had that been the case, its
effects would still have been perceptible in the
variations of the geographical latitudes. If we
suppose that such an event had taken place,
and that the disturbance had been very great,
equilibrium could then only have been restored,
with regard to a new axis of rotation, by the
rushing of the seas to the new equator, which
they must have continued to do till the surface
was everywhere perpendicular to the direction of
gravity. But it is probable that such an accumulation
of the waters would not be sufficient to
restore equilibrium if the derangement had been
great, for the mean density of the sea is only about
a fifth part of the mean density of the earth, and
the mean depth of the Pacific Ocean is, not more
than four miles, whereas the equatorial radius of
the earth exceeds the polar radius about twenty--
five miles; consequently, the influence of the sea
on the direction of gravity is very small; and as it
thus appears that a great change in the position
of the axis is incompatible with the law of equilibrium,
the geological phenomena in question must
be ascribed to an internal cause. Indeed, it is now
demonstrated that the strata containing marine diluvia,
which are in lofty situations, must have been
formed at the bottom of the ocean, and afterwards
upheaved by the action of subterraneous fires. Besides,
it is clear, from the mensuration of the arcs
of the meridian, and the length of the seconds
pendulum, as welI as from the lunar theory, that
the internal strata, and also the external outline
of the globe, are elliptical, their centres being
coincident, and their axes identical, with that of
the surface, — a state of things which, according to
the distinguished author lately quoted, is incompatible
with a subsequent accommodation of the
surface to a new and different state of rotation
from that which determined the original distribution
of the component matter. Thus, amidst the
mighty revolutions which have swept innumerable
races of organized beings from the earth, which
have elevated plains, and buried mountains in the
ocean, the rotation of the earth, and the position
of the axes on its surface, have undergone but
slight variations.
It not only appears that the strata of the terrestrial
spheroid are concentric and elliptical, but
the lunar inequalities show that they increase in
density from the surface of the earth to its centre.
This would certainly have happened if the earth
had originally been fluid, for the denser parts must
have subsided towards the centre, as it approached
a state of equilibrium; but the enormous pressure
of the superincumbent mass is a sufficient cause
for the phenomenon. Professor Leslie observes
that air, compressed into the fiftieth part of its
volume, has its elasticity fifty times augmented;
if it continue to contract at that rate, it would,
from its own incumbent weight, acquire the density
of water at the depth of thirty-four miles. But
water itself would have its density doubled at the
depth of ninety-three miles, and would even attain
the density of quicksilver at a depth of 362 miles.
In descending, therefore, towards the centre, through
nearly 4000 miles, the condensation of ordinary
substances would surpass the utmost powers of
conception. Dr. Young says that steel would be
compressed into one-fourth and stone into one--
eighth of its bulk at the earth's centre. However,
we are yet ignorant of the laws of compression of
solid bodies beyond a certain limit; though, from
the experiments of Mr. Perkins, they appear to be
capable of a greater degree of compression than
has generally been imagined.
But a density so extreme is not borne out by
astronomical observation. It might seem to follow,
therefore, that our planet must have a widely
cavernous structure, and that we tread on a crust
or shell whose thickness bears a very small proportion
to the diameter of its sphere. Possibly,
too, this great condensation at the central regions
may be counterbalanced by the increased elasticity
due to a very elevated temperature.
SECTION XII.
IT has been shown that the axis of rotation is
invariable on the surface of the earth, and observation,
as well as theory, prove that, were it not for
the action of the sun and moon on the matter at
the equator, it would remain parallel to itself in
every point of its orbit.
The attraction of an external body not only
draws a spheroid towards it, but, as the force
varies inversely as the square of the distance, it
gives it a motion about its centre of gravity, unless
when the attracting body is situate in the prolongation
of one of the axes of the spheroid. The
plane of the equator is inclined to the plane
of the ecliptic at an angle of 23° 27' 36".7;
and the inclination of the lunar orbit on the same
is 5° 8' 47".9; consequently, from the oblate
figure of the earth, the sun and moon acting
obliquely and unequally on the different parts of
the terrestrial spheroid, urge the plane of the
equator from its direction, and force it to move
from east to west, so that the equinoctial points
have a slow retrograde motion on the plane of the
ecliptic of 50".37572 annually. The direct tendency
of this action is to make the planes of the
equator and ecliptic coincide, but it is balanced
by the tendency of the earth to return to stable
rotation about the polar diameter, which is one of
its principal axes of rotation; therefore the inclination
of the two planes remains constant, as a
top spinning preserves the same inclination to the
plane of the horizon. Were the earth spherical,
this effect would not be produced, and the equinoxes
would always correspond with the same
points of the ecliptic, at least as far as this kind
of motion is concerned. But another and totally
different cause which operates on this motion has
already been mentioned. The action of the planets
on one another and on the sun occasions a very
slow variation in the position of the plane of
the ecliptic, which affects its inclination to
the plane of the equator, and gives the equinoctial
points a slow but direct motion on the
ecliptic of 0".15272 annually, which is entirely
independent of the figure of the earth, and would
be the same if it were a sphere. Thus the sun
and moon, by moving the plane of the equator,
cause the equinoctial points to retrograde on the
ecliptic, and the planets, by moving the plane of
the ecliptic, give them a direct motion, though
much less than the former; consequently, the
difference of the two is the mean precession, which
is proved, both by theory and observation, to be
about 50".223 annually.
As the longitudes of all the fixed stars are
increased by this quantity, the effects of precession
are soon detected; it was accordingly
discovered by Hipparchus, in the year 128 before
Christ, from a comparison of his own observations
with those of Timocharis, 155 years
before. In the time of Hipparchus, the entrance
of the sun into the constellation Aries was the
beginning of spring, but since that time the equinoctial
points have receded 30°, so that the constellations
called the signs of the zodiac are now
at a considerable distance from those divisions of
the ecliptic which bear their names. Moving at
the rate of 50".223 annually, the equinoctial
points will accomplish a revolution in 25805
years; but as the precession varies in different
centuries, the extent of this period will he slightly
modified. Since the motion of the sun is direct,
and that of the equinoctial points retrograde, he
takes a shorter time to return to the equator than
to arrive at the same stars; so that the tropical
year of 365.242219 mean solar days must be
increased by the time he takes to move through an
arc of 50".223, in order to have the length of the
sidereal year. By simple proportion, it is the
0.014154th part of a day, so that the sidereal year
contains 365.256373 mean solar days.
The mean annual precession is subject to a
secular variation; for, although the change in the
plane of the ecliptic, in which the orbit of the sun
lies, be independent of the form of the earth, yet,
by bringing the sun, moon, and earth into different
relative positions, from age to age, it alters the
direct action of the two first on the prominent
matter at the equator: on this account, the motion
of the equinox is greater by 0".455 now than it
was in the time of Hipparchus ; consequently, the
actual length of the tropical year is about 4s.21
shorter than it was at that time. The utmost
change that it can experience from this cause
amounts to 43 seconds.
Such is the secular motion of the equinoxes;
but it is sometimes increased and sometimes diminished
by periodic variations, whose periods depend
upon the relative positions of the sun and moon
with regard to the earth, and which are occasioned
by the direct action of these bodies on the equator.
Dr. Bradley discovered that by this action the moon
causes the pole of the equator to describe a small
ellipse in the heavens, the diameters of which are
16" and 20". The period of this inequality is 19
years, the time employed by the nodes of the lunar
orbit to accomplish a revolution. The sun causes
a small variation in the description of this ellipse;
it runs through its period in half a year. This
nutation in the earth's axis affects both the precession
and obliquity with small periodic variations;
but, in consequence of the secular variation
in the position of the terrestrial orbit, which is
chiefly owing to the disturbing energy of Jupiter
on the earth, the obliquity of the ecliptic is annually
diminished by 0".445, or, according to Bessel,
by 0".457. This variation in the course of ages
may amount to ten or eleven degrees; but the
obliquity of the ecliptic to the equator can never
vary more than 2° 42' or 3°, since the equator will
follow in some measure the motion of the ecliptic.
It is evident that the places of all the celestial
bodies are affected by precession and nutation,
and therefore all observations of them must be
corrected for these inequalities.
The densities of bodies are proportional to their
masses divided by their volumes; hence, if the
sun and planets be assumed to be spheres, their
volumes will be as the cubes of their diameters.
Now, the apparent diameters of the sun and earth,
at their mean distance, are 1922" .8 and 17".154,
and the mass of the earth is the 354936th part of
that of the sun taken as the unit: it follows, therefore,
that the earth is nearly four times as dense
as the sun; but the sun is so large, that his
attractive force would cause bodies to fall through
about 334.65 feet in a second; consequently, if
he were habitable by human beings, they would
be unable to move, since their weight would be
thirty times as great as it is here. A man of
moderate size would weigh about two tons at the
surface of the sun, whereas, at the surface of the
four new planets, he would be so light, that it
would be impossible to stand steady, since he would
only weigh a few pounds. All the planets and
satellites appear to be of less density than the earth.
The motions of Jupiter's satellites show that his
density increases towards his centre: were his mass
homogeneous, his equatorial and polar axes would
be in the ratio of 41 to 36, whereas they are observed
to be only as 41 to 38. The singular irregularities
in the form of Saturn, and the great
compression of Mars, prove the internal structure
of these two planets to be very far from uniform.
SECTION XIII.
ASTRONOMY has been of immediate and essential
use in affording invariable standards for measuring
duration, distance, magnitude, and velocity. The
sidereal day, measured by the time elapsed between
two consecutive transits of any star at the same
meridian, and the sidereal year, are immutable units
with which all great periods of time are compared;
the oscillations of the isochronous pendulum measure
its smaller portions. By these invariable standards
alone, we can judge of the slow changes that
other elements of the system may have undergone
in the lapse of ages.
The returns of the sun to the meridian, and to
the same equinox or solstice, have been universally
adopted as the measure of our civil days and years.
The solar or astronomical day is the time that
elapses between two consecutive noons or midnights;
it is consequently longer than the sidereal
day, on account of the proper motion of the sun
during a revolution of the celestial sphere; but,
as the sun moves with greater rapidity at the
winter than at the summer solstice, the astronomical
day is more nearly equal to the sidereal
day in summer than in winter. The obliquity of
the ecliptic also affects its duration, for in the equinoxes
the arc of the equator is less than the corresponding
arc of the ecliptic, and in the solstices
it is greater. The astronomical day is therefore
diminished in the first case, and increased in the
second. If the sun moved uniformly in the equator
at the rate of 59' 8".3 every day, the solar
days would be all equal; the time, therefore, which
is reckoned by the arrival of an imaginary sun at
and if, in addition to this, a bissextile be suppressed
every 4000 years, the length of the year will be
nearly equal to that given by observation. Were
the fraction neglected, the beginning of the year
would precede that of the tropical year, so that it
would retrograde through the different seasons in
a period of about 1507 years. The Egyptians
estimated the year at 365.25 days, by which they
lost one year in every 14601 — their Sothiac
period. The division of the year into months is
very old and almost universal; but the period of
seven days, by far the most permanent division of
time, and the most ancient monument of astronomical
knowledge, was used by the Brahmins in
India with the same denominations employed by
us, and was alike found in the calendars of the
Jews, Egyptians, Arabs, and Assyrians; it has
survived the fall of empires, and has existed
among all successive generations, a proof of their
common origin.
The new moon immediately following the winter
solstice in the 707th year of Rome was made the
1st of January of the first year of Julius Cæsar; the
25th of December of his forty-fifth year is considered
as the date of Christ's nativity; and Caesar's
forty-sixth year is assumed to be the first of our
era. The preceding year is called the first year
before Christ by chronologists, but by astronomers
it is called the year 0. The astronomical year
begins on the 31st of December, at noon; and the
date of an observation expresses the days and
hours which have actually elapsed since that
time.
Some remarkable astronomical eras are determined
by the position of the major axis of the
solar ellipse, which depends upon the direct motion
of the perigee and the precession of the equinoxes
conjointly, the annual motion of the one
being 11".2936, and that of the other 50".223;
hence the axis, moving at the rate of 61".5166 annually,
accomplishes a tropical revolution in 21067
years. It coincided with the line of the equinoxes
4000 or 4022 years before the Christian era,
much about the time chronologists assign for the
creation of man. In 6512 the major axis will again,
coincide with the line of the equinoxes, but then
the solar perigee will coincide with the equinox of
spring, whereas at the creation of man it coincided
with the autumnal equinox. In the year 1245,
the major axis was perpendicular to the line of
the equinoxes, then the solar perigee coincided
with the solstice of winter, and the apogee with
the solstice of summer. According to La Place,
who computed these periods from different data,
the last coincidence happened in the year 1250 of
our era, which induced him to propose that year
as a universal epoch, the vernal equinox of the
year 1250 to be the first day of the first year.
The variation in the position of the solar ellipse
occasions corresponding changes in the length of
the seasons. In its present position, spring is
shorter than summer, and autumn longer than
winter; and while the solar perigee continues as
it now is, between the solstice of winter and the
equinox of spring, the period including spring and
summer will be longer than that including autumn
and winter. In this century the difference is
between seven and eight days. The intervals
will be equal towards the year 6512, when the
perigee coincides with the equinox of spring, but
when it passes that point, the spring and summer,
taken together, will be shorter than the period
including the autumn and winter. These changes
will be accomplished in a tropical revolution of
the major axis of the earth's orbit, which includes
an interval of 21067 years; and as the seasons
are opposed to each other in the northern and
southern hemispheres, they alternately receive, for
a period of 10534 years, a greater portion of light
and heat. Were the orbit circular, the seasons
would be equal; their difference arises from the
excentricity of the orbit, small as it is; but the
changes are so trifling, as to be imperceptible in
the short space of human life.
No circumstance in the whole science of astronomy
excites a deeper interest than its application
to chronology. "Whole nations," says La Place,
"have been swept from the earth, with their languages,
arts, and sciences, leaving but confused
masses of ruins to mark the place where mighty
cities stood; their history, with the exception of a
few doubtful traditions, has perished; but the
perfection of their astronomical observations marks
their high antiquity, fixes the periods of their
existence, and proves that, even at that early time,
they must have made considerable progress in
science." The ancient state of the heavens may
now be computed with great accuracy; and by
comparing the results of computation with ancient
observations, the exact period at which they were
made may be verified if true, or, if false, their
error may be detected. If the date be accurate,
and the observation good, it will verify the accuracy
of modern tables, and will show to how many
centuries they may be extended, without the fear
of error. A few examples will show the importance
of the subject.
At the solstices the sun is at his greatest distance
from the equator, consequently his declination
at these times is equal to the obliquity of the
ecliptic, which, in former times, was determined
from the meridian length of the shadow of the
stile of a dial on the day of the solstice. The
lengths of the meridian shadow at the summer and
winter solstice are recorded to have been observed
at the city of Layang, in China, 1100 years before
the Christian era. From these, the distances of
the sun from the zenith of the city of Layang are
known. Half the sum of these zenith distances
determines the latitude, and half their difference
gives the obliquity of the ecliptic at the period of
the observation; and as the law of the variation
of the obliquity is known, both the time and place
of the observations have been verified by computations
from modern tables. Thus the Chinese had
made some advances in the science of astronomy
at that early period; their whole chronology is
founded on the observation of eclipses, which
prove the existence of that empire for more
than 4700 years. The epoch of the lunar tables
of the Indians, supposed by Bailly to be 3000
years before the Christian era, was proved by La
Place, from the acceleration of the moon, not to
be more ancient than the time of Ptolemy, who
lived in the second century after it. The great
inequality of Jupiter and Saturn, whose cycle
embraces 929 years, is peculiarly fitted for marking
the civilization of a people. The Indians had
determined the mean motions of these two planets
in that part of their periods when the apparent
mean motion of Saturn was at the slowest, and
that of Jupiter the most rapid. The periods in
which that happened was 3102 years before the
Christian era, and the year 1491 after it. The
returns of comets to their perihelia may possibly
mark the present state of astronomy to future
ages.
The places of the fixed stars are affected by the
precession of the equinoxes; and as the law of
that variation is known, their positions at any
time may be computed. Now Eudoxus, a contemporary
of Plato, mentions a star situate in the
pole of the equator, and it appears from computation,
that Draconis was not very far from that
place about 3000 years ago; but as it is only
about 2150 years since Eudoxus lived, he must
have described an anterior state of the heavens,
supposed to be the same that was mentioned by
Chiron, about the time of the siege of Troy.
Every circumstance concurs in showing that
astronomy was cultivated in the highest ages of
antiquity.
It is possible that a knowledge of astronomy
may lead to the interpretation of hieroglyphical
characters. Astronomical signs are often found
on the ancient Egyptian monuments, probably
employed by the priests to record dates. The
author had occasion to witness an instance of
this most interesting application of astronomy, in
ascertaining the date of a papyrus, sent from
Egypt by Mr. Salt, in the hieroglyphical researches
of the late Dr. Thomas Young, whose
profound and varied acquirements do honour to his
country and to the age in which he lived. The
manuscript was found in a mummy-case; it
proved to be a horoscope of the age of Ptolemy,
and its antiquity was determined from the configuration
of the heavens at the time of its construction.

The form of the earth furnishes a standard of
weights and measures for the ordinary purposes
of life, as well as for the determination of the
masses and distances of the heavenly bodies. The
length of the pendulum vibrating seconds of mean
solar time, in the latitude of London, forms the
standard of the British measure of extension. Its
length oscillating in vacuo at the temperature of
62° of Fahrenheit, and reduced to the level of the
sea was determined, by Captain Kater, to be
39'1392 inches. The weight of a cubic inch of
water at the temperature of 62° of Fahrenheit,
barometer 30 inches, was also determined in parts
of the imperial troy pound, whence a standard
both of weight and capacity is deduced. The
French have adopted the metre equal to 3.2808992
English feet for their unit of linear measure, which
is the ten-millionth part of that quadrant of the
meridian passing through Formentera and Greenwich,
the middle of which is nearly in the forty--
fifth degree of latitude. Should the national
standards of the two countries be lost in the
vicissitude of human affairs, both may be recovered,
since they are derived from natural standards
presumed to be invariable. The length of the
pendulum would be found again with more facility
than the metre ; but as no measure is mathematically
exact, an error in the original standard
may at length become sensible in measuring a
great extent, whereas the error that must necessarily
arise in measuring the quadrant of the
meridian is rendered totally insensible by subdivisions,
in taking its ten-millionth part. The French
have adopted the decimal division, not only in
time, but in their degrees, weights, and measures,
on account of the very great facility it affords in
computation. It has not been adopted by any
other people, though nothing is more desirable than
that all nations should concur in using the same
division and standards, not only on account of
convenience, but as affording a more definite idea
of quantity. It is singular that the decimal
division of the day, of degrees, weights, and
measures, was employed in China 4000 years
ago; and that at the time Ibn Junis made his
observations at Cairo, about the year 1000 of the
Christian era, the Arabs were in the habit of employing
the vibrations of the pendulum in their
astronomical observations as a measure of time.
SECTION XIV.
ONE of the most immediate and remarkable effects
of a gravitating force external to the earth, is the
alternate rise and fall of the surface of the sea twice
in the course of a lunar day, or 24h 50m 48s of mean
solar time. As it depends upon the action of the
sun and moon, it is classed among astronomical
problems, of which it is by far the most difficult
and its explanation the least satisfactory. The
form of the surface of the ocean in equilibrio, when
revolving with the earth round its axis, is an ellipsoid
flattened at the poles; but the action of the
sun and moon, especially of the moon, disturbs the
equilibrium of the ocean. If the moon attracted
the centre of gravity of the earth and all its particles
with equal and parallel forces, the whole
system of the earth and the waters that cover it
would yield to these forces with a common motion,
and the equilibrium of the seas would remain undisturbed.
The difference of the forces, and the
inequality of their directions alone, trouble the
equilibrium.
It is proved by daily experience, as well as by
strict mathematical reasoning, that if a number of
waves or oscillations be excited in a fluid by different
forces, each pursues its course, and has its
effect independently of the rest. Now in the tides
there are three distinct kinds of oscillations, depending
on different causes, and producing their effects
independently of each other, which may therefore
be estimated separately.
The oscillations of the first kind, which are
very small, are independent of the rotation of the
earth; and as they depend upon the motion of the
disturbing body in its orbit, they are of long periods.
The second kind of oscillations depends
upon the rotation of the earth, therefore their period
is nearly a day; and the oscillations of the third
kind vary with an angle equal to twice the angular
rotation of the earth; and consequently happen
twice in twenty-four hours. The first afford no
particular interest, and are extremely small; but
the difference of two consecutive tides depends
upon the second. At the time of the solstices,
this difference, which ought to be very great,
according to Newton's theory, is hardly sensible
on our shores. La Place has shown that this
discrepancy arises from the depth of the sea, and
that if the depth were uniform there would be no
difference in the consecutive tides but that which
is occasioned by local circumstances; it follows,
therefore, that as this difference is extremely small,
the sea, considered in a large extent, must be
nearly of uniform depth, that is to say, there is a
certain mean depth from which the deviation is
not great. The mean depth of the Pacific Ocean
is supposed to be about four miles, that of the
Atlantic only three. From the formulæ which
determine the difference of the consecutive tides,
it is also proved, that the precession of the equinoxes,
and the nutation of the earth's axis, are
the same as if the sea formed one solid mass with
the earth.
Oscillations of the third kind are the semi--
diurnal tides, so remarkable on our coasts; they
are occasioned by the combined action of the sun
and moon, but as the effect of each is independent
of the other, they may be considered separately.
The particles of water under the moon are more
attracted than the centre of gravity of the earth,
hi the inverse ratio of the square of the distances;
hence they have a tendency to leave the earth,
but are retained by their gravitation, which is
diminished by this tendency. On the contrary, the
moon attracts the centre of the earth more powerfully
than she attracts the particles of water in the
hemisphere opposite to her ; so that the earth has
a tendency to leave the waters, but is retained by
gravitation, which is again diminished by this tendency.
Thus the waters immediately under the
moon are drawn from the earth at the same time
that the earth is drawn from those which are diametrically
opposite to her ; in both instances producing
an elevation of the ocean of nearly the same
height above the surface of equilibrium; for the
diminution of the gravitation of the particles in
each position is almost the same, on account of the
distance of the moon being great in comparison of
the radius of the earth. Were the earth entirely
covered by the sea, the water thus attracted by the
moon would assume the form of an oblong spheroid,
whose greater axis would point towards the moon,
since the columns of water under the moon and
in the direction diametrically opposite to her are
rendered lighter in consequence of the diminution
of their gravitation ; and in order to preserve
the equilibrium, the axes 90° distant would
be shortened. The elevation, on account of the
smaller space to which it is confined, is twice as
great as the depression, because the contents of
the spheroid always remain the same. The effects
of the sun's attraction are in all respects similar
to those of the moon's, though greatly less in
degree, on account of his distance; he therefore only
modifies the form of this spheroid a little. If the
waters were capable of assuming the form of equiLibrium
instantaneously, that is, the form of the
spheroid, its summit would always point to the
moon, notwithstanding the earth's rotation; but
on account of their resistance the rapid motion
produced in them by rotation, prevents them from
assuming at every instant the form which the equilibrium
of the forces acting upon them requires.
Hence, on account of the inertia of the waters, if
the tides be considered relatively to the whole
earth, and open sea, there is a meridian about
30° eastward of the moon, where it is always high
water both in the hemisphere where the moon is
and in that which is opposite. On the west side
of this circle the tide is flowing, on the east it is
ebbing, and on every part of the meridian at 90°
distant, it is low water. These tides must necessarily
happen twice in a day, since the rotation
of the earth brings the same point twice
under the meridian of the moon in that time, once
under the superior, and once under the inferior,
meridian.
In the semidiurnal tides there are two phenomena
particularly to be distinguished, one occurring
twice in a month, and the other twice in
a year.
The first phenomenon is, that the tides are much
increased in the syzigies, or at the time of new
and full moon. In both cases the sun and moon
are in the same meridian, for when the moon is
new they are in conjunction, and when she is full,
they are in opposition. In each of these positions
their action is combined to produce the highest or
spring tides under that meridian, and the lowest
in those points that are 90° distant. It is observed
that the higher the sea rises in full tide,
the lower it is in the ebb. The neap tides take
place when the moon is in quadrature; they neither
rise so high nor sink so low as the spring
tides. The spring tides are much increased when
the moon is in perigee, because she is then nearest
to the earth. It is evident that the spring tides
must happen twice in a month, since in that time
the moon is once new and once full.
The second phenomenon in the tides is the
augmentation, which occurs at the time of the
equinoxes, when the sun's declination is zero,
which happens twice every year. The greatest
tides take place when a new or full moon happens
near the equinoxes while the moon is in perigee.
The inclination of the moon's orbit on the ecliptic
is 5° 8' 47".9; hence, in the equinoxes, the action
of the moon would be increased if her node were
to coincide with her perigee. The equinoctial
gales often raise these tides to a great height. Besides
these remarkable variations, there are others
arising from the declination of the sun and moon,
which have a great influence on the ebb and flow
of the waters. The moon takes about twenty-nine
days and a half to vary through all her declinations,
which sometimes extend about 28 degrees
on each side of the equator, while the sun requires
about 365 1/4 days to accomplish his motion from
tropic to tropic through about 23 1/2 degrees, so that
their combined motion causes great irregularities,
and, at times, their attractive forces counteract
each other's effects to a certain extent; but, on an
average, the mean monthly range of the moon's
declination is nearly the same as the annual range
of the declination of the sun ; consequently the
highest tides take place within the tropics, and the
lowest towards the poles.
Both the height and time of high eater are
thus perpetually changing; therefore, in solving
the problem, it is required to determine the
heights to which the tides rise, the times at which
they happen, and the daily variations. Theory
and observation show, that each partial tide
creases as the cube of the apparent diameter or of
the parallax of the body which produces it, and
that it diminishes as the square of the cosine of
the declination of that body.
The periodic motions of the waters of the ocean,
on the hypothesis of an ellipsoid of revolution
entirely covered by the sea, are very far from
according with observation; this arises from the
very great irregularities in the surface of the earth,
which is but partially covered by the sea, from
the variety in the depths of the ocean, the manner
in which it is spread out on the earth, the position
and inclination of the shores, the currents, and
the resistance the waters meet with, causes
it is impossible to estimate, but which modify
the oscillations of the great mass of the ocean.
However, amidst all these irregularities, the ebb
and flow of the sea maintain. a ratio to the forces
producing them sufficient to indicate their nature,
and to verify the law of the attraction of the sun
and moon on the sea. La Place observes, that
the investigation of such relations between cause
and effect is no less useful in natural philosophy
than the direct solution of problems, either to
prove the existence of the causes or to trace the
laws of their effects. Like the theory of probabilities,
it is a happy supplement to the ignorance
and weakness of the human mind. Thus the
problem of the tides does not admit of a general
solution; it is certainly necessary to analyse the
general phenomena which ought to result from the
attraction of the sun and moon, but these must be
corrected in each particular case by local observations
modified by the extent and depth of the sea,
and the peculiar circumstances of the place.
Since the disturbing action of the sun and moon
can only become sensible in a very great extent of
water, it is evident that the Pacific Ocean is one
of the principal sources of our tides; but, in consequence
of the rotation of the earth, and the
inertia of the ocean, high water does not happen
till some time after the moon's southing. The
tide raised in that world of waters is transmitted
to the Atlantic, from which sea it moves in a
northerly direction along the coasts of Africa and
Europe, arriving later and later at each place.
This great wave, however, is modified by the tide
raised in the Atlantic, which sometimes combines
with that from the Pacific in raising the sea, and
sometimes is in opposition to it, so that the tides
only rise in proportion to their difference. This
vast combined wave, reflected by the shores of the
Atlantic, extending nearly from pole to pole, still
coming northward, pours through the Irish and
British Channels into the North Sea, so that the
tides in our ports are modified by those of another
hemisphere. This the theory of the tides in each
port, both as to their height and the times at
which they take place, is really a matter of experiment,
and can only be perfectly determined by the
Mean of a very great number of observations, including
several revolutions of the moon's nodes.
The height to which the tides rise is much
greater in narrow channels than in the open sea,
on account of the obstructions they meet with.
The sea is so pent up in the British Channel, that
the tides sometimes rise as much as fifty feet at
St. Malo, on the coast of France, whereas, on the
shores of some of the South Sea islands, they do
not exceed one or two feet. The winds have a
great influence on the height of the tides, according
as they conspire with or oppose them; hut the
actual effect of the wind in exciting the waves of
the ocean extends very little below the surface:
even in the most violent storms, the water is probably
calm at the depth of ninety or a hundred
feet. The tidal wave of the ocean does not reach
the Mediterranean nor the Baltic, partly from their
position and partly from the narrowness of the
Straits of Gibraltar and of the Categat, but it is
very perceptible in the Red Sea and in Hudson's
Bay. In high latitudes, where the ocean is less
directly under the influence of the luminaries, the
rise and fall of the sea is inconsiderable, so that,
in all probability, there is no tide at the poles, or
only a small annual and monthly tide. The ebb
and flow of the sea are perceptible in rivers to a
very great distance from their estuaries. In the
Straits of Pauxis, in the river of the Amazons,
more than five hundred miles from the sea, the
tides are evident. It requires so many days for
the tide to ascend this mighty stream, that the
returning tides meet a succession of those which
are coming up; so that every possible variety
occurs in some part or other of its shores, both as
to magnitude and time. It requires a very wide
expanse of water to accumulate the impulse of the
sun and moon, so as to render their influence
sensible; on that account, the tides in the Mediterranean
and Black Sea are scarcely perceptible.
These perpetual commotion in the waters are
occasioned by forces that bear a very small proportion
to terrestrial gravitation: the sun's action
in raising the ocean is only 1/38448000 of gravitation
at the earth's surface, and the action of the
moon is little more than twice as much; these
forces being in the ratio of 1 to 2.35333, when
the sun and moon are at their mean distances from
the earth. From this ratio, the mass of the moon
is found to be only of that of the earth. Had
the action of the sun on the ocean been exactly
equal to that of the moon, there would have been
no neap tides, and the spring tides would have
been of twice the height which the action of either
the sun or moon would have produced separately;
a phenomenon depending upon the interference of
the undulations.
A stone plunged into a pool of still water
occasions a series of waves to advance along
the surface, though the water itself is not carried
forward, but only rises into heights and sinks into
hollows, each portion of the surface being elevated
and depressed in its turn. Another stone of the
same size, thrown into the water near the first,
will occasion a similar set of undulations. Then,
if an equal and similar wave from each stone arrive
at the same spot at the same time, so that the
elevation of the one exactly coincides with the
elevation of the other, their united effect will produce
a wave twice the size of either; but if one
wave precede the other by exactly half an undulation,
the elevation of the one will coincide with
the hollow of the other, and the hollow of the one
with the elevation of the other, and the waves will
so entirely obliterate one another, that the surface
of the water will remain smooth and level. Hence,
if the length of each wave be represented by 1,
they will destroy one another at intervals of  1/3, 3/2,
5/2, &c., and will combine their effects at the intervals
1, 2, 3, &c. It will be found, according to
this principle, when still water is disturbed by the
fall of two equal stones, that there are certain
lines on its surface of a hyperbolic form, where
the water is smooth in consequence of the waves
obliterating each other; and that the elevation of
the water in the adjacent parts corresponds to
both the waves united. Now, in the spring and
neap tides, arising from the combination of the
simple soli-lunar waves, the spring tide is the
joint result of the combination when they coincide
in time and place; and the neap tide happens
when they succeed each other by half an interval,
so as to leave only the effect of their difference
sensible. It is therefore evident that, if the solar
and lunar tides were of the same height, there
would be no difference, consequently no neap tides,
and the spring tides would be twice as high as
either separately. In the port of Batsha, in Tonquin,
where the tides arrive by two channels, of
lengths corresponding to half an interval, there is
neither high nor low water, on account of the
interference of the waves.
The initial state of the ocean has no influence
on the tides; for, whatever its primitive conditions
may have been, they must soon have vanished by
the friction and mobility of the fluid. One of the
most remarkable circumstances in the theory of
the tides is the assurance that, in consequence of
the density of the sea being only one-fifth of the
mean density of the earth, and that the earth
itself increases in density toward the centre, the
stability of the equilibrium of the ocean never can
be subverted by any physical cause whatever. A
general inundation, arising from the mere instability
of the ocean, is therefore impossible. A variety
of circumstances, however, tend to produce partial
variations in the equilibrium of the seas, which is
restored by means of currents. Winds, and the
periodical melting of the ice at the poles, occasion
temporary water-courses; but by far the most
important causes are the centrifugal force induced
by the velocity of the earth's rotation and variations
in the density of the sea.
The centrifugal force may be resolved into
two forces — one perpendicular, and another tangent
to the earth's surface. The tangential
force, though small, is sufficient to make the fluid
particles within the polar circles tend towards
the equator, and the tendency is much increased
by the immense evaporation in the equatorial
regions, from the heat of the sun, which disturbs
the equilibrium of the ocean; to this may
also be added the superior density of the waters
near the poles, partly from their low temperature,
and partly from their gravitation being less diminished
by the action of the sun and moon than
that of the seas of lower latitudes. In consequence
of the combination of all these circumstances, two
great currents perpetually set from each pole
towards the equator; but as they come from latitudes
where the rotatory motion of the surface of
the earth is very much less than it is between the
tropics, on account of their inertia, they do not
immediately acquire the velocity with which the
solid part of the earth's surface is revolving at the
equatorial regions, from whence it follows that,
within twenty-five or thirty degrees on each side
of the line, the ocean appears to have a general
motion from east to west, which is much increased
by the action of the trade-winds. This mighty
mass of rushing waters, at about the tenth degree
of south latitude, is turned towards the north-west
by the coast of America, runs through the Gulf of
Mexico, and, passing the Straits of Florida at the
rate of five miles an hour, forms the well-known
current of the Gulf-stream, which sweeps along
the whole coast of America, and runs northward
as far as the bank of Newfoundland, whence, bending
to the east, it flows past the Azores and Canary
Islands, till it joins the great westerly current of
the tropics about latitude 21° north. According
to Humboldt, this great circuit of 3800 leagues,
which the waters of the Atlantic are perpetually
describing between the parallels of eleven and
forty-three degrees of latitude, may be accomplished
by any one particle in two years and ten
months. Besides this, there are branches of the
Gulf-stream, which convey the fruits, seeds, and a
portion of the warmth of the tropical climates, to
our northern shores.
The general westward motion of the South Sea,
together with the south polar current, produce various
water-courses in the Pacific and Indian Oceans,
according as the one or the other prevails. The
western set of the Pacific causes currents to pass
on each side of Australia, while the polar stream
rushes along the Bay of Bengal; but the westerly
current again becomes most powerful towards Ceylon
and the Maldives, from whence it stretches by
the extremity of the Indian peninsula, past Madagascar,
to the most northern point of the continent
of Africa, where it mingles with the general motion
of the seas. Icebergs are sometimes drifted as far
as the Azores from the north pole, and from the
south pole they have come even to the Cape of Good
Hope. In consequence of the polar current, Sir
Edward Parry was obliged to give up his attempt
to reach the north pole in the year 1821, because
he found that the fields of ice were drifting to the
south faster than his party could travel over them
to the north.
SECTION XV.
THE oscillations of the atmosphere, and the changes
in its temperature, are measured by variations in
the heights of the barometer and thermometer, but
the actual length of the liquid columns in these
instruments not only depends upon the force of
gravitation, but upon capillary attraction, or the
force of cohesion, which is a reciprocal attraction
between the molecules of the liquid and those of
the tube containing it.
All bodies consist of an assemblage of material
particles held in equilibrio by a mutual affinity
or cohesive force which tends to unite them,
and also by a repulsive force — probably caloric,
the principle of heat — which tends to separate
them. The intensity of these forces decreases
rapidly, as the distance between the atoms augments,
and becomes altogether insensible as soon
as that distance has acquired a sensible magnitude.
The particles of matter are so small, that nothing
is known of their form further than the dissimilarity
of their different sides in certain cases, which
appears from their reciprocal attractions during
crystallization being more or less powerful, according
to the sides they present to one another. It
is evident that the density of substances will
depend upon the ratio which the opposing forces
of cohesion and repulsion bear to one another.
When particles of the same kind of matter are at
such distances from each other, that the cohesion
which retains them is insensible, the repulsive
principle remains unbalanced, and the particles
have a tendency to fly from one another, as in
aëriform fluids. If the particles approach sufficiently
near to produce equilibrium between the
attractive and repulsive forces, but not near enough
to admit of any influence from their form, perfect
mobility will exist among them, resulting from the
similarity of their attractions, and they will offer
great resistance when compressed, properties which
characterize fluids, in which the repulsive principle
is greater than in the gases. When the distance
between the particles is still less, solids are formed
in consequence of the preponderating force of
cohesion; but the nature of their structure will
vary, because, at such small distances, the power
of the mutual attraction of the particles will depend
upon their form, and will be modified by the sides
they present to one another during their aggregation.

All the phenomena of capillary attraction depend
upon the cohesion of the particles of matter. If a.
glass tube of extremely fine bore, such as a small
thermometer-tube, be plunged into a cup of water
or alcohol, the liquid will immediately rise in the
tube above the level of that in the cup, and the
surface of the little column thus suspended will be
concave. If the same tube be plunged into a cup
full of mercury, the liquid will also rise in the
tube, but it will never attain the level of that in the
cup, and its surface will be convex. The elevation
or depression of the same liquid in different tubes
of the same matter is in the inverse ratio of their
internal diameters, and altogether independent of
their thickness. Whence it follows that the molecular
action is insensible at sensible distances, and
that it is only the thinnest possible film of the
interior surface of the tubes that exerts a sensible
action on the liquid. So much indeed is this the
case, that, when tubes of the same bore are completely
wetted with water throughout their whole
extent, mercury will rise to the same height in all
of them, whatever be their thickness or density,
because the minute coating of moisture is sufficient
to remove the internal column of mercury beyond
the sphere of attraction of the tube, and to supply
the place of a tube by its own capillary attraction.
The forces which produce the capillary phenomena
are the reciprocal attraction of the tube and the
liquid, and of the liquid particles to one another;
and in order that the capillary column may be in
equilibria the weight of that part of it which rises
above or sinks below the level of the liquid in the
cup must balance these forces.
The estimation of the action of the liquid is a difficult
part of this problem. La Place, Dr. Young, and
other mathematicians, have considered the liquid
within the tube to be of uniform density; but Poisson,
in one of those masterly productions in which
he elucidates the most abstruse subjects, has recently
proved that the phenomena of capillary
attraction depend upon a rapid decrease in the density
of the liquid column throughout an extremely
small space at its surface. Every indefinitely thin
layer of a liquid is compressed by the liquid above
it, and supported by that below; its degree of
condensation depends upon the magnitude of the
compressing force, and as this force decreases
rapidly towards the surface, where it vanishes, the
density of the liquid decreases also. M. Poisson has
shown that, when this force is omitted, the capillary
surface becomes plane, and that the liquid in
the tube will neither rise above nor sink below the
level of that in the cup ; but, in estimating the
forces, it is also necessary to include the variation
in the density of the capillary surface round the
edges, from the attraction of the tube.
The direction of the resulting force determines
the curvature of the surface of the capillary column.
In order that a liquid may be in equilibrio, the force
resulting from all the forces acting upon it must be
perpendicular to the surface. Now, it appears that,
as glass is more dense than water or alcohol, the
resulting force will be inclined towards the interior
side of the tube, therefore the surface of the liquid
must be more elevated next the sides of the tube
than in the centre, in order to be perpendicular to
it, so that it will be concave, as in the thermometer.
But as glass is less dense than mercury, the resulting
force will be inclined from the interior side of
the tube, so that the surface of the capillary column
must be more depressed next the sides of the tube
than in the centre, in order to be perpendicular to
it, and is consequently convex, as may be perceived
in the mercury of the barometer when rising. The
absorption of moisture by sponges, sugar, salt, &c.,
are familiar examples of capillary attraction.; indeed
the pores of sugar are so minute, that there seems
as the sun; but the sun is so large, that his
attractive force would cause bodies to fall through
about 334.65 feet in a second; consequently, if
he were habitable by human beings, they would
be unable to move, since their weight would be
thirty times as great as it is here. A man of
moderate size would weigh about two tons at the
surface of the sun, whereas, at the surface of the
four new planets, he would be so light, that it
would be impossible to stand steady, since he would
only weigh a few pounds. All the planets. and
satellites appear to be of less density than the earth.
The motions of Jupiter's satellites show that his
density increases towards his centre: were his mass
homogeneous, his equatorial and polar axes would
be in the ratio of 41 to 36, whereas they are observed
to be only as 41 to 38. The singular irregularities
in the form of Saturn, and the great
compression of Mars, prove the internal structure
of these two planets to be very far from uniform.
SECTION XIII.
ASTRONOMY has been of immediate and essential
use in affording invariable standards for measuring
duration, distance, magnitude, and velocity. The
sidereal day, measured by the time elapsed between
two consecutive transits of any star at the same
meridian, and the sidereal year, are immutable units
with which all great periods of time are compared;
the oscillations of the isochronous pendulum measure
its smaller portions. By these invariable standards
alone, we can judge of the slow changes that
other elements of the system may have undergone
in the lapse of ages.
The returns of the sun to the meridian, and to
the same equinox or solstice, have been universally
adopted as the measure of our civil days and years.
The solar or astronomical day is the time that
elapses between two consecutive noons or midnights;
it is consequently longer than the sidereal
day, on account of the proper motion of the sun
during a revolution of the celestial sphere; but,
as the sun moves with greater rapidity at the
winter than at the summer solstice, the astronomical
day is more nearly equal to the sidereal
day in summer than in winter. The obliquity of
the ecliptic also affects its duration, for in the equinoxes
the arc of the equator is less than the corresponding
arc of the ecliptic, and in the solstices
it is greater. The astronomical day is therefore
diminished in the first case, and increased in the
second. If the sun moved uniformly in the equator
at the rate of 59' 8".3 every day, the solar
days would be all equal; the time, therefore, which
is reckoned by the arrival of an imaginary sun at
reduced some of the gases to a liquid state by very
great compression; but, although, atmospheric air
is capable of a great diminution of volume, it always
retains its gaseous properties, which resume
their primitive volume the instant the pressure is
removed, in consequence of the elasticity occasioned
by the mutual repulsion of its particles.
SECTION XVI.
THE atmosphere is not homogeneous; it appears
from analysis that, of 100 parts, 79 are azotic gas,
and 21 oxygen, the great source of combustion
and animal heat. Besides these, there are three
or four parts of carbonic acid gas in 1000 parts of
atmospheric air. These proportions are found to
be the same at all heights hitherto attained by
man. The air is an elastic fluid, resisting pressure
in every direction, and is subject to the power of
gravitation: for, as the space in the top of the
tube of a barometer is a vacuum, the column of
mercury suspended by the pressure of the atmosphere
on the surface of the cistern is a measure
of its weight; consequently, every variation in the
density occasions a corresponding rise or fall in
the barometrical column. The pressure of the
atmosphere is about fifteen pounds on every square
inch, so that the surface of the whole globe sustains
a weight of 11449000000 hundreds of
millions of pounds. Shell-fish, which have the
power of producing a vacuum, adhere to the rocks
by a pressure of fifteen pounds upon every square
inch of contact.
Since the atmosphere is both elastic and heavy,
its density necessarily diminishes in ascending
above the surface of the earth, for each stratum of
air is compressed only by the weight above it;
therefore the upper strata are less dense, because
they are less compressed than those below them.
Whence it is easy to show, supposing the temperature
to be constant, that, if the heights above
the earth be taken in increasing arithmetical progression,
— that is, if they increase by equal quantities,
as by a foot or a mile, the densities of the
strata of air, or the heights of the barometer, which
are proportional to them, will decrease in geometrical
progression. For example, at the level of
the sea, if the mean height of the barometer be
29.922 inches, at the height of 18000 feet it will
be 14.961 inches, or one-half as great; at the
height of 36000 feet it will be one-fourth as great;
at 54000 feet it will be one-eighth, and so on,
which affords a method of measuring the heights
of mountains with considerable accuracy, and
would be very simple if the decrease in the density
of the air were exactly according to the preceding
law; but it is modified by several circumstances,
and chiefly by the changes of temperature, because
heat dilates the air and cold contracts it, the variation
being 1/480, for every degree of Fahrenheit's
thermometer. Experience shows that the heat of
the air decreases as the height above the surface
of the earth increases; and it appears, from recent
investigations, that the mean temperature of space
is 58° below the freezing point of Fahrenheit,
which would probably be the temperature of the
surface of the earth also, were it not for the nonconducting
power of the air, whence it is enabled
to retain the heat of the sun's rays, which the
earth imbibes and radiates in all directions.
The decrease in heat is very irregular, but from
the mean of many observations, it appears to be
about 14° or 15° for every 9843 feet, which is the
cause of the severe cold and eternal snows on the
summits of the Alpine chains. The expansion of
the atmosphere from the heat of the sun occasions
diurnal variations in the height of the barometer.
Of the.various methods of computing heights from
barometrical measurements, that of Ivory has the
advantage of combining accuracy with the greatest
simplicity. The most remarkable result of
barometrical measurement was recently obtained
by Baron Von Humboldt, showing that about
eighteen thousand square leagues of the northwest
of Asia, including the Caspian Sea and the
Lake of Aral, are more than three hundred and
twenty feet below the level of the surface of the
ocean in a state of mean equilibrium. This enormous
basin is similar to some of those large cavities
on the surface of the moon, and is attributed,
by Humboldt, to the upheaving of the surrounding
mountain-chains of the Himalaya, of Kuen-Lun,
of Thian-Chan, to those of Armenia, of Erzerum,
and of Caucasus, which, by undermining the
country to so great an extent, caused it to settle
below the usual level of the sea. The very contemplation
of the destruction that would ensue
from the bursting of any of those barriers which
now shift out the sea is fearful. In consequence
of the diminished pressure of the atmosphere,
water boils at a lower temperature on the mountain-tops
than in the valleys, which induced Fahrenheit
to propose this mode of observation as a.
method of ascertaining their heights; but although
an instrument was constructed for that purpose by
Archdeacon Wollaston, it does not appear to have
been much employed.
The atmosphere, when in equilibrio, is an
ellipsoid flattened at the poles from its rotation
with the earth: in that state its strata are of
uniform density at equal heights above the level
of the sea, and it is sensibly of finite extent, whether
it consists of particles infinitely divisible or
not. On the latter hypothesis, it must really be
finite, and even if its particles be infinitely divisible,
it is known, by experience, to be of extreme
tenuity at very small heights. The barometer
rises in proportion to the superincumbent pressure.
At the level of the sea, in the latitude of 45°, and
at the temperature of melting ice, the mean height
of the barometer being 29.922 inches, the density
of air is to the density of a similar volume of mercury,
as 1 to 10477.9, consequently the height of
the atmosphere, supposed to be of uniform density,
would be about 4.95 miles; but as the density decreases
upwards in geometrical progression, it is
considerably higher, probably about fifty miles. The
air, even on the mountain-tops, is sufficiently rare
to diminish the intensity of sound, to affect respiration,
and to occasion a loss of muscular strength.
The blood burst from the lips and ears of M. de
Humboldt as he ascended the Andes, and he experienced
the same difficulty in kindling and maintaining
a fire at great heights that Marco Polo, the
Venetian, did on the mountains of Central Asia.
At the height of thirty-seven miles, the atmosphere
is still dense enough to reflect the rays of the sun
when eighteen degrees below the horizon; and
although at the height of fifty miles, the bursting
of the meteor of 1783 was heard on earth like the
report of a cannon, it only proves the immensity
of the explosion of a mass, half a mile in diameter,
which could produce a sound capable of penetrating
air three thousand times more rare than that
we breathe; but even these heights are extremely
small when compared with the radius of the earth.
The action of the sun and moon disturbs the
equilibrium of the atmosphere, producing oscillations
similar to those in the ocean, which ought to
occasion periodic variations in the heights of the
barometer. These, however, are so extremely small,
that their existence in latitudes far removed from
the equator is doubtful. M. Arago has lately been
even led to conclude that the barometrical variations
corresponding to the phases of the moon are
the effects of some special cause, totally different
from attraction, of which the nature and mode of
action are unknown. La Place seems to think
that the flux and reflux distinguishable at Paris
may be occasioned by the rise and fall of the
ocean, which forms a variable base to so great a
portion of the atmosphere.
The attraction of the sun and moon has no
sensible effect on the trade winds; the heat of the
sun occasions these aerial currents, by rarefying
the air at the equator, which causes the cooler
and more dense part of the atmosphere to rush
along the surface of the earth to the equator,
while that which is heated is carried along the
higher strata to the poles, forming two counter
currents in the direction of the meridian. But
the rotatory velocity of the air, corresponding to
its geographical position, decreases towards the
poles; in approaching the equator, it must therefore
revolve more slowly than the corresponding
parts of the earth, and the bodies on the surface
of the earth must strike against it with the excess
of their velocity, and, by its reaction, they will
meet with a resistance contrary to their motion of
rotation : so that the wind will appear, to a person
supposing himself to be at rest, to blow in a contrary
direction to the earth's rotation, or from east
to west, which is the direction of the trade winds.
The equator does not exactly coincide with the
line which separates the trade winds north and
south of it; that line of separation depends upon
the total difference of heat in the two hemispheres,
arising from the unequal length of their summers,
the distribution of land and water, and other
causes. There are many proofs of the existence
of a counter current above the trade winds. On
the Peak of Teneriffe, the prevailing winds are from
the west. The ashes of the volcano of St. Vincent's,
in the year 1812, were carried to windward
as far as the island of Barbadoes by the upper
current. The captain of a Bristol ship declared
that, on that occasion, dust from St. Vincent's fell
to the depth of five inches on the deck at the distance
of 500 miles to the eastward; and light
clouds have frequently been seen moving rapidly
from west to east, at a very great height above the
trade winds, which were sweeping along the surface
of the ocean in a contrary direction.
SECTION XVII.
WITHOUT the atmosphere, death-like silence would
prevail through nature, for it, in common with all
substances, has a tendency to impart vibrations
to those in contact with it, therefore undulations
received by the air, whether it be from a sudden
impulse, such as an explosion, or the vibrations of
a musical chord, are propagated equally in every
direction, and produce the sensation of sound upon
the auditory nerves. In the small undulations of
deep water in a calm, the vibrations of the liquid
particles are made in the vertical plane, that is,
at right angles to the direction of the transmission
of the waves; but the vibrations of the particles of
air which produce sound differ, being performed
in the same direction in which the waves of sound
travel. The propagation of sound may be illustrated
by a field of corn agitated by a gust of
wind; for however irregular the motion of the
corn may seem, on a superficial view, it will be
found, if the intensity of the wind be constant,
that the waves are all precisely similar and equal,
and that all are separated by equal intervals, and
move in equal times.
A sudden blast depresses each ear equally and
successively in the direction of the wind, but in
consequence of the elasticity of the stalks and the
force of the impulse, each car not only rises again
as soon as the pressure is removed, but bends
back nearly as much in the contrary direction,
and then continues to oscillate backwards and
forwards in equal times like a pendulum, to a less
and less extent, till the resistance of the air puts a
stop to the motion. These vibrations are the same
for every individual ear of corn; yet as their oscillations
do not all commence at the same time, but
successively, the ears will have a variety of positions
at any one instant. Some of the advancing
ears will meet others in their returning vibrations,
and as the times of oscillation are equal for all,
they will be crowded together at regular intervals;
between these, there will occur equal spaces where
the ears will be few, in consequence of being bent
in opposite directions; and at other equal intervals
they will be in their natural upright positions;
so that over the whole field there will be a regular
series of condensations and rarefactions among the
ears of corn, separated by equal intervals where
they will be in their natural state of density. In
consequence of these changes the field will be
marked by an alternation of bright and dark
bands. Thus the successive waves which fly over
the corn with the speed of the wind are totally
distinct from, and entirely independent of, the
extent of the oscillations of each individual ear,
though both take place in the same direction.
The length of a wave is equal to the space between
two ears precisely in the same state of
motion, or which are moving similarly, and the
time of the vibration of each ear is equal to that
which elapses between the arrival of two successive
waves at the same point. The only difference
between the undulations of a corn-field and those
of the air which produce sound is, that each ear
of corn is set in motion by an external cause, and
is uninfluenced by the motion of the rest, whereas
in air, which is a compressible and elastic fluid,
when one particle begins to oscillate, it communicates
its vibrations to the surrounding particles,
which transmit them to those adjacent, and so on
continually. Hence, from the successive vibrations
of the particles of air, the same regular condensations
and rarefactions take place as in the
field of corn, producing waves throughout the
whole mass of air, though each molecule, like each
individual ear of corn, never moves far from its
state of rest. The small waves of a liquid, and
the undulations of the air, like waves in the corn,
are evidently not real masses moving in the direction
in which they are advancing, but merely
outlines, motions, or forms rushing along, and
comprehending all the particles of an undulating
fluid, which are at once in a vibratory state. Or,
in other words, an undulation is merely the continued
transmission in one direction of particles
bearing a relative position to one another. It is thus
that an impulse given to any one point of the
atmosphere is successively propagated in all directions,
in waves diverging as from the centre of a
sphere to greater and greater distances, but with
decreasing intensity, in consequence of the increasing
number of particles of inert matter which
the force has to move; like the waves formed in
still water by a falling stone, which are propagated
circularly all around the centre of disturbance.
These successive spherical waves are only
the repercussions of the condensations and motions
of the first particles to which the impulse was given.
The intensity of sound depends upon the violence
and extent of the initial vibrations of air,
but whatever they may be, each undulation, when
once formed, can only be transmitted straight
forwards, and never returns back again unless
when reflected by an opposing obstacle. The
vibrations of the aerial molecules are always
extremely small, whereas the waves of sound vary
from a few inches to several feet. The various
kinds of musical instruments, the human voice,
and that of animals, the singing of birds, the
hum of insects, the roar of the cataract, the
whistling of the wind, and the other nameless
peculiarities of sound, at once show an infinite
variety in the modes of aerial vibrations, and the
astonishing acuteness and delicacy of the ear, thus
capable of appreciating the minutest differences
in the laws of molecular oscillation.
All mere noises are occasioned by irregular impulses
communicated to the ear, and if they be
short, sudden, and repeated beyond a certain degree
of quickness, the ear loses the intervals of
silence, and the sound appears continuous, because,
like the eye, it retains the perception of excitement
for a moment after the impulse has ceased.
Or, in other words, the auditory nerves continue
their vibrations for an extremely short period after
the impulse, before they return to a state of repose.
Still such sounds will be mere noise; in order to
produce a musical sound, the impulses, and, consequently,
the undulations of the air, must be all
exactly similar in duration and intensity, and must
recur after exactly equal intervals of time. The
quality of a musical note depends upon the abrupt
ness, and its intensity upon the violence and extent
of the original impulse. But the whole theory
of harmonics is founded upon the pitch which
varies with the rapidity of the vibrations. The
grave, or low tones are produced by very slow
vibrations, which increase in frequency progressively,
as the note becomes more acute. When
the vibrations of a musical chord, for example,
are less than sixteen in a second, it will not
communicate a continued sound to the ear; the
vibrations or pulses increase in number with the
acuteness of the note till, at last, all sense of pitch
is lost. The whole extent of human hearing,
from the lowest note of the organ to the highest
known cry of insects, as of the cricket, includes
about nine octaves. All ears, however, are by no
means gifted with so great a range of hearing;
many people, though not at all deaf, are quite
insensible to the cry of the bat or the cricket,
while to others it is painfully shrill. According
to recent experiments by M. Savart, the human
ear is capable of hearing sounds arising from
about 24000 vibrations in a second, and is consequently
able to appreciate a sound which only
lasts the twenty-four thousandth part of a second.
All people do not hear the deep sounds alike; that
faculty seems to depend upon the frequency of the
vibrations, and not on the intensity or loudness.
But, although there are limits to the vibrations
of our auditory nerves, Dr. Wollaston, who has
investigated this curious subject with his usual
originality, observes, that "as there is nothing in
the nature of the atmosphere to prevent the existence
of vibrations incomparably more frequent
than any of which we are conscious, we may
imagine that animals, like the Grylli, whose
powers appear to commence nearly where ours
terminate, may have the faculty of hearing still
sharper sounds which we do not know to exist,
and that there may be other insects hearing nothing
in common with us, but endowed with a
power of exciting, and a sense which perceives
vibrations of the same nature indeed as those
which constitute our ordinary sounds, but so remote,
that the animals who perceive them may be
said to possess another sense agreeing with our
own solely in the medium by which it is excited."
The velocity of sound is uniform, and is independent
of the nature, extent, and intensity of the
primitive disturbance. Consequently sounds, of
every quality and pitch, travel with equal speed;
the smallest difference in their velocity is incompatible
either with harmony or melody, for notes
of different pitches and intensities, sounded together
at a little distance, would arrive at the ear
in different times; and a rapid succession of notes
would produce confusion and discord. But as the
rapidity with which sound is transmitted depends
upon the elasticity of the medium through which
it has to pass, whatever tends to increase the
elasticity of the air must also accelerate the motion
of sound; on that account its velocity is
greater in warm than in cold weather, supposing
the pressure of the atmosphere constant. In dry
air, at the freezing temperature, sound travels at
the rate of 1089 feet in a second, and at 62° of
Fahrenheit, its speed is 1090 feet in the same time,
or 765 miles an hour, which is about three-fourths
of the diurnal velocity of the earth's equator. Since
all the phenomena of sound are simple consequences
of the physical properties of the air, they
have been predicted and computed rigorously by the
laws of mechanics. It was found, however, that
the velocity of sound, determined by observation,
exceeded what it ought to have been theoretically
by 173 feet, or about one-sixth of the whole
amount. La Place suggested that this discrepancy
might arise from the increased elasticity of the air,
in consequence of a development of latent heat
during the undulations of sound, and the result
of calculation fully confirmed the accuracy of his
views. The aerial molecules being suddenly compressed
give out their latent heat, and as air is too
bad a conductor to carry it rapidly off, it occasions
a momentary and local rise of temperature, which
increasing the consecutive expansion of the air,
causes a still greater development of heat, and as
it exceeds that which is absorbed in the next
rarefaction, the air becomes yet warmer, which
favours the transmission of sound. Analysis gives
the true velocity of sound, in terms of the elevation
of temperature that a mass of air is capable
of communicating to itself, by the disengagement
of its own latent heat, when it is suddenly compressed
in a given ratio. This change of temperature,
however, cannot be obtained directly by
experiment; but by inverting the problem, and
assuming the velocity of sound as given by experiment,
it was computed that the temperature of a
mass of air is raised nine-tenths of a degree when
the compression is equal to 1/116 of its volume.
Probably all liquids are elastic, though considerable
force is required to compress them. Water
suffers a condensation of nearly 0.0000496 for
every atmosphere of pressure, and is consequently
capable of conveying sound even more rapidly
than air, the velocity being 4708 feet in a second.
A person under water hears sounds made in air
feebly, but those produced in water very distinctly.
According to the experiments of M. Colladon, the
sound of a bell was conveyed under water through
the Lake of Geneva to the distance of about nine
miles. He also perceived that the progress of
sound through water is greatly impeded by the
interposition of any object, such as a projecting
wall; consequently sound under water resembles
light, in having a distinct shadow. It has much
less in air, being transmitted all round buildings,
or other obstacles, so as to be heard in every,
direction, though often with a considerable diminution
of intensity, as when a carriage turns the
corner of a street.
The velocity of sound, in passing through solids,
is in proportion to their hardness, and is much
greater than in air or water. A sound which
takes some time in travelling through the air,
passes almost instantaneously along a wire six
hundred feet long, consequently it is heard twice, —
first as communicated by the wire, and afterwards
through the medium of the air. The
facility with which the vibrations of sound are
transmitted along the grain of a log of wood
is well known; indeed they pass through iron,
glass, and some kinds of wood at the rate of
18530 feet in a second. The velocity of sound
is obstructed by a variety of circumstances, such
as falling snow, fog, rain, or any other cause
which disturbs the homogeneity of the medium
through which it has to pass. Humboldt says,
that it is on account of the greater homogeneity of
the atmosphere during the night that sounds are then
better heard than during the day, when its density
is perpetually changing from partial variations of
temperature. His attention was called to this
subject by the rushing noise of the great cataracts
of the Orinoco, which seemed to be three times
as loud during the night as in the day, from the
plain surrounding the Mission of the Apures.
This he illustrated by the celebrated experiment
of Chladni. A tall glass, half full of champagne,
cannot be made to ring as long as the effervescence
lasts; in order to produce a musical note, the
glass, together with the liquid it contains, must
vibrate in unison as a system, which it cannot do,
in consequence of the fixed air rising through the
wine and disturbing its homogeneity, because the
vibrations of the gas being much slower than
those of the liquid, the velocity of the sound is
perpetually interrupted. For the same reason, the
transmission of sound as well as light is impeded
in passing through an atmosphere of variable
density. Sir John Herschel, in his admirable
Treatise on Sound, thus explains the phenomenon.
"It is obvious," he says, "that sound as well as
light must be obstructed, stifled, and dissipated
from its original direction by the mixture of air
of different temperatures, and consequently elasticities;
and thus the same cause which produces
that extreme transparency of the air at night,
which astronomers alone fully appreciate, renders
it also more favourable to sound. There is no
doubt, however, that the universal and dead
silence, generally prevalent at night, renders
our auditory nerves sensible to impressions which
would otherwise escape notice. The analogy between
sound and light is perfect in this as in so
many other respects. In the general light of day
the stars disappear. In the continual hum of
voices, which is always going on by day, and
which reach us from all quarters, and never leave
the ear time to attain complete tranquillity, those
feeble sounds which catch our attention at night
make no impression. The ear, like the eye, requires
long and perfect repose to attain its utmost
sensibility."
Many instances may be brought in proof of the
strength and clearness with which sound passes
over the surface of water or ice. Lieutenant
Foster was able to carry on a conversation across
Port Bowen harbour, when frozen, a distance of a
mile and a half.
The intensity of sound depends upon the extent
of the excursions of the fluid molecules, on the
energy of the transient condensations and dilatations,
and on the greater or less number of particles
which experience these effects; and we
estimate that intensity by the impetus of these
fluid molecules on our organs, which is consequently
as the square of the velocity, and not by
their inertia, which is as the simple velocity; for
were the latter the case, there would be no sound,
because the inertia of the receding waves of air
would destroy the equal and opposite inertia of
those advancing, whence it may be concluded,
that the intensity of sound diminishes inversely
as the square of the distance from its
origin. In a tube, however, the force of sound
does not decay as in open air, unless, perhaps, by
friction against the sides. M. Biot found, from a
number of highly-interesting experiments which
he made on the pipes of the aqueducts in Paris,
that a continued conversation could be carried on,
in the lowest possible whisper, through a cylindrical
tube about 3120 feet long, the time of
transmission through that space being 2.79 seconds.
In most cases sound diverges in all
directions; but a very elegant experiment of Dr.
Young's shows that there are exceptions. When
a tuning-fork vibrates, its two branches alternately
recede from and approach one another;
each communicates its vibrations to the air, and
a musical note is the consequence. If the fork
be held upright, about a foot from the ear, and
turned round its axis while vibrating, at every
quarter revolution the sound will scarcely be
heard, while at the intermediate points it will be
strong and clear. This phenomenon is occasioned
by the air rushing between the two branches of
the fork when they recede from one another, and
being squeezed out when they approach, so that it is
in one state of motion in the direction in which the
fork vibrates, and in another at right angles to it.
It appears from theory as well as daily experience,
that sound is capable of reflection from
surfaces, according to the same laws as light.
Indeed any one who has observed the reflection of
the waves from a wall on the side of a river, or
very wide canal, after the passage of a steam-boat,
will have a perfect idea of the reflection of sound
and of light. As every substance in nature is more
or less elastic, it may be agitated according to its
own law, by the impulse of a mass of undulating
air; but reciprocally, the surface by its reaction
will communicate its undulations back again into
the air. Such reflections produce echos, and as a
series of them may take place between two or
more obstacles, each will cause an echo of the
original sound, growing fainter and fainter till it
dies away; because sound, like light, is weakened
by reflection. Should the reflecting surface be
concave towards a person, the sound will converge
towards him with increased intensity, which will
be greater still if the surface be spherical and
concentric with him. Undulations of sound diverging
from one focus of an elliptical shell converge
in the other after reflection; consequently
a sound from the one will be heard in the other
as if it were close to the ear. The rolling noise
of thunder has been attributed to reverberation
between different clouds, which may possibly be
the case to some degree; but Sir John Herschel
is of opinion, that an intensely prolonged peal is
probably owing to a combination of sounds, because
the velocity of electricity being incomparably
greater than that of sound, the thunder may be
regarded as originating in every point of a flash of
lightning at the same instant. The sound from the
nearest point will arrive first, and if the flash run in
a direct line from a person, the noise will come later
and later from the remote points of its path in a
continued roar. Should the direction of the flash
be inclined, the succession of sounds will be more
rapid and intense, and if the lightning describe
a circular curve round a person, the sound will
arrive from every point at the same instant with
a stunning crash. In like manner, the subterranean
noises heard during earthquakes, like distant
thunder, may arise from the consecutive arrival
at the ear of undulations propagated at the same
instant from nearer and more remote points; or,
if they originate in the same point, the sound
may come by different routes through strata of
different densities.
Sounds under water are heard very distinctly in
the air immediately above, but the intensity decays
with great rapidity as the observer goes farther
off; and is altogether inaudible at the distance of
two or three hundred yards: so that waves of
sound, like those of light, in passing from a dense
to a rare medium, are not only refracted but suffer
total reflection at very oblique incidences.
The laws of interference extend also to sound.
It is clear that two equal and similar musical
strings will be in unison if they communicate the
same number of vibrations to the air in the same
time. But if two such strings be so nearly in
unison that one performs a hundred vibrations in
a second, and the other a hundred and one in the
same period, — during the first few vibrations, the
two resulting sounds will combine to form one of
double the intensity of either, because the
waves will sensibly coincide in time and place,
but the one will gradually gain on the other, till, at
the fiftieth vibration, it will be half an oscillation
in advance; then the waves of air which produce
the sound being sensibly equal, but the receding
part of the one coinciding with the advancing part
of the other, they will destroy one another, and
occasion an instant of silence. The sound will be
renewed immediately after, and will gradually increase
till the hundredth vibration, when the two
waves will combine to produce a sound double the
intensity of either. These intervals of silence and
greatest intensity, called beats, will recur every
second, but if the notes differ much from one
another, the alternations will resemble a rattle;
and if the strings be in perfect unison, there will
be no beats, since there will be no interference.
Thus by interference is meant the coexistence of
two undulations, in which the lengths of the waves
are the same; and as the magnitude of an undulation
may be diminished by the addition of another
transmitted in the same direction, it follows, that
one undulation may be absolutely destroyed by
another, when waves of the same length are transmitted
in the same direction, provided that the
maxima of the undulations are equal, and that
one follows the other by half the length of a wave.
SECTION XVIII.
WHEN the particles of elastic bodies are suddenly
disturbed by an impulse, they return to their
natural position by a series of isochronous vibrations,
whose rapidity, force, and permanency
depend upon the elasticity, the form, and the
mode of aggregation which unites the particles of
the body. These oscillations are communicated
to the air, and on account of its elasticity they
excite alternate condensations and dilatations in
the strata of the fluid nearest to the vibrating
body: from thence they are propagated to a distance.
A string or wire stretched between two
pins, when drawn aside and suddenly let go, will
vibrate till its own rigidity and the resistance of
the air reduce it to rest. These oscillations may
be rotatory, in every plane, or confined to one
plane, according as the motion is communicated.
In the piano-forte, where the strings are struck
by a hammer at one extremity, the vibrations probably
consist of a bulge running to and fro from
end to end. The vibrations of sonorous bodies,
however, are compound. Suppose a vibrating string
to give the lowest C of the piano-forte, which is the
fundamental note of the string; if it be lightly
touched exactly in the middle, so as to retain that
point at rest, each half will then vibrate twice as
fast as the whole, but in opposite directions; the
ventral or bulging segments will be alternately
above and below the natural position of the string,
and the resulting note will be the octave above C.
When a point at a third of the length of the
string is kept at rest, the vibration will be three
times as fast as those of the whole string, and will
give the twelfth above C. When the point of rest
is one-fourth of the whole, the oscillations will be
four times as fast as those of the fundamental note,
and will give the double octave, and so on. Now, if
the whole string vibrate freely, a good ear will not
only hear the fundamental note, but will detect
all the others sounding along with it, though with
less and less intensity as the pitch becomes higher.
These acute sounds, being connected with the
fundamental note by the laws of harmony, are
called its harmonics. It is clear, from what has
been stated, that the string thus vibrating freely
could not give all these harmonics at once, unless
it divided itself spontaneously at its aliquot parts
into segments in opposite states of vibration,
separated by points actually at rest. In proof of
this, pieces of paper placed on the string at the
half, third, fourth, and other aliquot points, will
remain on it during its vibration, but will instantly
fly off from any of the intermediate points. Thus,
according to the law of co-existing undulations,
the whole string and each of its aliquot parts are
in different and independent states of vibration at
the same time; and as all the resulting notes are
heard simultaneously, not only the air, but the ear
also, vibrates in unison with each at the same
instant. The points of rest, called the nodal points
of the string, are a mere consequence of the law of
interferences. For if a rope fastened at one end
be moved to and fro at the other extremity, so as
to transmit a succession of equal waves along it,
they will be successively reflected when they arrive
at the other end of the rope by the fixed point, and
in returning they will occasionally interfere with
the advancing waves; and as these opposite undulations
will at certain points destroy one another,
the point of the rope in which this happens will
remain at rest. Thus a series of nodes and ventral
segments will be produced, whose number will
depend upon the tension and the frequency of the
alternate motions communicated to the moveable
end. So, when a string fixed at both ends is put
in motion by a sudden blow at any point of it, the
primitive impulse divides itself into two pulses
running opposite ways, which are each totally
reflected at the extremities, and, running back
again along the whole length, are again reflected
at the other ends; and thus they will continue to
run backwards and forwards, crossing one another
at each traverse, and occasionally interfering so as
to produce nodes; so that the motion of a string
fastened at both ends consists of a wave or pulse,
continually doubled back on itself by reflection at
the fixed extremities.
A blast of air passing over the open end of a
tube, as over the reeds in Pan's pipes; over a hole
in one side, as in the flute; or through the aperture
called a reed, with a flexible tongue, as in the
clarinet, puts the internal column of air into
longitudinal vibrations by the alternate condensations
and rarefactions of its particles; at the same
time the column spontaneously divides itself into
nodes, between which the air also vibrates longitudinally,
but with a rapidity proportional to the
number of divisions, giving the fundamental note
and all its harmonics. The nodes are produced
on the principle of interferences, by the reflection
of the longitudinal undulations, at the closed end
or ends of the pipe, as in the musical string, only
that in the one case the undulations are longitudinal,
and in the other transverse. Glass and
metallic rods, when struck at one end, or rubbed
in the direction of their length with a wet finger,
vibrate longitudinally, like a column of air, by the
alternate condensation and expansion of their
constituent particles, which produces a clear and
beautiful musical note of a high pitch, on account
of the rapidity with which these substances transmit
sound. Rods, surfaces, and in general all
undulating bodies, resolve themselves into nodes;
but in surfaces, the parts which remain at rest
during their vibrations are lines, which are curved
or plane according to the substance, its form, and
the mode of vibration. If a little fine dry sand be
strewed over the surface of a plate of glass or
metal, ground smooth at the edges, and if undulations
be excited by drawing the bow of a violin
across its edge, it will emit a musical sound, and
the sand will immediately arrange itself in the
nodal lines, where alone it will accumulate and
remain at rest, because the segments of the surface
on each side will be in different states of
vibration, the one being always elevated while the
other is depressed, and as these two motions meet
in the nodal lines, they neutralize one another.
These lines vary in form and position with the
part where the bow is drawn across, and the
point by which the plate is held being at rest,
must necessarily be in a nodal line; the smallest
variation in the pitch changes the nodal lines. A
sound may thus be detected though inaudible.
The motion of the sand shows in what direction
the vibrations take place: if they be perpendicular
to the surface, the sand will be violently tossed
up and down, till it finds the points of rest; if
they be tangential, the sand will only creep along
the surface to the nodal lines. Sometimes the
undulations are oblique, or compounded of both
the preceding. The air of a room, when thrown
into undulations by the continued sound of an
organ-pipe, or any other means, divides itself into
masses separated by nodal curves of double curvature,
such as spirals, on each side of which the
air is in opposite states of vibration.
All solids which ring when struck, as bells,
drinking-glasses, gongs, &c. have their shape
momentarily and forcibly changed by the blow,
and from their elasticity, or tendency to resume
their natural form, a series of undulations take
place, owing to the alternate condensations and
rarefactions of the particles of solid matter. These
have also their harmonic tones, and, consequently,
nodes. Indeed generally when a rigid system of
any form whatever vibrates either transversely or
longitudinally, it divides itself into a certain number
of parts, which perform their vibrations without
disturbing one another. These parts are at
every instant in alternate states of undulation,
and as the points or lines where they join partake
of both, they remain at rest because the opposing
motions destroy one another.
All bodies have a tendency to impart their
undulations both to the air and to substances in
contact with them. A musical string gives a very
feeble sound when vibrating alone, on account of
the small quantity of air set in motion ; but when
attached to a sounding-board, as in the harp and
piano-forte, it communicates its undulations to
that surface, and from thence to every part of the
instrument, so that the whole system vibrates
isochronously, and by exposing an extensive undulating
surface, which transmits its undulations to
a great mass of air, the sound is much reinforced.
It is evident that the sounding-board and the
whole instrument are agitated at once by all the
superposed vibrations excited by the simultaneous
or consecutive notes that are sounded, each having
its perfect effect independently of the rest. The
air, notwithstanding its rarity, is capable of
transmitting its undulations when in contact with
a body susceptible of admitting and exciting them.
It is thus that sympathetic undulations are excited
by a body vibrating near insulated tended strings,
capable of following its undulations, either by
vibrating entire, or by separating themselves into
their harmonic divisions. When a tuning-fork
receives a blow, and is made to rest upon a pianoforte,
during its vibration every string which, either
by its natural length, or by its spontaneous subdivisions,
is capable of executing corresponding
vibrations, responds in a sympathetic note. Some
one or other of the notes of an organ are generally
in unison with one of the panes, or with the whole
sash of a window, which consequently resound
when these notes are sounded. A peal of thunder
has frequently the same effect. The sound of
very large organ-pipes is generally inaudible till
the air be set in motion by the undulations of
some of the superior accords, and then its sound
becomes extremely energetic. Recurring vibrations
occasionally influence each other's periods.
For example: two adjacent organ-pipes, nearly
in unison, may force themselves into concord, and
two clocks, whose rates differed considerably when
separate, have been known to beat together when
fixed to the same wall.
Every one is aware of the reinforcement of
sound by the resonance of cavities. When singing
or speaking near the aperture of a wide--
mouthed vessel, the intensity of some one note
in unison with the air in the cavity is often
augmented to a great degree. Any vessel will
resound if a body vibrating the natural note
of the cavity be placed opposite to its orifice,
and be large enough to cover it; or, at least,
to set a large portion of the adjacent air in motion.
For the sound will be alternately reflected
by the bottom of the cavity and the undulating
body at its mouth. The first impulse of
the undulating substance will be reflected by the
bottom of the cavity, and then by the undulating
body, in time to combine with the second new
impulse; this reinforced sound will also be twice
reflected in time to conspire with the third new
impulse; and as the same process will be repeated
on every new impulse, each will combine with all
its echos to reinforce the sound prodigiously.
Several attempts have been made to imitate the
articulation of the letters of the alphabet. About
the year 1779, MM. Kratzenstein, of St. Petersburgh,
and Kempelen, of Vienna, constructed instruments
which articulated many letters, words,
and even sentences; Mr. Willis, of Cambridge,
has recently adapted cylindrical tubes to a reed,
whose length can be varied at pleasure by sliding
joints. Upon drawing out the tube, while a column
of air from the bellows of an organ is passing
through it, the vowels are pronounced in the
order i, e, a, o, u; on extending the tube, they are
repeated, after a certain interval, in the inverted
order u, o, a, e, i; after another interval, they are
again obtained in the direct order, and so on.
When the pitch of the reed is very high, it is
impossible to sound some of the vowels, which is
in perfect correspondence with the human voice,
female singers being unable to pronounce u and o
in their high notes. From the singular discoveries
of M. Savart, on the nature of the human voice,
and the investigations of Mr. Willis on the mechanism
of the larynx, it may be presumed that
ultimately the utterance or pronunciation of modern
languages will be conveyed, not only to the
eye, but also to the ear, of posterity. Had the
ancients possessed the means of transmitting such
definite sounds, the civilized world would still
have responded in sympathetic notes at the distance
of hundreds of ages.
SECTION XIX.
THE action of the atmosphere on light is not less
interesting than the theory of sound, for in consequence
of the refractive power of the air, no distant
object is seen in its true position.
All the celestial bodies appear to be more elevated
than they really are, because the rays of
light, instead of moving through the atmosphere
in straight lines, are continually inflected towards
the earth. Light passing obliquely out of a rare
into a denser medium, as from vacuum into air,
or from air into water, is bent or refracted from
its course towards a perpendicular to that point of
the denser surface where the light enters it. In
the same medium, the sine of the angle contained
between the incident ray and the perpendicular
is in a constant ratio to the sine of the angle contained
by the refracted ray and the same perpendicular;
but this ratio varies with the refracting
medium. The denser the medium the more the
ray is bent. The barometer shows that the density
of the atmosphere decreases as the height above
the earth increases; and direct experiments prove,
that the refractive power of the air increases with
its density; it follows, therefore, that if the temperature
be uniform, the refractive power of the
air is greatest at the earth's surface and diminishes
upwards.
A ray of light from a celestial object falling
obliquely on this variable atmosphere, instead of
being refracted at once from its course, is gradually
more and more bent during its passage
through it, so as to move in a vertical curved line,
in the same manner as if the atmosphere consisted
of an infinite number of strata of different densities.
The object is seen in the direction of a tangent
to that part of the curve which meets the eye,
consequently the apparent altitude of the heavenly
bodies is always greater than their true altitude.
Owing to this circumstance, the stars are seen
above the horizon after they are set, and the day
is lengthened from a part of the sun being visible,
though he really is behind the rotundity of the
earth. It would be easy to determine the direction
of a ray of light through the atmosphere, if the
law of the density were known; but as this law is
perpetually varying with the temperature, the cause
is very complicated. When rays pass perpendicularly
from one medium into another, they are not
bent; and experience shows, that in the same surface,
though the sines of the angles of incidence
and refraction retain the same ratio, the refraction
increases with the obliquity of incidence. Hence
it appears, from what precedes, that the refraction
is greatest at the horizon, and at the zenith there
is none; but it is proved that at all heights above
ten degrees, refraction varies nearly as the tangent
of the angular distance of the object from the
zenith, and wholly depends upon the heights of
the barometer and thermometer; for the quantity
of refraction at the same distance from the zenith
varies nearly as the height of the barometer, the
temperature being constant; and the effect of the
variation of temperature is to diminish the quantity
of refraction by about its 480th part for every
degree in the rise of Fahrenheit's thermometer.
Not much reliance can be placed on celestial
observations within less than ten or twelve degrees
of the horizon, on account of irregular variations
in the density of the air near the surface of the
earth, which are sometimes the cause of very
singular phenomena. The humidity of the air produces
no sensible effect on its refractive power.
Bodies, whether luminous or not, are only
visible by the rays which proceed from them; and
as the rays must pass through strata of different
densities in coming to us, it follows that, with the
exception of stars in the zenith, no object either in or
beyond our atmosphere is seen in its true place; but
the deviation is so small in ordinary cases, that it
causes no inconvenience, though in astronomical
and trigonometrical observations a due allowance
must be made for the effects of refraction. Dr.
Bradley's tables of refraction were formed by observing
the zenith distances of the sun at his
greatest declinations, and the zenith distances of
the pole-star above and below the pole; the sum
of these four quantities is equal to 180°, diminished
by the sum of the four refractions; whence the sum
of the four refractions was obtained; and from
the law of the variation of refraction determined
by theory, he assigned the quantity due to each
altitude. The mean horizontal refraction is about
35' 6", and at the height of forty-five degrees it is
58".36. The effect of refraction upon the same
star above and below the pole was noticed by
Alhazen, a Saracen astronomer of Spain, in the
ninth century; but its existence was known to
Ptolemy in the second, though he was ignorant of
its quantity.
The refraction of a terrestrial object is estimated
differently from that of a celestial body; it
is measured by the angle contained between the
tangent to the curvilineal path of the ray, where
it meets the eye, and the straight line joining the
eye and the object. Near the earth's surface the
path of the ray may be supposed to be circular;
and the angle of this path between tangents at the
two extremities of this arc is called the horizontal
angle. The quantity of terrestrial refraction is obtained
by measuring contemporaneously the elevation
of the top of a mountain above a point in the
plain at its base, and the depression of that point
below the top of the mountain. The distance between
these two stations is the chord of the horizontal
angle; and it is easy to prove that double the
refraction is equal to the horizontal angle, diminished
by the difference between the apparent
elevation and the apparent depression. Whence
it appears that, in the mean state of the atmosphere,
the refraction is about the fourteenth part
of the horizontal angle.
Some very singular appearances occur from the
accidental expansion or condensation of the strata
of the atmosphere contiguous to the surface of the
earth, by which distant objects, instead of being
elevated, are depressed; and sometimes, being at
once both elevated and depressed, they appear
double, one of the images being direct, and the
other inverted. In consequence of the upper edges
of the sun and moon being less refracted than the
lower, they often appear to be oval when near the
horizon. The looming also, or elevation of coasts,
mountains and ships, when viewed across the sea,
arises from unusual refraction. A friend of the
author's, on the plains of Hindostan, saw the
whole upper chain of the Himalaya mountains
start into view, from a sudden change in the density
of the air, occasioned by a heavy shower after
a very long course of dry and hot weather. Single
and double images of objects at sea, arising from
sudden changes of temperature, which are not so
soon communicated to the water on account of
its density as to the air, occur more rarely, and
are of shorter duration than similar appearances
on land. In 1818, Captain Scoresby, whose observations
on the phenomena of the polar seas are
so valuable, recognised his father's ship by its inverted
image in the air, although the vessel itself
was below the horizon. He afterwards found that
she was seventeen miles beyond the horizon, and
thirty miles distant. Two images are sometimes
seen suspended in the air over a ship, one direct
and the other inverted, with their topmasts or
their hulls meeting, according as the inverted
image is above or below the direct image. Dr.
Wollaston has proved that these appearances are
owing to the refraction of the rays through media
of different densities, by the very simple experiment
of looking along a red hot poker at a distant
object. Two images are seen, one direct and
another inverted, in consequence of the change
induced by the heat in the density of the adjacent
air. He produced the same effect by a saline or
saccharine solution with water and spirit of wine
floating upon it.
Many of the phenomena that have been ascribed
to extraordinary refraction seem to be occasional
by a partial or total reflection of the rays of light
at the surfaces of strata of different densities. It
is well known that when light falls obliquely upon
the external surface of a transparent medium, as
on a plate of glass, or stratum of air, one portion
is reflected and the other transmitted, but when
light falls very obliquely upon the internal surface,
the whole is reflected and not a ray is transmitted;
in all cases the angles made by the incident
and reflected rays with a perpendicular to
the surface being equal. As the brightness of the
reflected image depends on the quantity of light,
those arising from total reflection must be by far
the most vivid. The delusive appearance of water,
so well known to African travellers, and to the
Arab of the desert, as the Lake of the Gazelles,
is ascribed to the reflection which takes place
between strata of air of different densities, owing
to radiation of heat from the arid sandy plains.
The mirage described by Captain Mundy, in his
Journal of a Tour in India, probably arises from
this cause. 'A deep precipitous valley below us,
at the bottom of which I had seen one or two
miserable villages in the morning, bore in the
evening a complete resemblance to a beautiful
lake; the vapour, which played the part of water,
ascending nearly half way up the sides of the
vale, and on its bright surface trees and rocks
being distinctly reflected. I had not been long
contemplating the phenomenon, before a sudden
storm came on and dropped a curtain of clouds
over the scene.'
An occurrence which happened on the 18th of
November, 1804, was probably produced by reflection.
Dr. Buchan, while watching the rising sun
from the cliff about a mile to the east of Brighton,
at the instant the solar disc emerged from the surface
of the ocean, saw the cliff on which he was
standing, a wind-mill, his own figure and that of
a friend, depicted immediately opposite to him on
the sea. This appearance lasted about ten minutes,
till the sun had risen nearly his own diameter
above the surface of the waves. The whole
then seemed to be elevated into the air and successively
vanished. The rays of the sun fell upon
the cliff at an incidence of 73° from the perpendicular,
and the sea was covered with a dense fog
many yards in height, which gradually receded
before the rising sun. When extraordinary refraction
takes place laterally, the strata of variable
density are perpendicular to the horizon, and when
it is combined with vertical refraction, the objects
are magnified as if seen through a telescope.
From this cause, on the 26th of July, 1798, the
cliffs of France, fifty miles off, were seen as distinctly
from Hastings as if they had been close
at hand, and even Dieppe was said to have been
visible in the afternoon.
The stratum of air in the horizon is so much
thicker and more dense than the Stratum in the
vertical, that the sun's light is diminished 1300
times in passing through it, which enables us to
look at him when setting without being dazzled:
The loss of light, and consequently of heat, by
the absorbing power of the atmosphere, increases
with the obliquity of incidence. Of ten thousand
rays falling on its surface, 8123 arrive at a given
point of the earth if they fall perpendicularly;
1024 arrive if the angle of direction be fifty degrees;
2831 if it be seven degrees; and only five
rays will arrive through a horizontal stratum.
Since so great a quantity of light is lost in passing
through the atmosphere, many celestial objects
may be altogether invisible from the plain, which
may be seen from elevated situations. Diminished
splendour and the false estimate we make of distance
from the number of intervening objects;
lead us to suppose the sun and moon to be much
larger when in the horizon than at any other
altitude, though their apparent diameters are then
somewhat less. Instead of the sudden transitions
of light and darkness, the reflective power of the
air adorns nature with the rosy and golden hues
of the Aurora, and twilight. Even when the sun is
eighteen degrees below the horizon, a sufficient
portion of light remains to show that, at the height
of thirty miles, it is still dense enough to reflect
light. The atmosphere scatters the sun's rays,
and gives all the beautiful tints and cheerfulness
of day. It transmits the blue light in greatest
abundance; the higher we ascend, the sky assumes
a deeper hue, but in the expanse of space,
the sun and stars must appear like brilliant specks
in profound blackness.
SECTION XX.
IT is impossible thus to trace the path of a sunbeam
through our atmosphere without feeling a
desire to know its nature, by what power it traverses
the immensity of space, and the various
modifications it undergoes at the surfaces and the
interior of terrestrial substances.
Sir Isaac Newton proved the compound nature
of white light, as emitted from the sun, by passing
a sunbeam through a glass prism, which,
separating the rays by refraction, formed a spectrum
or oblong image of the sun, consisting of
seven colours, red, orange, yellow, green, blue,
indigo, and violet; of which the red is the least
refrangible, and the violet the most; but when
he reunited these seven rays by means of a lens,
the compound beam became pure white as before.
He insulated each coloured ray, and finding that
it was no longer capable of decomposition by refraction,
concluded that white light consists of
seven kinds of homogeneous light, and that to the
same colour the same refrangibility ever belongs,
and to the same refrangibility the same colour.
Since the discovery of absorbent media, however,
it appears that this is not the constitution of the
solar spectrum.
We know of no substance that is either perfectly
opaque or perfectly transparent; for even
gold may be beaten so thin as to be pervious to
light; and, on the contrary, the clearest crystal,
the purest air or water, stop or absorb its rays
when transmitted, and gradually extinguish them
as they penetrate to greater depths. On this
account, objects cannot be seen at the bottom of
very deep water, and many more stars are visible
to the naked eye from the tops of mountains than
from the valleys. The quantity of light that is
incident on any transparent substance is always
greater than the sum of the reflected and refracted
rays. A small quantity is irregularly reflected in
all directions by the imperfections of the polish
by which we are enabled to see the surface; but
a much greater portion is absorbed by the body.
Bodies that reflect all the rays appear white;
those that absorb them all seem black; but most
substances, after decomposing the white light
which falls upon them, reflect some colours and
absorb the rest. A violet reflects the violet rays
alone, and absorbs the others; scarlet cloth absorbs
almost all the colours except red; yellow cloth
reflects the yellow rays most abundantly, and blue
cloth those that are blue; consequently colour is
not a property of matter, but arises from the
action of matter upon light. Thus a white ribbon
reflects all the rays, but when dyed red, the particles
of the silk acquire the property of reflecting
the red rays most abundantly and of absorbing
the others. Upon this property of unequal
absorption, the colours of transparent media depend;
for they also receive their colour from their
power of stopping or absorbing some of the colours
of white light and transmitting others; as, for
example, black and red ink, though equally homogeneous,
absorb different kinds of rays; and
when exposed to the sun, they become heated in
different degrees, while pure water seems to transmit
all rays equally, and is not sensibly heated by
the passing light of the sun. The rich dark light
transmitted by a smalt-blue finger-glass is not a
homogeneous colour, like the blue or indigo of the
spectrum, but is a mixture of all the colours of
white light which the glass has not absorbed; and
the colours absorbed are such as, mixed with the
blue tint, would form white light. When the
spectrum of seven colours is viewed through a
thin plate of this glass, they are all visible; and
when the plate is very thick, every colour is
absorbed between the extreme red and the extreme
violet, the interval being perfectly black.
But if the spectrum be viewed through a certain
thickness of the glass intermediate between the
two, it will be found that the middle of the red
space, the whole of the orange, a great part of the
green, a considerable part of the blue, a little of
the indigo, and a very little of the violet, vanish,
being absorbed by the blue glass; and that the
yellow rays occupy a larger space, covering part
of that formerly occupied by the orange on one
side, and by the green on the other; so that the
blue glass absorbs the red light, which, when
mixed with the yellow, constitutes orange; and
also absorbs the blue light, which when mixed
with the yellow forms the part of the green
space next to the yellow. Hence, by absorption,
green light is decomposed into yellow and blue,
and orange light into yellow and red. Consequently
the orange and green rays, though incapable
of decomposition by refraction, can be
resolved by absorption, and actually consist of
two different colours possessing the same degree
of refrangibility. Difference of colour, therefore,
is not a test of difference of refrangibility, and the
conclusion deduced by Newton is no longer admissible
as a general truth. By this analysis of
the spectrum, not only with blue glass but with a
variety of coloured media, Sir David Brewster, so
justly celebrated for his optical discoveries, has
proved, that the solar spectrum consists of three
primary colours, red, yellow, and blue, each of
which exists throughout its whole extent, but with
different degrees of intensity in different parts;
and that the superposition of these three produces
all the seven hues according as each primary colour
is in excess or defect. Since a certain portion of
red, yellow, and blue rays constitute white light,
the colour of any point of the spectrum may be
considered as consisting of the predominating colour
at that point mixed with white light; consequently,
by absorbing the excess of any colour at
any point of the spectrum above what is necessary
to form white light, such white light will appear
at that point as never mortal eye looked upon
before this experiment, since it possesses the remarkable
property of remaining the same after
any number of refractions, and of being capable
of decomposition by absorption alone.
When the prism is very perfect and the sunbeam
small, so that the spectrum may be received
on a sheet of white paper in its utmost state of
purity, it presents the appearance of a riband
shaded with all the prismatic colours, having its
breadth irregularly striped or subdivided by an
indefinite number of dark and sometimes black
lines. The greater number of these rayless lines
are so extremely narrow that it is impossible to
see them in ordinary circumstances. The best
method is to receive the spectrum on the object--
glass of a telescope, so as to magnify them sufficiently
to render them visible. This experiment
may also be made, but in an imperfect manner,
by viewing a narrow slit between two nearly-closed
window-shutters through a very excellent glass
prism held close to the eye, with its refracting
angle parallel to the line of light. When the
spectrum is formed by the sun's rays, either direct
or indirect, — as from the sky, clouds, rainbow,
moon, or planets, — the black bands are always
found to be in the same parts of the spectrum,
and under all circumstances to maintain the same
relative positions, breadths, and intensities. Similar
dark lines are also seen in the light of the
stars, in the electric light, and in the flame of
combustible substances, though differently arranged,
each star and each flame having a system
of dark lines peculiar to itself, which remains the
same under every circumstance. Dr. Wollaston
and Fraunhofer of Munich discovered these lines
deficient of rays independently of each other.
Fraunhofer found that their number extends to
nearly six hundred. From these he selected seven
of the most remarkable, and determined their
distances so accurately, that they now form standard
and invariable points of reference for measuring
the refractive powers of different media on the
rays of light, which renders this department of
optics as exact as any of the physical sciences.
The rays that are wanting in the solar spectrum,
which occasion the dark lines, are possibly absorbed
by the atmosphere of the sun. If they
were absorbed by the earth's atmosphere, the very
same rays would be wanting in the spectra from
the light of the fixed stars, which is not the case,
for it has already been stated that the position of
the dark lines is not the same in spectra from
star-light and from the light of the sun. The
solar rays reflected from the moon and planets
would most likely be modified also by their atmospheres,
but they are not, — for the dark lines have
precisely the same positions in the spectra, from
the direct and reflected light of the sun.
A perfectly homogeneous colour is very rarely
to be found, but the tints of all substances are
most brilliant when viewed in light of their own
colour. The red of a wafer is much more vivid in
red than in white light; whereas, if placed in
homogeneous yellow light, it can no longer appear
red, because there is not a ray of red in the yellow
light; and were it not that the wafer, like all
other bodies, whether coloured or not, reflects
white light at its outer surface, it would appear
absolutely black when placed in yellow light.
After looking steadily for a short time at a
coloured object, such as a red wafer, on turning
the eyes to a white substance, a green image of
the wafer will appear, which is called the accidental
colour of red. All tints have their accidental
colours: — thus the accidental colour of orange is
blue; that of yellow is indigo; of green, reddish--
white; of blue, orange-red; of violet, yellow;
and of white, black; and vice versa. When the
direct and accidental colours are of the same intensity,
the accidental is then called the complementary
colour, because any two colours are said
to be complementary to one another which produce
white when combined.
Recent experiments by Plateau of Brussels
prove that direct and accidental colours differ
essentially. From these it appears that two complementary
colours from direct impression, which
would produce white when combined, produce
black, or extinguish one another by their union,
when accidental; and also that the combination
of all the tints of the solar spectrum produces
white light if they be from a direct impression on
the eye, whereas blackness results from a union
of the same tints if they be accidental. M. Plateau
attributes the phenomena of accidental colours
to a reaction of the retina after being excited by
direct vision. When the image of an object is
impressed on the retina only for a few moments,
the picture left is exactly of the same colour with
the object, but in an extremely short time the
picture is succeeded by the accidental image. If
the prevailing impression be a very strong white
light, its accidental image is not black, but a variety
of colours in succession. With a little attention
it will generally be found that, whenever the
eye is affected by one prevailing colour, it sees at
the same time the accidental colour, in the same
manner as in music the ear is sensible at once to
the fundamental note and its harmonic sounds.
The imagination has a powerful influence on our
optical impressions, and has been known to revive
the images of highly luminous objects months and
even years afterwards.
SECTION XXI.
NEWTON and most of his immediate successors
imagined light to be a material substance emitted
by all self-luminous bodies in extremely minute
particles, moving in straight lines with prodigious
velocity, which, by impinging upon the optic
nerves, produce the sensation of light. Many of
the observed phenomena have been successfully
explained by this theory; it seems, however,
totally inadequate to account for the following
circumstances.
When two equal rays of red light, proceeding
from two luminous points, fall upon a sheet of
white paper in a dark room, they will produce a
red spot on it, which will be twice as bright as
either ray would produce singly, provided the
difference in the lengths of the two beams, from
the luminous points to the red spot on the paper,
be exactly the 0.0000258th part of an inch. The
same effect will take place if the difference in
their lengths be twice, three times, four times,
&c., that quantity. But if the difference in the
lengths of the two rays be equal to one-half of the
0 0000258th part of an inch, or to its 1 1/2, 2 1/2, 3 1/2,
&c. part, the one light will entirely extinguish the
other, and will produce absolute darkness on the
paper where the united beams fall. If the difference
in the lengths of their paths be equal to the
1 1/4,2 1/4, 3 1/4 &c. of the 0.0000258th part of an
inch, the red spot arising from the combined
beams will be of the same intensity which one
alone would produce. If violet light be employed,
the difference in the lengths of the two beams
must be equal to the 0.0000157th part of an inch,
in order to produce the same phenomena; and
for the other colours the difference must be intermediate
between the 0.0000258th and the
0.0000157th part of an inch. Similar phenomena
may be seen by viewing the flame of a
candle through two very fine slits in a card extremely
near to one another; or by admitting the
sun's light into a dark room through a pin-hole
about the fortieth of an inch in diameter, and
receiving the image on a sheet of white paper.
When a slender wire is held in the light, its
shadow consists of a bright white bar or stripe in
the middle, with a series of alternate black and
brightly coloured stripes on each side. The rays
which bend round the wire in two streams are of
equal lengths in the middle stripe; it is consequently
doubly bright from their combined effect;
but the rays which fall on the paper on each side
of the bright stripe, being of such unequal lengths
as to destroy one another, form black lines. On
each side of these black lines the rays are again
of such lengths as to combine to form bright
stripes, and so on alternately, till the light is too
faint to be visible. When any homogeneous light
is used, such as red, the alternations are only
black and red; but on account of the heterogeneous
nature of white light, the black lines alternate
with vivid stripes or fringes of prismatic
colours, arising from the superposition of systems
of alternate black lines and lines of each homogeneous
colour. That the alternation of black
lines and coloured fringes actually does arise from
the mixture of the two streams of light which flow
round the wire, is proved by their vanishing the
instant one of the streams is interrupted. It may
therefore be concluded, as often as these stripes of
light and darkness occur, that they are owing to
the rays combining at certain intervals to produce
a joint effect, and at others to extinguish one
another. Now it is contrary to all our ideas of
matter to suppose that two particles of it should
annihilate one another under any circumstances
whatever; while, on the contrary, it is impossible
not to be struck with the perfect similarity between
the interferences of small undulations of air and
water and the preceding phenomena. The analogy
is indeed so perfect, that philosophers of the
highest authority concur in the supposition that
the celestial regions are filled with an extremely
rare, imponderable, and highly elastic medium or
ether, whose particles are capable of receiving the
vibrations communicated to them by self-luminous
bodies, and of transmitting them to the optic
nerves, so as to produce the sensation of light.
The acceleration in the mean motion of Encke's
comet renders the existence of such a medium
almost certain. It is clear that, in this hypothesis,
the alternate stripes of light and darkness are
entirely the effect of the interference of the undulations;
for, by actual measurement, the length of
a wave of the mean red rays of the solar spectrum
is equal to the 0.0000258th part of an inch; consequently,
when the elevation of the waves combine,
they produce double the intensity of light that
each would do singly; and when half a wave
combines with a whole, — that is, when the hollow
of one wave is filled up by the elevation of another,
darkness is the result. At intermediate
points between these extremes, the intensity of
the light corresponds to intermediate differences
in the lengths of the rays.
The theory of interferences is a particular case
of the general mechanical law of the superposition
of small motions; whence it appears that the
disturbance of a particle of an elastic medium,
produced by two coexistent undulations, is the
sum of the disturbances which each undulation
would produce separately; consequently the particle
will move in the diagonal of a parallelogram,
whose sides are the two undulations. If, therefore,
the two undulations agree in direction, or
nearly so, the resulting motion will be very nearly
equal to their sum, and in the same direction: if
they nearly oppose one another, the resulting motion
will be nearly equal to their difference; and
if the undulations be equal and opposite, the
resultant will be zero, and the particle will remain
at rest.
The preceding experiments, and the inferences
deduced from them, which have led to the establishment
of the doctrine of the undulations of
light, are the most splendid memorials of our
illustrious countryman Dr. Thomas Young, though
Huygens was the first to originate the idea.
It is supposed that the particles of luminous
bodies are in a state of perpetual agitation, and
that they possess the property of exciting regular
vibrations in the ethereal medium, corresponding
to the vibrations of their own molecules; and that,
on account of its elastic nature, one particle of
the ether, when set in motion, communicates its
vibrations to those adjacent, which in succession
transmit them to those farther off, so that the
primitive impulse is transferred from particle to
particle, and the undulating motion darts through
ether like a wave in water. Although the progressive
motion of light is known by experience to
be uniform, and in a straight line, the vibrations
of the particles are always at right angles to the
direction of the ray. The propagation of light is
like the spreading of waves in water; but if one
ray alone be considered, its motion may he conceived
by supposing a rope of indefinite length
stretched horizontally, one end of which is held in
the hand. If it be agitated to and fro at regular
intervals, with a motion perpendicular to its
length, a series of similar and equal tremors or
waves will be propagated along it; and if the
regular impulses be given in a variety of planes,
as up and down, from right to left, and also in
oblique directions, the successive undulations will
take place in every possible plane. An analogous
motion in the ether, when communicated to the
optic nerves, would produce the sensation of common
light. It is evident that the waves which
flow from end to end of the cord in a serpentine
form are altogether different from the perpendicular
vibratory motion of each particle of the rope,
which never deviates far from a state of rest. So
in ether each particle vibrates perpendicularly to
the direction of the ray; but these vibrations are
totally different from, and independent of, the
undulations which are transmitted through it, in
the same manner as the vibrations of each particular
ear of corn are independent of the waves
that rush from end to end of a harvest-field when
agitated by the wind.
The intensity of light depends upon the amplitude
or extent of the vibrations of the particles
of ether; while its colour depends upon their
frequency. The time of the vibration of a particle
of ether is, by theory, as the length of a wave
directly, and inversely as its velocity. Now, as
the velocity of light is known to be 192000 miles
in a second, if the lengths of the waves of the
different coloured rays could be measured, the
number of vibrations in a second corresponding
to each could be computed; but that has been
accomplished as follows: — All transparent substances
of a certain thickness, with parallel surfaces,
reflect and transmit white light, but if they
he extremely thin, both the reflected and transmitted
light is coloured. The vivid hues on soap--
bubbles, the iridescent colours produced by heat
on polished steel and copper, the fringes of colour
between the laminæ of Iceland spar and sulphate
of lime, all consist of a succession of lines disposed
in the same order, totally independent of the
colour of the substance, and determined solely by
its greater or less thickness, — a circumstance
which affords the means of ascertaining the length
of the waves of each coloured ray, and the frequency
of the vibrations of the particles producing
them. If a plate of glass be laid upon a lens of
almost imperceptible curvature, before an open window,
when they are pressed together a black spot
will be seen in the point of contact, surrounded by
seven rings of vivid colours, all differing from one
another. In the first ring, estimated from the black
spot, the colours succeed each other in the following
order; — black, very faint blue, brilliant white,
yellow, orange, and red. They are quite different
in the other rings, and in the seventh the only
colours are pale bluish-green and very pale pink.
That these rings are formed between the two surfaces
in apparent contact may be proved by laying
a prism on the lens, instead of the plate of glass,
and viewing the rings through the inclined side
of it that is next to the eye, which arrangement
prevents the light reflected from the upper surface
mixing with that from the surfaces in contact, so
that the intervals between the rings appear perfectly
black, — one of the strongest circumstances
in favour of the undulatory theory; for, although
the phenomena of the rings can be explained by
either hypothesis, there is this material difference,
that, according to the undulatory theory, the intervals
between the rings ought to be absolutely
black, which is confirmed by experiment; whereas,
by the emanating doctrine, they ought to be half
illuminated, which is not found to be the case.
M. Fresnel, whose opinion is of the first authority,
thought this test conclusive. It may therefore be
concluded that the rings arise entirely from the
interference of the rays: the light reflected from
each of the surfaces in apparent contact reaches
the eye by paths of different lengths, and produces
coloured and dark rings alternately, according as
the reflected waves coincide or destroy one another.
The breadths of the rings are unequal; they decrease
in width, and the colours become more
crowded, as they recede from the centre. Coloured
rings are also produced by transmitting light
through the same apparatus; but the colours are
less vivid, and are complementary to those reflected,
consequently the central spot is white.
The size of the rings increases with the obliquity
of the incident light; the same colour requiring
a greater thickness or space between the
glasses to produce it than when the light falls
perpendicularly upon them. Now if the apparatus
be placed in homogeneous instead of white
light, the rings will all be of the same colour with
that of the light employed. That is to say, if the
light be red, the rings will be red divided by
black intervals. The size of the rings varies with
the colour of the light. They are largest in red;
and decrease in magnitude with the succeeding
prismatic colours, being smallest in violet light.
Since one of the glasses is plane and the other
spherical, it is evident that, from the point of contact,
the space between them gradually increases
in thickness all round, so that a certain thickness
of air corresponds to each colour, which, in the
undulatory system, measures the length of the
wave producing it. By actual measurement Sir
Isaac Newton found that the squares of the diameters
of the brightest parts of each ring are as
the odd numbers, 1, 3, 5, 1, &c.; and that the
squares of the diameters of the darkest parts are
as the even numbers 0, 2, 4, 6, &c. Consequently
the intervals between the glasses at these points
are in the same proportion. If, then, the thickness
of the air corresponding to any one colour
could be found, its thickness for all the others
would be known. Now, as Sir Isaac Newton
knew the radius of curvature of the lens, and the
actual breadth of the rings in parts of an inch, it
was easy to compute that the thickness of air at
the darkest part of the first ring is the 1/89000th
part of an inch, whence all the others have been
deduced. As these intervals determine the lengths
of the waves on the undulatory hypothesis, it
appears that the length of a wave of the extreme
red of the solar spectrum is equal to the
0.0000266th part of an inch; that the length of
a wave of the extreme violet is equal to the
0.0000167th part of an inch; and as the time of
a vibration of a particle of ether producing any
particular colour is directly as the length of a
wave of that colour, and inversely as the velocity
of light, it follows that the molecules of ether
producing the extreme red of the solar spectrum
perform 458 millions of millions of vibrations in
a second; and that those producing the extreme
violet accomplish 727 millions of millions of vibrations
in the same time. The lengths of the
waves of the intermediate colours and the number
of their vibrations being intermediate between
these two, white light, which consists of all the
colours, is consequently a mixture of waves of all
lengths between the limits of the extreme red and
violet. The determination of these minute portions
of time and space, both of which have a real
existence, being the actual results of measurement,
do as much honour to the genius of Newton
as that of the law of gravitation.
The phenomenon of the coloured rings takes
place in vacuo as well as in air ; which proves
that it is the distance between the lenses alone,
and not the air, which produces the colours.
However, if water or oil be put between them, the
rings contract, but no other change ensues, and
Newton found that the thickness of different media
at which a given tint is seen is in: the inverse
ratio of their refractive indices, so that the thickness
of laminæ may be known by their colour,
which could not otherwise be measured; and as the
position of the colours in the rings is invariable,
they form a fixed standard of comparison, well
known as Newton's scale of colours; each tint
being estimated according to the ring to which. it
belongs from the central spot inclusively. Not
only the periodical colours which have been described,
but the colours seen in thick plates of
transparent substances, the variable hues of feathers,
of insects' wings, and of striated substances,
and the coloured fringes surrounding the shadows
of all bodies held in an extremely small beam
of light, all depend upon the same principle.
Whence it appears, that material substances derive
their colours from two different causes — some
from the law of interference, such as iridescent
metals, peacock's feathers, &c., and others from
the unequal absorption of the rays of white light,
such as vermilion, ultramarine, blue or green
cloth, flowers, and the greater number of coloured
bodies.
The ethereal medium pervading space is supposed
to penetrate all material substances, occupying
the interstices between their molecules;
but in the interior of refracting media it exists
in a state of less elasticity compared with its
density in vacuo; and the more refractive the
medium the less the elasticity of the ether within
it. Hence the waves of light are transmitted
with less velocity in such media as glass and
water than in the external ether. As soon as a
ray of light reaches the surface of a diaphanous
reflecting substance, for example, a plate of glass,
it communicates its undulations to the ether next
in contact with the surface, which thus becomes a
new centre of motion, and two hemispherical waves
are propagated from each point of this surface;
one of which proceeds forward into the interior of
the glass,with a less velocity than the incident wave;
and the other is transmitted back into the air with
a velocity equal to that with which it came. Thus
when refracted, the light moves with a different
velocity without and within the glass; when reflected,
the ray comes and goes with the same
velocity. The particles of ether without the glass
which communicate their motions to the particles
of the dense and less elastic ether within it, are
analogous to small elastic balls striking large ones;
for some of the motion will be communicated
to the large balls, and the small ones will be
reflected. The first would cause the refracted
wave, and the last the reflected. Conversely,
when the light passes from glass to air, the action
is similar to large balls striking small ones. The
small balls receive a motion which would cause
the refracted ray, and the part of the motion
retained by the large ones would occasion the
reflected wave ; so that when light passes through
a plate of glass or of any other medium differing
in density from the air, there is a reflection at
both surfaces. But this difference exists between
the two reflections, that one is caused by a vibration
in the same direction with that of the incident
ray, and the other by a vibration in the opposite
direction.
A single wave of air or ether would not produce
the sensation of sound or light. In order to excite
vision, the vibrations of the molecules of ether
must be regular, periodical,and very often repeated;
and as the ear continues to be agitated for a short
time after the impulse, by which alone a sound
becomes continuous, so also the fibres of the retina,
according to M. d'Arcet, continue to vibrate
for about the eighth part of a second, after the
exciting cause has ceased. Every one must have
observed when a strong impression is made by a
bright light, that the object remains visible for ra
short time after shutting the eyes, which is supposed
to be in consequence of the continued vibrations
of the fibres of the retina. It is quite possible
that many vibrations may be excited in the ethereal
medium incapable of producing undulations in the
fibres of the human retina, which yet have a powerful
effect on those of other animals or of insects.
Such may receive luminous impressions of which
we are totally unconscious, and at the same time
they may be insensible to the light and colours
which affect our eyes, their perceptions beginning
where ours end.
SECTION XXII.
IN giving a sketch of the constitution of light,
it is impossible to omit the extraordinary property
of its polarization, 'the phenomena of which,'
Sir John Herschel says, 'are so singular and
various, that to one who has only studied the common
branches of physical optics, it is like entering
into a new world, so splendid as to render it one
of the most delightful branches of experimental
inquiry, and so fertile in the views it lays open of
the constitution of natural bodies, and the minuter
mechanism of the universe, as to place it in the
very first rank of the physico-mathematical sciences,
which it maintains by the rigorous application
of geometrical reasoning its nature admits
and requires.'
In general, when a ray of light is reflected from
a pane of plate-glass, or any other substance, it
may be reflected a second time from another surface,
and it will also pass freely through trans.
parent bodies; but if a ray of light be reflected
from a pane of plate-glass at an angle of 57°, it is
rendered totally incapable of reflection at the surface
of another pane of glass in certain definite
positions, but will be completely reflected by the
second pane in other positions. It likewise loses
the property of penetrating transparent bodies in
particular positions, whilst it is freely transmitted
by them in others. Light so modified, as to be
incapable of reflection and transmission in certain
directions, is said to be polarized. This name was
originally adopted from an imaginary analogy in
the arrangement of the particles of light on the
Corpuscular doctrine to the poles of a magnet,
and is still retained in the undulatory theory.
Light may be polarized by reflection from any
polished surface, and the same property is also
imparted by refraction. It is proposed to explain
these methods of polarizing light, to give a short
account of its most remarkable properties, and to
endeavour to describe a few of the splendid phenomena
it exhibits.
If a brown tourmaline, which is a mineral generally
crystallized in the form of a long prism, be
cut longitudinally, that is, parallel to the axis of
the prism, into plates about the thirtieth of an
inch in thickness, and the surfaces polished,
luminous objects may be seen through them, as
through plates of coloured glass. The axis of
each plate is, in its longitudinal section, parallel
to the axes of the prism whence it was cut. If
one of these plates be held perpendicularly between
the eye and a candle, and turned slowly
round in its own plane, no change will take place
in the image of the candle; but if the plate he
held in a fixed position, with its axis or longitudinal
section vertical, when a second plate is interposed
between it and the eye, parallel to the
first, and turned slowly round in its own plane,
a remarkable change will be found to have taken
place in the nature of the light, for the image of the
candle will vanish and appear alternately at every
quarter revolution of the plate, varying through all
degrees of brightness down to total, or almost total,
evanescence, and then increasing again by the same
degrees as it had before decreased. These changes
depend upon the relative positions of the plates.
When the longitudinal sections of the two plates
are parallel, the brightness of the image is at its
maximum; and when the axes of the sections cross
at right angles, the image of the candle vanishes.
Thus the light, in passing through the first plate
of tourmaline, has acquired a property totally different
from the direct light of the candle. The direct
light would have penetrated the second plate equally
well in all directions, whereas the refracted ray will
only pass through it in particular positions, and
is altogether incapable of penetrating it in others.
The refracted ray is polarized in its passage through
the first tourmaline, and experience shows that it
never loses that property, unless when acted upon
by a new substance. Thus one of the properties
of polarized light is proved to be the incapability
of passing through a plate of tourmaline perpendicular
to it, in certain positions, and its ready
transmission in other positions at right angles to
the former.
Many other substances have the property of
polarizing light. If a ray of light falls upon a
transparent medium which has the same temperature,
density and structure throughout every part,
as fluids, gases, glass, &c., and a few regularly
crystallized minerals, it is refracted into a single
pencil of light by the laws of ordinary refraction,
according to which the ray, passing through the
refracting surface from the object to the eye, never
quits a plane perpendicular to that surface. Almost
all other bodies, such as the greater number
of crystallized minerals, animal and vegetable substances,
gums, resins, jellies, and all solid bodies
having unequal tensions, whether from unequal
temperature or pressure, possess the property of
doubling the image or appearance of an object
seen through them in certain directions; became
a ray of natural light falling upon them is refracted
into two pencils which move with different
velocities, and are more or less separated, according
to the nature of the body and the direction of
the incident ray. Iceland spar, a carbonate of
lime, which, by its natural cleavage, may be split
into the form of a rhombohedron, possesses this
property in an eminent degree, as may be seen by
passing a piece of paper, with a large pin hole in
it, on the side of the spar farthest from the eye.
The hole will appear double when held to the light.
One of these pencils is refracted according to the
same law, as in glass or water, never quitting the
plane perpendicular to the refracting surface, and
therefore called the ordinary ray; but the other
does quit that plane, being refracted according to
a different and much more complicated law, and
on that account is called the extraordinary ray.
For the same reason one image is called the ordinary,
and the other the extraordinary image. When
the spar is turned round in the same plane, the
extraordinary image of the hole revolves about the
ordinary image which remains fixed, both being
equally bright. But if the spar be kept in one
position, and viewed through a plate of tourmaline,
it will be found that, as the tourmaline revolves,
the images vary in their relative brightness — one
increases in intensity till it arrives at a maximum,
at the same time that the other diminishes till
it vanishes, and so on alternately at each quarter
revolution, proving both rays to be polarized; for in
one position the tourmaline transmits the ordinary
ray, and reflects the extraordinary, and after revolving
90°, the extraordinary ray is transmitted,
and the ordinary ray is reflected. Thus another
property of polarized light is, that it cannot be
divided into two equal pencils by double refraction,
in positions of the doubly refracting bodies, in
which a ray of common light would be so divided.
Were tourmaline like other doubly refracting
bodies, each of the transmitted rays would be
double, but that mineral, when of a certain thickness,
after separating the light into two polarized
pencils, absorbs one of them, and consequently
shows only one image of an object.
The pencils of light, on leaving a doubly refracting
substance, are parallel; and it is clear, from
the preceding experiments, that they are polarized
in planes at right angles to each other. But that
will be better understood by considering the change
produced in common light by the action of the
polarizing body. It has been shown that the
undulations of ether, which produce the sensation
of common light, arc performed in every possible
plane, at right angles to the direction in which the
ray is moving; but the case is very different after
the ray has passed through a doubly refracting
substance, like Iceland spar. The light then
proceeds in two parallel pencils, whose undulations
are still, indeed, transverse to the direction
of the rays, but they are accomplished in planes
at right angles to one another, analogous to two
parallel stretched cords, one of which performs its
undulations only in a horizontal plane, and the
other in a vertical, or upright plane. Thus the
polarizing action of Iceland spar, and of all doubly
refracting substances, is, to separate a ray of common
light whose waves, or undulations, are in
every plane, into two parallel rays, whose waves
or undulations lie in planes at right angles to each
other. The ray of common light may be assimilated
to a round rod, whereas the two polarized
rays are like two parallel long flat rulers, one of
which is laid horizontally on its broad surface, and
the other horizontally on its edge. The alternate
transmission and obstruction of one of these flattened
beams by the tourmaline is similar to the
facility with which a thin sheet of paper, or a card,
may be passed between the bars of a grating, or
wires of a cage, if presented edgeways, and the
impossibility of its passing in a direction transverse
to the openings of the bars or wires.
Although it generally happens that a ray of
light, in passing through Iceland spar, is separated
into two polarized rays; yet there is one
direction along which it is refracted in one ray
only, and that according to the ordinary law.
This direction is called the optic axis. Many
crystals and other substances have two optic axes,
inclined to each other, along which a ray of light
is transmitted in one pencil by the law of ordinary
refraction. The extraordinary ray is sometimes
refracted towards the optic axis, as in quartz,
zircon, ice, &c., which are, therefore, said to be
positive crystals; but when it is bent from the
optic axis, as in Iceland spar, tourmaline, emerald,
beryl, &c., the crystals are negative, which
is the most numerous class. The ordinary ray
moves with uniform velocity within a doubly refracting
substance, but the velocity of the extraordinary
ray varies with the position of the ray
relatively to the optic axis, being a maximum
when its motion within the crystal is at right
angles to the optic axis, and a minimum when
parallel to it. Between these extremes its velocity
varies according to a determinate law.
It had been inferred from the action of Iceland
spar on light, that, in all doubly refracting substances,
one only of the two rays is turned aside
from the plane of ordinary refraction, while the
other follows the ordinary law; and the great
difficulty of observing the phenomena tended to
confirm that opinion. M. Fresnel, however,
proved, by a most profound mathematical inquiry,
a priori, that the extraordinary ray must be wanting
in glass and other uncrystallized substances,
and that it must necessarily exist in carbonate of
lime, quartz, and other bodies having one optic
axis, but that, in the numerous class of substances
which possess two optic axes, both rays must
undergo extraordinary refraction, and consequently
that both must deviate from their original plane;
and these results have been perfectly confirmed by
subsequent experiments. This theory of refraction,
which, for generalization, is perhaps only
inferior to the law of gravitation, has enrolled the
name of Fresnel among those which pass not
away, and make his early loss a subject of deep
regret to all who take an interest in the higher
paths of scientific research.
Panes of glass, if sufficiently numerous, will
give a polarized beam by refraction. It appears
that, when a beam of common light is partly reflected
at, and partly transmitted through, a transparent
surface, the reflected and refracted pencils
contain equal quantities of polarized light, and
that their planes of polarization are at right angles
to one another; hence, a pile of panes of glass
will give a polarized beam by refraction. For if
a ray of common light pass through them, part of
it will be polarized by the first plate, the second
plate will polarize a part of what passes through
it, and the rest will do the same in succession, till
the whole-beam is polarized, except what is lost
reflection at the diiferent surfaces, or by absorption.
This beam is polarized in a plane at right
angles to the plane of reflection, that is, at right
angles to the plane passing through the incident
and reflected ray. But by far the most convenient
way of polarizing light is by reflection.
A pane of plate glass laid upon a piece of black
cloth, on a table at an open window, will appear
of a uniform brightness from the reflection of the
sky, pr clouds; but if it be viewed through a plate
of tourmaline, having its, axis vertical, instead of
being illuminated as before, it will be obscured by
a large cloudy spot, having its centre quite dark,
which will readily be found by elevating or depressing
the eye, and will only be visible when the
angle of incidence is 57°, that is, when a line from
the eye to the centre of the black spot makes an
angle of 33° with the surface of the reflector.
When the tourmaline is turned round in its own
plane, the dark cloud will diminish, and entirely
vanish when the axis of the tourmaline is horizontal,
and then every part of the surface of the
glass will be equally illuminated. As the tourmaline
revolves, the cloudy spot will appear and
vanish alternately at every quarter revolution.
Thus, when a ray of light is incident on a pane of
plate glass at an angle of 57°, the reflected ray is
rendered incapable of penetrating a plate of tourmaline
whose axis is in the plane of incidence;
consequently it has acquired the same character
as if it had been polarized by transmission through
a plate of tourmaline with its axis at right angles
to the plane of reflection. It is found by experience
that this polarized ray is incapable of a
second reflection at certain angles and in certain
positions of the incident plane. For if another
pane of plate glass, having one surface blackened,
be so placed as to make an angle of 33° with the
reflected ray, the image of the first pane will be
reflected in its surface, and will be alternately-illuminated
and obscured at every quarter revolution
of the blackened pane, according as the plane of
reflection is parallel or perpendicular to the plane
of polarization. Since this happens by whatever
means the light has been polarized, it evinces
another general property of polarized light, which
is, that it is incapable of reflection in a plane at
right angles to the plane of polarization.
All reflecting surfaces are capable of polarizing
light, but the angle of incidence at which it is
completely polarized, is different in each substance.
It appears that the angle for plate-glass
is 57°; in crown-glass it is 56° 55', and no ray
will be completely polarized by water, unless the
angle of incidence be 53° 11'. The angles at
which different substances polarize light are determined
by a very simple and elegant law, discovered
by Sir David Brewster, That the tangent
of the polarizing angle for any medium is
equal to the sine of the angle of incidence divided
by the sine of the angle of refraction of that medium.'
Whence also the refractive power even of
an opaque body is known when its polarizing
angle has been determined.
Metallic substances, and such as are of high
refractive powers, like the diamond, polarize imperfectly.

If a ray polarized by refraction or by reflection
from any substance not metallic be viewed
through a piece of Iceland spar, each image will
alternately vanish and re-appear at every quarter
revolution of the spar, whether it revolves from
right to left, or from left to right; which shows
that the properties of the polarized ray are symmetrical
on each side of the plane of polarization.
Although there be only one angle in each substance
at which light is completely polarized by
one reflection, yet it may be polarized at any angle
of incidence by a sufficient number of reflections.
For if a ray falls upon the upper surface of a pile
of glass at an angle greater or less than the polarizing
angle, a part only of the reflected ray will
be polarized, but a part of what is transmitted will
be polarized by reflection at the surface of the
second plate, part at the third, and so on till the
whole is polarized. This is the best apparatus;
but a plate of glass having its inferior surface
blackened, or even a polished table, will answer
the purpose.
SECTION XXIII.
SUCH is the nature of polarized light and the laws
it follows; but it is hardly possible to convey an
idea of the splendour of the phenomena it exhibits
under circumstances which an attempt will now
be made to describe.
If light polarized by reflection from a pane of
glass be viewed through a plate of tourmaline with
its longitudinal section vertical, an obscure cloud,
with its centre totally dark, will be seen on the
glass. Now let a plate of mica, uniformly about
the thirtieth of an inch in thickness, be interposed
between the tourmaline and the glass; the dark
spot will instantly vanish, and instead of it, a
succession of the most gorgeous colours will appear,
varying with every inclination of the mica,
from the richest reds, to the most vivid greens,
blues, and purples. That they may be seen in
perfection, the mica must revolve at right angles to
its own plane. When the mica is turned round in
a plane perpendicular to the polarized ray, it will
be found that there are two lines in it where the
colours entirely vanish: these are the optic axes of
the mica; which is a doubly refracting substance,
with two optic axes, along which light is refracted
in one pencil.
No colours are visible in the mica, whatever its
position may be with regard to the polarized light,
without the aid of the tourmaline, which separates
the transmitted ray into two pencils of coloured
light complementary to one another, that is, which
taken together would make white light; one of
these it absorbs and transmits the other: it is
therefore called the analyzing plate. The truth
of this will appear more readily if a film of sulphate
of lime between the twentieth and sixtieth of
an inch thick be used instead of the mica. When
the film is of uniform thickness, only one colour
will he seen when it is placed between the analyzing
plate and the reflecting glass; as, for example,
red: but when the tourmaline revolves, the
red will vanish by degrees, till the film is colourless,
then it will assume a green hue, which will
increase and arrive at its maximum when the
tourmaline has turned through ninety degrees;
after that the green will vanish and the red will
re-appear, alternating at each quadrant. Whence
it appears that the tourmaline separates the light
which has passed through the film into a red and
a green pencil, and that in one position it absorbs
the green and lets the red pass, and in another it
absorbs the red and transmits the green. This is
proved by analyzing the ray with Iceland spar instead
of tourmaline, for since the spar does not
absorb the light, two images of the sulphate of
lime will be seen, one red and the other green, and
these exchange colours every quarter revolution of
the spar, the red becoming green and the green
red, and where the images overlap, the colour is
white, proving the red and green to be complementary
to each other. The tint depends on the
thickness of the film. Films of sulphate of lime
the 0.00124 and 0.01818 of an inch respectively,
give white light in whatever position they may be
held, provided they be perpendicular to the polarized
ray; but films of intermediate thickness will
give all colours. Consequently a wedge of sulphate
of lime, varying in thickness between the
0.00124 and the 0.01818 of an inch, will appear
to be striped with all colours when polarized light
is transmitted through it. A change in the inclination
of the film, whether of mica or sulphate of
lime, is evidently equivalent to a variation in thickness.

When a plate of mica held as close to the eye as
possible, at such an inclination as to transmit the
polarized ray along one of its optic axes, is viewed
through the tourmaline with its axis vertical, a
most splendid appearance is presented. The
cloudy spot, which is in the direction of the optic
axis, is seen surrounded by a set of vividly coloured
rings of an oval form, divided into two
unequal parts by a black curved band passing
through the cloudy spot about which the rings are
formed. The other optic axis of the mica-exhibits
a similar image.
When the two optic axes of a crystal make a
small angle with one another, as in nitre, the two
sets of rings touch externally; and if the plate of
nitre be turned round in its own plane, the black
transverse bands undergo a variety of changes,
till at last the whole richly coloured image assumes
the form of the figure 8, traversed brit
black cross. Substances having one optic axis
have but one set of coloured circular rings, with
broad black cross passing through its centre and
dividing the rings into four equal parts. When
the.analyzing plate revolves, this figure recurs at
every quarter revolution, but in the intermediate
positions it assumes the complementary colours,
the black cross becoming white.
It is in vain to attempt to describe the beautiful
phenomena exhibited by innumerable bodies, all
of which undergo periodic changes in form and
colour when the analyzing plate revolves, but not
one of them shows a trace of colour without the
aid of tourmaline or something equivalent to analyze
the light, and as it were to call these beautiful
phantoms into existence. Tourmaline has the
disadvantage of being itself a coloured substance,
but that inconvenience may be avoided by employing
a reflecting surface as an analyzing plate.
When polarized light is reflected by a plate of
glass at the polarizing angle, it will be separated
into two coloured pencils, and when the analyzing
plate is turned round in its own plane, it will
alternately reflect each ray at every quarter revolution,
so that all the phenomena that have been
described will be seen by reflection on its surface.
Coloured rings are produced by analyzing polarized
light transmitted through glass melted and
suddenly or unequally cooled, also in thin plates
of glass bent with the hand, in jelly indurated or
compressed &c. &c.; in short, all the phenomena
of coloured rings may be produced, either
the plane ''of polarization revolves from right to
left, and in others from left to right, although
the crystals themselves differ apparently only by
a very slight, almost imperceptible, variety in form.
In these phenomena, the rotation to the right is
accomplished according to the same laws, and with
the same energy, as that to the left. But if two
plates of quartz be interposed which possess different
affections, the second plate undoes, either
wholly or partly, the rotatory motion which the
first had produced, according as the plates are
of equal or unequal thickness. When the plates
are of unequal thickness, the deviation is in the
direction of the strongest, and exactly the same
with that which a third plate would produce equal
in thickness to the difference of the two.
M. Biot has discovered the same properties in a
variety of liquids. Oil of turpentine and an essential
oil of laurel cause the plane of polarization to
turn to the left, whereas the syrup of the sugar-cane
and a solution of natural camphor by alcohol turn
it to the right. A compensation is effected by the
superposition or mixture of two liquids which possess
these opposite properties, provided no chemical
action takes place. A remarkable difference
was also observed by M. Biot between the action
of` the particles of the same substances when in a
liquid or solid state. The syrup of grapes, for
example, turns the plane of polarization to the
left as long as it remains liquid, but as soon as it
acquires the solid form of sugar, it causes the
plane of polarization to revolve towards the right,
a property which it retains even when again dissolved.
Instances occur also in which these circumstances
are reversed.
A ray of light passing through a liquid possessing
the power of circular polarization is not
affected by mixing other fluids with the liquid, —
such as water, ether, alcohol, &c., which do not
possess circular polarization themselves, the angle
of deviation remaining exactly the same as before
the mixture; whence M. Biot infers that the
action exercised by the liquids in question does
not depend upon their mass, but that it is a molecular
action, exercised by the ultimate particles
of matter, which only depends upon their individual
constitution, and is entirely independent of
the positions and mutual distances of the particles
with regard to each other. This peculiar action
of matter on light affords the means of detecting
varieties in the nature of substances which have
eluded chemical research. For example, no chemical
difference has been discovered between syrup
from the sugar-cane and syrup from grapes; yet
the first causes the plane of polarization to revolve
to the right, and the other to the left, therefore some
essential difference must exist in the nature of
their ultimate molecules. The same difference is
to be traced between the juices of such plants as
give sugar similar to that from the cane and those
which give sugar like that obtained from grapes.
M. Biot has shown, by these important discoveries,
that circular polarization surpasses the
power of chemical analysis in giving certain and
direct evidence of the similarity or difference
existing in the molecular constitution of bodies, as
well as of the permanency of that constitution, or
of the fluctuations to which it may be liable.
This eminent philosopher is now engaged in a
series of experiments on the progressive changes
in the sap of vegetables at different distances from
their roots, and on the products that are formed
at the various epochs of vegetation, from their
action on polarized light.
One of the many brilliant discoveries of M.
Fresnel is the production of circular and elliptical
polarization by the internal reflection of light from
plate-glass. He has shown that if light, polarized
by any of the usual methods, be twice reflected
within a glass rhomb of a given form, the vibrations
of the ether that are perpendicular to the
plane of incidence will be retarded a quarter of a
vibration, which causes the vibrating particles to
describe a circular helix, or curve, like a cork--
screw. However, that only happens when the
plane of polarization is inclined at an angle of 45°
to the plane of incidence. When these two planes
form an angle, either greater or less, the vibrating
particles move in an elliptical helix, which curve
may be represented by twisting a thread in a spiral
about an oval rod. These curves will turn to the
right or left according to the position of the incident
plane.
The motion of the ethereal medium in elliptical
and circular polarization may be represented by
the analogy of a stretched cord; for if the extremity
of such a cord be agitated at equal and regular
intervals by a vibratory motion entirely confined
to one plane, the cord will be thrown into an undulating
curve lying wholly in that plane. If to
this motion there be superadded another, similar
and equal, but perpendicular to the first, the cord
will assume the form of an elliptical helix; its
extremity will describe an ellipse, and every molecule
throughout its length will successively do the
same. But if the second system of vibrations
commence exactly a quarter of an undulation later
than the first, the cord will take the form of a
circular helix, or corkscrew; the extremity of it
will move uniformly in a circle, and every molecule
throughout the cord will do the same in succession.
It appears, therefore, that both circular
and elliptical polarization may be produced by the
composition of the motions of two rays in which
the particles of ether vibrate in planes at right
angles to one another.
Professor Airy, in a very profound and able
paper lately published in the Cambridge Transactions,
has proved that all the different kinds of
polarized light are obtained from rock crystal.
When polarized light is transmitted through the
axis of a crystal of quartz in the emergent ray,
the particles of ether move in a circular helix ;
and when it is transmitted obliquely, so as to
form an angle with the axis of the prism, the
particles of ether move in an elliptical helix,
the ellipticity increasing with the obliquity of
the incident ray; so that, when the incident
ray falls perpendicularly to the axis, the particles
of ether move in a straight line. Thus
quartz exhibits every variety of elliptical polarization,
even including the extreme cases where
the excentricity is zero, or equal to the greater
axis of the ellipse. In many crystals the two
rays are so little separated, that it is only from
the nature of the transmitted light that they are
known to have the property of double refraction.
M. Fresnel discovered, by experiments on
the properties of light passing through the axis of
quartz, that it consists of two superposed rays
moving with different velocities; and Professor
Airy has proved that, in these two rays, the molecules
of ether vibrate in similar ellipses at right
angles to each other, but in different directions;
that their ellipticity varies with the angle which
the incident ray makes with the axis; and that,
by the composition of their motions, they produce
allI the phenomena of the polarized light observed
in quartz.
It appears from what has been said, that the
molecules of ether always perform their vibrations
at right angles to the direction of the ray, but very
differently in the various kinds of light. In natural
light the vibrations are rectilinear, and in
every plane; in ordinary polarized light they are
rectilinear, but confined to one plane; in circular
polarization the vibrations are circular; and in
elliptical polarization the molecules vibrate in
ellipses. These vibrations are communicated from
molecule to molecule in straight lines when they
are rectilinear, in a circular helix when they are
circular, and in an oval or elliptical helix when
elliptical.
Some fluids possess the property of circular
polarization, as oil of turpentine; and elliptical
polarization, or something similar, seems to be
produced by reflection from metallic surfaces.
The coloured images from polarized light arise
from the interference of the rays. MM. Fresnel
Arago proved by experiment that two rays of
polarized light interfere and produces coloured
fringes if they be polarized in the same plane, but
that they do not interfere when polarized in different
planes. In all intermediate positions, fringes
of intermediate brightness are produced. The analogy
of a stretched cord will show how this happens.
Suppose the cord to be moved backwards.
and forwards horizontally at equal intervals it
will be thrown into an undulating curve lying all
in one plane. If to this motion there be super--
added another, similar and equal, commencing
exactly half an undulation later than the first, it
is evident that the direct motion every molecule
will assume, in consequence of the first system of
waves, will at every instant be exactly neutralized
by the retrogade motion it would take in virtue
of the second; and the cord itself will be quiescent,
in consequence of the interference. But if
the second system of waves be in a plane perpendicular
to the first, the effect would only be to
twist the rope, so that no interference would take
place. Rays polarized at right angles to each
other may subsequently be brought into the same
plane without acquiring the property of producing
coloured fringes; but if they belong to a pencil, the
whole of which was originally polarized in the
same plane, they will interfere.
The manner in which the coloured rays are
formed may be conceived by considering that,
when polarized light passes through the optic axis
of a doubly refracting substance, — as mica, for
example, — it is divided into two pencils by the
analyzing tourmaline; and as one ray is absorbed,
there can be no interference. But when the polarized
light passes through the mica in any other
direction, it is separated into two white rays, and
these are again divided into four pencils by the
tourmaline, which absorbs two of them; and the
other two, being transmitted in the same plane,
with different velocities, interfere and produce the
coloured phenomena. If the analysis be made
with Iceland spar, the single ray passing through
the optic axis of the mica will be refracted into
two rays polarized in different planes, and no
interference will happen: but when two rays are
transmitted by the mica, they will be separated
into four by the spar, two of which will interfere
to form one image, and the other two, by their
interference, will produce the complementary colours
of the other image, when the spar has
revolved through 90°; because, in such positions
of the spar as produce the coloured images, only
two rays are visible at a time, the other two being
reflected. When the analysis is accomplished by
reflection, if two rays are transmitted by the mica,
they are polarized in planes at right angles to each
other ; and if the plane of reflection of either of
these rays be at right angles to the plane of polarization,
only one of them will be reflected, and
therefore no interference can take place; but in
all other positions of the analyzing plate, both
rays will be reflected in the same plane, and consequently
will produce coloured rings by their
interference.
It is evident that a great deal of the light we see
must be polarized, since most bodies which have
the power of reflecting or refracting light also have
the power of polarizing it. The blue light of the
sky is completely polarized at an angle of 74° from
the sun in a plane passing through his centre.
A constellation of talent, almost unrivalled
any period in the history of science, has contributed
to the theory of polarization, though the
original discovery of that property of light was
accidental, and arose from an occurrence which,
like thousands of others, would have passed unnoticed,
had it not happened to one of those rare
minds capable of drawing the most important
inferences from circumstances apparently trifling.
In 1808, while M. Malus was accidentally viewing,
with a doubly refracting prism, a brilliant
sunset reflected from the windows of the Luxembourg
palais in Paris, on turning the prism slowly
round, he was surprised to see a very great difference
in the intensity of the two images, the most
refracted alternately changing from brightness to
obscurity at each quadrant of revolution. A phenomenon
so unlooked for induced him to investigate
its cause, whence sprung one of the most
elegant and refined branches of physical optics.
SECTION XXIV.
THE numerous phenomena of periodical colours
arising from the interference of light, which do
not admit of satisfactory explanation on any other
principle than the undulatory theory, are the
strongest arguments in favour of that hypothesis;
and even cases which at one time seemed unfavourable
to that doctrine have proved, upon investigation,
to proceed from it alone. Such is the
erroneous objection which has been made in consequence
of a difference in the mode of action of
light and sound under the same circumstances in
one particular instance. When a ray of light
from a luminous point, and a diverging sound, are
both transmitted through a very small hole into a
dark room, the light goes straight forward, and
illuminates a small spot on the opposite wall,
leaving the rest in darkness; whereas the sound,
on entering, diverges in all directions, and it
heard in every part of the room. These phenomena,
however, instead of being at variance with
the undulatory theory, are direct consequences of
it, arising from the very great difference between
the magnitude of the undulations of sound and
those of light. The undulations of light are incomparably
less than the minute aperture, while
those of sound are much greater; therefore, when
light, diverging from a luminous point, enters the
hole, the rays round its edges are oblique, and
consequently of different lengths, while those in
the centre are direct, and nearly or altogether of
the same lengths; so that the small undulations
between the centre and the edges are in different
phases, that is, in different states of undulation;
and therefore the greater number of them interfere,
and, by destroying one another, produce darkness
all around the edges of the aperture; whereas the
central rays, having the same phases, combine
and produce a spot of bright light on a wall or
screen directly opposite the hole. The waves of
air producing sound, on the contrary, being very,
large compared with the hole, do not sensibly
diverge in passing through it, and are therefore all
so nearly of the same length, and consequently in
the same phase, or state of undulation, that none
of them interfere sufficiently to destroy one another;
hence all the particles of air in the room
are set into a state of vibration, so that the intensity
of the sound is very nearly everywhere the
same. It is probable, however, that, if the aperture
were large enough, sound diverging from a
point without would scarcely be audible, except
immediately opposite the opening. Strong as the
preceding cases may be, the following experiment,
recently published by Professor Airy, seems to be
decisive in favour of the undulatory doctrine. Suppose
a plano-convex lens of very great radius to be
placed upon a plate of very highly polished metal.
When a ray of polarized light falls upon this apparatus
at a very great angle of incidence, Newton's
rings are seen at the point of contact. But as
the polarizing angle of glass differs from that of
metal, when the light falls on the lens at the polarizing
angle of glass, the black spot and the system
of rings vanish: for although light in abundance
continues to be reflected from the surface of the
metal, not a ray is reflected from the surface of
the glass that is in contact with it, consequently
no interference can take place; which proves,
beyond a doubt, that Newton's rings result from
the interference of the light reflected from the surfaces
apparently in contact.
Notwithstanding the successful adaptation of
the undulatory system to phenomena, it cannot be
denied that an objection still exists in the dispersion
of light, unless the explanation given by
Professor Airy be deemed sufficient. A sunbeam
falling on a prism, instead of being refracted to
a single point, is dispersed, or scattered over a
considerable space, so that the rays of the coloured
spectrum, whose waves are of different lengths,
have different degrees of refrangibility, and consequently
move with different velocities, either in
the medium which conveys the light from the
sun, or in the refracting medium, or in both;
whereas it has been shown that rays of all colours
move with the same velocity. If, indeed, the
velocities of the various rays were different in
space, the aberration of the fixed stars, which is
inversely as the velocity, would be different for
different colours, and every star would appear as
a spectrum whose length would be parallel to the
direction of the earth's motion, which is not found
to agree with observation. Besides, there is no
such difference in the velocities of the long and
short waves of air in the analogous case of sound,
since notes of the lowest and highest pitch are
heard in the order in which they are struck. The
solution of this anomalous case suggested by Professor
Airy from a similar instance in the theory
of sound, already mentioned, will be best understood
in his own words. 'We have every reason,'
he observes, 'to think that a part of the velocity
of sound depends upon the circumstance that the
law of elasticity of the air is altered by the instantaneous
development of latent heat on compression,
or the contrary effect on expansion. Now, if this
heat required time for its development, the quantity
of heat developed would depend upon the time
during which the particles remained in nearly the
same relative state, that is, on the time of vibration.
Consequently, the law of elasticity would
be different for different times of vibration, or for
different lengths of waves; and therefore the
velocity of transmission would be different for
waves of different lengths. If we suppose some
cause which is put in action by the vibration of
the particles to affect in a similar manner the
elasticity of the medium of light, and if we conceive
the degree of development of that cause to
depend upon time, we shall have a sufficient explanation
of the unequal refrangibility of different
coloured rays.' Even should this view be objectionable,
instead of being surprised that one discrepant
case should occur, it is astonishing to find
the theory so nearly complete, if it be considered
that no subject in the whole course of physicomathematical
inquiry is more abstruse than the
doctrine of the propagation of motion through
elastic media, perpetually requiring the aid of
analogy from the unconquerable difficulties of the
subject.
SECTION XXV.
It is not by vision alonne that a knowledge of the
sun's rays is acquired, — touch proves that they
have the power of raising the temperature of substances
exposed to their action; and experience
likewise teaches that remarkable changes are
effected by their chemical agency. Sir William
Herschel discovered that rays of caloric, which
produce the sensation of heat, exist independently
of those of light; when he used a prism of flint
glass, he found the warm rays most abundant in
the dark space a little beyond the red extremity
of the solar spectrum, from whence they decrease
towards the violet, beyond which they are
insensible. It may therefore be concluded that
the calorific rays vary in refrangibility, and that
those:-beyond the extreme red are less refrangible
than any rays of light. Wollaston, Ritter, and
Beckman discovered simultaneously that invisible
rays, known only by their chemical action, exist
in the dark space beyond the extreme violet, where
there is no sensible heat: these are more refrangible
than any of the rays of light or heat, and
gradually decrease in refrangibility towards the
other end of the spectrum, where they cease.
Thus the solar spectrum is proved to consist of
five superposed spectra, only three of which are
visible — the red, yellow, and blue; each of the
five varies in refrangibility and intensity throughout
the whole extent, the visible part being overlapped
at one extremity by the chemical, and at
the other by the calorific rays. The action of the
chemical rays blackens the salts of silver, and
their influence is daily seen in the fading of vegetable
colours: what object they are destined to
accomplish in the economy of nature remains
unknown, but certain it is, that the very existence
of the animal and vegetable creation depends upon
the calorific rays. That the heat-producing rays
exist independently of light is a matter of constant
experience in the abundant emission of them from
boiling water, yet there is every reason to believe
that both the calorific and chemical rays are modifications
of the same agent which produces the
sensation of light. The rays of heat are subject
to the same laws of reflection and refraction with
those of light; they pass through the gases with
the same facility, but a remarkable difference
obtains in the transmission of light and heat
through most solid and liquid substances; the same
body being often perfectly transparent to the luminous,
and altogether impermeable to the calorific
rays. The experiments of M. de Laroche show
that glass, however thin, totally intercepts the
obscure rays of caloric when they flow from a
body whose temperature is lower than that of boiling
water; that, as the temperature increases, the
calorific rays are transmitted more and more abundantly;
and when the body becomes highly luminous,
that they penetrate the glass with perfect
ease. The very feeble heat of moonlight must be
incapable of penetrating glass, consequently it
does not sensibly affect the thermometer, even
when concentrated; and, on the contrary, the extreme
brilliancy of the sun is probably the reason
why his heat, when brought to a focus by a lens,
is more intense than any that can be produced
artificially; and it is owing to the same cause
that glass screens, which entirely exclude the heat
of a common fire, are permeable by the solar
caloric.
The results of de Laroche have been confirmed
by the recent experiments of M. Melloni, whence
it appears that the calorific rays pass less abundantly,
not only through glass, but through rock--
crystal, Iceland spar, and other diaphanous bodies,
both solid and liquid, according as the temperature
of their origin is diminished, and that they
are altogether intercepted when the temperature
is about that of boiling water. It is singular that
transparency with regard to light is totally different
from the power of transmitting heat. In
bodies possessing the same degree of transparency
for light, the quantities of heat which they transmit
differ immensely, though proceeding from the
same source. The transmissive power of certain
substances having a dark colour exceeds by four
or five times that of others perfectly diaphanous,
and the calorific rays pass instantaneously through
black glass perfectly opaque to light.
The property of transmitting the calorific rays
diminishes, to a certain degree, with the thickness
of the body they have to traverse, but not so much
as might be expected: a piece of very transparent
alum transmitted three or four times less radiant
heat from the flame of a lamp than a piece of
nearly opaque quartz about a hundred times as
thick. However, the influence of thickness upon
the phenomena of transmission increases with the
decrease of temperature in the origin of the rays,
and becomes very great when that temperature is
low — a circumstance intimately connected with the
law established by de Laroche, for M. Melloni
observed that the differences between the quantities
of caloric transmitted by the same plate of glass,
exposed successively to several sources of heat,
diminished with the thinness of the plate, and
vanished altogether at a certain limit, and that a
film of mica transmitted the same quantity of
caloric whether it was exposed to incandescent
platina or to a mass of iron heated to 360°.
Since the power of penetrating glass increases
in proportion as the radiating caloric approaches
the state of light, it seemed to indicate that the
same principle takes the form of light or heat
according to the modification it receives, and that
the hot rays are only invisible light, and light
luminous caloric; and it was natural to infer that,
in the gradual approach of invisible caloric to the
condition and properties of luminous caloric, the
invisible rays must at first be analogous to the
least calorific part of the spectrum, which is at the
violet extremity, an analogy which appeared to be
greater, by all flame being at first violet or blue,
and only becoming white when it has attained
the greatest intensity. Thus, as diaphanous
bodies transmit light with the same facility whether
proceeding from the sun or from a glow-worm,
and that no substance had hitherto been found
which instantaneously transmits radiant caloric
coming from a source of low temperature, it was
concluded that no such substance exists, and
the great difference between the transmission of
light and radiant heat was thus referred to the
nature of the agent of heat, and not to the action
of matter upon the calorific rays. M. Melloni
has, however, discovered in rock-salt a substance
which transmits radiant heat with the same facility
whether it originates in the brightest flame
or lukewarm water, and which consequently possesses
the same permeability with regard to heat
that all diaphanous bodies have for light. It follows,
therefore, that the impermeability of glass and
other substances for heat arises from their action
upon the calorific rays, and not from the principle
of heat. But, although this discovery changes the
received ideas drawn from de Laroche's experiments,
it establishes a new and unlooked-for
analogy between these two great agents of nature.
The probability of light and heat being modifications
of the same principle is not diminished
by the calorific rays being unseen, for the
condition of visibility or invisibility may only
depend upon the construction of our eyes, and
not upon the nature of the agent which produces
these sensations in us. The sense of
seeing, like that of hearing, may be confined
within certain limits; the chemical rays beyond
the violet end of the spectrum may be too rapid
or not sufficiently excursive in their vibrations to
be visible to the human eye ; and the calorific
rays beyond the other end of the spectrum may
not be sufficiently rapid or too extensive in their
undulations to affect our optic nerves, though both
may be visible to certain animals or insects. We
are altogether ignorant of the perceptions which
direct the carrier-pigeon to his home, and the
vulture to his prey, before he himself is visible
even as a speck in the heavens; or of those in
the antennæ of insects which warn them of the
approach of danger: so likewise beings may
exist on earth, in the air, or in the waters, which
hear sounds our ears are incapable of hearing,
and which see rays of light and heat of which we
are unconscious. Our perceptions and faculties
are limited to a very small portion of that immense
chain of existence which extends from the Creator
to evanescence. The identity of action under
similar circumstances is one of the strongest arguments
in favour of the common nature of the
chemical, visible, and calorific rays. They are all
capable of reflection from polished surfaces, of
refraction through diaphanous substances, of polarization
by reflection and by doubly refracting
crystals; none of these rays add sensibly to the
weight of matter; their velocity is prodigious, they
may be concentrated and dispersed by convex
and concave mirrors; light and heat pass with
equal facility through rock-salt, and both are capable
of radiation; the chemical rays are subject
to the same law of interference with those of
light; and although the interference of the calorific
rays has not yet been proved, there is no
reason to suppose that they differ from the others
in this instance. As the action of matter in so
many cases is the same on the whole assemblage
of rays, visible and invisible, which constitute a
solar beam, it is more than probable that the
obscure, as well as the luminous part, is propagated
by the undulations of an imponderable ether,
and consequently comes under the same laws of
analysis.
Liquids, the various kinds of glass, and probably
all substances, whether solid or liquid, that do
not crystallize regularly, are more pervious to the
calorific rays according as they possess a greater
refracting power. For example, the chlorid of
sulphur, which has a high refracting power, transmits
more of the calorific rays than the oils which
have a less refracting power: oils transmit more
radiant heat than the acids, the acids more than
aqueous solutions, and the latter more than pure
water, which, of all the series, has the least refracting
power, and is the least pervious to heat. M.
Melloni observed also that each ray of the solar
spectrum follows the same law of action with that
of terrestrial rays having their origin in sources of
different temperatures, so that the very refrangible
rays may be compared to the heat emanating from
a focus of high temperature, and the least refrangible
to the heat which comes from a source of
low temperature. Thus, if the calorific rays
emerging from a prism be made to pass through a
layer of water contained between two plates of
glass, it will be found that these rays suffer a loss
in passing through the liquid as much greater as
their refrangibility is less. The rays of heat that
are mixed with the blue or violet light pass in
great abundance, while those in the obscure part
which follows the red light arc almost totally intercepted.
The first, therefore, act like the heat
of a lamp, and the last like that of boiling water.
These circumstances explain the phenomena
observed by several philosophers with regard to
the point of greatest heat in the solar spectrum,
which varies with the substance of the prism. ft
has already been observed that Sir William Herschelovho
employed a prism of flint glass, found
that point to be a little beyond the red extremity
of the spectrum, but, according to M. Seebeck, it
is found to be upon the yellow, upon the orange,
on the red, or at the dark limit of the red, according
as the prism consists of water, sulphuric
acid, crown or flint glass. If it be recollected
that, in the spectrum from crown glass, the
maximum heat is in the red part, and that the
solar rays, in traversing a mass of water, suffer
losses inversely as their refrangibility, it will be
easy to understand the reason of the phenomenon
in question. The solar heat which comes to the
anterior face of the prism of water consists of rays
of all degrees of refrangibility. Now, the rays
possessing the same index of refraction with the
red light suffer a greater loss in passing through
the prism than the rays possessing the refrangibility
of the orange light, and the latter lose less in
their passage than the heat of the yellow. Thus,
the losses, being inversely proportional to the
degree of refrangibility of each ray, cause the
point of maximum heat to tend from the red
towards the violet, and therefore it rests upon the
yellow part. The prism of sulphuric acid, acting
similarly, but with less energy than that of water,
throws the point of greatest heat on the orange;
for the same reason the crown and flint glass
prisms transfer that point respectively to the red
and to its limit. M, Melloni, observing that the
maximum point of heat is transferred farther and
farther towards the red end of the spectrum, according
as the substance of the prism is more and
more permeable to heat, inferred that a prism
of rock-salt, which possesses a greater power of
transmitting the calorific rays than any known
body, ought to throw the point of greatest heat to
a considerable distance beyond the visible part of
the spectrum — an anticipation which experiment
fully confirmed, by placing it as much beyond the
dark limit of the red rays as the red part is distant
from the bluish-green band of the spectrum.
When radiant heat falls upon a surface, part of
it is reflected and part of it is absorbed, consequently
the best reflectors possess the least absorbing
powers. The absorption of the sun's rays
is the cause both of the colour and temperature
of solid bodies. A black substance absorbs all
the rays of light, and reflects none; and since it
absorbs at the same time all the calorific rays, it
becomes sooner warm, and rises to a higher temperature,
than bodies of any other colour. Blue
bodies come next to black in their power of absorption.
Of all the colours of the solar spectrum,
the blue possesses least of the heating power; and
since substances of a blue tint absorb all the other
colours of the spectrum, they absorb by far the
greatest part of the calorific rays, and reflect the
blue where they are least abundant. Next in
order come the green, yellow, red, and, last of all,
white bodies, which reflect nearly all the rays both
of light and heat. The temperature of very transparent
fluids is not raised by the passage of the
sun's rays, because they do not absorb any of
them, and as his heat is very intense, transparent
solids arrest a very small portion of it.
Rays of heat proceed in diverging straight lines
from each point in the surfaces of hot bodies, in
the same manner as diverging rays of light dart
from every point of the surfaces of those that are
luminous. Heated substances, when exposed to
the open air, continue to radiate caloric till they
become nearly of the temperature of the surrounding
medium. The radiation is very rapid at first,
but diminishes, according to a known law, with the
temperature of the heated body. It appears also
that the radiating power of a surface is inversely
as its reflecting power; and bodies that are most
impermeable to heat radiate least. According to the
experiments of Sir John Leslie, radiation proceeds
not only from the surfaces of substances, but also
from the particles at a minute depth below it. He
found that the emission is most abundant in a direction
perpendicular to the radiating surface, and
is more rapid from a rough than from a polished
surface: radiation, however, can only take place
in air and in vacuo; it is altogether insensible
when the hot body is inclosed in a solid or liquid.
All substances may be considered to radiate caloric,
whatever their temperature may be, though
with different intensities, according to their nature,
the state of their surfaces, and the temperature of
the medium into which they arc brought. But
every surface absorbs, as well as radiates, caloric;
and the power of absorption is always equal to
that of radiation, for it is found that, under the
same circumstances, matter which becomes soon
warm also cools rapidly. There is a constant
tendency to an equal diffusion of caloric, since
every body in nature is giving and receiving it at
the same instant; each will be of uniform temperature
when the quantities of caloric given and
received during the same time are equal, that is,
when a perfect compensation takes place between
each and all the rest. Our sensations only measure
comparative degrees of heat: when a body,
such as ice, appears cold, it imparts fewer calorific
rays than it receives; and when a substance seems
to be warm, — for example, a fire, — it gives more
caloric than it takes. The phenomena of dew and
hoar-frost are owing to this inequality of exchange,
for the caloric radiated during the night by substances
on the surface of the earth into a clear
expanse of sky is lost, and no return is made from
the blue vault, so that their temperature sinks
below that of the air, from whence they abstract a
part of that caloric which holds the atmospheric
humidity in solution, and a deposition of dew
takes place. If the radiation be great, the dew is
frozen, and becomes hoar-frost, which is the ice
of dew. Cloudy weather is unfavourable to the
formation of dew, by preventing the free radiation
of caloric, and actual contact is requisite for its
deposition, since it is never suspended in the air,
like fog. Plants derive a great part of their
nourishment from this source; and as each possenses
a power of radiation peculiar to itself, they
are capable of procuring a sufficient supply for
their wants.
Rain is formed by the mixing of two masses of
air of different temperatures; the colder part, by
abstracting from the other the heat which holds
it in solution, occasions the particles to approach
each other and form drops of water, which, becoming
too heavy to be sustained by the atmosphere,
sink to the earth by gravitation in the
form of rain. The contact of two strata of air of
different temperatures, moving rapidly in opposite
directions, occasions an abundant precipitation of
rain.
An accumulation of caloric invariably produces
light: with the exception of the gases, all bodies
which can endure the requisite degree of heat
without decomposition begin to emit light at the
same temperature; but when the quantity of caloric
is so great as to render the affinity of their
component particles less than their affinity for the
oxygen of the atmosphere, a chemical combination
takes place with the oxygen, light and heat are
evolved, and fire is produced. Combustion — so
essential for our comfort, and even existence — takes
place very easily from the small affinity between
the component parts of atmospheric air, the oxygen
being nearly in a free state; but as the cohesive
force of the particles of different substances
is very variable, different degrees of heat are requisite
to produce their combustion. The tendency
of heat to a state of equal diffusion or equilibrium,
either by radiation or contact, makes it necessary
that the chemical combination which occasions
combustion should take place instantaneously; for
if the heat were developed progressively, it would
be dissipated by degrees, and would never accumulate
sufficiently to produce a temperature high
enough for the evolution of flame.
Though it is a general law that all bodies expand
by heat and contract by cold, yet the absolute
change depends upon the nature of the substance.
Gases expand more than liquids, and
liquids more than solids. The expansion of air is
more than eight times that of water, and the
increase in the bulk of water is at least forty-five
times greater than that of iron. The expansion
of solids and liquids increases uniformly
with the temperature, between certain limits,
this change of bulk, corresponding to the variation
of heat, is one of the most important of
its effects, since it furnishes the means of measuring
relative temperature by the thermometer
and pyrometer. The expansive force of caloric
has a constant tendency to overcome the attraction
of cohesion, and to separate the constituent partides
of solids and fluids; by this separation the
attraction of aggregation is more and more weakened,
till at last it is entirely overcome, or even
changed into repulsion. By the continual addition
of caloric, solids may be made to pass into
liquids, and from liquids to the aëriform state, the
dilatation increasing with the temperature; but
every substance expands according to a law of its
own. Metals dilate uniformly from the freezing
to the boiling points of the thermometer; the
uniform expansion of the gases extends between
still wider limits; but as liquidity is a state of
transition from the solid to the aeriform condition,
the equable dilatation of liquids has not so extensive
a range. The rate of expansion of solids
varies at their transition to liquidity, and that of
liquids is no longer equable near their change to
an aëriform state. There are exceptions, however,
to the general laws of expansion; some liquids
have a maximum density corresponding to a certain
temperature, and dilate whether that temperature
be increased or diminished. For example, —
water expands whether it be heated above or cooled
below 40°. The solidification of some liquids,
and especially their crystallization, is always accompanied
by an increase of bulk. Water dilates
rapidly when converted into ice, and with a force
sufficient to split the hardest substances. The
formation of ice is therefore a powerful agent in
the disintegration and decomposition of rocks,
operating as one of the most efficient causes of
local changes in the structure of the crust of the
earth, of which we have experience in the tremendous
éboulemens of mountains in Switzerland.
Heat is propagated with more or less rapidity
through all bodies; air is the worst conductor,
and consequently mitigates the severity of cold
climates by preserving the heat imparted to the
earth by the sun. On the contrary, dense bodies,
especially metals, possess the power of conduction
in the greatest degree, but the transmission requires
time. If a bar of iron, twenty inches long,
be heated at one extremity, the caloric takes four
minutes in passing to the other. The particle of
the metal that is first heated communicates its
caloric to the second, and the second to the third;
so that the temperature of the intermediate molecule
at any instant is increased by the excess of
the temperature of the first above its own, and
diminished by the excess of its own temperature
above that of the third., That, however, will not
be the temperature indicated by the thermometer,
because, as soon as the particle is more heated
than the surrounding atmosphere, it will lose its
caloric by radiation, in proportion to the excess
of its actual temperature above that of the air.
The velocity of the discharge is directly proportional
to the temperature, and inversely as
the length of the bar. As there are perpetual
variations in the temperature of all terrestrial
substances, and of the atmosphere, from the rotation
of the earth and its revolution round the sun,
from combustion, friction, fermentation, electricity,
and an infinity of other causes, the tendency
to restore the equability of temperature by the
transmission of caloric must maintain all the
particles of matter in a state of perpetual oscillation,
which will be more or less rapid according
to the conducting powers of the substances. From
the motion of the heavenly bodies about their
axes, and also round the sun, exposing them to
perpetual changes of temperature, it may be inferred
that similar causes will produce like effects
in them too. The revolutions of the double stars
show that they are not at rest, and though we are
totally ignorant of the changes that may be going
on in the nebulæ and millions of other remote
bodies, it is more than probable that they are not
in absolute repose; so that, as far as our knowledge
extends, motion seems to be a law of matter.
Heat applied to the surface of a fluid is propagated
downwards very slowly, the warmer, and
consequently lighter strata always remaining at
the top. This is the reason why the water at the
bottom of lakes fed from alpine chains is so cold;
for the heat of the sun is transfused but a little
way below the surface. When heat is applied
below a liquid, the particles continually rise as
they become specifically lighter, in consequence
of the caloric, and diffuse it through the mass,
their place being perpetually supplied by those
that are more dense. The power of conducting
heat varies materially in different liquids. Mercury
conducts twice as fast as an equal bulk of
water, which is the reason why it appears to be
so cold. A hot body diffuses its caloric in the air
by a double process. The air in contact with it,
being heated, and becoming lighter, ascends and
scatters its caloric, while at the same time another
portion is discharged in straight lines by the radiating
powers of the surface. Heinle a substance
cools more rapidly in air than in vacuo, because
in the latter case the process is carried on by
radiation alone. It is probable that the earth,
having originally been of very high temperature,
has become cooler by radiation only. The ethereal
medium must be too rare to carry off much caloric.
Besides the degree of heat indicated by the
thermometer, caloric pervades bodies in an imperceptible
or latent state; and their capacity for
heat is so various, that very different quantities of
caloric are required to raise different substances
to the same sensible temperature; it is therefore
evident that much of the caloric is absorbed, or
latent and insensible to the thermometer. The
portion of caloric requisite to raise a body to a
given temperature is its specific heat; but latent
heat is that portion of caloric which is employed
in changing the state of bodies from solid to liquid,
and from liquid to vapour. When a solid is converted
into a liquid, a greater quantity of caloric
enters into it than can be detected by the thermometer;
this accession of caloric does not make
the body warmer, though it converts it into a
liquid, and is the principal cause of its fluidity.
Ice remains at the temperature of 32° of Fahrenheit
till it has combined with or absorbed 140°
of caloric, and then it melts, but without raising
the temperature of the water above 32°; so that
water is a compound of ice and caloric. On the
contrary, when a liquid is converted into a solid,
a quantity of caloric leaves it without any diminution
of its temperature. Water at the temperature
of 32° must part with 140° of caloric
before it freezes. The slowness with which water
freezes, or ice thaws, is a consequence of the time
required to give out or absorb 140° of latent
heat. A considerable degree of cold is often
felt during a thaw, because the ice, in its transition
from a solid to a liquid state, absorbs sensible
heat from the atmosphere and other bodies,
and, by rendering it latent, maintains them at
the temperature of 32° while melting. According
to the same principle, vapour is a combination
of caloric with a liquid. About 1000° of
latent heat exists in steam without raising its
temperature: that is, boiling water, at the temperature
of 212°, must absorb about 1000° of
caloric before it becomes steam; and steam at
212° must part with the same quantity of latent
caloric when condensed into water. The elasticity
of steam may be increased to an enormous
degree by increasing its temperature under pressure,
yet its latent heat remains the same; however,
it acquires an additional quantity, if allowed
to expand; so that the latent heat of high-pressure
steam issuing from a boiler is really two-fold — the
latent heat of elastic fluidity and that of expansion.
High-pressure steam expands the instant
it comes into the air; the latent heat of expansion
is increased at the expense of the latent heat of
fluidity, in consequence of which, a portion of the
steam is instantly condensed, and then the remaining
portion, being mixed with air and particles
of water, is so much reduced in temperature, that
the hand may be plunged, without injury, into
high-pressure steam, the instant it issues from the
orifice of a boiler.
The latent heat of air, and of all elastic fluids,
may be forced out by sudden compression, like
squeezing water out of a sponge. The quantity
of heat brought into action in this way is very
well illustrated in the experiment of igniting a
piece of tinder by the sudden compression of air by
a piston thrust into a cylinder closed at one end:
the developement of heat on a stupendous scale
is exhibited in lightning, which is produced by the
violent compression of the atmosphere during the
passage of the electric fluid. Prodigious quantities
of heat are constantly becoming latent, or are
disengaged by the changes of condition to which
substances are liable in passing from the solid to
the liquid, and from the liquid to the gaseous
form, or the contrary, occasioning endless vicissitudes
of temperature over the globe.
The application of heat to the various branches
of the mechanical and chemical arts has, within a
few years, effected a greater change in the condition
of man than had been accomplished in any
equal period of his existence. Armed by the expansion
and condensation of fluids with a power
equal to that of the lightning itself, conquering
time and space, he flies over plains, and travels
on paths cut by human industry even through
mountains, with a velocity and smoothness more
like planetary than terrestrial motion; he crosses
the deep in opposition to wind and tide; by
releasing the strain on the cable, he rides at
anchor fearless of the storm ; he makes the elements
of air and water the carriers of warmth, not
only to banish winter from his home, but to adorn
it even during the snow-storm with the blossoms
of spring; and like a magician, he raises from the
gloomy and deep abyss of the mine, the spirit of
light to dispel the midnight darkness.
It has been observed that heat, like light and
sound, probably consists in the undulations of an
elastic medium. All the principal phenomena of
heat may actually be illustrated by a comparison
with those of sound. The excitation of heat and
sound are not only similar, but often identical, as
in friction and percussion; they are both communicated
by contact and radiation; and Dr. Young
observes, that the effect of radiant heat in raising
the temperature of a body upon which it
falls resembles the sympathetic agitation of a
string, when the sound of another string, which
is in unison with it, is transmitted to it through
the air. Light, heat, sound, and the waves of
fluids, are all subject to the same laws of reflection,
and, indeed, their undulatory theories are perfectly
similar. If, therefore, we may judge from analogy,
the undulations of some of the heat-producing rays
must be less frequent than those of the extreme red
of the solar spectrum; but if the analogy were perfect,
the interference of two hot rays ought to produce
cold, since darkness results from the interference
of two undulations of light, silence ensues
from the interference of two undulations of sound;
and still water, or no tide, is the consequence of
the interference of two tides. The propagation of
sound, however, requires a much denser medium
than that either of light or heat, its intensity diminishes
as the rarity of the air increases; so that
at a very small height above the surface of the
earth, the noise of the tempest ceases, and the
thunder is heard no more in those boundless regions
where the heavenly bodies accomplish their
periods in eternal and sublime silence.
A consciousness of the fallacy of our judgment
is one of the most important consequences of the
study of nature. This study teaches us that
no object is seen by us in its true place, owing
to aberration; that the colours of substances
are solely the effects of the action of matter upon
light, and that light itself, as well as heat and
sound, are not real beings, but mere modes of
action communicated to our perceptions by the
nerves. The human frame may therefore be regarded
as an elastic system, the different parts
of which are capable of receiving the tremors of
elastic media, and of vibrating in unison with
any number of superposed undulations, all of
which have their perfect and independent effect.
Here our knowledge ends; the mysterious influence
of matter on mind will in all probability
be for ever hid from man.
SECTION XXVI.
THE sun and some of the planets appear to be
surrounded with atmospheres of considerable density.
According to the observations of Schröeter,
the atmosphere of Ceres is more than 668 miles
high, and that of Pallas has an elevation of 465
miles. It is remarkable that not a trace of atmosphere
can be perceived in Vesta, and that Jupiter,
Saturn, and Mars, have very little. The attraction
of the earth has probably deprived the moon
of hers, for the refractive power of the air at the
surface of the earth is at least a thousand times
as great as the refraction at the surface of the
moon. The lunar atmosphere, therefore, must be
of a greater degree of rarity than can be produced
by our best air-pumps; consequently no terrestrial
animal could exist in it.
What the body of the sun may be, it is impossible
to conjecture; but he seems to be surrounded
by a mottled ocean of flame, through which his
dark nucleus appears like black spots, often of
enormous size. These spots are almost always
comprised within a zone of the sun's surface,
whose breadth, measured on a solar meridian, does
not extend beyond 30 1/2° on each side of his equator,
though they have been seen at the distance of
39 1/2°. From their extensive and rapid changes,
there is every reason to suppose that the exterior
and incandescent part of the sun is gaseous. The
solar rays probably arising from chemical processes
that continually take place at his surface
are transmitted through space in all directions;
but notwithstanding the sun's magnitude, and the
inconceivable heat that must exist at his surface,
as the intensity both of his light and heat
diminishes as the square of the distance increases,
his kindly influence can hardly be felt
at the boundaries of our system. The power of
the solar rays depends much upon the manner
in which they fall, as we readily perceive from
the different climates on our globe. In winter
the earth is nearer the sun by about a thirtieth
than in summer, but the rays strike the northern
hemisphere more obliquely in winter than in the
other half of the year. In Uranus the sun must
be seen like a small but brilliant star, not above
the hundred and fiftieth part so bright as he appears
to us; but that is 2000 times brighter
than our moon to us, so that he really is a sun to
Uranus, and probably imparts some degree of
warmth. But if we consider that water would not
remain fluid in any part of Mars, even at his
equator, and that in the temperate zones of the
same planet even alcohol and quicksilver would
freeze, we may form some idea of the cold that
must reign in Uranus, though it cannot exceed
that of the surrounding space.
It is found by experience that heat is developed
in opaque and translucent substances by their
absorption of solar light, but that the sun's rays
do not alter the temperature of perfectly transparent
bodies through which they pass. As the
temperature of the pellucid planetary space cannot
be affected by the passage of the sun's light
and heat, neither can it be raised by the heat radiated
from the earth, consequently its temperature
must be invariable. The atmosphere, on the
contrary, gradually increasing in density towards
the surface of the earth, becomes less pellucid, and
therefore gradually increases in temperature both
from the direct action of the sun, and from the
radiation of the earth. Lambert had proved that
the capacity of the atmosphere for heat varies
according to the same law with its capacity for
absorbing a ray of light passing through it from
the zenith, whence M. Svanberg found that the
temperature of space is 58° below the zero point
of Fahrenheit's thermometer; and from other researches,
founded upon the rate and quantity of
atmospheric refraction, he obtained a result which
only differs from the preceding by half a degree.
M. Fourier has arrived at nearly the same conclusion,
from the law of the radiation of the heat of
the terrestrial spheroid, on the hypothesis of its
having nearly attained its limit of temperature in
cooling down from its supposed primitive state of
fusion. The difference in the result of these three
methods, totally independent of one another, only
amounts to the fraction of a degree. Thus, as the
temperature of space is uniform, it follows that no
part of Uranus can experience more than 90° of
cold, which only exceeds that which Sir Edward
Parry suffered during one day at Melville Island,
by 3°.
The climate of Venus more nearly resembles
that of the earth, though, excepting perhaps at her
poles, much too hot for animal and vegetable life
as they exist here: but in Mercury, the mean
heat, arising only from the intensity of the sun's
rays, must be above that of boiling quicksilver,
and water would boil even at his poles. Thus the
planets, though kindred with the earth in motion
and structure, are totally unfit for the habitation
of such a being as man.
The direct light of the sun has been estimated
to be equal to that of 5563 wax candles of moderate
size, supposed to be placed at the distance of
one foot from the object: that of the moon is
probably only equal to the light of one candle at
the distance of twelve feet; consequently the light
of the sun is more than three hundred thousand
times greater than that of the moon; for which
reason the light of the moon either imparts no
heat, or it is too feeble to penetrate the glass of
the thermometer, even when brought to a focus
by a mirror. The intensity of the sun's light
diminishes from the centre to the circumference of
the solar disc; but in the moon the gradation is
reversed.
Much has been done within a few years to
ascertain the manner in which heat is distributed
over the surface of our planet, and the variations
of climate; which in a general view mean every
change of the atmosphere, such as of temperature,
humidity, variations of barometric pressure, purity
of air, the serenity of the heavens, the effects of
winds, and electric tension. Temperature depends
upon the property Which all bodies possess, more
or less, of perpetually absorbing and emitting or
radiating heat. When the interchange is equal,
the temperature of a body remains the same; but
when the radiation exceeds the absorption, it becomes
colder, and vice versa. But in order to
determine the distribution of heat over the surface
of the earth, it is necessary to find a standard by
which the temperature in different latitudes may
be compared. For that purpose it is requisite to
ascertain by experiment the mean temperature of
the day, of the month, and of the year, at as many
places as possible throughout the earth. The
annual average temperature may be found by adding
the mean temperatures of all the months in
the year, and dividing the sum by twelve. The
average of ten or fifteen years will give it with
tolerable accuracy; for although the temperature
in any place may be subject to very great variations,
yet it never deviates more than a few degrees
from its mean state, which consequently offers
good standard of comparison.
If climate depended solely upon the heat of the
sun, all places having the same latitude would
have the same mean annual temperature. The
motion of the sun in the ecliptic, indeed, occasions
perpetual variations in the length of the day, and
in the direction of the rays with regard to the
earth; yet, as the cause is periodic, the mean
annual temperature from the sun's motion alone
must be constant in each parallel of latitude. For
it is evident that the accumulation of heat in the
long days of summer, which is but little diminished
by radiation during the short nights, is balanced
by the small quantity of heat received during the
short days in winter and its radiation in the long
frosty and clear nights. In fact, if the globe were
everywhere on a level with the surface of the sea,
and also of the same substance, so as to absorb
heat equally, and radiate the same, the mean heat
of the sun would be regularly distributed over its
surface in zones of equal annual temperature parallel
to the equator, from which it would decrease
to each pole as the square of the cosine of the
latitude; and its quantity would only depend upon
the altitudes of the sun, atmospheric currents, and
the internal heat of the earth evinced by the vast
number of volcanos and hot springs, in every
region from the equator to the polar circles, which
has probably been cooling down to its present
state for thousands of ages. The distribution of
heat, however, in the same parallel is very irregular
in all latitudes, except between the tropics,
where the isothermal lines, or the lines passing
through places of equal mean annual temperature,
arc parallel to the equator. The causes of disturbance
are very numerous; but such as have the
greatest influence, according to Humboldt, to whom
we are indebted for the greater part of what is
known on the subject, are the elevation of the
continents, the distribution of land and water over
the surface of the globe, exposing different absorbing
and radiating powers; the variations in the
surface of the land, as forests, sandy deserts, verdant
plains, rocks, &c., mountain-chains covered
with masses of snow, which diminish the temperature;
the reverberation of the sun's rays in the
valleys, which increases it; and the interchange
of currents, both of air and water, which mitigate
the rigour of climates; the warm currents from
the equator softening the severity of the polar
frosts, and the cold currents from the poles tempering
the intense heat of the equatorial regions.
To these may be added cultivation, though its influence
extends over but a small portion of the globe,
only a fourth part of the land being inhabited.
Temperature does not vary so much with latitude
as with the height above the level of the sea;
and the decrease is more rapid in the higher strata
of the atmosphere than in the lower, because they
are farther removed from the radiation of the
earth, and being highly rarefied, the heat is diffused
through a larger space. A portion of air
at the surface of the earth, whose temperature is
70° of Fahrenheit, if carried to the height of two
miles and a half, will expand so much that its
temperature will be reduced 50°; and in the ethereal
regions the temperature is 90° below the point
of congelation.
The height at which snow lies perpetually decreases
from the equator to the poles, and is higher
in summer than in winter; but it varies from
many circumstances. Snow rarely falls when the
cold is intense and the atmosphere dry. Extensive
forests produce moisture by their evaporation, and
high table-lands, on the contrary, dry and warm
the air. In the Cordilleras of the Andes, plains
of only twenty-five square leagues raise the temperature
as much as three or four degrees above
what is found at the same altitude on the rapid
declivity of a mountain, consequently the line of
perpetual snow varies according as one or other
of these causes prevails. Aspect has also a great
influence; the line of perpetual snow is much
more elevated on the southern than on the northern
side of the Himalaya mountains; but on the
whole it appears that the mean height between
the tropics at which the snow lies perpetually
is about 15207 feet above the level of the sea;
whereas snow does not cover the ground continually
at the level of the sea till near the north pole.
In the southern hemisphere, however, the cold is
greater than in the northern. In Sandwich land,
between the 54th and 55th degrees of latitude,
perpetual snow and ice extend to the sea-beach;
and in the island of St. George's, in the 53rd
degree of south latitude, which corresponds with
the latitude of the central counties of England,
perpetual snow descends even to the level of the
ocean. This preponderance of cold in the southern
hemisphere cannot be altogether attributed to
the winter being longer than ours by so small a
quantity as 7 3/4 days, even allowing to that its due
influence; but it is probably owing to the open
sea round the south pole, which permits the icebergs
to descend to a lower latitude by ten degrees
than they do in the northern hemisphere, on account
of the numerous obstructions opposed to
them by the islands and continents about the
north pole. Icebergs seldom float farther to the
south than the Azores; whereas those that come
from the south pole descend as far as the Cape of
Good Hope, and occasion a continual absorption
of heat in melting.
The influence of mountain-chains does not
wholly depend upon the line of perpetual congelation;
they attract and condense the vapours
floating in the air, and send them down in torrents
of rain; they radiate heat into the atmosphere at
a lower elevation, and increase the temperature of
the valleys by the reflection of the sun's rays, and
by the shelter they afford against prevailing winds.
But, on the contrary, one of the most general and
powerful causes of cold arising from the vicinity of
mountains is the freezing currents of wind which
rush from their lofty peaks along the rapid declivities,
chilling the surrounding valleys: such is the
cutting north wind called the bise in Switzerland.
Next to elevation, the difference in the radiating
and absorbing powers of the sea and land has the
greatest influence in disturbing the regular distribution
of heat. The extent of the dry land is not
above the fourth part of that of the ocean, so that
the general temperature of the atmosphere, regarded
as the result of the partial temperatures
of the whole surface of the globe, is most powerfully
modified by the sea; besides, the ocean acts
more uniformly on the atmosphere than the diversified
surface of the solid mass does, both by the
equality of its curvature and its homogeneity. In
opaque substances the accumulation of heat is
confined to the stratum nearest the surface; but
the seas become less heated at their surface than
the land, because the solar rays, before being extinguished,
penetrate the transparent liquid to a
greater depth, and in greater numbers than in the
opaque masses. On the other hand, water has a
considerable radiating power, which, together with
evaporation, would reduce the surface of the ocean
to a very low temperature, if the cold particles did
not sink to the bottom, on account of their. superior
density. The seas preserve a considerable
portion of the heat they receive in summer; and,
from their saltness, do not freeze so soon as fresh
water: so that, in consequence of all these circumstances,
the ocean is not subject to such variations
of heat as the land; and, by imparting its
temperature to the winds, it diminishes the intensity
of climate on the coasts and in the islands,
which are never subject to such extremes of heat
and cold as are experienced in the interior of continents,
though they are liable to fogs and rain
from the evaporation of the adjacent seas. On
each side of the equator, to the 48th degree of
latitude, the surface of the ocean is in general
warmer than the air above it : the mean of the
difference of temperature at noon and midnight is
about 1°.37, the greatest deviation never exceeding
from 0°.36 to 2°.16, which is much cooler
than the air over the land.
On land the temperature depends upon the
nature of the soil and its products, its habitual
moisture or dryness. From the eastern extremity
of the Sahara desert quite across Africa, the
soil is almost entirely barren sand, and the Sahara
desert itself, without including Dafour or Dongola,
extends over an area of 194000 square leagues,
equal to twice the area of the Mediterranean Sea,
and raises the temperature of the air by radiation
from 90° to 100° which must have a most extensive
influence. On the contrary, vegetation cools
the air by evaporation and the apparent radiation
of cold from the leaves of plants, because they
absorb more caloric than they give out. The
graminiferous plains of South America cover an
extent ten times greater than France, occupying
no less than about 50000 square leagues, which
is more than the whole chain of the Andes,
and all the scattered mountain-groups of Brazil :
these, together with the plains of North America
and the steppes of Europe and Asia, must have
an extensive cooling effect on the atmosphere, if
it be considered that, in calm and serene nights,
they cause the thermometer to descend 12° or
14°, and that, in the meadows and heaths in
England, the absorption of heat by the grass is
sufficient to cause the temperature to sink to the
point of congelation during the night for ten
months in the year. Forests cool the air also by
shading the ground from the rays of the sun, and
by evaporation from the boughs, Hales found
that the leaves of a single plant of helianthus,
three feet high, exposed nearly forty feet of surface;
and if it be considered that the woody regions of
the river Amazons, and the higher part of the Oroonoko,
occupy an area of 260000 square leagues,
some idea may be formed of the torrents of vapour
which arise from the leaves of the forests all over
the globe. However, the frigorific effects of their
evaporation are counteracted in some measure by
the perfect calm which reigns in the tropical wildernesses.
The innumerable rivers, lakes, pools,
and marshes interspersed through the continents
absorb caloric, and cool the air by evaporation;
but on account of the chilled and dense particles
sinking to the bottom, deep water diminishes the
cold of winter, so long as ice is not formed.
In consequence of the difference in the radiating
and absorbing powers of the sea and land, their
configuration greatly modifies the distribution of
heat over the surface of the globe. Under the
equator only one-sixth part of the circumference is
land; and the superficial extent of land in the
northern and southern hemispheres is in the proportion
of three to one: the effect of this unequal
division is greater in the temperate, than in the
torrid zones, for the area of land in the northern
temperate zone is to that in the southern as thirteen
to one, whereas the proportion of land between
the equator and each tropic is as five to four;
and it is a curious fact, noticed by Mr. Gardner,
that only one twenty-seventh part of the land of
the globe has land diametrically opposite to it.
This disproportionate arrangement of the solid
part of the globe has a powerful influence on the
temperature of the southern hemisphere. But,
besides these greater modifications, the peninsulas,
promontories, and capes, running out into the
ocean, together with bays and internal seas, all
affect the temperature : to these may be added, the
position of continental masses with regard to the
cardinal points. All these diversities of land and
water affect the temperature by the agency of the
winds. On this account the temperature is lower
on the eastern coasts both of the New and Old
World, than on the western; for, considering
Europe as an island, the general temperature is
mild in proportion as the aspect is open to the
western ocean, the superficial temperature of which,
as far north as the 45° and 50° of latitude, does
not fall below 48° or 51° of Fahrenheit, even in
middle of winter. On the contrary, the cold of
Russia arises from its exposure to the northern
and eastern winds; but the European part of that
empire has a less rigorous climate than the Asiatic,
because the whole northern extremity of Europe
is separated from the polar ice by a zone of open
sea, whose winter temperature is much above that
of a continental country under the same latitude.
The interposition of the atmosphere modifies
all the effects of the sun's heat; but the earth
communicates its temperature so slowly, that M.
Arago has occasionally found as much as from
14° to 18° of difference between the heat of the soil
and that of the air two or three inches above it.
The circumstances which have been enumerated,
and many more, concur in disturbing the regular
distribution of heat over the globe, and occasion
numberless local irregularities: nevertheless the
mean annual temperature becomes gradually lower
from the equator to the poles; but the diminution
of mean heat is most rapid between the 40°
and 45° of latitude both in Europe and America,
which accords perfectly with theory, whence it appears
that the variation in the square of the cosine
of the latitude which expresses the law of the
change of temperature, is a maximum towards the
45° of latitude. The mean annual temperature
under the line in Asia and America is about 81 1/2°
of Fahrenheit; in Africa it is said to be nearly
83°. The difference probably arises from the
winds of Siberia and Canada, whose chilly influence
is sensibly felt in Asia and America, even
within 18° of the equator.
The isothermal lines are parallel to the equator,
till about the 22° of latitude on each side of it,
where they begin to lose their parallelism, and
continue to do so more and more as the latitude
augments. With regard to the northern
hemisphere, the isothermal line of 59° of Fahrenheit
passes between Rome and Florence, in latitude
43°; and near Raleigh, in North Carolina,
latitude 36°; that of 50° of equal annual temperature
runs through the Netherlands, latitude 51°;
and near Boston, in the United States, latitude
42 1/2°; that of 41° passes near Stockholm, latitude
59 1/2°; and St. George's Bay, Newfoundland, latitude
48°; and lastly, the line of 32°, the freezing
point of water, passes between Ulea, in Lapland,
latitude 66°, and Table Bay, on the coast of Labradore,
latitude 54°.
Thus it appears, that the isothermal lines which
are parallel to the equator for nearly 22°, afterwards
deviate more and more; and from the observations
of Sir Charles Giesecke in Greenland,
of Mr. Scoresby in the Arctic seas, and also from
those of Sir Edward Parry and Sir John Franklin,
it is found that the isothermal lines of Europe and
America entirely separate in the high latitudes,
and surround two poles of maximum cold, one in
America and the other in the north of Asia, neither
of which coincides with the pole of the earth's
rotation. These poles are both situate in about
the eightieth parallel of north latitude; the Transatlantic
pole is in the 100° of west longitude, about
5° to the north of Sir Graham Moore's Bay, in
the Polar Seas, and the Asiatic pole is in the 95°
of east longitude, a little to the north of the Bay
of Taimura, near the North-East Cape. According
to the estimation of Sir David Brewster, from
the observations of M. de Humboldt and Captains
Parry and Scoresby, the mean annual temperature
of the Asiatic pole is nearly 1° of Fahrenheit's
thermometer, and that of the transatlantic pole
about 3 1/2° below zero, whereas he supposes the
mean annual temperature of the pole of rotation
to be 4° or 5°. It is believed that two corresponding
poles of maximum cold exist in the southern
hemisphere, though observations are wanting to
trace the course of the southern isothermal lines
with the same accuracy as the northern.
The isothermal lines, or such as pass through
places where the mean annual temperature of the
air is the same, do not always coincide with the
isogeothermal lines, which are those passing
through places where the mean temperature of
the, ‘ground is the same. The mean heat of the
earth is determined from that of springs, and if
the spring be on elevated ground, the temperature
is reduced by computation to what it would he at
the level of the sea, assuming that the heat of the
soil varies according to the same law as the heat
of the atmosphere, which is about a degree of Fahrenheit's
thermometer for every 656 feet. From
a comparison of the temperature of numerous
springs with that of the air, Sir David Brewster
concludes that there is a particular line passing
nearly through Berlin, at which the temperature
of springs and that of the atmosphere coincide;
that in approaching the Arctic Circle the temperature
of springs is always higher than that of the
air, while proceeding towards the equator it is
lower. He likewise found that the isogeothermal
lines are always parallel to the isothermal lines,
consequently the same general formulæ will serve
to determine both, since the difference is a constant
quantity, obtained by observation, and depending
upon the distance of the place from the neutral
isothermal line. These results are confirmed by
the observations of M. Kupffer, of Kasan, during
his excursions to the north, which show that the
European and the American portions of the isogeothermal
line of 32° Fahrenheit actually separate,
and go round the two poles of maximum cold.
This traveller remarked also, that the temperature
both of the air and of the soil decreases most rapidly
towards the 45° of latitude. The temperature
of the ground at the equator is lower on the
coasts and islands than in the interior of the continents;
the warmest part is in the interior of
Africa, but the temperature is obviously affected by
the nature of the soil, especially if it be volcanic.
It is evident that places may have the same
mean annual temperature, and yet differ materially
in climate. In one the winters may be mild and
the summers cool : whereas another may experience
the extremes of heat and cold. Lines passing
through places having the same mean summer
or winter temperature, are neither parallel to the
isothermal, the geothermal lines, nor to one another,
and they differ still more from the parallels
of latitude. In Europe, the latitude of two
places which have the same annual heat never
differs more than 8° or 9°; whereas the difference
in the latitude of those having the same mean
winter temperature is sometimes as much as 18°
or 19°. At Kasan, in the interior of Russia, in latitude
55°•48, nearly the same with that of Edinburgh,
the mean annual temperature is about
37°.6 ; at Edinburgh it is 41°.84. At Kasan, the
mean summer temperature is 64°.84, and that of
winter 2°.12, whereas at Edinburgh the mean
summer temperature is 58°.28, and that of winter
38°.66. Whence it appears that the difference of
winter temperature is much greater than that of
the summer. At Quebec, the summers are as
warm as those in Paris, and grapes sometimes
ripen in the open air; whereas the winters are as
severe as in Petersburg; the snow lies five feet
deep for several months, wheel-carriages cannot
be used, the ice is too hard for skating, travelling
is performed in sledges, and frequently on the ice
of the river St. Lawrence. The cold at Melville
Island, on the 15th of January, 1820, according
to Sir Edward Parry, was 55° below the zero of
Fahrenheit's thermometer, only 3° above the temperature
of the ethereal regions, yet the summer
heat in these high latitudes is insupportable.
SECTION XXVII.
THE gradual decrease of temperature in the air
and in the earth, from the equator, to the poles, is
clearly indicated by its influence on vegetation.
In the valleys of the torrid zone, where the mean
annual temperature is very high, and where there
is abundance, of moisture, nature adorns the soil
with all the luxuriance of perpetual summer. The
palm, the bombax ceiba, and a variety of magnificent
trees, tower to the height of a hundred and
fifty or two hundred feet above the banana, the
bamboo, the arborescent fern, and numberless
other tropical productions, so interlaced by creeping
and parasitical plants, as often to present an
impenetrable barrier. But the richness of vegetation
gradually diminishes with the temperature ;
the splendour of the tropical forest is succeeded
by the regions of the olive and vine; these again
yield to the verdant meadows of more temperate
climes; then follow the birch and the pine, which
probably owe their existence in very high latitudes
more to the warmth of the soil than to that of
the air; but even these enduring plants become
dwarfish, stunted shrubs, till a verdant carpet of
mosses and lichens, enamelled with flowers, exhibits
the last signs of vegetable life during the
short but fervent summers at the polar regions.
Such is the effect of cold on the vegetable kingdom,
that the numbers of species growing under
the line and in the northern latitudes of 45° and
68°, are in the proportion of the numbers 12, 4,
and 1. But notwithstanding the remarkable difference
between a tropical and polar Flora, moisture
seems to be almost the only requisite for
vegetation, since neither heat, cold, nor even darkness
destroy the fertility of nature; in salt plains
and sandy deserts alone hopeless barrenness prevails.
Plants grow on the borders of hot springs
— they form the oases, wherever moisture exists,
among the burning sands of Africa — they are
found in caverns void of light, though generally
blanched and feeble — the ocean teems with vegetation
— the snow itself not only produces a red
alga, discovered by Saussure in the frozen declivities
of the Alps, found in abundance by the
author crossing the Col de Bonhomme from Savoy
to Piedmont, and by the polar navigators in
the arctic regions, but it affords shelter to the
productions of those inhospitable climes, against
the piercing winds that sweep over fields of everlasting
ice. Those interesting mariners narrate
that, under this cold defence, plants spring
up, dissolve the snow a few inches round, and
that the part above, being again quickly frozen
into a transparent sheet of ice, admits the sun's
rays, which warm and cherish the plant in this
natural hot-house, till the returning summer renders
such protection unnecessary.
By far the greater part of the hundred and ten
thousand known species of plants are indigenous
in equinoctial America; Europe contains about
half the number; Asia with its islands somewhat
less than Europe; New Holland, with the islands
in the Pacific, still less; and in Africa there are
fewer vegetable productions than in any part of
the globe, of equal extent. Very few social plants,
such as grasses and heaths that cover large tracts
of land, are to be found between the tropics, except
on the sea coasts, and elevated plains. In
the equatorial regions, where the heat is always
great, the distribution of plants depends upon the
mean annual temperature; whereas in temperate
zones the distribution is regulated in some degree
by the summer heat. Some plants require a gentle
warmth of long continuance, others flourish most
where the extremes of heat and cold are greater.
The range of wheat is very great: it may be cultivated
as far north as the 60° of latitude, but in
the torrid zone, it will seldom form an ear below an
elevation of 4500 feet above the level of the sea
from the exuberance of vegetation; nor will it ripen
above the height of 10800 feet, though much depends
upon local circumstances. The best wines
are produced between the 30° and 45° of north
latitude. But with regard to the vegetable kingdom,
elevation is equivalent to latitude, as far as
temperature is concerned. In ascending the mountains
of the torrid zone, the richness of the tropical
vegetation diminishes with the height; a
succession of plants similar, though not identical
with those found in latitudes of corresponding
mean temperature takes place; the lofty forests
lose by degrees their splendour, stunted shrubs
succeed, till at last the progress of the lichen is
checked by eternal snow. On the volcano of
Teneriffe, there are five successive zones, each producing
a distinct race of plants. The first is the
region of vines, the next that of laurels, these are
followed by the districts of pines, of mountain
broom, and of grass; the whole covering the declivity
of the peak through an extent of 11200 feet
of perpendicular height.
Near the equator the oak flourishes at the height
of 9200 feet above the level of the sea, and on the
lofty range of the Hymalaya the primula, the convallaria,
and the veronica blossom, but not the
primrose, the lily of the valley, or the veronica
which adorn our meadows; for although the herbarium
collected by Mr. Moorcroft on his route
from Neetee to Daba and Garlope in Chinese Tartary,
at elevations as high or even higher than
Montblanc, abounds in Alpine and European
genera, the species are universally different, with
the single exception of the rhodiola rosea, which is
identical with the species that blooms in Scotland.
It is not in this instance alone that similarity of
climate obtains without identity of productions ;
throughout the whole globe, a certain analogy
both of structure and appearance is frequently
discovered between plants under corresponding circumstances,
which are yet specifically different.
It is even said, that a distance of 25° of latitude
occasions a total change not only of vegetable productions,
but of organised beings. Certain it is,
that each separate region both of land and water,
from the frozen shores of the polar circles, to the
burning regions of the torrid zone, possesses a flora
of species peculiarly its own. The whole globe has
been divided by botanical geographers into twenty--
seven botanical districts, differing almost entirely
in their specific vegetable productions; the limits
of which are most decided when they are separated
by a wide expanse of ocean, mountain chains,
sandy deserts, salt plains, or internal seas. A considerable
number of plants are common to the
northern regions of Asia, Europe, and America,
where these continents almost unite ; but in approaching
the south, the floras of these three great
divisions of the globe differ more and more even
in the same parallels of latitude, which shows that
temperature alone is not the cause of the almost
complete diversity of species that everywhere prevails.
The floras of China, Siberia, Tartary, of
the European district including central Europe
and the coasts of the Mediterranean, and the oriental
region, comprising the countries round the
Black and Caspian Seas, all differ in specific character.
Only twenty-four species were found by
MM. Boni)land and Humboldt in equinoctial
America, that are identical with those of the Old
World; and Mr. Brown not only found that a
peculiar vegetation exists in New Holland, between
the thirty-third and thirty-fifth parallels of
south latitude, but that, at the eastern and western
extremities of these parallels, not one species is
common to both, and that certain genera also are
almost entirely confined to these spots. The
number of species common to Australia and Europe
are only 166 out of 4100, and probably some
of these have been conveyed thither by the colonists.
This proportion exceeds what is observed
in southern Africa, and from what has been already
stated, the proportion of European species in equinoctial
America is still less.
Islands partake of the vegetation of the nearest
continents, but when very remote from land their
floras are altogether peculiar. The Aleutian
islands extending between Asia and America, partake
of the vegetation of the northern parts of both
these continents, and may have served as a channel
of communication. In Madeira and Teneriffe,
the plants of Portugal, Spain, the Azores, and of
the north coast of Africa are found, and the Canaries
contain a great number of plants belonging
to the African coast. But each of these islands
possesses a flora that exists nowhere else, and
St. Helena, standing alone in the midst of the
Atlantic ocean, out of sixty-one indigenous species,
produces only two or three recognised as belonging
to any other part of the world.
It appears from the investigations of Humboldt
that between the tropics the monocotyledonous
plants, such as grasses and palms, which have
only one seed-lobe, are to the dicotyledonous tribe,
which have two seed-lobes, like most of the European
species, in the proportion of one to four; in
the temperate zones they are as one to six; and in
the arctic regions, where mosses and lichens, which
form the lowest order of the vegetable creation,
abound, the proportion is as one to two. The annual
monocotyledonous and dicotyledoneus plants
in the temperate zones amount to one-sixth of the
whole, omitting the cryptogamia; in the torrid zone
they scarcely form one-twentieth, and in Lapland
one-thirtieth part. In approaching the equator, the
ligneous exceed the number of herbaceous plants;
in America, there are a hundred and twenty different
species of forest-trees, whereas in the same
latitude in Europe only thirty-four are to be found.
Similar laws appear to regulate the distribution
of marine plants. M. Lamouroux has discovered
that the groups of algæ affect particular temperatures
or zones of latitude, though some few genera
prevail throughout the ocean. The polar Atlantic
basin, to the 40° of north latitude, presents a
well-defined vegetation. The West Indian seas,
including the gulf of Mexico, the eastern coast of
South America, the Indian ocean and its gulfs,
the shores of New Holland, and the neighbouring
islands, have each their assemblage of distinct
species. The Mediterranean possesses a vegetation
peculiar to itself, extending to the Black Sea;
and the species of marine plants on the coasts of
Syria and in the port of Alexandria differ almost
entirely from those of Suez and the Red Sea,
notwithstanding the proximity of their geographical
situation. It is observed that shallow seas
have a different set of plants from such as are
deeper and colder; and, like terrestrial vegetation,
the algæ are most numerous towards, the, equator,
where the quantity must be prodigious, if we may
judge from the gulf-weed, which certainly has its
origin in the tropical seas, and is drifted, though
not by the gulf-stream, to higher latitudes, where
it accumulates in such quantities, that the early
Portuguese navigators, Columbus and Lerius, compared
the sea to extensively inundated meadows,
in which it actually impeded their ships and
alarmed their sailors. Humboldt, in his Personal
Narrative, mentions, that the most extensive bank
of sea-weed is in the northern Atlantic, a little
west of the meridian of Fayal, one of the Azores,
between the 25° and 36° of latitude. Vessels
returning to Europe from Monte Video, or from
the Cape of Good Hope, cross this bank nearly at
an equal distance from the Antilles and Canary
islands. The other occupies a smaller space, between
the 22° and 26° of north latitude, about
eighty leagues west of the meridian of the Bahama
islands, and is generally traversed by vessels on
their passage from the Caicos to the Bermuda
islands. These masses consist chiefly of one or
two species of Sargassum, the most extensive genus
of the order Fucoidea.
Some of the sea-weeds grow to the enormous
length of several hundred feet, and all are highly
coloured, though many, of them must grow in the
deep caverns. of the ocean in total, or almost total
darkness; light, however, may not be the only
principle on which the colour of vegetables depends,
since Humboldt met with green plants
growing in complete darkness at the bottom of
one of the mines at Freuberg.
It appears that in the dark and tranquil caves
of the ocean, on the shores alternately covered and
deserted by the restless waves, on the lofty Mountain
and extended plain, in the chilly regions of
the north, and in the genial warmth of the south,
specific diversity is a general law of the vegetable
kingdom, which cannot be accounted for by diversity
of climate; and yet the similarity thuogh not
identity of species is such, under the same isothermal
lines, that if the number of species belonging
to one of the great families. of plants be known in
any part of the globe, the whole number of the
phanerogamous or more perfect plants, and also
the number of species composing the other vegetable
families, may be estimated with considerable
accuracy.
Various opinions have been formed on the original
or primitive distribution of plants over the
surface of the globe, but since botanical geography
became a regular science, the phenomena observed
have led to the conclusion that vegetable
creation must have taken place in a number of
distinctly different centres, each of which was the
original seat of a certain number of peculiar species,
which at first grew there and no where else.
Heaths are exclusively confined to the old world,
and no indigenous rose-tree has ever been discovered
in the new; the whole southern hemisphere
being destitute of that beautiful and fragrant plant.
But this is still more confirmed by multitudes
of particular plants having an entirely local and
insulated existence, growing spontaneously in some
particular spot and in no other place; as, for example,
the cedar of Lebanon, which grows indigenously
on that mountain and in no other part of
the world.
The same laws obtain in the distribution of the
animal creation. The zoophite, occupying the
lowest place in animated nature, is widely scattered
through the seas of the torrid zone, each species
being confined to the district best fitted to its existence.
Shell-fish decrease in size and beauty with
their distance from the equator ; and as far as is
known, each sea has its own kind, and every basin
of the ocean is inhabited by its peculiar tribe
of fish. Indeed, MM. Peron and Le Sueur assert,
that among the many thousands of marine animals
which they had examined, there is not a single
animal of the southern regions which is not distinguishable
by essential characters from the analogous
species in the northern seas. Reptiles are not exempt
from the general law. The Saurian tribes of
the four quarters of the globe differ in species, and
although warm countries abound in venomous
snakes, they are specifically different, and decrease
both in the numbers and in the virulence of their
poison with decrease of temperature. The dispersion
of insects necessarily follows that of the
vegetables which supply them with food, and in
general it is observed, that each kind of plant is
peopled by its peculiar inhabitants. Each species
of bird has its particular haunt, notwithstanding
the locomotive powers of the winged tribes. The
emu is confined to Australia, the condor never
leaves the Andes, nor the great eagle the Alps;
and although some birds are common to every
country, they are few in number. Quadrupeds
are distributed in the same manner wherever man
has not interfered. Such as are indigenous in one
continent are not the same with their congeners in
another; and with the exception of some kinds of
bats, no warm-blooded animal is indigenous in the
Polynesian Archipelago, nor in any of the islands
on the borders of the central part of the Pacific.
In reviewing the infinite variety of organised
beings that people the surface of the globe, nothing
is more remarkable than the distinctions
which characterise the different tribes of mankind,
from the ebony skin of the torrid zone to the fair
and ruddy complexion of Scandinavia, a difference
which existed in the earliest recorded times, since
the African is represented in the sacred writings
to have been as black in the first ages of mankind
as he is at the present day, and the most ancient
Egyptian paintings, confirm that truth; yet it
appears from a comparison of the principal circumstances
relating to the animal economy or
physical character of the various tribes of mankind,
that the different races are identical in species.
Many attempts have been made to trace the
various tribes back to a common origin, by collating
the numerous languages which are, or have
been, spoken. Some classes of these have few or
no words in common, yet exhibit a remarkable
analogy in the laws of their grammatical construction.
The languages spoken by the native American
nations afford examples of these; indeed the
refinement in the granunatical construction of the
tongues of the American savages leads to the belief
that they must originally have been spoken
by a much more civilized class of mankind. Some
tongues have little or no resemblance in structure,
though they correspond extensively in their vocabularies,
as in the Syrian dialects. In all of these
cases it may be inferred, that the nations speaking
the languages in question are descended from the
same stock; but the probability of a common
origin is much greater in the Indo-European nations,
whose languages, such as the Sanscrit,
Greek, Latin, German, &c. have an affinity both
in structure and correspondence of vocables. In
many tongues not the smallest resemblance can be
traced; length of time, however, may have obliterated
the original identity. The conclusion drawn
from the whole investigation is, that although the
distribution of organized beings does not follow the
direction of the isothermal lines, temperature has
a very great influence on their physical development.
Possibly, too, the nature of animated and
inanimated creatures may be powerfully modified
by the invisible agencies of electricity and magnetism,
which probably pervade all the particles
of matter; indeed the temperature of the air seems
to be intimately connected with its electrical condition.

SECTION XXVIII.
ELECTRICITY is one of those imponderable agents
pervading the earth and all substances, without
affecting their volume or temperature, or even
giving any visible sign of its existence when in a
latent state, but when elicited, developing forces
capable of producing the most sudden, violent, and
destructive effects in some cases, while in others
their action, though less energetic, is of indefinite
and uninterrupted continuance. These modifications
of the electric force, incidentally depending
upon the manner in which it is excited, present
phenomena of great diversity, but yet so connected
as to justify the conclusion that they originate in
a common principle.
Electricity may be called into activity by mechanical
power, by chemical action, by heat, and
by magnetic influence; but we are totally ignorant
why it is roused from its neutral state by
such means, or of the manner of its existence in
bodies; whether it be a material agent, or merely
a property of matter. However, as some hypothesis
is necessary for explaining the phenomena
observed, it is assumed to be a highly-elastic fluid,
capable of moving with various degrees of facility
through the pores or even the substance of matter;
and as experience shows that bodies in one electric
state attract, and in another repel each other, the
hypothesis of two kinds, called positive and negative
electricity, is adopted, but whether there really
be two different fluids, or that the mutual attraction
and repulsion of bodies arises from the redundancy
and defect of their electricities, is of no
consequence, since all the phenomena can be explained
on either hypothesis. As each electricity
has its peculiar properties, the science may be divided
into branches, of which the following notice
is intended to convey some idea.
Substances in which the positive and negative
electricities are combined, being in a neutral state,
neither attract nor repel; but there is a numerous
class called electrics, in which the electric equilibrium
is destroyed by friction: then the positive
and negative electricities are called into action or
separated; the positive is impelled in one direction,
and the negative in another; those of the
same kind repel, whereas those of different kinds
attract each other. The attractive power is exactly
equal to the repulsive force at equal distances,
and when not opposed, they coalesce with
great rapidity and violence, producing the electric
flash, explosion, and shock; then equilibrium is
restored, and the electricity remains latent till
again called forth by a new exciting cause. One
kind of electricity cannot be evolved without the
evolution of an equal quantity of the opposite
kind: thus, when a glass rod is rubbed with
a piece of silk, as much positive electricity is
elicited in the glass as there is negative in
the silk. The kind of electricity depends more
upon the mechanical condition than on the nature
of the surface, for when two plates of
glass, one polished and the other rough, are
rubbed against each other, the polished surface
acquires positive, and the rough negative electricity.
The manner in which the friction is performed
also alters the kind of electricity. Equal
lengths of black and white ribbon, applied longitudinally
to one another, and drawn between the
finger and thumb, so as to rub their surfaces
together, become electric; when separated, the
black ribbon is found to have acquired negative
electricity, and the white positive: but if the
whole length of the black ribbon be drawn across
the breadth of the white, the black will be positively,
and the white negatively electric when separate.
Electricity may be transferred from one body
to another in the same manner as heat is communicated,
and, like it too, the body loses by the
transmission. Although no substance is altogether
impervious to the electric fluid, nor is there any
that does not oppose some resistance to its passage,
yet it moves with much more facility through a
certain class of substances called conductors, such
as metals, water, the human body, &c., than
through atmospheric air, glass, silk, &c., which
are therefore called non-conductors; but the conducting
power is affected both by temperature and
moisture.
Bodies surrounded with non-conductors are said
to be insulated, because, when charged, the electricity
cannot escape; but when that is not the
case, the electricity is conveyed to the earth, which
is formed of conducting matter ; consequently it
is impossible to accumulate electricity in a conducting
substance that is not insulated. There
are a great many substances called non-electrics,
in which electricity is not sensibly developed by
friction, unless they be insulated, probably because
it is carried off by their conducting power
as soon as elicited. Metals, for example, which
are said to be non-electrics, can be excited, but,
being conductors, they cannot retain this state if
in communication with the earth. It is probable
that no bodies exist which are either perfect nonelectrics
or perfect non-conductors; but it is evident
that electrics must be non-conductors to a
certain degree, otherwise they could not retain
their electric state.
It has been supposed that an insulated body remains
at rest, because the tension of the electricity,
or its pressure on the air which restrains it, is
equal on all sides; but when a body in a similar
state, and charged with the same kind of electricity,
approaches it, that the mutual repulsion of
the particles of the electric fluid diminishes the
pressure of the fluid on the air on the adjacent
sides of the two bodies, and increases it on their
remote ends; consequently that equilibrium will be
destroyed, and the bodies, yielding to the action
of the preponderating force, will recede from or
repel each other. When, on the contrary, they
are charged with opposite electricities, it is alleged
that the pressure upon the air on the adjacent sides
will be increased by the mutual attraction of the
particles of the electric fluid, and that on the further
sides diminished; consequently that the force
will urge the bodies towards one another, the motion
in both cases corresponding to the forces producing
it. An attempt has thus been made to
attribute electrical attractions and repulsions to
the mechanical pressure of the atmosphere; it is,
however, more than doubtful whether these phenomena
can be referred to that cause, but certain
it is that, whatever the nature of these forces may
be, they are not impeded in their action by the
intervention of any substance whatever, provided
it he not itself in an electric state.
A body charged with electricity, although perfectly
insulated, so that all escape of electricity is
precluded, tends to produce an electric state of the
opposite kind in all bodies in its vicinity; positive
electricity tends to produce negative electricity in
a body near it, and vice versa, the effect being
greater as the distance diminishes. This power
which electricity possesses of causing an opposite
electrical state in its vicinity is called induction.
When a body charged with either species of electricity
is presented to a neutral one, its tendency,
in consequence of the law of induction, is to disturb
the electrical condition of the neutral body.
The electrified body induces electricity contrary to
its own in the adjacent part of the neutral one,
and therefore an electrical state similar to its own
in the remote part; hence the neutrality of the
second body is destroyed by the action of the first,
and the adjacent parts of the two, having now
opposite electricities, will attract each other. The
attraction between electrified and unelectrified substances
is therefore merely a consequence of their
altered state, resulting directly from the law of
induction, and not an original law. The effects
of induction depend upon the facility with which
the equilibrium of the neutral state of a body can
be overcome, a facility which is proportional to
the conducting power of the body; consequently,
the attraction exerted by an electrified substance
upon another substance previously neutral will be
much more energetic if the latter be a conductor
than if it be a non-conductor.
The law of electrical attraction and repulsion
has been determined by suspending a needle of
gum lac horizontally by a silk fibre, the needle
carrying at one end a piece of electrified gold--
leaf. A globe charged with the same, or with the
opposite kind of electricity, when presented to the
gold-leaf, will repel or attract it, and will therefore
cause the needle to vibrate more or less rapidly
according to the distance of the globe. A comparison
of the number of oscillations performed in
a given time, at different distances, will determine
the law of the variation of the electrical intensity,
in the same manner that the force of gravitation
is measured by the oscillations of the pendulum.
Coulomb invented an instrument which balances
the forces in question by the force of the torsion
of a thread, which consequently measures their
intensity. By this method he found that the intensity
of the electrical attraction and repulsion varies
inversely as the square of the distance. Since electricity
can only be in equilibrio from the mutual
repulsion of its particles, — which, according to
these experiments, varies inversely as the square
of the distance, — its distribution in different bodies
depends upon the laws of mechanics, and therefore
becomes a subject of analysis and calculation.
The distribution of electricity has been so successfully
determined by the analytical investigations of
M. Poisson and Mr. Ivory, that all the computed
phenomena have been confirmed by observation.
It is found by direct experiment that a metallic
globe or cylinder contains the same quantity of
electricity when hollow that it does when solid;
therefore electricity is entirely confined to the
surfaces of bodies, or, if it does penetrate their
substance, the depth is inappreciable: consequently
the quantity bodies are capable of receiving
does not follow the proportion of their bulk,
but depends principally upon the extent of surface
over which it is spread; so that the exterior may
be positively or negatively electric, while the interior
is in a state of perfect neutrality.
Electricity of either kind may be accumulated
to a great extent in insulated bodies, and as long
as it is quiescent it occasions no sensible change
in their properties, though it is spread over their
surfaces in indefinitely thin layers. When restrained
by the non-conducting power of the atmosphere,
the tension or pressure exerted by the
electric fluid against the air which opposes its
escape is in the ratio compounded of the repulsive
force of its own particles at the surface of the
stratum of the fluid and of the thickness of that
stratum; but as one of these elements is always
proportional to the other, the total pressure on
every point must be proportional to the square of
the thickness. If this pressure be less than the
coercive force of the air, the electricity is retained;
but the instant it exceeds that force in any one
point the electricity escapes, which it will do when
the air is attenuated, or becomes saturated with
moisture.
The power of retaining electricity depends also
upon the shape of the body. It is most easily
retained by a sphere, next to that by a spheroid,
but it readily escapes from a point; and, on the
contrary, a pointed object receives it with most
facility. It appears from analysis that electricity,
when in equilibrio, spreads itself in a thin stratum
over the surface of a sphere, in consequence of the
repulsion of its particles, which force is directed
from the centre to the surffice. In an oblong
spheroid the intensity or thickness of the stratum
of electricity at the extremities of the two axes is
exactly in the proportion of the axes themselves;
hence, when the ellipsoid is much elongated, the
electricity becomes very feeble at the equator and
powerful at the poles. A still greater difference
in the intensities takes place in bodies of a cylindrical
or prismatic form, and the more so in proportion
as their length exceeds their breadth;
therefore the electrical intensity is very powerful
at a point, where nearly the whole electricity in
the body will be concentrated.
A perfect conductor is not mechanically affected
by the passage of electricity, if it be of sufficient
size to carry off the whole; but it is shivered to
pieces in an instant, if it be too small to carry off
the charge: this also happens to a bad conductor.
In that case the physical change is generally a
separation of the particles, though it may occasionally
be attributed to chemical action, or expansion
from the heat evolved during the passage
of the fluid; but all these effects are in proportion
to the obstacles opposed to the freedom of its
course. The heat produced by the electric shock
is intense, fusing metals, and even volatilizing
substances, though it is only accompanied by
light when the fluid is obstructed in its passage.
Electrical light is perfectly similar to solar light
in its composition; it seems to arise from the condensation
of the air, during the rapid motion of
the electricity, and varies both in intensity and
colour with the density of the atmosphere. Electricity
is occasionally produced by pressure and
fracture; several crystalline substances also become
electric when heated, especially tourmaline,
one end of which acquires positive, and the other
negative electricity, while the intermediate part is
neutral; but when broken through the middle
each fragment is found to possess positive electricity
at one end, and negative at the other, like
the entire crystal. Electricity is evolved by bodies
passing from a liquid to a solid state, also by the
production and condensation of vapour, which is
consequently a great source of atmospheric electricity.

The atmosphere, when clear, is almost always
positively electric; its electricity is stronger in
winter than in summer, during the day than in
the night. The intensity increases for two or
three hours from the time of sunrise, then decreases
towards the middle of the day, and again augments
as the sun declines, till about the time of sunset,
after which it diminishes, and continues feeble
during the night. Atmospheric electricity arises
from an evolution of the electric fluid during the
evaporation that is so abundant at the surface of
the earth; and clouds probably owe their existence,
or at least their form, to it, for they consist
of hollow vesicles of vapour coated with electricity;
as the electricity is either entirely positive or negative,
the vesicles repel each other, which prevents
them from uniting and falling down in rain.
The friction of the surfaces of two strata of air
moving in different directions, probably developes
electricity; and if the strata be of different temperatures,
a portion of the vapour they always
contain will be deposited; the electricity evolved
will be taken up by the vapour, and will cause it
to assume the vesicular state constituting a cloud.
A vast deal of electricity may be accumulated in
this manner, which may either be positive or
negative, and should two clouds charged with
opposite kinds approach within a certain distance,
the thickness of the coating of electricity will
increase on the two sides of the clouds that are
nearest to one another; and when the accumulation
becomes so great as to overcome the coercive
pressure of the atmosphere, a discharge takes
place, which occasions a flash of lightning. The
actual quantity of electricity in any one part of a
cloud is extremely small; the intensity of the
flash arises from the very great extent of surface
occupied by the electricity, so that the clouds may
be compared to enormous Leyden jars thinly
coated with the electric fluid, which only acquires
its intensity by its instantaneous condensation.
An interchange frequently takes place between
the clouds and the earth, but on account of the
extreme rapidity of lightning it is difficult to ascertain
whether it goes from the clouds to the earth, or
shoots upwards from the earth to the clouds, though
there can be no doubt that it does both. M. Halvig
measured the velocity of lightning by means of the
camera lucida, and estimates that it is probably eight
or ten miles in a second, or about forty times greater
than that of sound; and M. Gay-Lussac has ascertained
that a flash of lightning sometimes darts
more than three miles at once in a straight line.
A person may be killed by lightning, although
the explosion takes place at the distance of twenty
miles, by what is called the back stroke. Suppose
that the two extremities of a cloud highly charged
with electricity hang down towards the earth, they
will repel the electricity from the earth's surface,
if it be of the same kind with their own, and will
attract the other kind ; and if a discharge should
suddenly take place at one end of the cloud, the
equilibrium will instantly be restored by a flash at
that point of the earth which is under the other.
The pure air, at all times negatively electric,
becomes intensely so on the approach of rain,
snow, wind, hail, or sleet, but it afterwards varies
on opposite sides, and the transitions are very
rapid on the approach of a thunder-storm. An
insulated conductor then gives out such quantities
of sparks that it is dangerous to approach it, as was
fatally experienced by Professor Richman, at Petersburg,
who was struck dead by a globe of fire
from the extremity of a conductor, while making
experiments on atmospheric electricity. There is
no instance on record of an electric cloud being
dispelled by a conducting rod silently withdrawing
the electric fluid; yet it may mitigate the
stroke, or render it harmless if it should come.
Sir John Leslie observes, that the efficacy of
conductors depends upon the rapidity with which
they transmit the electric energy; and as copper
is found to transmit the fluid twenty times faster
than iron, and as iron conducts it 400000000 times
more rapidly than water, which conveys it several
thousand times faster than dry stone, copper conductors
afford the best protection, especially if they
expose a broad surface, since the electric fluid is
conveyed chiefly along the exterior of bodies. The
object of a conductor being to carry off the electricity
in case of a stroke, and not to invite an
enemy, it ought to project very little, if at all,
above the building.
The aurora borealis is decidedly an electrical phenomenon,
which takes place in the highest regions
of the atmosphere, since it is visible at the same
time from places very far distant from each other.
It is somehow connected with the magnetic poles of
the earth, but it has never been seen so far north
as the pole of the earth's rotation, nor does it
extend to low latitudes. It generally appears in
the form of a luminous arch, stretching more or
less from east to west, but never from north to
south; across the arch the coruscations are rapid,
vivid, and of various colours. A similar phenomenon
occurs in the high latitudes of the southern
hemisphere. Mr. Faraday conjectures that the
electric equilibrium of the earth is restored by
means of the aurora conveying the electricity from
the poles to the equator.
SECTION XXIX.
GALVANISM is a peculiar kind of electricity, elicited
by the force of chemical action, instead of
friction. It is connected with one of the most
brilliant periods of British science, from the splendid
discoveries to which it led Sir Humphry Davy;
but it has acquired additional interest since it has
been proved, by the reciprocal action of galvanic
and magnetic currents, that magnetism has no
existence as a distinct or separate principle, but is
only an effect of electricity : therefore, galvanism,
as immediately connected with the theory of the
earth and planets, forms a part of the physical
account of their nature.
The disturbance of electric equilibrium, and a development
of electricity, invariably accompanies the
chemical action of a fluid on metallic substances,
and is most plentiful when that action occasions
oxidation. Metals vary ill the quantity of electricity
afforded by their combination with oxygen;
but the greatest abundance is developed by the
oxidation of zinc by weak sulphuric acid; and in
conformity with the law, that one kind of electricity
cannot be evolved without an equal quantity
of the other being brought into activity, it is found
that the acid is positively, and the zinc negatively
electric. It has not yet been ascertained why
equilibrium is not restored by the contact of these
two substances, which are both conductors, and
in opposite electrical states ; however, the electrical
and chemical changes are so connected, that unless
the equilibrium be restored, the action of the acid
will go on languidly, or stop as soon as a certain
quantity of electricity is accumulated in the acid.
The equilibrium, however, will be restored, and
the action of the acid will be continuous, if a plate
of copper be placed in contact with the zinc, both
being partly immersed in the fluid ; for the copper,
not being acted upon by the acid, will serve as a
conductor to convey the positive electricity from
the acid to the zinc, and will at every instant
restore the equilibrium, and then the oxidation of
the zinc will go on rapidly. Thus three substances
are concerned in forming a galvanic circuit,
but it is indispensable that one of them be a fluid.
The electricity so obtained will be very feeble, but
it may be augmented by increasing the number of
plates. In the common galvanic battery, the electricity
which the fluid has acquired from the first
plate of zinc exposed to its action, is taken up by
the copper plate belonging to the second pair, and
transferred to the second zinc plate with which it
is connected. This second plate of zinc having
thus acquired a larger portion of electricity than
its natural share, communicates a larger quantity
of electricity to the fluid in the second cell. This
increased quantity is again transferred to the next
pair of plates; and thus every succeeding alternation
is productive of a further increase in the
quantity of the electricity developed. This action,
however, would stop unless a vent were given to
the accumulated electricity, by establishing a communication
between the positive and negative
poles of the battery, by means of wires attached
to the extreme plate at each end. When the
wires are brought into contact, the galvanic circuit
is completed, the electricities meet and neutralize
each other, producing the shock and other
electrical phenomena, and then the electric current
continues to flow uninterruptedly in the circuit,
as long as the chemical action lasts. The
stream of positive electricity flows from the zinc
to the copper, but as the battery ends in a zinc
plate which communicates with the wire, the zinc
end becomes the positive, and the copper the negative
poles of a compound battery, which is exactly
the reverse of what obtains in a single circuit.
Galvanic or voltaic, like common electricity,
may either be considered to consist of two fluids
passing in opposite directions through the circuit,
the positive stream coming from the zinc, and the
negative from the copper end of the battery ; or,
if the hypothesis of one fluid be adopted, the zinc
end of the battery may be supposed to have an
excess of electricity, and the copper end a deficiency.

Voltaic electricity is distinguished by two
marked characters. Its intensity increases with
the number of plates—its quantity with the extent
of their surfaces. The most intense concentration
of force is displayed by a numerous series of
large plates, light and heat are copiously evolved,
and chemical decomposition is accomplished with
extraordinary energy ; whereas, the electricity
from one pair of plates is so feeble, whatever their
size may be, that it gives no sign either of attraction
or repulsion ; and, even with a battery consisting
of a very great number of plates, it is
difficult to render the mutual attraction of its two
wires sensible, though of opposite electricities.
The action of voltaic electricity differs materially
from that of the ordinary kind. When a
quantity of common electricity is accumulated,
the restoration of equilibrium is attended by an
instantaneous violent explosion, accompanied by
the development of light, heat, and sound. The
concentrated power of the fluid forces its way
through every obstacle, disrupting and destroying
the cohesion of the particles of the bodies through
which it passes, and occasionally increasing its
destructive effects by the conversion of fluids into
steam from the intensity of the momentary heat,
as when trees are torn to pieces by a stroke of
lightning : even the vivid light which marks the
path of the electric fluid is probably owing to
the sudden compression of the air and other
particles of matter during the rapidity of its
passage; but the instant equilibrium is restored
by this energetic action, the whole is at an end.
On the contrary, when an accumulation takes
place in a voltaic battery, equilibrium is restored
the moment the circuit is completed; but so far
is the electric stream from being exhausted, that
it continues to flow silently and invisibly in an
uninterrupted current supplied by a perpetual reproduction
; and although its action on bodies'is
neither so sudden nor so intense as that of common
electricity, yet it acquires such power from
constant accumulation and continued action, that
it ultimately surpasses the energy of the other.
The two kinds of electricity differ in no circumstance
more than in the development of heat.
Instead of a momentary evolution, which seems to
arise from a forcible compression of the particles
of matter during the passage of the common electric
fluid, the circulation of the voltaic electricity
is accompanied by a continued development of
heat, lasting as long as the circuit is complete,
without producing either light or sound; and this
appears to be its immediate direct effect, inde-,
pendent of mechanical action. Its intensity is
greater than that of any heat that can be obtained
by artificial means, so that it fuses substances
which resist the action of the most powerful furnaces.
The temperature of every part of a galvanic
battery itself is raised during its activity.
When the battery is powerful, the luminous
effects of galvanism are very brilliant ; but considerable
intensity is requisite to enable the electricity
to force its way through the air on bringing
the wires together from the opposite poles. Its
transit is accompanied by light, and in consequence
of the continuous supply of the fluid,
sparks occur every time the contact of the wires
is either broken or renewed. The most splendid
artificial light known is produced by fixing pencils
of charcoal at the extremities of the wires, and
bringing them into contact. This light is the
more remarkable as it appears to be independent
of combustion, since the charcoal suffers no
change, and likewise because it is equally vivid
in such gases as do not contain oxygen. Though
nearly as bright as solar light, it differs from it in
possessing some of those rays of which the sunbeams
are deficient, according to the experiments
of M. Fraunhofer. Voltaic electricity is a powerful
agent in chemical analysis ; numerous instances
might be given, but the decomposition of water is
perhaps the most simple and elegant. Suppose a
glass tube filled with very pure water, and corked
at both ends ; if one of the wires of an active galvanic
battery be made to pass through one cork,
:and the other through the other cork, into the
water, so that the extremities of the two wires shall
be opposite and about a quarter of an inch asunder,
chemical action will immediately take place, and
gas will continue to rise from the extremities of
both wires till the water has vanished. If an
electric spark be then sent through the tube, the
water will reappear. By arranging the experiment
so as to have the gas given out by each wire
separately, it is found that water consists of two
parts of hydrogen and one of oxygen. The positive
wire of the battery has a stronger affinity for
oxygen than oxygen has for hydrogen ; it consequently
combines with the oxygen of the water,
and sets the hydrogen free; but as the negative
wire has a stronger affinity for hydrogen than hydrogen
has for oxygen, it combines with the hydrogen
of the water, and sets the oxygen free. If,
therefore, an electric spark be sent through a mixture
consisting of two parts of hydrogen and one
of oxygen, the gases will combine and form water.
The decomposition of the alkalies and earths by
Sir Humphry Davy, and all chemical changes produced
by the electric fluid, are accomplished on
the same principle, and it appears that, in general,
combustible substances go to the negative wire,
while oxygen is evolved at the positive. The
powerful efficacy of voltaic electricity in chemical
decomposition arises from the continuance of its
action, and its agency appears to be most exerted
on fluids and substances which, by conveying the
electricity partially and imperfectly, impede its
progress. But it is now proved to be as efficacious
in the composition as in the decomposition
or analysis of bodies.
It had been observed that, when metallic solutions
are subjected to galvanic action, a deposition
of metal, generally in the form of minute crystals,
takes place on the negative wire : by extending
this principle, and employing a very feeble voltaic
action, M. Becquerel has succeeded in forming
crystals of a great proportion of the mineral substances
precisely similar to those produced by
nature. The electric state of metallic veins
makes it possible that many natural crystals may
have taken their form from the action of electricity
bringing their ultimate particles, when in solution,
within the narrow sphere of molecular attraction
already mentioned as the great agent in the formation
of solids. Both light and motion favour crystallization.
Crystals which form in different liquids
x 2
are generally more abundant on the side of the jar
exposed to the light ; and it is a well-known fact
that still water, cooled below 32°, starts into crystals
of ice the instant it is agitated. Light and
motion are intimately connected with electricity,
which may therefore have some influence on the
laws of aggregation; this is the more likely, as a
feeble action is alone necessary, provided it be
continued for a sufficient time. Crystals formed
rapidly are generally imperfect and soft, and M.
Becquerel found that even years of constant voltaic
action were necessary for the crystallization of
some of the hard substances. If this law be general,
how many ages may be required for the formation
of a diamond!
Several fish possess the faculty of producing
electrical effects. The most remarkable are the
gymnotus electricus, found in South America, and
the torpedo, a species of ray, frequent in the Mediterranean.
The absolute quantity of electricity
brought into circulation by the torpedo is so great
that it effects the decomposition of water, has
power sufficient to make magnets, and gives very
severe shocks; it is identical in kind with that of
the galvanic battery, the electricity of the under
surface of the fish being the same with the negative
pole, and that in the upper surface the same
with the positive pole : its manner of action is,
however, somewhat different, for, although the
evolution of the electricity is continued for a sensible
time, it is interrupted, being communicated
by a succession of discharges.
SECTION XXX.
IN order to explain the other methods of exciting
electricity, and the recent discoveries that have
been made in that science, it is necessary to be
acquainted with the general theory of magnetism,
and also with the magnetism of the earth, the
director of the mariner's compass, and his guide
through the ocean. Its influence extends over
every part of the earth's surface, but its action on
the magnetic needle determines the poles of this
great magnet, which by no means coincide with
the poles of the earth's rotation. In consequence
of their attraction and repulsion, a needle freely
suspended, whether it be magnetic or not, only
remains in equilibrio when in the magnetic meridian,
that is, in the plane which passes through
the north and south magnetic poles. There are
places where the magnetic meridian coincides with
the terrestrial meridian ; in these a magnetic
needle freely suspended points to the true north;
but if it be carried successively to different places
on the earth's surface, its direction will deviate
sometimes to the east and sometimes to the west
of north. Lines drawn on the globe, through all
the places where the needle points due north and
south, are called lines of no variation,• and they
are extremely complicated. The direction of the
needle is not even constant in the same place, but
changes in a few years according to a law not yet
determined. In 1657, the line of no variation
passed through London ; from that time it has
moved slowly, but irregularly, westward, and is
now in North America. In the year 1819, Sir
Edward Parry, in his voyage to discover the northwest
passage round America, sailed near the
magnetic pole ; and in 1824; Captain Lyon, on
an expedition for the same purpose, found that
the magnetic pole was then situate in 63° 26' 51"
north latitude, and in 80° 51' 25" west longitude.
It appears, from later researches, that the law of
terrestrial magnetism is of considerable complexity
and the existence of more than one magnetic
pole in either hemisphere has been rendered highly
probable ; that there is one in Siberia seems to be
decided by the recent observations of M. Hansteen,—it
is in longitude 102° east of Greenwich,
and a little to the north of the 60th degree of
latitude : so that, by these data, the two magnetic
poles in the northern hemisphere are about 180°
distant from each other ; hut Captain Ross, who
is just returned from a voyage in the polar seas,
has ascertained that the American magnetic pole
is in '10° 14' north latitude, and 96° 40' west
longitude. The magnetic equator does not exactly
coincide with the terrestrial equator ; it
appears to be an irregular curve inclined to the
earth's equator at an angle of about 12°, and
crossing it in at least three points in longitude
113° 14' west, and 66° 46' east of the meridian of
Greenwich, and again somewhere between 156° 30'
of west longitude, and 116° east.
The needle is also subject to diurnal variations ;
in our latitudes it moves slowly eastward during
the forenoon, and returns to its mean position
about ten in the evening ; it then deviates to the
westward, and again returns to its mean position
about ten in the morning. M. Kupffer, of Casan,
ascertained, in the year 1831, that there is a
nightly, as well as a diurnal variation, depending,
in his opinion, upon a variation in the magnetic
equator.
A magnetic needle, suspended so as to be
moveable only in the vertical plane, dips, or
becomes more and more inclined to the horizon
the nearer it is brought to the magnetic pole, and
there becomes vertical. At the magnetic equator
it is horizontal, and between these two positions
it assumes every degree of inclination. Captain
Lyon found that the dip in the latitude and longitude
mentioned, very near the magnetic pole, was
86° 32', and Captain Segelke determined it to be
69° 38' at Woolwich in 1830. According to Captain
Sabine, it appears to have been decreasing for
the last fifty years at the rate of three minutes
annually.
If a magnetised needle freely suspended, and at
rest in the magnetic meridian, be drawn any
-number of degrees from its position, it will make
a certain number of oscillations before it resumes
its state of rest. The intensity of the magnetic
force is determined from these oscillations in the
same manner that the intensity of the gravitating
and electrical forces are known from the vibrations
of the pendulum and the balance of torsion, and in
all these cases it is proportional to the square of the
number of oscillations performed in a given time ;
consequently a comparison of the number of vibrations
accomplished by the same needle, during
the same time, in different parts of the earth's
surface, will determine the variations in the magnetic
action. By this method Humboldt and
Russel have discovered that the intensity of the
magnetic force increases from the equator to the
poles, where it is probably at its maximum. It
appears to be doubled in the ascent from the equator
to the western limits of Baffin's Bay. According
to the magnetic observations of Professor
Hansteen, of Christiania, the magnetic intensity
has been decreasing annually at Christiania, London,
and Paris, at the rate of its 235th, 125th,
and 1020th parts, respectively, which he attributes
to the revolution of the Siberian magnetic
pole. There is, however, so much uncertainty in
the magnetic phenomena of the earth, that the
results require to be continually corrected by new
observations.
The inventor of the mariner's compass, like
most of the early benefactors of mankind, is
unknown ; it is even doubted which nation first
made use of magnetic polarity to determine
positions on the surface of the globe ; but it is
said that a rude form of the compass was invented
in Upper Asia, and conveyed thence by
the Tartars to China, where the Jesuit missionaries
found traces of this instrument having been employed
as a guide to land travellers in very remote
antiquity. From that the compass spread over the
east, and was imported into Europe by the Crusaders,
and its construction improved by an artist
of Amalfi, on the coast of Calabria. It seems that
the Romans and Chinese only employed eight cardinal
divisions, which the Germans successively
bisected till there were thirty-two, and gave the
points the names which they still bear.
The variation of the compass was unknown till
Columbus, during his first voyage, observed that
the needle declined from the meridian as he advanced
across the Atlantic. The dip of the magnetic
needle was first noticed by Robert Norman,
in the year 1576.
Very delicate experiments have shown that all
bodies are more or less susceptible of magnetism.
Many of the gems give signs of it ; cobalt, titanium,
and nickel sometimes even possess the properties
of attraction and repulsion; but the magnetic
agency is most powerfully developed in iron,
and in that particular ore of iron called the load-stone,
which consists of the protoxide and the
peroxide of iron, together with small portions of
silica and alumina. A metal is often susceptible
of magnetism if it only contains the 130000th
part of its weight of iron, a quantity too small to
be detected by anv chemical test.
The bodies in question are naturally magnetic,
but that property may be imparted by a variety of
methods, as by friction with magnetic bodies, or
juxtaposition to them, but none is more simple
than percussion. A bar of hard steel, held in the
direction of the dip, will become a magnet on
receiving a few smart blows with a hammer on its
upper extremity; and M. Hansteen has ascertained
that every substance has magnetic poles
when held in that position, whatever the materials
may be of which it is composed.
One of the most distinguishing marks of magnetism
is polarity, or the property a magnet possesses,
when freely suspended, of spontaneously
pointing nearly north and south, and always returning
to that position when disturbed. Another
property of a magnet is the attraction of unmagnetised
iron. Both poles of a magnet attract iron,
which in return attracts either pole of the magnet
with an equal and contrary force. The magnetic
intensity is most powerful at the poles, as may
easily be seen by dipping the magnet into iron
filings, which will adhere abundantly to each pole,
while scarcely any attach themselves to the intermediate
parts. The action of the magnet on unmagnetised
iron is confined to attraction, whereas
the reciprocal agency of magnets is characterized
by a repulsive as well as an attractive force, for a
north pole repels a north pole, and a south repels
a south pole ; but a north and a south pole mutually
attract one another, which proves that there
are two distinct kinds of magnetic forces, directly
opposite in their effects, though similar in their
mode of action.
Induction is the power which a magnet possesses
of exciting temporary or permanent magnetism
in such bodies in its vicinity as are capable of
receiving it. By this property the mere approach
of a magnet renders iron or steel magnetic, the
more powerfully the less the distance. When the
north pole of a magnet is brought near to, and in
the line with an unmagnetised iron bar, the bar acquires
all the properties of a perfect magnet, the
end next the north pole of the magnet becomes a
south pole, while the remote end becomes a north
pole. Exactly the reverse takes place when the
south pole is presented to the bar ; so that each
pole of a magnet induces the opposite polarity in
the adjacent end of the bar, and the same polarity
in the remote extremity ; consequently the nearest
extremity of the bar is attracted, and the farther
repelled, but as the action is greater on the adjacent
than on the distant part, the resulting force
is that of attraction. By induction, the iron bar
not only acquires polarity, but the power of inducing
magnetism in a third body ; and although
all these properties vanish from the iron as soon as
the magnet is removed, a lasting increase of intensity
is generally imparted to the magnet itself by the reaction
of the temporary magnetism of the iron. Iron
acquires magnetism more rapidly than steel, yet it
loses it as quickly on the removal of the magnet,
whereas the steel is impressedwith a lasting polarity.
A certain time is requisite for the induction of
magnetism, and it may be accelerated by anything
that excites a vibratory motion in the particles of
the steel, such as the smart stroke of a hammer,
or heat succeeded by sudden cold. A steel bar
may be converted into a magnet by the transmission
of an electric discharge through it, and as its
efficacy is the same in whatever direction the electricity
passes, the magnetism arises from its mechanical
operation exciting a vibration among the
particles of the steel. It has been observed that the
particles of iron easily resume their neutral state
after induction, but that those of steel resist the
restoration of magnetic equilibrium, or a return to
the neutral state : it is therefore evident, that any
cause which removes or diminishes the resistance
of the particles will tend to destroy the magnetism
of the steel ; consequently, the same mechanical
means which develope magnetism will also destroy
it. On that account, a steel bar may lose its magnetism
by any mechanical concussion, such as by
falling on a hard substance, a blow with a hammer,
and heating to redness, which reduces the steel to
the state of soft iron. The circumstances which
determine whether it shall gain or lose being its
position with respect to the magnetic equator, and
the higher or lower intensity of its previous magnetic
state.
Polarity of one kind only cannot exist in any
portion of iron or steel, for in whatever manner
the intensities of the two kinds of polarity may be
diffused through a magnet, they exactly balance
or compensate one another. The northern polarity
is confined to one half of a magnet, and the
southern to the other, and they are generally concentrated
in or near the extremities of the bar.
When a magnet is broken across its middle, each
fragment is at once converted into a perfect magnet;
the part which originally had a north pole,
acquires a south pole at the fractured end, the
part that originally had a south pole gets a north
pole ; and as far as mechanical division can be
carried, it is found that each fragment, however
small, is a perfect magnet.
A comparison of the number of vibrations accomplished
by the same needle, during the same
time, at different distances from a magnet, gives
the law of magnetic intensity, which, like every
known force that emanates from a centre, follows
the inverse ratio of the square of the distance, a
law that is not affected by the intervention of any
substance whatever between the magnet and the
needle, provided that substance be not itself susceptible
of magnetism. Induction and the reciprocal
action of magnets are, therefore, subject to
the laws of mechanics, but the composition and
resolution of the forces are complicated, in consequence
of four forces being constantly in activity,
two in each magnet.
The phenomena of magnetism may be explained
on the hypothesis of two extremely rare fluids pervading
all the particles of iron, and incapable of
leaving them. Whether the particles of these fluids
are coincident with the molecules of the iron, or
that they only fill the interstices between them, is
unknown and immaterial ; but it is certain that the
sum of all the magnetic molecules, added to the
sum of all the spaces between them, whether occupied
by matter or not, must be equal to the
whole volume of the magnetic body. When the
two fluids in question are combined they are inert,
so that the substances containing them show no
signs of magnetism ; but when separate they are
active, the molecules of each of the fluids attracting
those of the opposite kind, and repelling those
of the same kind. The decomposition of the
united fluids is accomplished by the inductive
influence of either of the separate fluids ; that is
to say, a ferruginous body acquires polarity by the
approach of either the south or north pole of a
magnet. The electric fluids are confined to the
surfaces of bodies, whereas the magnetic fluids pervade
each molecule of the mass ; besides, the electric
fluid has a perpetual tendency to escape, and
does escape, when not prevented by the coercive
power of the surrounding air and other non-conducting
bodies. Such a tendency does not exist
in the magnetic fluids, which never quit the substance
that contains them under ally circumstances
whatever ; nor is any sensible quantity of either
kind of polarity ever transferred from one part to
another of the same piece of steel. It appears
that the two magnetic fluids, when decomposed by
the influence of magnetising forces, only undergo
a displacement to an insensible degree within the
body. The action of all the particles so displaced
upon a particle of the magnetic fluid in any particular
situation, compose a resultant force, the
intensity and direction of which it is the province
of the analyst to determine. In this manner
M. Poisson has proved that the result of the
action of all the magnetic elements of a magnetised
body is a force equivalent to the action of
a very thin stratum covering the whole surface of
a body, and consisting of the two fluids—the
austral and the boreal, occupying different parts
of it ; or, in other words, the attractions and
repulsions externally exerted by a magnet are
exactly the same as if they proceeded from a very
thin stratum of each fluid occupying the surface
only, both fluids being in equal quantities, and so
distributed that their total action upon all the
points in the interior of the body are equal to
nothing. Since the resulting force is the difference
of the two polarities, its intensity must be
greatly inferior to that of either.
It may be observed that, in addition to the
forces already mentioned, there must be some
coercive force analogous to friction which arrests
the particles of both fluids, so as first to oppose
the separation of the fluids, and then to prevent
their reuniting. In soft iron the coercive force is
either wanting or extremely feeble, since the iron
is easily rendered magnetic by induction, and as
easily loses its magnetism ; whereas in steel the
coercive force is extremely energetic, because it
prevents the steel from acquiring the magnetic
properties rapidly, and entirely hinders it from
losing them when acquired. The feebleness of
the coercive force in iron, and its energy in steel,
with regard to the magnetic fluids, is perfectly
analogous to the facility of transmission afforded
to the electric fluids by non-electrics, and the
resistance they experience in electrics. At every
step the analogy between magnetism and electricity
becomes more striking. The agency of
attraction and repulsion is common to both, the
positive and negative electricitics are similar to
the northern and southern polarities, and are
governed by the same laws, namely, that between
like powers there is repulsion, and between unlike
powers there is attraction ; each of these four
forces is capable of acting most energetically when
alone, but the electric equilibrium is restored by
the union of the two electricities, and magnetic
neutrality by the combination of the two polarities,
thus respectively neutralizing each other when
joined. All these forces vary inversely as the
square of the distance, and consequently come
under the same mechanical laws. A like analogy
extends to magnetic and electrical induction.
Iron and steel are in a state of equilibrium when
the two magnetic polarities conceived to reside in
them are equally diffused throughout the whole
mass, so that they are altogether neutral. But
this equilibrium is immediately disturbed on the
approach of the pole of a magnet, which by induction
transfers one kind of polarity to one end of
the iron or steel bar, and the opposite kind to
the other,—effects exactly similar to electrical
induction. There is even a correspondence between
the fracture of a magnet and that of an
electric conductor ; for if an oblong conductor be
electrified by induction, its two extremities will
have opposite electricities ; and if in that state it
be divided across the middle, the two portions,
when removed to a distance from one another,
will each retain the electricity that has been induced
upon it. The analogy, however, does not
extend to transference. A body may transfer a
redundant quantity of positive or negative electricity
to another, the one gaining at the expense
of the other ; but there is no instance of a body
possessing only one kind of polarity. With this
exception, there is such perfect correspondence
between the theories of magnetic attractions and
repulsions and electric forces in conducting bodies,
that they not only are the same in principle, but
are determined by the same formulae. Experiment
concurs with theory in proving the identity
of these two unseen influences.
SECTION XXXI.
THE disturbing effects of the aurora borealis and
of lightning on the mariner's compass had been
long known, but in the year 1819, M. Oersted,
Professor of Natural Philosophy at Copenhagen,
discovered that a current of voltaic electricity
exerts a powerful influence on a magnetised
needle, an observation which has given rise to the
theory of electro-magnetism, the most interesting
science of modern times, whether it be considered
as leading us a step farther in generalization, by
identifying two agencies hitherto referred to different
causes, or as developing a new force unparalleled
in the system of the world, which, overcoming
the retardation from friction, and the obstacle of
a resisting medium, maintains a perpetual motion,
often vainly attempted, but which it seems altoY2

gether impossible to accomplish by means of any
other force or combination of forces than the one
in question.
When the two poles of a voltaic battery are
connected by a metallic wire, so as to complete
the circuit, the electricity flows without ceasing ;
and if a straight portion of that wire be placed
parallel to, and horizontally above, a magnetised
needle at rest in the magnetic meridian, but freely
poised like the mariner's compass, the action of
the electric current flowing through the wire will
instantly cause the needle to change its position :
its extremity will deviate from the north towards
the east or west, according to the direction in
which the current is flowing ; and on reversing
the direction of the current, the motion of the
needle will be reversed also. The numerous experiments
that have been made on the magnetic
and electric fluids, as well as those on the various
relative motions of a magnetic needle under the
influence of galvanic electricity, arising from all
possible positions of the conducting wire, and
every direction of the voltaic current, together
with all the other phenomena of electromagnetism,
are explained by Dr. Roget in some excellent
articles on these subjects in the Library of
Useful Knowledge.
• All the experiments tend to prove that the force
emanating from the electric current, which produces
such effects on the magnetic needle, acts at
right angles to the current, and is therefore unlike
any force hitherto known. The action of all the
forces in nature is directed in straight lines, as far
as we know, for the curves described by the heavenly
bodies result from the composition of two forces,
whereas, that which is exerted by an electrical
current upon either pole of a magnet has no tendency
to cause the pole to approach or recede,
but to rotate about it. If the stream of electricity
be supposed to pass through the centre of a circle
whose plane is perpendicular to the current, the
direction of the force exerted by the electricity
will always be in the tangent to the circle, or at
right angles to its radius; consequently the tangential
force of the electricity has a tendency to
make the pole of a magnet move in a circle round
the wire of the battery. Mr. Barlow has proved
that the action of each particle of the electric fluid
in the wire, on each particle of the magnetic fluid
in the needle, varies inversely as the square of the
distance.
Rotatory motion was suggested by Dr. Wollaston;
Mr. Faraday was the first who actually
succeeded in making the pole of a magnet rotate
about a vertical conducting wire. In order to
limit the action of the electricity to one pole, about
two-thirds of a small magnet was immersed in mercury,
the lower end being fastened by a thread to the
bottom of the vessel containing the mercury. When
the magnet was thus floating almost vertically
with its north pole above the surface, a current
of positive electricity was made to descend perpendicularly
through a wire touching the mercury,
and immediately the magnet began to rotate from
left to right about the wire. As the force is uniform,
the rotation was accelerated till the tangential
force was balanced by the resistance of the
mercury, when it became constant. Under the
same circumstances, the south pole of the magnet
rotates from right to left. It is evident from this
experiment that the wire may also be made to
perform a rotation round the magnet, since the
action of the current of electricity on the pole of
the magnet must necessarily be accompanied by a
corresponding reaction of the pole of the magnet
on the electricity in the wire. This experiment
has been accomplished by a vast number of contrivances,
and even a small battery, consisting of
two plates, has performed the rotation. Mr. Faraday
produced both motions at the same time in
a vessel containing mercury ; the wire and the
magnet revolved in one direction about a common
centre of motion, each following the other.
The next step was to make a magnet and
also a cylinder revolve about their own axes, which
they do with great rapidity. Mercury has been
made to rotate by means of voltaic electricity,
and Professor Ritchie has exhibited in the Royal
Institution the singular spectacle of the rotation
of water by the same means, while the vessel containing
it remained stationary. The water was
in a hollow double cylinder of glass, and on being
made the conductor of electricity, was observed to
revolve in a regular vortex, changing its direction
as the poles of the battery were alternately reversed.
Professor Ritchie found that all the different
conductors hitherto tried by him, such as
water, charcoal, &c. give the same electromagnetic
results, when transmitting the same quantity of
electricity, and that they deflect the magnetic
needle in an equal degree when their respective
axes of conduction are at the same distance from
it. But one of the most extraordinary effects of
the new force is exhibited by coiling a copper
wire, so as to form a helix or corkscrew, and connecting
the extremities of the wires with the poles
of a galvanic battery. If a magnetised steel bar
or needle be placed within the screw, so as to rest
upon the lower and interior part, the instant a
current of electricity is sent through the wire of
the helix, the steel bar starts up by the influence
of this invisible power, and remains suspended in
the air in opposition to the force of gravitation.
The effect of the electromagnetic power exerted
by each turn of the wire is to urge the north pole
of the magnet in one direction, and the south pole
in the other ; the force thus exerted is multiplied
in degree and increased in extent by each repetition
of the turns of the wire, and in consequence
of these opposing forces the bar remains suspended.
This helix has all the properties of a
magnet while the electrical current is flowing
through it, and may be substituted for one in
almost every experiment. It acts as if it had a
north pole at one extremity and a south pole at
the other, and is attracted and repelled by the
poles of a magnet exactly as if it were one itself.
All these effects depend upon the course of the
electricity, that is, on the direction of the turns of
the screw, according as they are from right to
left, or from left to right, being in the one case
exactly the contrary of what it is in the other.
The effects of electricity in motion on magnets
are not only precisely the same as the reciprocal
action of magnetised bodies, but its influence in
inducing magnetism in unmagnetised iron and steel
is also the same with magnetic induction. The
term induction, when applied to electric currents,
expresses the power which these currents possess
of inducing any particular state upon matter in
their immediate neighbourhood, otherwise neutral
or indifferent. For example, the connecting wire
of a galvanic battery holds iron filings suspended
like an artificial magnet, as long as the current
continues to flow through it ; and the most powerful
temporary magnets that have ever been made
are obtained by bending a thick cylinder of soft
iron into the form of a horseshoe, and surrounding
it with a coil of thick copper wire covered
with silk, to prevent communication between its
parts. When this wire forms part of a galvanic
circuit, the iron becomes so highly magnetic, that
a temporary magnet of this kind made by Professor
Henry of the Albany Academy, in the
United States, sustained nearly a ton weight. The
iron loses its magnetic power the instant the
electricity ceases to circulate, and acquires it
again as instantaneously when the circuit is renewed.
Steel needles are rendered permanently
magnetic by electrical induction; the effect is produced
in a moment, and as readily by juxtaposition
as by contact; the nature of the poles depends
upon the direction of the current, and the intensity
is proportional to the quantity of electricity.
It appears from what precedes, that the principle
and characteristic phenomena of the electromagnetic
science are, the evolution of a tangential
and rotatory force exerted between a conducting
body and a magnet; and the transverse induction
of magnetism by the conducting body in such
substances as are susceptible of it.
The action of an electric current causes a deviation
of the compass from the plane of the magnetic
meridian. In proportion as the needle recedes
from the meridian, the intensity of the force
of terrestial magnetism increases, while at the
same time the electromagnetic force diminishes;
the number of degrees at which the needle stops,
and which mark where the equilibrium between
these two forces takes place, will indicate the intensity
of the galvanic current. The galvanometer,
constructed upon this principle, is employed
to measure the intensity of galvanic currents collected
and conveyed to it by wires. This instrument
is rendered much more sensible by neutralizing
the effects of the earth's magnetism on
the needle, which is accomplished by placing a
second magnetised needle so as to counteract the
action of the earth on the first, a precaution requisite
in all delicate magnetical experiments.
SECTION XXXII.
THE science of electro-magnetism which has been
under consideration, and must render the name
of M. Oersted ever memorable, relates to the reciprocal
action of electrical and magnetic currents:
M. Ampère, by discovering the mutual action of
electrical currents on one another, has added a
new branch to the subject, to which he has given
the name of electro-dynamics.
When electric currents are passing through two
conducting wires so suspended or supported as to
be capable of moving both towards and from one
another, they show mutual attraction or repulsion,
according as the currents are flowing in the same
or in contrary directions; the phenomena varying
with the relative inclinations and positions of the
streams of electricity. It appears that the mutual
action of such currents, whether they flow in the
same or in contrary directions, whether they be
parallel, perpendicular, diverging, converging, circular,
or heliacal, all produce different kinds of motion,
in a conducting wire, both rectilineal and circular,
and also the rotation of a wire helix, such as
that described and now called an electrodynamic
cylinder on account of some improvements in its
construction; and as the hypothesis of a force
varying inversely as the square of the distance
accords perfectly with all the observed phenomena,
these motions come under the same laws of dynamics
and analysis as any other branch of physics.
The theory of electrodynamics, as well as
actual experiment, confirms the identity between
the agencies of electrodynamic cylinders, or
helices, and magnets. The law of the reciprocal
action of a cylinder and an electric current is
precisely the same, and all the experiments that
can be performed with the cylinder might be
accomplished with a magnet. It has already been
observed that the two extremities of an electrodynamic
cylinder or helix exhibit all the properties
possessed by the poles of a magnet; that end
in which the current of positive electricity is
moving in a direction similar to the motion of the
hands of a watch, acting as a south pole, and the
other end, in which the current is flowing in a
contrary direction, exhibiting northern polarity.
In conformity with this resemblance, electrodynamic
cylinders act on each other precisely as
if they were magnets, during the time the electricity
is flowing through them.
The phenomena mark a very decided difference
between the action of electricity in motion or at
rest, that is, between voltaic and common electricity;
the laws they follow are in many respects
of an entirely different nature. Since voltaic
electricity flows perpetually, it cannot be accumulated,
and consequently has no tension or tendency
to escape from the wires which conduct it. Nor
do these wires either attract or repel light bodies
in their vicinity, whereas ordinary electricity can
be accumulated in insulated bodies to a great degree,
and in that state of rest the tendency to
escape is proportional to the quantity accumulated
and the resistance it meets with. In ordinary
electricity, the law of action is, that dissimilar
electricities attract, and similar electricities repel
one another. In voltaic electricity, on the contrary,
similar currents, or such as are moving in
the same direction, attract one another, while a
mutual repulsion is exerted between dissimilar
currents, or such as flow in opposite directions.
The common electricity escapes when the pressure
is removed, but the electrodynamical effects are
the same whether the conductors be in air or in
vacuo.
Although the effects produced by a current of
electricity depend upon the celerity of its motion,
the velocity with which it moves through a conducting
wire is unknown. We are equally ignorant
whether it be uniform or varied, but the
method of transmission has a marked influence on
the results ; for when it flows without intermission,
it occasions a deviation in the magnetic
needle, but it has no effect whatever when its
motion is discontinuous or interrupted, like the
current produced by the common electrical machine
when a communication is made between the
positive and negative conductors.
M. Ampère has established a theory of electromagnetism
suggested by the analogy between
electro-dynamic cylinders and magnets, founded
upon the reciprocal attraction of electric currents,
to which all the phenomena of magnetism and
electromagnetism may be reduced, by assuming
that the magnetic properties which bodies possess
derive these properties from currents of electricity
circulating about every part in one uniform
direction. It has been observed that, although
every particle of a magnet possess like properties
with the whole, yet the general effect is the same
as if the magnetic properties were confined to the
surface: consequently the internal electro-currents
must compensate one another, and therefore
the magnetism of a body is supposed to arise
from a superficial current of electricity constantly
circulating in a direction perpendicular to the
axis of the magnet; so that the reciprocal action
of magnets, and all the phenomena of electromagnetism,
are reduced to the action and reaction
of superficial currents of electricity acting at right
angles to the direction of the currents. Notwithstanding
some experiments made by M. Ampère
to elucidate the subject, there is still an uncertainty
in the theory of the induction of magnetism
by an electric current in a body near it; for it
does not appear whether electric currents which
did not previously exist are actually produced by
induction, or if its effect be only to give one uniform
direction to the infinite number of electric
currents previously existing in the particles of the
body, and thus rendering them capable of exhibiting
magnetic phenomena, in the same manner
as polarization reduces those undulations of light
to one plane which had previously been performed
in every plane. Possibly both may be combined
in producing the effect; for the action of an
electric current may not only give a common
direction to those already existing, but may also
increase their intensity. However that may be,
by assuming that the attraction and repulsion of
the elementary portions of electric currents vary
inversely as the square of the distance, the action
being at right angles to the direction of the current,
it is found that the attraction and repulsion
of a current of indefinite length on the elementary
portion of a parallel current at any distance from
it, is in the simple ratio of the shortest distance
between them ; consequently the reciprocal action
of electric currents is reduced to the composition
and resolution of forces, so that the phenomena
of electromagnetism are brought under the laws
of dynamics by the theory of Ampère.
SECTION XXXIII.
FROM the law of action and reaction being equal
and contrary, it might be expected that, as electricity
powerfully affects magnets, so, conversely,
magnetism ought to produce electrical phenomena.
By proving this very important fact from a series
of highly interesting and ingenious experiments,
Mr. Faraday has added another branch to the
science, which he has named magneto-electricity.
A great quantity of copper wire was coiled
in the form of a helix round one half of a ring
of soft iron, and connected with a galvanic battery,
while a similar helix connected with a galvanometer
was wound round the other half of the
ring, but not touching the first helix. As soon
as contact was made with the battery, the needle
of the galvanometer was deflected, but the action
was transitory, for when the contact was continued
the needle returned to its usual position, and
was not affected by the continual flow of the electricity
through the wire connected with the battery.
As soon, however, as the contact was broken, the
needle of the galvanometer was again deflected, but
in the contrary direction. Similar effects were produced
by an apparatus consisting of two helices of
copper wire coiled round a block of wood, instead
of iron, from which Mr. Faraday infers that the
electric current passing from the battery through
one wire induces a similar current through the
other wire, but only at the instant of contact, and
that a momentary current is induced in a contrary
direction when the passage of the electricity is
suddenly interrupted. These brief currents or
waves of electricity were found to be capable of
magnetizing needles, of passing through a small
extent of fluid, and when charcoal points were
interposed in the current of the induced helix, a
minute spark was perceived as often as the contacts
were made or broken, but neither chemical
action nor any other electric effects were obtained.
A deviation of the needle of the galvanometer
took place when common magnets were employed
instead of the voltaic current; so that the magnetic
and electric fluids are identical in their
effects in this interesting experiment. Again,
when a helix formed of 220 feet of copper wire,
into which a cylinder of soft iron was introduced,
was placed between the north and south poles of
two bar magnets, and connected with the galvanometer
by means of wires from each extremity, as
often as the magnets were brought into contact
with the iron cylinder, it became magnetic by
induction, and produced a deflection in the needle
of the galvanometer. On continuing the contact,
the needle resumed its natural position, and when
the contact was broken, the deflection took place
in the opposite direction; when the magnetic
contacts were reversed, the deflection was reversed
also. With strong magnets, so powerful was the
action, that the needle of the galvanometer whirled
round several times successively; and similar
effects were produced by the mere approximation
or removal of the helix to the poles of the magnets.
Thus magnets produce the very same effects
on the galvanometer that electricity does. Though
at that time no chemical decomposition was effected
by these momentary currents which emanated from
the magnets, they agitated the limbs of a frog, and
Mr. Faraday justly observes, that 'an agent which
is conducted along metallic wires in the manner
described, which, whilst so passing, possesses the
peculiar magnetic actions and force of a current
of electricity, which can agitate and convulse the
limbs of a frog, and which finally can produce a
spark by its discharge through charcoal, can only
be electricity.' Hence it appears that electrical
currents are evolved by magnets, which produce
the same phenomena with the electrical currents
from the voltaic battery; they, however, differ
materially in this respect — that time is required
for the exercise of the magneto-electric induction,
whereas volta-electric induction is instantaneous.
After Mr. Faraday had proved the identity of
the magnetic and electric fluids by producing the
spark, heating metallic wires, and accomplishing
chemical decomposition, it was easy to increase
these effects by more powerful magnets and other
arrangements. The following apparatus is now
in use, which is in effect a battery, where the agent
is the magnetic, instead of the voltaic fluid, or, in
other words, electricity.
A very powerful horse-shoe magnet, formed of
twelve steel plates in close approximation, is
placed in a horizontal position. An armature
consisting of a bar of the purest soft iron has
each of its ends bent at right angles, so that the
faces of those ends may be brought directly opposite
and close to the poles of the magnet when
required. Two series of copper wires — covered
with silk, in order to insulate them — are wound
round the bar of soft iron as compound helices.
The extremities of these wires, having the same
direction, are in metallic connexion with a circular
disc, which dips into a cup of mercury, while the
ends of the wires in the opposite direction are
soldered to a projecting screw-piece, which carries
a slip of copper with two opposite points. The
steel magnet is stationary; but when the armature,
together with its appendages, is made to
rotate horizontally, the edge of the disc always
remains immersed in the mercury, while the points
of the copper slip alternately dip in it and rise
above it. By the ordinary laws of induction, the
armature becomes a temporary magnet while its
bent ends are opposite the poles of the steel magnet,
and ceases to be magnetic when they are at
right angles to them. It imparts its temporary
magnetism to the helices which concentrate it;
and while one set conveys a current to the disc,
the other set conducts the opposite current to the
copper slip. But as the edge of the revolving disc
is always immersed in the mercury, one set of
wires is constantly maintained in contact with it,
and the circuit is only completed when a point of
the copper slip dips in the mercury also; but the
circuit is broken the moment that point rises
above it. Thus, by the rotation of the armature,
the circuit is alternately broken and renewed; and
as it is only at these moments that electric action
is manifested, a brilliant spark takes place every
time the copper point touches the surface of the
mercury. Platina wire is ignited, shocks smart
enough to be disagreeable are given, and water is
decomposed with astonishing rapidity, by the same
means, which proves beyond a doubt the identity
of the magnetic and electric agencies, and places
Mr. Faraday, whose experiments established the
principle, in the first rank of experimental philosophers.

SECTION XXXIV.
M. ARAGO discovered an entirely new source of
magnetism in rotatory motion. If a circular plate
of copper be made to revolve immediately above
or below a magnetic needle or magnet, suspended
in such a manner that the needle may rotate in
a plane parallel to that of the copper plate, the
magnet tends to follow the circumvolution of the
plate; or if the magnet revolves, the plate tends
to follow its motion; and so powerful is the effect,
that magnets and plates of many pounds weight
have been carried round. This is quite independent
of the motion of the air, since it is the same
when a pane of glass is interposed between the
magnet and the copper. When the magnet and
the plate are at rest, not the smallest effect, attractive,
repulsive, or of any kind, can be perceived
between them. In describing this phenomenon,
M. Arago states that it takes place not
only with metals, but with all substances, solids,
liquids, and even gases, although the intensity depends
upon the kind of substance in motion. Experiments
recently made by Mr. Faraday explain
this singular action. A plate of copper, twelve
inches in diameter and one-fifth of an inch thick,
was placed between the poles of a powerful horseshoe
magnet, and connected at certain points with
a galvanometer by copper wires. When the plate
was at rest no effect was produced, but as soon
as the plate was made to revolve rapidly, the
galvanometer needle was deflected sometimes as
much as 90°, and by a uniform rotation, the
deflection was constantly maintained at 45°.
When the motion of the copper plate was reversed,
the needle was deflected in the contrary
direction, and thus a permanent current of electricity
was evolved by an ordinary magnet. The
intensity of the electricity collected by the wires,
and conveyed by them to the galvanometer, varied
with the position of the plate relatively to the
poles of the magnet.
The motion of the electricity in the copper
plate may be conceived, by considering, that merely
from moving a single wire like the spoke of a
wheel before a magnetic pole, a current of electricity
tends to flow through it from one end to the
other; hence, if a wheel be constructed of a great
many such spokes, and revolved near the pole of a
magnet in the manner of the copper disc, each
radius or spoke will tend to have a current produced
in it as it passes the pole. Now, as the circular
plate is nothing more than an infinite number
of radii or spokes in contact, the currents will
flow in the direction of the radii if a channel be
open for their return, and in a continuous plate
that channel is afforded by the lateral portions on
each side of the particular radius close to the
magnetic pole. This hypothesis is confirmed
by observation, for the currents of positive electricity
set from the centre to the circumference,
and the negative from the circumference to the
centre, and vice versa, according to the position of
the magnetic poles and the direction of rotation.
So that a collecting wire at the centre of the copper
plate conveys positive electricity to the galvanometer
in one case, and negative in another;
that collected by a conducting wire in contact with
the circumference of the plate is always the opposite
of the electricity conveyed from the centre.
It is evident that when the plate and magnet are
both at rest, no effect takes place, since the electric
currents which cause the deflection of the galvanometer
cease altogether. The same phenomena
may be produced by electromagnets. The effects
are the same when the magnet rotates and the
plate remains at rest. When the magnet revolves
uniformly about its own axis, electricity of the
same kind is collected at its poles, and the opposite
electricity at its equator.
The phenomena which take place in M. Arago's
experiments may be explained on this principle,
for when both the copper plate and the magnet
are revolving, the action of the electric current,
induced in the plate by the magnet in consequence
of their relative motion, tends continually to diminish
that relative motion; that is, to bring the
moving bodies into a state of relative rest, so
that if one be made to revolve by an extraneous
force, the other will tend to revolve about it in
the same direction, and with the same velocity.
When a plate of iron, or of any substance capable
of being made either a temporary or permanent
magnet, revolves between the poles of a
magnet, it is found that dissimilar poles on opposite
sides of the plate neutralize each other's effects,
so that no electricity is evolved, while similar poles
on each side of the revolving plate increase the
quantity of electricity, and a single pole end-on is
sufficient. But when copper, and substances not
sensible to ordinary magnetic impressions, revolve,
similar poles on opposite sides of the plate neutralize
each other, dissimilar poles on each side exalt
the action; and a single pole at the edge of the
revolving plate, or end-on, does nothing. This
forms a test for distinguishing the ordinary magnetic
force from that produced by rotation. If
unlike poles, that is a north and a south pole,
produce more effect than one pole, the force will
be due to electric currents; if similar poles produce
more effect than one, then the power is not
electric. These investigations show that there
are really very few bodies magnetic in the manner
of iron. Mr. Faraday therefore arranges substances
in three classes, with regard to their relation
to magnets. Those affected by the magnet
when at rest like iron, steel, and nickel, which
possess ordinary magnetic properties; those affected
when in motion, in which electric currents
are evolved by the inductive force of the magnet,
such as copper ; and lastly, those which are perfectly
indifferent to the magnet, whether at rest
or in motion.
It has already been observed, that three bodies
are requisite to form a galvanic circuit, one of
which must be fluid; but in 1822, Professor
Seebeck, of Berlin, discovered that electric currents
may be produced by the partial application
of heat to a circuit formed of two solid conductors.
For example, when a semicircle of bismuth, joined
to a semicircle of antimony, so as to form a ring,
is heated at one of the junctions by a lamp, a current
of electricity flows through the circuit from the
antimony to the bismuth, and such thermoelectric
currents produce all the electromagnetic effects.
A compass needle placed either within or without
the circuit, and at a small distance from it, is deflected
from its natural position, in a direction
corresponding to the way in which the electricity
is flowing. If such a ring be suspended so as to
move easily in any direction, it will obey the action
of a magnet brought near it, and may even be
made to revolve. According to the researches of
M. Nobili, the same substance, unequally heated,
exhibits electrical currents. The experiments of
Professor Cumming show that the mutual action of
a magnet and a thermo-electric current, is subject
to the same laws as those of magnets and galvanic
currents, consequently all the phenomena of repulsion,
attraction, and rotation may be exhibited
by a thermo-electric current. It is, however, so
feeble, that neither heat, the spark, nor chemical
action have been observed, nor can repulsion,
attraction of light substances at sensible distances,
or any other effects of tension, be perceived.
SECTION XXXV.
IN all the experiments hitherto described, artificial
magnets alone were used, but it is obvious that the
magnetism of the terrestrial spheroid which has
so powerful an influence on the mariner's compass,
must also affect electrical currents. It consequently
appears that a piece of copper wire bent
into a rectangle, and free to revolve on a vertical
axis, arranges itself with its plane at right angles
to the magnetic meridian, as soon as a stream of
electricity is sent through it. Under the same
circumstances a similar rectangle, suspended on a
horizontal axis at right angles to the magnetic
meridian, assumes the same inclination with the
dipping needle. So that terrestrial magnetism
has the same influence on electrical currents as
an artificial magnet. But the magnetic action of
the earth also induces electric currents. When a
hollow helix of copper wire, whose extremities are
connected with the galvanometer, is placed in the
magnetic dip, and suddenly inverted several times,
accommodating the motion to the oscillations of
the needle, the latter is soon made to vibrate
through an arc of 80° or 90°. Hence it is evident,
that whatever may be the cause of terrestrial
magnetism, it produces currents of electricity
by its direct inductive power upon a metal not
capable of exhibiting any of the ordinary magnetic
properties. The action on the galvanometer is
much greater when a cylinder of soft iron is inserted
into the helix, and the same results follow
the simple introduction of the iron cylinder into,
or removal out of the helix. These effects arise
from the iron being made a temporary magnet by
the inductive action of terrestrial magnetism, for
a piece of iron, such as a poker, becomes a magnet
for the time, when placed in the line of the magnetic
dip.
M. Biot has formed a theory of terrestrial magnetism
upon the observations of M. de Humboldt
as data. Assuming that the action of the two
opposite magnetic poles of the earth upon any
point is inversely as the square of the distance,
he obtains a general expression for the direction
of the magnetic needle, depending upon the distance
between the north and south magnetic poles;
so that if one of these quantities varies, the corresponding
variation of the other will be known.
By making the distance between the poles vary,
and comparing the resulting direction of the needle
with the observations of M. de Humboldt, he
found that the nearer the poles are supposed to
approach to one another, the more did the computed
and observed results agree; and when the
poles were assumed to coincide, or nearly so, the
difference between theory and observation was the
least possible. It is evident, therefore, that the
earth does not act as if it were a permanently
magnetic body, the distinguishing characteristic of
which is, to have two poles at a distance from one
another. Mr. Barlow has investigated this subject
with much skill and success. He first proved
that the magnetic power of an iron sphere resides
in its surface; he then inquired what the superficial
action of an iron sphere in a state of transient
magnetic induction, on a magnetised needle, would
be, if insulated from the influence of terrestrial
magnetism. The results obtained, corroborated
by the profound analysis of M. Poisson, on the
hypothesis of the two poles being indefinitely near
the centre of the sphere, are identical with those
obtained by M. Biot for the earth from M. de
Humboldt's observations. Whence it follows,
that the laws of terrestrial magnetism deduced
from the formulæ of M. Biot, are inconsistent
with those which belong to a permanent magnet,
but that they are perfectly concordant with those
belonging to a body in a state of transient magnetic
induction. It appears, therefore, that the
earth is to be considered as only transiently magnetic
by induction, and not a real magnet. Mr.
Barlow has rendered this extremely probable by
forming a wooden globe, with grooves admitting
of a copper wire being coiled round it parallel to
the equator from pole to pole. When a current
of electricity was sent through the wire, a magnetic
needle suspended above the globe, and neutralized
from the influence of the earth's magnetism,
exhibited all the phenomena of the dipping
and variation needles, according to its positions
with regard to the wooden globe. As there can
be no doubt that the same phenomena would be
exhibited by currents of thermo, instead of voltaic,
electricity, if the grooves of the wooden globe
were filled by rings constituted of two metals, it
seems highly probable that the heat of the sun
may be the great agent in developing electric
currents in or near the surface of the earth, by its
action upon the substances of which the globe is
composed, and, by the changes in its intensity,
may occasion the diurnal variation of the compass,
and the other vicissitudes in terrestrial magnetism
evinced by the disturbance in the directions of the
magnetic lines, in the same manner as it influences
the parallelism of the isothermal lines. That such
currents do exist in metalliferous veins appears
from the experiments of Mr. Robert Fox in the
Cornish copper-mines. However, it is probable
that the secular and periodic disturbances in the
magnetic force are occasioned by a variety of combining
circumstances. Among others, M. Biot
mentions the vicinity of mountain chains to the
place of observation, and still more the action of
extensive volcanic fires, which change the chemical
state of the terrestrial surface, they themselves
varying from age to age, some becoming extinct,
while others burst into activity.
It is moreover probable that terrestrial magnetism
may be owing, to a certain extent, to the
earth's rotation. Mr. Faraday has proved that
all the phenomena of revolving plates may be
produced by the inductive action of the earth's
magnetism alone. If a copper plate be connected
with a galvanometer by two copper wires, one
from the centre and another from the circumference,
in order to collect and convey the electricity,
it is found that, when the plate revolves in a
plane passing through the line of the dip, the
galvanometer is not affected; but as soon as the
plate is inclined to that plane, electricity begins to
be developed by its rotation; it becomes more
powerful as the inclination increases, and arrives
at a maximum when the plate revolves at right
angles to the line of the dip. When the revolution
is in the same direction with that of the hands
of a watch, the current of electricity flows from
its centre to the circumference; and when the
rotation is in the opposite direction, the current
sets the contrary way. The greatest deviation of
the galvanometer amounted to 50° or 60°, when
the direction of the rotation was accommodated to
the oscillations of the needle. Thus a copper
plate, revolving in a plane at right angles to the
line of the dip, forms a new electrical machine,
differing from the common plate-glass machine,
by the material of which it is composed being the
most perfect conductor, whereas glass is the most
perfect non-conductor; besides, insulation, which
is essential in the glass machine, is fatal in the
copper one. The quantity of electricity evolved
by the metal does not appear to be inferior to that
developed by the glass, though very different in
intensity.
From the experiments of Mr. Faraday, and
also from theory, it is possible that the rotation
of the earth may produce electric currents in its
own mass. In that case, they would flow superficially
in the meridians, and if collectors could
be applied at the equator and poles, as in the
revolving plate, negative electricity would be collected
at the equator, and positive at the poles;
but without something equivalent to conductors
to complete the circuit, these currents could not
exist.
Since the motion, not only of metals but even
of fluids, when under the influence of powerful
magnets, evolves electricity, it is probable that the
gulf stream may exert a sensible influence upon
the forms of the lines of magnetic variation, in
consequence of electric currents moving across it,
by the electromagnetic induction of the earth.
Even a ship passing over the surface of the water,
in northern or southern latitudes, ought to have
electric currents running directly across the line
of her motion. Mr. Faraday observes, that such
is the facility with which electricity is evolved by
the earth's magnetism, that scarcely any piece of
metal can be moved in contact with others without
a development of it, and that consequently,
among the arrangements of steam engines and
metallic machinery, curious electromagnetic combinations
probably exist, which have never yet
been noticed.
What magnetic properties the sun and planets
may have, it is impossible to conjecture, although
their rotation might lead us to infer that they are
similar to the earth in this respect. According
to the observations of MM. Biot and Gay-Lussac,
during their aerostatic expedition, the magnetic
action is not confined to the surface of the earth,
but extends into space. A decrease in its intensity
was perceptible, and as it most likely follows
the ratio of the inverse square of the distance, it
must extend indefinitely. It is probable that the
moon has become highly magnetic by induction,
in consequence of her proximity to the earth, and
because her greatest diameter always points towards
it. Should the magnetic, like the gravitating
force, extend through space, the induction
of the sun, moon, and planets must occasion perpetual
variations in the intensity of terrestrial
magnetism, by the continual changes in their
relative positions.
In the brief sketch that has been given of the
five kinds of electricity, those points of resemblance
have been pointed out which are characteristic
of one individual power; but as many
anomalies have been lately removed, and the identity
of the different kinds placed beyond a doubt,
by Mr. Faraday, it may be satisfactory to take a
summary view of the various coincidences in their
modes of action on which their identity has been
so ably and completely established by that great
electrician.
The points of comparison are attraction and
repulsion at sensible distances, discharge from
points through air, the heating power, magnetic
influence, chemical decomposition, action on the
human frame, and lastly the spark.
Attraction and repulsion at sensible distances,
which are so eminently characteristic of ordinary
electricity, and, in a lesser degree, also, of the
voltaic and magnetic currents, have not been perceived
in either the thermo or animal electricities,
not on account of difference of kind, but entirely
owing to inferiority in tension; for even the ordinary
electricity, when much reduced in quantity
and intensity, is incapable of exhibiting these phenomena.

Ordinary electricity is readily discharged from
points through air, but Mr. Faraday found that no
sensible effect took place from a battery consisting
of 140 double plates, either through air or in the
exhausted receiver of an air-pump, the tests of
the discharge being the electrometer and chemical
action, — a circumstance entirely owing to the
small degree of tension, for an enormous quantity
of electricity is required to make these effects sensible,
and for that reason they cannot be expected
from the other kinds, which are much inferior in
degree. Common electricity passes easily through
rarefied and hot air, and also through flame. Mr.
Faraday effected chemical decomposition and a
deflection of the galvanometer by the transmission
of voltaic electricity through heated air, and observes
that these experiments are only cases of the
discharge which takes place through air between
the charcoal terminations of the poles of a powerful
battery when they are gradually separated after
contact — for the air is then heated; and Sir
Humphry Davy mentions that, with the original
voltaic apparatus at the Royal Institution, the
discharge passed through four inches of air; that,
in the exhausted receiver of an air-pump, the
electricity would strike through nearly half an inch
of space, and that the combined effects of rarefaction
and heat were such, upon the included air, as
to enable it to conduct the electricity through a
space of six or seven inches. A Leyden jar may
be instantaneously charged with voltaic, and also
with magneto-electricity — another proof of their
tension. Such effects cannot be obtained from
the other kinds, on account of their weakness
only.
The heating powers of ordinary and voltaic
electricity have long been known, but the world is
indebted to Mr. Faraday for the wonderful discovery
of the heating power of the magnetic fluid:
there is no indication of heat either from the
animal or thermo-electricities. All the kinds of
electricity have strong magnetic powers, those of
the voltaic fluid are highly exalted, and the existence
of the magneto and thermo-electricities was
discovered by their magnetic influence alone. The
needle has been deflected by all in the same manner,
and, with the exception of thermoelectricity,
magnets have been made by all according to the
same laws. Ordinary electricity was long supposed
incapable of deflecting the needle, and it required
all Mr. Faraday's ingenuity to produce that effect.
He has, however, proved that, in this respect, also,
ordinary electricity agrees with voltaic, but that
time must be allowed for its action. It deflected
the needle, whether the current was sent through
rarefied air, water, or wire. Numerous chemical
decompositions have been effected by ordinary and
voltaic electricity, according to the same laws and
modes of arrangement. Dr. Davy decomposed
water by the electricity of the torpedo, — Mr. Faraday
accomplished its decomposition, and Dr.
Ritchie its composition, by means of magnetic
action ; but the chemical effects of the thermoelectricity
have not yet been observed. The electric
and galvanic shock, the flash in the eyes, and
the sensation on the tongue, are well known. All
these effects are produced by magneto-electricity,
even to a painful degree. The torpedo and gymnotus
electricus give severe shocks, and the limbs
of a frog have been convulsed by thermo-electricity.
The last point of comparison is the spark,
which is already mentioned as common to the
ordinary, voltaic, and magnetic fluids ; and although
it has not yet been seen from the thermo
and animal electricities, there can be no doubt
that it is only on account of their feebleness.
Indeed, the conclusion drawn by Mr. Faraday is
that the five kinds of electricity are identical, and
that the differences of intensity and quantity are
quite sufficient to account for what were supposed
to be their distinctive qualities. He has given
still greater assurance of their identity by showing
that the magnetic force and the chemical action of
electricity are in direct proportion to the absolute
quantity of the fluid which passes through the galvanometer,
whatever its intensity may be.
In light, heat, and electricity, or magnetism, nature
has exhibited principles which do not occasion
any appreciable change in the weight of bodies,
although their presence is manifested by the most
remarkable mechanical and chemical action. These
agencies are so connected, that there is reason to
believe they will ultimately be referred to some
one power of a higher order, in conformity with
the general economy of the system of the world,
where the most varied and complicated effects
Are produced by a small number of universal
laws. These principles penetrate matter in all directions;
their velocity is prodigious, and their
intensity varies inversely as the square of the distance.
The development of electric currents, as
well by magnetic as electric induction, the similarity
in their mode of action in a great variety of
circumstances, but above all the production of the
spark from a magnet, the ignition of metallic wires,
and chemical decomposition, show that magnetism
can no longer be regarded as a separate, independent
principle. That light is visible heat seems
highly probable; and although the evolution of
light and heat during the passage of the electric
fluid may be from the compression of the air, yet
the development of electricity by heat, the influence
of heat on magnetic bodies, and that of light on
the vibrations of the compass, show an occult
connexion between all these agents, which probably
will one day be revealed; and in the
mean time it opens a noble field of experimental
research to philosophers of the present, perhaps of
future ages.
SECTION XXXVI.
IN considering the constitution of the earth and
the fluids which surround it, various subjects have
presented themselves to our notice, of which some,
for aught we know, are confined to the planet we
inhabit; some are common to it and to the other
bodies of our system; but an all-pervading ether
probably fills the whole visible creation, and conveys,
in the form of light, tremors which may
have been excited in the deepest recesses of the
universe thousands of years before we were called
into being. The existence of such a medium,
though at first hypothetical, is nearly proved by
the undulatory theory of light, and rendered all
but certain, within a few years, by the motion of
comets, and by its action upon the vapours of which
they are chiefly composed. It has often been
imagined that, in addition to the effects of heat
and electricity, the tails of comets have infused
new substances into our atmosphere. Possibly
the earth may attract some of that nebulous matter,
since the vapours raised by the sun's heat,
when the comets are in perihelio and which form
their tails, are scattered through space in their
passage to their aphelion; but it has hitherto
produced no effect, nor have the seasons ever been
influenced by these bodies. In all probability, the
tails of comets may have passed over the earth
without its inhabitants being conscious of their
presence.
The passage of comets has never sensibly disturbed
the stability of the solar system; their
nucleus, being in general only a mass of vapours,
is so rare, and their transit so rapid, that the time
has not been long enough to admit of a sufficient
accumulation of impetus to produce a perceptible
action. Indeed, M. Dusejour has proved that,
under the most favourable circumstances, a comet
cannot remain longer than two hours and a
half at a less distance than 10500 leagues from
the earth. The comet of 1770 passed within
about six times the distance of the moon from
the earth, without even affecting our tides; and
as the moon has no sensible influence on the equilibrium
of the atmosphere, a comet must have
still less. According to La Place, the action of
the earth on the comet of 1770 augmented the
period of its revolution by more than two days ;
and if comets had any perceptible disturbing
energy, the reaction of the comet ought to have
increased the length of our year. Had the mass
of that comet been equal to the mass of the earth,
its disturbing action would have increased the
length of the sideral year by 2h 53m; but as
Delambre's computations from the Greenwich
observations of the sun, show that the length of
the year has not been increased by the fraction of
a second, its mass could not have been equal to
the 1/5000 part of that of the earth. This accounts
for the same comet having twice swept through
the system of Jupiter's satellites without deranging
the motions of these moons. Dusejour has
computed that a comet, equal in mass to the earth,
passing at the distance of 12150 leagues from our
planet, would increase the length of the year to
367d 16h 5m, and the obliquity of the ecliptic as
much as 2°. So the principal action of comets
would be to alter the calendar, even if they were
dense enough to affect the earth.
Comets traverse all parts of the heavens;
their paths have every possible inclination to
the plane of the ecliptic, and, unlike the planets,
the motion of more than half of those that
have appeared have been retrograde. They
are only visible when near their perihelia; then
their velocity is such, that its square is twice as
great as that of a body moving in a circle at the
same distance, they consequently remain a very
short time within the planetary orbits; and as all
the conic sections of the same focal distance sensibly
coincide, through a small arc on each side
of the extremity of their axis, it is difficult to
ascertain in which of these curves the comets
move, from observations made, as they necessarily
must be, at their perihelia; but probably they all
move in extremely excentric ellipses, although in
most cases the parabolic curve coincides most
nearly with their observed motions. Some few
seem to describe hyperbolas; such being once
visible to us, would vanish for ever, to wander
through boundless space, to the remote systems
of the universe. If a planet be supposed
to revolve in a circular orbit, whose radius is
equal to the perihelion distance of a comet moving
in a parabola, the areas described by these
two bodies in the same time will be as unity
to the square root of two, which forms such a
connexion between the motion of comets and
planets, that, by Kepler's law, the ratio of the
areas described during the same time by the comet
and the earth may be found; so that the place of
a comet at any time in its parabolic orbit, estimated
from the instant of its passage at the perihelion,
may be computed. But it is a problem of
very great difficulty to determine all the other
elements of parabolic motion — namely, the comet's
perihelion distance, or shortest distance from the
sun, estimated in parts of the mean distance of
the earth from the sun; the longitude of the perihelion;
the inclination of the orbit on the plane of
the ecliptic; and the longitude of the ascending
node. Three observed longitudes and latitudes of
a comet are sufficient for computing the approximate
values of these quantities; but an accurate
estimation of them can only be obtained by successive
corrections from a number of observations,
distant from one another. When the motion of a
comet is retrograde, the place of the ascending
node is exactly opposite to what it is when the
motion is direct; hence the place of the ascending
node, together with the direction of the comet's
motion, show whether the inclination of the orbit
is on the north or south side of the plane of the
ecliptic. If the motion be direct, the inclination
is on the north side; if retrograde, it is on the
south side.
The identity of the elements is the only proof
of the return of a comet to our system. Should
the elements of a new comet be the same, or nearly
the same, with those of any one previously known,
the probability of the identity of the two bodies is
very great, since the similarity extends to no less
than four elements, every one of which is capable
of an infinity of variations. But even if the orbit
he determined with all the accuracy the case admits
of, it may be difficult, or even impossible, to
recognise a comet on its return, because its orbit
would be very much changed if it passed near any
of the large planets of this, or of any other system,
in consequence of their disturbing energy, which
would be very great on bodies of so rare a nature.
Halley computed the elements of the orbit of a
comet that appeared in the year 1682, which
agreed so nearly with those of the comets of 1607
and 1531, that he concluded it to be the same
body returning to the sun, at intervals of about
seventy-five years. He consequently predicted its
re-appearance in the year 1758, or in the beginning
of 1759. Science was not sufficiently advanced
in the time of Halley, to enable him to
determine the perturbations this comet might experience;
but Clairaut computed that it would be
retarded in its motion a hundred days by the
attraction of Saturn, and 518 by that of Jupiter,
and consequently, that it would pass its perihelion
about the middle of April, 1759, requiring
618 days more to arrive at that point than in its
preceding revolution. This, however, he considered
only to be an approximation, and that it
might be thirty days more or less: the return
of the comet on the 12th of March, 1759, proved
the truth of the prediction. MM. Damoiseau
and Pontecoulant have ascertained that this comet
will return either on the 4th or the 7th of November,
1835; the difference of three days in
their computations arises from their having employed
different values for the masses of the
planets. This is the first comet whose periodicity
has been established; it is also the first
whose elements have been determined from observations
made in Europe, for although the comets
which appeared in the years 240, 539, 565, and
837, are the most ancient whose orbits have been
traced, their elements were computed from Chinese
observations.
By far the most curious and interesting instance
of the disturbing action of the great bodies of our
system is found in the comet of 1770. The elements
of its orbit, determined by Messier, did not
agree with those of any comet that had hitherto
been computed, yet Lexel ascertained that it described
an ellipse about the sun, whose major
axis was only equal to three times the length of
the diameter of the terrestrial orbit, and consequently
that it must return to the sun at intervals of
five years and a half. This result was confirmed by
numerous observations, as the comet was visible
through an arc of 170°; yet this comet had never
been observed before the year 1770, nor has it ever
again been seen, though very brilliant The disturbing
action of the larger planets afford a solution
of this anomaly, as Lexel ascertained that in
1767 the comet must have passed Jupiter at a
distance less than the fifty-eighth part of its distance
from the sun, and that in 1779 it would be
500 times nearer Jupiter than the sun; consequently
the action of the sun on the comet would
not be the fiftieth part of what it would experience
from Jupiter, so that Jupiter became the primum
mobile. Assuming the orbit to be such as Lexel
had determined in 1770, La Place found that the
action of Jupiter, previous to the year 1770,
had so completely changed the form of it, that
the comet which had been invisible to us before
1770, was then brought into view, and that the
action of the same planet producing a contrary
effect, has, subsequently to that year, removed it,
probably for ever, from our system. This comet
might have been seen from the earth in 1716, had
its light not been eclipsed by that of the sun.
Besides Halley's comet, two others are now
proved to form part of our system ; that is to
say, they return to the sun at intervals, one of
1207 days, and the other of 6 years, nearly.
The first, generally called Encke's comet, or the
comet of the short period, was first seen by MM.
Messier and Mechain in 1786, again by Miss
Herschel in 1795, and its returns in the years 1805
and 1819 were observed by other astronomers,
under the impression that all four were different
bodies; however, Professor Encke not only proved
their identity, but determined the circumstances
of the comet's motion. Its reappearance in the
years 1825, 1828, and 1832 accorded with the
orbit assigned by M. Encke, who thus established
the length of its period to be 1207 days, nearly.
This comet is very small, of feeble light, and invisible
to the naked eye, except under very favourable
circumstances, and in particular positions; it
has no tail, it revolves in an ellipse of great excentricity
inclined at an angle of 13° 22' to the plane
of the ecliptic, and is subject to considerable perturbations
from the attraction of the planets. It
has already been mentioned, that among the many
perturbations to which the planets are liable, their
mean motions, and, therefore, the major axes of
their orbits, experience no change; while, on the
contrary, the mean motion of the moon is accelerated
from age to age, a circumstance at first
attributed to the resistance of an etherial medium
pervading space, but subsequently proved to arise
from the secular diminution of the excentricity of
the terrestrial orbit. Although the resistance of
such a medium has not hitherto been perceived in
the motions of such dense bodies as the planets
and satellites, its effects on the revolutions of the
two small periodic comets hardly leave a doubt of
its existence. From the numerous observations that
have been made on each return of the comet of the
short period, the elements have been computed
with great accuracy on the hypothesis of its moving
in vacuo; its perturbations occasioned by the disturbing
action of the planets have been determined;
and after every thing that could influence
its motion had been duly considered, M. Encke
found that an acceleration of about two days on
each revolution has taken place in its mean motion,
precisely similar to that which would be
occasioned by the resistance of an etherial medium
; and as it cannot be attributed to a cause
like that which produces the acceleration of the
moon, it must be concluded that the celestial
bodies do not perform their revolutions in an absolute
void, and that although the medium be too
rare to have a sensible effect on the masses of the
planets and satellites, it nevertheless has a considerable
influence on so rare a body as a comet.
Contradictory as it may seem, that the motion of
a body should be accelerated by the resistance of
an etherial medium, the truth becomes evident if
it be considered that both planets and comets are
retained in their orbits by two forces which exactly
balance one another; namely, the centrifugal
force producing the velocity in the tangent,
and the attraction of the gravitating force directed
to the centre of the sun. If one of these forces
be diminished by any cause, the other will be
proportionally increased. Now, the necessary
effect of a resisting medium is to diminish the
tangential velocity, so that the balance is destroyed,
gravity preponderates, the body descends
towards the sun till equilibrium is again restored
between the two forces; and as it then describes
a smaller orbit, it moves with increased velocity.
Thus, the resistance of an etherial medium actually
accelerates the motion of a body, but as the
resisting force is confined to the plane of the orbit
it has no influence whatever on the inclination of
the orbit, or on the place of the nodes. The other
comet belonging to our system, which returns to
its perihelion after a period of 6 3/4 years, has been
accelerated in its motion by a whole day during its
last revolution, which puts the existence of ether
beyond a doubt, and forms a strong presumption
in corroboration of the undulating theory of light.
The comet in question was discovered by M. Biela
at Johannisberg on the 27th of February, 1826,
and ten days afterwards it was seen by M. Gambart
at Marseilles, who computed its parabolic
elements, and found that they agreed with those
of the comets which had appeared in the years
1789 and 1795, whence he concluded them to be
the same body moving in an ellipse, and accomplishing
its revolution in 2460 days. The perturbations
of this comet were computed by M. Damoiseau,
who predicted that it would cross the plane
of the ecliptic on the 29th of October, 1832, a
little before midnight, at a point nearly 18484
miles within the earth's orbit; and as M. Olbers,
of Bremen, in 1805, had determined the radius of
the comet's head to be about 21136 miles, it was
evident that its nebulosity would envelope a portion
of the earth's orbit, a circumstance which
caused great alarm in France, and not altogether
Without reason, for if any disturbing cause had
delayed the arrival of the comet for one month,
the earth must have passed through its head.
M. Arago dispelled their fears by the excellent
treatise on comets which appeared in the Annuaire
of 1832, where he proves that, as the earth would
never be nearer the comet than 24800000 British
leagues, there could be no danger of collision.
If a comet were to impinge on the earth, so as
to destroy its centrifugal force, it would fall to the
sun in 64 1/2 days. What the earth's primitive
velocity may have been it is impossible to say;
therefore a comet may have given it a shock
Without changing the axis of rotation, but only
destroying part of its tangential velocity, so as
to diminish the size of the orbit, a thing by no
means impossible, though highly improbable; at
all events, there is no proof that such has been
the case ; and it is manifest that the axis of the
earth's rotation has not been changed, because, as
there is no resistance, the libration would to this
day be evident in the variation it must have occasioned
in the terrestrial latitudes. Supposing the
nucleus of a comet to have a diameter only equal
to the fourth part of that of the earth, and that its
perihelion is nearer to the sun than we are ourselves,
its orbit being otherwise unknown, M.
Arago has computed that the probability of the
earth receiving a shock from it is only one in 281
millions, and that the chance of our coming in
contact with its nebulosity is about ten or twelve
times greater. But in general comets are so rare,
that it is likely they would not do much harm if
they were to impinge; and even then the mischief
would probably be local, and the equilibrium soon
restored, provided there was only a gaseous or
very small nucleus. It is, however, more probable
that the earth would only be deflected a
little from its course by the approach of a comet,
without being touched by it. The comets that
seem to have come nearest to the earth were that
of the year 837, which remained four days within
less than 1240000 leagues from our orbit; that
of 1770, which approached within about six
times the distance of the moon. The celebrated
comet of 1680 also came very near to us; and
the comet whose period is 6 3/4 years was ten times
nearer the earth in 1805 than in 1832, when it
caused so much alarm.
Comets, when in or near their perihelion, move
with prodigious velocity. That of 1680 appears
to have gone half round the sun in ten hours and a
half, moving at the rate of 880000 miles an hour.
If its enormous centrifugal force had ceased when
passing its perihelion, it would have fallen to the
sun in about three minutes, as it was then only
147000 miles from his surface. So near the
sun, it would be exposed to a heat 27500 times
greater than that received by the earth; and as
the sun's heat is supposed to be in proportion to
the intensity of his light, it is probable that a degree
of heat so very intense would be sufficient to
convert into vapour every terrestrial substance
with which we are acquainted. At the perihelion
distance the sun's diameter would be seen from
the comet under an angle of 73°, so that the sun,
viewed from the comet, would nearly cover the
whole extent of the heavens from the horizon to
the zenith; and as this cornet is presumed to
have a period of 575 years, the major axis of its
orbit must be so great, that at the aphelion the
sun's diameter would only subtend an angle of
about fourteen seconds, which is not so great as
half the diameter of Mars appears to us when in
opposition. The sun would consequently impart
no heat, so that the comet would then
be exposed to the temperature of the etherial
regions, which is 58° below the zero point of
Fahrenheit. A body so rare as the comet, and
moving with such velocity, must have met with
great resistance from the dense atmosphere of the
sun, while passing so near his surface at its perihelion.
The centrifugal force must consequently
have been diminished, and the sun's attraction
proportionally augmented, so that it must have
come nearer to the sun in 1680 than in its preceding
revolution, and would subsequently describe
a smaller orbit. As this diminution of its
orbit will be repeated at each revolution, the comet
will infallibly end by falling on the surface of the
sun, unless its course be changed by the disturbing
influence of some large body in the unknown
expanse of creation. Our ignorance of the actual
density of the sun's atmosphere, of the density of
the comet, and of the period of its revolution,
renders it impossible to form any idea of the number
of centuries which must elapse before this
singular event takes place.
But this is not the only comet threatened with
such a catastrophe; Encke's, and that discovered
by M. Biela, are both slowly tending to the same
fate. By the resistance of the ether, they will
perform each revolution nearer and nearer to the
sun, till at last they will be precipitated on his
surface. The same cause may affect the motions
of the planets, and be ultimately the means of destroying
the solar system; but, as Sir John Herschel
observes, they could hardly all revolve in
the same direction round the sun for so many ages
without impressing a corresponding motion on the
etherial fluid, which may preserve them from the
accumulated effects of its resistance. Should this
material fluid revolve about the sun like a vortex,
it will accelerate the revolutions of such comets
as have direct motions, but it will retard those
that have retrograde motions.
Though already so well acquainted with the
motions of comets, we know nothing of their
physical constitution. A vast number, especially
of telescopic comets, are only like clouds or masses
of vapour often without tails. Such were the comets
which appeared in the years 1795, 1797,
and 1798; but the head commonly consists of a
mass of light, like a planet surrounded by a very
transparent atmosphere, the whole, viewed with a
telescope, being so diaphanous, that the smallest
star may be seen even through the densest part of
the nucleus; and in general their masses, when they
have any, are so minute that they have no sensible
diameter, like that of the comet of 1811, which
appeared to Sir Wm. Herschel like a luminous
point in the middle of the nebulous matter. The
nuclei, which seem to be formed of the denser
strata of that nebulous matter in successive coatings,
are often of great magnitude; those of the
comets which came to the sun in the years 1199
and 1801 had nuclei whose diameters measured
180 and 215 leagues respectively, and the second
comet of 1811 had a nucleus 1350 leagues in diameter.

The nebulosity immediately round the nucleus
is so diaphanous that it gives little light ; but
at a small distance the nebulous matter becomes
suddenly brilliant, so as to look like a bright
ring round the body. Sometimes there are as
many as two or three of these luminous concentric
rings separated by dark intervals, but
they are generally incomplete on the side next
the tail. In the comet of 1811, the luminous
ring was 12400 leagues thick, and the distance
between its interior surface and the centre of the
nucleus was as much as 14880 leagues. The
thickness of these bright diaphanous coatings in
the comets of 1807 and 1799 were 14880 and
9920 leagues respectively. The transit of a comet
over the sun would afford the best information
with regard to the nature of the nuclei. It
was computed that such an event was to take
place in the year 1827; unfortunately the sun
was hid by clouds from the British astronomers,
but it was examined at Viviers and at Marseilles,
at the time the comet must have been projected
on its disc, but no spot or cloud was to be seen.
The tails of comets proceed from the head in
two streams of light somewhat like that of the
aurora; these in most cases unite at a greater or
less distance from the nucleus, and are generally
situate in the planes of their orbits; they
follow the comets in their descent towards the
sun, but precede them in their return with a
small degree of curvature, probably owing to the
resistance of the ether, but their extent and form
must vary in appearance according to the positions
of their orbits with regard to the ecliptic. In some
cases, the tail has been at right angles to the line
joining the sun and comet. They are generally of
enormous lengths, — the comet of 1811 had a tail
no less than 34 millions of leagues in length, and
those which appeared in the years 1618, 1680,
and 1769, had tails which extended respectively
over 104, 90, and 97 degrees of space; consequently,
when the heads of these comets were set,
a portion of the extremity of their tails was still in
the zenith. Sometimes the tail is divided into
several branches, like the comet of 1744, which
had six, separated by dark intervals, each of them
about 4° broad, and from 30° to 44° long. The
tails do not attain their full magnitude till the
comet has left the sun. When these bodies first
appear, they resemble round films of vapour with
little or no tail; as they approach the sun, they
increase in brilliancy, and their tail in length, till
they are lost in his rays; and it is not till they
emerge from the sun's more vivid light that they
assume their full splendour. They then gradually
decrease by the same degrees; their tails diminish
and disappear nearly or altogether before the
comet is beyond the sphere of telescopic vision.
Many comets have no tails at all, as, for example,
Encke's comet and that discovered by M. Biela,
both of which are small and insignificant objects.
The comets which appeared in the years 1585,
1763, and 1682, were also without tails, though
the latter is recorded to have been as bright as
Jupiter. The matter of the tail must be extremely
buoyant to precede a body moving with such velocity;
indeed the rapidity of its ascent can only
be accounted for by the fervent heat of the sun.
Immediately after the great comet of 1680 had
passed its perihelion, its tail was 20000000 leagues
in length, and was projected from the comet's head
in the short space of two days. A body of such
extreme tenuity as a comet is most likely incapable
of an attraction powerful enough to recall matter
sent to such an enormous distance; it is therefore,
in all probability, scattered in space, which may
account for the rapid decrease observed in the tails
of comets every time they return to their perihelia.
It is remarkable that, although the tails of comets
increase in length as they approach their perihelia,
there is reason to believe that the real diameter
of the nebulous matter or nucleus contracts
on coming near the sun, and expands rapidly on
leaving him. Hevelius first observed this phenomenon,
which Encke's comet has exhibited in a
very extraordinary degree. On the 28th of October,
1828, this comet was about three times as far
from the sun as it was on the 24th of December,
yet at the first date its apparent diameter was
twenty-five times greater than at the second, the
decrease being progressive. M. Valz attributes
the circumstance to a real condensation of volume
from the pressure of the ethereal medium, which
increases most rapidly in density towards the surface
of the sun, and forms an extensive atmosphere
around him. Sir John Herschel, on the contrary,
conjectures that it may be owing to the alternate
conversion of evaporable materials in the upper
regions of a transparent atmosphere into the states
of visible cloud and invisible gas by the effects of
heat and cold. Not only the tails, but the nebulous
part of comets diminishes every time they return
to their perihelia; after frequent returns they
ought to lose it altogether, and present the appearance
of a fixed nucleus: this ought to happen
sooner to comets of short periods. La Place supposes
that the comet of 1682 must be approaching
rapidly to that state. Should the substances be
altogether, or even to a great degree, evaporated,
the comet would disappear for ever. Possibly
comets may have vanished from our view sooner
than they would otherwise have done from this
cause.
In those positions of comets where only half of
their enlightened hemisphere ought to be seen if
they shine by reflected light, they ought to exhibit
phases, but even with high magnifying powers
none have been detected, though some slight indications
are said to have been once observed by
Hevelius and La Hire in 1682. In general the
light of comets is dull, — that of the comet of 1811
was only equal to the tenth part of the light of
the full moon, but some have been brilliant enough
to be visible in full daylight, especially the comet
of 1744, which was seen without a telescope at
one o'clock in the afternoon, while the sun was
shining; whence it may be inferred that, although
some comets may be altogether diaphanous, others
seem to possess a solid mass resembling a planet;
but whether they shine by their own or by reflected
light has never been satisfactorily made out till
now. As light is polarized by reflection at certain
angles, it would afford a decisive test, were it
not that a body is capable of reflecting light,
though it shines by its own; so that it would not
be conclusive, even if the light of a comet were
polarized light. M. Arago, however, has with
great ingenuity discovered a method of ascertaining
this point, independent both of phases and
polarization.
Since the rays of light diverge from a luminous
point, they will be scattered over a greater space
as the distance increases, so that the intensity of
the light on a screen two feet from the object is
four times less than at the distance of one foot;
three feet from the object it is nine times less, and
so on, decreasing in intensity as the square of the
distance increases. As a self-luminous surface
consists of an infinite number of luminous points,
it is clear that, the greater the extent of surface,
the more intense will be the light; whence it
may he concluded that the illuminating power of
such a surface is proportional to its extent, and
decreases inversely as the square of the distance.
Notwithstanding this, a self-luminous surface,
plane or curved, viewed through a hole in a plate
of metal, is of the same brilliancy at all possible
distances as long as it subtends a sensible angle,
because, as the distance increases, a greater
portion comes into view, and as the augmentation
of surface is as the square of the diameter
of the part seen through the hole, it increases
as the square of the distance. Hence,
though the number of rays from any one point of
the surface which pass through the hole decrease
inversely as the square of the distance, yet, as the
extent of surface which comes into view increases
also in that ratio, the brightness of the object is
the same to the eye as long as it has a sensible
diameter. For example — Uranus is about nineteen
times farther from the sun than we are, so
that the sun, seen from that planet, must appear
like a star with a diameter of a hundred seconds,
and must have the same brilliancy to the inhabitants
that he would have to us if viewed through
a small circular hole having a diameter of a hundred
seconds. For it is obvious that light comes
from every point of the sun's surface to Uranus,
whereas a very small portion of his disc is visible
through the hole; so that extent of surface exactly
compensates distance. Since, then, the visibility
of a self-luminous object does not depend
upon the angle it subtends as long as it is of
sensible magnitude, if a comet shines by its own
light, it should retain its brilliancy as long as its
diameter is of a sensible magnitude; and even
after it has lost an apparent diameter, it ought,
like the fixed stars, to be visible, and should only
vanish in consequence of extreme remoteness.
That, however, is far from being the case — comets
gradually become dim as their distance increases,
and vanish merely from loss of light, while they
still retain a sensible diameter, which is proved
by observations made the evening before they
disappear. It may therefore be concluded that
comets shine by reflecting the sun's light. The
most brilliant comets have hitherto ceased to be
visible when about five times as far from the sun
as we are. Most of the comets that have been
visible from the earth have their perihelia within
the orbit of Mars, because they are invisible when
as distant as the orbit of Saturn: on that account
there is not one on record whose perihelion is
situate beyond the orbit of Jupiter. Indeed, the
comet of 1156, after its last appearance, remained
five whole years within the ellipse described by
Saturn without being once seen. A hundred and
forty comets have appeared within the earth's
orbit during the last century that have not again
been seen. If a thousand years be allowed as the
average period of each, it may be computed, by
the theory of probabilities, that the whole number
which range within the earth's orbit must be
1400; but Uranus being about nineteen times
more distant, there may be no less than 11200000
comets that come within the known extent of our
system. M. Arago makes a different estimate :
he considers that, as thirty comets are known to
have their perihelion distance within the orbit of
Mercury, if it be assumed that comets are uniformly
distributed in space, the number having
their perihelion within the orbit of Uranus must
be to thirty as the cube of the radius of the orbit
of Uranus to the cube of the radius of the orbit of
Mercury, which makes the number of comets
amount to 3529470; but that number may be
doubled if it be considered that, in consequence of
day-light, fogs, and great southern declination,
one comet out of two is concealed from us. So,
according to M. Arago, more than seven millions
of comets frequent the planetary orbits.
SECTION XXXVI.
GREAT as the number of comets appears to be, it
is absolutely nothing when compared to the number
of the fixed stars. About two thousand only
are visible to the naked eye; but when we view
the heavens with a telescope, their number seems
to be limited only by the imperfection of the instrument.
In one hour Sir William Herschel estimated
that 50000 stars passed through the field

and supposed to be the nearest of the fixed stars.
If Sirius had a parallax of half a second, its distance
from the earth would be 525481 times the
distance of the sun from the earth; and therefore
Sirius, placed where the sun is, would appear to
us to be 3.7 times as large as the sun, and would
give 13.8 times more light: but many of the fixed
stars must be infinitely larger than Sirius.
Many stars have vanished from the heavens;
the star 42 Virginis seems to be of this number,
having been missed by Sir John Herschel on the
9th of May, 1828, and not again found, though
he frequently had occasion to observe that part of
the heavens. Sometimes stars have all at once
appeared, shone with a bright light, and vanished.
Several instances of these temporary stars are on
record; a remarkable instance occurred in the
year 125, which is said to have induced Hipparchus
to form the first catalogue of stars. Another
star appeared suddenly near a Aquilæ in
the year 389, which vanished after remaining for
three weeks as bright as Venus. On the 10th of
October, 1604, a brilliant star burst forth in the
constellation of Serpentarius, which continued
visible for a year; and a more recent case occurred
in the year 1610, when a new star was discovered
in the head of the Swan, which, after becoming
invisible, reappeared, and after many variations
in light vanished after two years, and has never
since been seen. In 1572, a star was discovered
in Cassiopeia, which rapidly increased in
brightness till it even surpassed that of Jupiter ;
it then gradually diminished in splendour, and
after exhibiting all the variety of tints that indicates
the changes of combustion, vanished sixteen
months after its discovery without altering its
position. It is impossible to imagine anything
more tremendous than a conflagration that could
be visible at such a distance. It is however suspected
that this star may be periodical and identical
with the stars which appeared in the years 945
and 1264. There are probably many stars which
alternately vanish and reappear among the innumerable
multitudes that spangle the heavens,
the periods of thirteen have already been pretty
well ascertained. Of these the most remarkable
is the star Omicron in the constellation Cetus. It
appears about twelve times in eleven years, and
is of variable brightness, sometimes appearing
like a star of the second magnitude; but it neither
always arrives at the same lustre, nor does it increase
or diminish by the same degrees. According
to Hevelius, it did not appear at all for four
years. γ Hydro also vanishes and reappears
every 494 days, and a very singular instance of
periodicity is given by Sir John Herschel in the
star Algol or β Persei, which is described as retaining
the size of a star of the second magnitude
for two days and fourteen seconds; it then; suddenly
begins to diminish in splendour, and in
about three hours and a half is reduced to the
size of a star of the fourth magnitude: it then
begins again to increase, and in three hours and
a half more regains its usual brightness, going
through all these vicissitudes in two days,
twenty hours, and forty-eight minutes. The
cause of the variations in most of the periodical
stars is unknown, but, from the changes of Algol,
M. Goodricke has conjectured that they may be
occasioned by the revolution of some opaque
body, coming between us and the star, obstructing
part of its light. Sir John Herschel is struck
with the high degree of activity evinced by
these changes in regions where, 'but for such
evidences, we might conclude all to be lifeless.'
He observes that our own sun requires nine times
the period of Algol to perform a revolution on its
own axis; while, on the other hand, the periodic
time of an opaque revolving body sufficiently huge
to produce a similar temporary obscuration of the
sun, seen from a fixed star, would be less than
fourteen hours.
Many thousands of stars that seem to be only
brilliant points, when carefully examined are found
to be in reality systems of two or: more suns, some
revolving about a common centre. These binary
and multiple stars are extremely remote, requiring
the most powerful telescopes, to show them separately.
The first catalogue of double stars, in
which their places and relative positions are, determined,
was accomplished by the talents, and industry
of.Sir Herschel, to whom astronomy
is indebted for so many brilliant discoveries, and
with whom the idea of their combination in binary
and multiple systems originated idea completely
established by his own observations, recently
confirmed by those of his son. The motions
of revolution of many round a common centre
have been ascertained, and their periods determined
with considerable accuracy. Some have,
since their first discovery, already accomplished
nearly a whole revolution, and one, η Coronæ, is
actually considerably advanced in its second period.
These, interesting systems thus present a species
of sidereal chronometer, by which; the chronologygy
of the heavens, will be marked out to future ages
by epochs of their, own, liable to no fluctuations
from planetary disturbances, such as obtain in our
system.
In observing the relative position of the stars
of a binary system, the distance between them,
and also the angle of position, that is, the angle
which the meridian or a parallel to the equator
makes with the line joining the two stars are
measured. The accuracy of each result depends
upon taking the mean of a great number of the
best observations, and eliminating error by mutual
comparison. The distances between the
stars are so minute that they cannot be measured
with the same accuracy as the angles of
position ; therefore, to determine the orbit of a
star independently of the distance, it is necessary
to assume, as the most probable hypothesis, that
the stars are subject to the law of gravitation, and
consequently, that one of the two stars revolves in
an ellipse about the other, supposed to be at rest,
though not necessarily in the focus. A curve is
thus constructed graphically by means of the
angles of position and the corresponding times of
observation. The angular velocities of the stars
are obtained by drawing tangents to this curve at
stated intervals, whence the apparent distances, or
radii vectores, of the revolving star become known
for each angle of position; because, by the laws
of elliptical motion, they are equal to the square
roots of the apparent angular velocities. Now
that the angles of position estimated from a given
line, and the corresponding distances of the two
stars, are known, another curve may be drawn,
which will represent on paper the actual orbit of
the star projected on the visible surface of the
heavens; so that the elliptical elements of the true
orbit and its position in space may be determined
by a combined system of measurements and computation.
But as this orbit has been obtained
on the hypothesis that gravitation prevails in these
distant regions, which could not be known à priori,
it must be compared with as many observations as
can be obtained, to ascertain how far the computed
ellipse agrees with the curve actually described by
the star.
By this process Sir John Herschel has discovered
that several of these systems of stars are
subject to the same laws of motion with our system
of planets: he has determined the elements of their
elliptical orbits, and computed the periods of their
revolution. One of the stars of γ Virginis revolves
about the other in 629 years; the periodic time of
σ Coronæ is 287 years; that of Castor is 253
years; that of ε Bootes is 1600; that of 70 Ophiuci
is ascertained by M. Savary to be 80 years; and
Professor Encke has shown that the revolution of
ξ Ursæ is completed in 58 years. The two first
of these stars are approaching their perihelia, —
γ Virginis will arrive at it on the 18th of August,
1834, and Castor some time in 1855. The actual
proximity of the two component stars in each case
will then be extreme, and the apparent angular
velocity so great, that, in the case of γ Virginis,
an Angle of 68° may be described in a single year.
σ Coronæ will also attain its perihelion about 1835.
Sir John Herschel, Sir James South, and Professor
Struve of Dorpat, have increased Sir, William
Herschel's original catalogue to more than 3000,
of which thirty or forty are known to form revolving
or binary systems, and Mr. Dunlop has
formed a catalogue of 253 double stars in the
southern hemisphere, The motion of Mercury is
more rapid than that of any other planet, being at
the rate of 107000 miles in an hour; the perihelion
velocity of the. ,comet of 1680 was no less
than 880000 miles an hour; but if the two
stars of ξ Ursæ be as remote from one another
as the nearest fixed star is from the sun, the
velocity of the revolving stars must exceed imagination.
The discovery of the elliptical emotion
of the double stars excites the highest interest,
since it shows that gravitation is not peculiar to
our system of planets, but that systems of suns in
the far distant regions of the universe are also
obedient to its laws.
Possibly, among the multitudes of small stars,
whether double or insulated, some may be found
near enough to exhibit distinct parallactic motions,
arising from the revolution of the earth in its
orbit. Of two stars apparently in close approximation,
one may be far behind the other in space.
These may seem near to one another when viewed
from the earth in one part of its orbit, but may
separate widely when seen from the earth in another
position, just as two terrestrial objects appear
to be one when viewed in the same straight line,
but separate as the observer changes his position.
In this case the stars would not have real, but
only apparent motion. One of them would seem
to oscillate annually to and fro in a straight line
on each side of the other — a motion which could
not be mistaken for that of a binary system, where
one star describes an ellipse about the other.
Such parallax does not yet appear to have been
made out, so that the actual distance of the stars
is still a matter of conjecture.
The double stars are of various hues, but
most frequently exhibit the contrasted colours.
The large star is generally yellow, orange, or red;
and the small star blue, purple, or green. Sometimes
a white star is combined with a blue or
purple, and more rarely a red and white are united.
In many cases, these appearances are due to the
influences of contrast on our judgment of colours.
For example, in observing a double star, where the
large one is a full ruby-red or almost blood-colour,
and the small one a fine green, the latter loses its
colour when the former is hid by the cross wires
of the telescope. But there are a vast number of
instances where the colours are too strongly
marked to be merely imaginary. Sir John Herschel
observes in one of his papers in the Philosophical
Transactions, as a very remarkable fact,
that, although red stars are common enough, no
example of an insulated blue, green, or purple one
has yet been produced.
Besides the revolutions about one another, some
of the binary systems are carried forward in space
by a motion common to both stars, towards some
unknown point in the firmament. The two stars
of 61 Cygni, which are nearly equal, and have
remained at the distance of about 15" from each
other for fifty years, have changed their place in
the heavens during that period, by a motion which
for ages must appear uniform and rectilinear:
because, even if the path be curved, so small a
portion of it must be sensibly a straight line to us.
Multitudes of the single stars also have proper
motions, yet so minute that that of μ Cassiopeiæ,
which is only 3".74 annually, is the greatest yet
observed; but the enormous distances of the stars
make motions appear small to us Which are in
reality very great. Sir William Herschel conceived
that, among many irregularities, the motions of
the stars have a general tendency towards a point
diametrically opposite to that occupied by the star
ζ Herculis, which he attributed to a motion of
the solar system in the contrary direction. Should
this really be the case, the stars, from the effects
of perspective alone, would seem to diverge in the
direction to which we are tending, and would apparently
converge in the space we leave, and there
would be a regularity in these apparent motions
which would in time be detected; but if the solar
system and the whole of the stars visible to us be
carried forward in space by a motion common to
all, like ships drifting in a current, it would be
impossible for us, who move with the rest, to
ascertain its direction. There can be no doubt of
the progressive motion of the sun and many of
the stars, but sidereal astronomy is not far enough
advanced to determine what relations these bear
to one another.
The stars are scattered very irregularly over the
firmament. In some places they are crowded together,
in others thinly dispersed. A few groups
more closely condensed form very beautiful objects
even to the naked eye, of which the Pleiades and
the constellation Coma Berenices are the most
striking examples; but the greater number of
these clusters of stars appear to unassisted vision
like thin white clouds or vapours: such is the
milky way, which, as Sir William Herschel has
proved, derives its brightness from the diffused
light of the myriads of stars that form it. Most
of them are extremely small on account of their
enormous distances, and they are so numerous
that, according to his estimation, no fewer than
50000 passed through the field of his telescope in
the course of one hour in a zone 2° broad. This
singular portion of the heavens, constituting part
of our firmament, consists of an extensive stratum
of stars, whose thickness is small compared with
its length and breadth; the earth is placed about
midway between its two surfaces, near the point
where it diverges into two branches. Many clusters
of stars appear like white clouds or round
comets without tails, either to unassisted vision
or with ordinary telescopes; but with powerful
instruments Sir John Herschel describes them as
conveying the idea of a globular space filled full
of stars insulated in the heavens, and constituting
a family or society apart from the rest, subject
only to its own internal laws. To attempt to
count the stars in one of these globular clusters,
he says, would be a vain task, — that they are not
to be reckoned by hundreds, — and, on a rough
computation, it appears that many clusters of this
description must contain ten or twenty thousand
stars compacted and wedged together in a round
space whose area is not more than a tenth part of
that covered by the moon; so that its centre,
where the stars are seen projected on each, other,
is one blaze of light. If each of these stars
sun, and if they be separated by intervals equal to
that which separates our sun from the nearest
fixed star, the distance which renders the whole
cluster barely visible to the naked eye must he so
great, that the existence of this splendid assemblage
can only be known to us by light which
must have left it at least a thousand years ago
Occasionally these clusters are so irregular and so
undefined in their outline as merely to suggest the
idea of a richer part of the heavens. They contain
fewer stars than the globular clusters, and
sometimes a red star forms a conspicuous object
among them. These Sir William Herschel regarded
as the rudiments of globular clusters in a
less advanced state of condensation, but tending to
that form by their mutual attraction.
Multitudes of nebulous spots are to be seen on
the clear vault of heaven which have every appearance
of being clusters like those described,
but are too distant to be resolved into stars by the
most excellent telescopes. This nebulous matter
exists in vast abundance in space. No fewer than
2000 nebulae and clusters of stars were observed
by Sir William Herschel, whose places have been
computed from his observations, reduced to a common
epoch, and arranged into a catalogue in order
of right ascension by his sister, Miss Caroline Herschel,
a lady so justly eminent for astronomical
knowledge and discovery. Six or seven hundred
nebulæ have already been ascertained in the southern
hemisphere; of these the magellanic clouds
are the most remarkable. The nature and use of
this matter, scattered over the heavens in such a variety
of forms, is involved in the greatest obscurity.
That it is a self-luminous, phosphorescent, material
substance, in a highly dilated or gaseous state, but
gradually subsiding by the mutual gravitation of
its particles into stars and sidereal systems, is
the hypothesis which seems to be most generally
received; but the only way that any real knowledge
on this mysterious subject can be obtained
is by the determination of the form, place, and
present state of each individual nebula; and a
comparison of these with future observations will
show generations to come the changes that may
now be going on in these supposed rudiments
of future systems. With this view, Sir John
Herschel began in the year 1825 the arduous and
pious task of revising his illustrious father's observations,
which he finished a short time before
he sailed for the Cape of Good Hope, in order to
disclose the mysteries of the Southern hemisphere,
because he considers our firmament to be exhausted
till farther improvements in the telescope
shall enable astronomers to penetrate deeper into
space. In a truly splendid paper read before the
Royal Society on the 21st of November, 1833, he
gives the places of 2500 nebulæ and clusters of
stars. Of these, 500 are new, — the rest he mentions
with peculiar pleasure as having been most
accurately determined by his father. This work is
the more extraordinary, as, from bad weather, fogs,
twilight, and moonlight, these shadowy appearances
are not visible, at an average, above thirty nights
in the year.
The nebulæ have a great variety of forms. Vast
multitudes are so faint as to be with difficulty
discerned at all till they have been for some time
in the field of the telescope, or are just about to
quit it. Many present a large ill-defined surface,
in which it is difficult to say where the centre of
the greatest brightness is. Some cling to stars
like wisps of cloud; others exhibit the wonderful
appearance of an enormous flat ring seen very
obliquely, with a lenticular vacancy in the centre.
A very remarkable instance of an annular nebula
is to be seen exactly half-way between β and
γ Lvræ. It is elliptical in the ratio of 4 to 5,
is sharply defined, the internal opening occupying
about half the diameter. This opening
is not entirely dark, but filled up with a faint
hazy light, aptly compared by Sir John Herschel
to fine gauze stretched over a hoop. Two
are described as most amazing objects: — one
like a dumb-bell or hour-glass of bright matter,
surrounded by a thin hazy atmosphere, so as to
give the whole an oval form, or the appearance of
an oblate spheroid. This phenomenon bears no
resemblance to any known object. The other consists
of a bright round nucleus, surrounded at a
distance by a nebulous ring split through half its
circumference, and having the split portions separated
at an angle of 45° each to the plane of the
other. This nebula bears a strong similitude to
the milky way, and suggested to Sir John Herschel,
the idea of a brother system bearing a real physical
resemblance and strong analogy of structure
to our own.' It appears that double nebulae are
not unfrequent, exhibiting all the varieties of distance,
position, and relative brightness with their
counterparts the double stars. The rarity of single
nebulae as large, faint, and as little condensed
the centre as these, makes it extremely improbable
that two such bodies should be accidentally so
near as to touch, and often in part to overlap each
other as these do. It is much more likely that
they constitute systems; and if so, it will form an,
interesting subject of future inquiry to discover
whether they possess orbitual motion round one
another.
Stellar nebulæ form another class. These have
a round or oval shape, increasing in density towards
the centre. Sometimes the matter is so
rapidly condensed as to give the whole the appearance
of a star with a blur, or like a candle shining
through horn. In some instances the central
matter is so highly and suddenly condensed, so
vivid and sharply defined, that the nebula might
be taken for a bright star surrounded by a thin
atmosphere. Such are nebulous stars. The zodiacal
light, or lenticular-shaped atmosphere of
the sun, which may be seen extending beyond the
orbits of Mercury and Venus soon after sunset in
the months of April and May, is supposed to be a
condensation of the ethereal medium by his attractive
force, and seems to place our sun among
the class of stellar nebulæ. The stellar nebulæ
and nebulous stars assume all degrees of ellipticity.
Not unfrequently they are long and narrow,
like a spindle-shaped ray, with a bright nucleus
in the centre. The last class are the planetary
nebulæ. These bodies have exactly the appearance
of planets, with sensibly round or oval discs,
sometimes sharply terminated, at other times hazy
and ill defined. Their surface, which is blue or
bluish-white, is equable or slightly mottled, and
their light occasionally rivals that of the planets
in vividness. They are generally attended by minute
stars which give the idea of accompanying
satellites. These nebulæ are of enormous dimensions.
One of them, near ν Aquarii, has a sensible
diameter of about 20", and another presents
a diameter of 12". Sir John Herschel has computed
that, if these objects be as far from us as
the stars, their real magnitude must, even on the
lowest estimation, be such as would fill the orbit
of Uranus. He concludes that, if they be solid
bodies of a solar nature, their intrinsic splendour
must be greatly inferior to that of the sun, because
a circular portion of the sun's disc, subtending an
angle of 20", would give a light equal to that of
a hundred full moons, while, on the contrary, the
objects in question are hardly, if at all, visible to
the naked eye. From the uniformity of the discs
of the planetary nebulæ, and their want of apparent
condensation, he presumes that they may be
hollow shells, only emitting light from their surfaces.

The existence of every degree of ellipticity in
the nebulæ — from long lenticular rays to the exact
circular form, — and of every shade of central
condensation — from the slightest increase of density
to apparently a solid nucleus, — may be accounted
for by supposing the general constitution
of these nebulæ to be that of oblate spheroidal
masses of every degree of flatness, from the sphere
to the disc, and of every variety in their density
and ellipticity towards the centre. It would be
erroneous however to imagine, that the forms of
these systems are maintained by forces identical
with those already described, which determine the
form of a fluid mass in rotation; because, if the
nebulæ be only clusters of separate stars, as in the
greater number of cases there is every reason to
believe them to be, no pressure can be propagated
through them. Consequently, since no general
rotation of such a system as one mass can be supposed,
it may be conceived to be a quiescent form,
comprising within its limits an indefinite muItitude
of stars, each of which may be moving in an
orbit about the common centre of the whole, in
virtue of a law of internal gravitation resulting
from the compound gravitation of all its parts.
Sir John Herschel has proved that the existence
of such a system is not inconsistent with the law
of gravitation under certain conditions.
The distribution of the nebulæ over the heavens
is even more irregular than that of the stars. In
some places they are so crowded together as
scarcely to allow one to pass through the field of
the telescope before another appears, while in
other parts hours elapse without a single nebula
occurring in the zone under observation. They
are in general only to be seen with the very best
telescopes, and are most abundant in a zone whose
general direction is not far from the hour circles
0h, and 12h, and which crosses the milky way
nearly at right angles. Where that zone crosses
the constellations Virgo, Coma Berenices, and the
Great Bear, they are to be found in multitudes.
Such is a brief account of the discoveries contained
in Sir John Herschel's paper, which, for
sublimity of views and patient investigation, has
not been surpassed in any age or country. To
him and to Sir William Herschel is due almost all
that is known of sidereal astronomy; and, in the
inimitable works of that highly-gifted father and
sons the reader will find this subject treated of in
a style altogether worthy of it, and of them.
So numerous are the objects which meet our
view in the heavens, that we cannot imagine
part of space where some light would not strike
the eye; — innumerable stars, thousands of double
and multiple systems, clusters in one blaze with
their tens of thousands of stars, and the nebulæ
amazing us by the strangeness of their forms and
the incomprehensibility of their nature, till at last,
from the imperfection of our senses, even these
thin and airy phantoms vanish in the distance.
If such remote bodies shine by reflected light, we
should be unconscious of their existence; each
star must then be a sun, and may be presumed
to have its system of planets, satellites; and comets,
like our own; and, for aught we know;
myriads' ;of bodies may be wandering in space unseen
by us, of whose nature we can form no idea,
and still less of the part they perform in the economy
of the universe; nor is this an unwarranted
presumption; many such do come within the
sphere of the earth's attraction, are ignited by the
velocity with which they pass through the atmosphere;
and are precipitated with great violence
on the earth. The fall of meteoric stones is much
more frequent than is generally believed; hardly
a year passes without instances occurring,
and if it be considered that only a small part of
the earth is inhabited; it may be presumed that
numbers fall in the ocean or on the uninhabited
part of the land, unseen by man. They are sometimes
of great magnitude; the volume of several
has exceeded that of the planet Ceres, which is
about 70 miles in diameter. One which passed
within 25 miles of us was estimated to weigh about
600000 tons, and to move with velocity of
about 20 miles in second, — a fragment of it
alone reached the earth. The obliquity of the
descent of meteorites, the peculiar substances they
are composed of, and the explosion accompanying
their fall, show that they are foreign to
our system. Luminous spots, altogether independent
of the phases, have occasionally appeared
on the dark part of the moon; these
have been ascribed to the light arising from the
eruption of volcanos; whence it has been supposed
that meteorites have been projected from
the moon by the impetus of volcanic eruption.
It has even been computed that, if a stone were
projected from the moon in a vertical line, with
an initial velocity of 10992 feet in a second, —
more than four times the velocity of a ball when
first discharged from a cannon, — instead of falling
back to the moon by the attraction of gravity, it
would come within the sphere of the earth's
attraction, and revolve about it like a satellite.
These bodies, impelled either by the direction of
the primitive impulse, or by the disturbing action
of the sun, might ultimately penetrate the earth's
atmosphere, and arrive at its surface. But from
whatever source meteoric stones may come, it
seems highly probable that they have a common
origin, from the uniformity — we may almost say
identity — of their chemical composition.
SECTION XXXVII.
THE known quantity of matter bears a very small
proportion to the immensity of space. Large as
the bodies are, the distances which separate them
are immeasurably greater; but as design is manifest
in every part of creation, it is probable that,
if the various systems in the universe had been
nearer to one another, their mutual disturbances.
would have been inconsistent with the harmony
and stability of the whole. It is clear that space.
is not pervaded by atmospheric air, since its.
resistance would, long ere this, have destroyed
the velocity of the planets; neither can we affirm
it to be a void, since it is replete with ether, and
traversed in all directions by light, heat, gravitation,
and possibly by influences whereof we can.
form no idea.
Whatever the laws may be that obtain in the
more distant regions of creation, we are assured that
one alone regulates the motions not only of our own
system, but also the binary systems of the fixed stars;
and as general laws form the ultimate object of philosophical
research, we cannot conclude these remarks
without considering the nature of gravitation
— that extraordinary power whose effects we have
been endeavouring to trace through some of their
mazes. It was at one time imagined that the
acceleration in the moon's mean motion was occasioned
by the successive transmission of the graviting
force; but it has been proved that, in
order to produce this effect, its velocity must be
about fifty millions of times greater than that of
light, which flies at the rate of 200000 miles in a
second: its action, even at the distance of the
sun, may, therefore be regarded as instantaneous;
yet so remote are the nearest of the fixed stars,
that it may be doubted whether the sun has any
sensible influence on them.
The curves in which the celestial bodies move
by the force, of gravitation are only lines of the
second order; the attraction of spheroids, according
to any other law of force than that of gravitation,
would be much more complicated; and
as it is easy to prove that matter might have
been moved according to an infinite variety of
laws, it may be concluded that gravitation must
have been selected by Divine Wisdom out of an
infinity of others, as being the most simple, and
that which gives the greatest stability to the celestial
motions.
It is a singular result of the simplicity of the
laws of nature, which admit only of the observation
and comparison of ratios, that the gravitation
and theory of the motions of the celestial bodies
are, independent of their absolute magnitudes and
distances; consequently, if all the bodies of the
solar system, their mutual distances, and their
velocities, were diminish proportionally, they
would describe curves in all respects similar to
those in which they now move; and the system
might be successively reduced to the smallest
sensible dimensions, and still exhibit the same
appearances. We learn by experience that a very
different law of attraction prevails when the particles
of matter are placed within inappreciable distances
from each other, as in chemical and capillary
attraction and the attraction of cohesion: whether
it be a modification of gravity; or that some new
and unknown power comes into action, does not
appear; but as a change in the law of the force
takes place at one end of the scale, it is possible
that gravitation may not remain the same throughout
every part of space. Perhaps the day may
come when even gravitation, no longer regarded
as an ultimate principle, may be resolved into a
yet more general cause, embracing every law that
regulates the material world.
The action of the gravitating force is not inpeded
by the intervention even of the densest
substances. If the attraction of the sun for the
centre of the earth, and of the hemisphere diametrically
opposite to him, were diminished by a
difficulty in penetrating the interposed matter, the
tides would be more obviously affected. Its attraction
is the same also, whatever the substances of
the celestial bodies may be; for if the action of
the sun upon the earth differed by a millionth
part from his action upon the moon, the difference
would occasion a periodical variation in the moon's
parallax whose maximum would be the 1/15 of a
second, and also a variation in her longitude
amounting to several seconds, a supposition proved
to be impossible, by the agreement of theory with
observation. Thus all matter is pervious to gravitation,
and is equally attracted by it.
As far as human knowledge extends, the intensity
of gravitation has never varied within the limits of
the solar system; nor does even analogy lead us
to expect that it should; on the contrary, there is
every reason to be assured that the great laws, of
the universe are immutable, like their Author.
Not only the sun and planets, but the minutest
particles, in all the varieties of their attractions
and repulsions, — nay, even the imponderable matter
of the electric, galvanic, or magnetic fluid, —
are all obedient to permanent laws, though we
may not be able in every case to resolve their
phenomena into general principles. Nor can we
suppose the structure of the globe alone to be
exempt from the universal fiat, though ages may
pass before the changes it has undergone, or that
are now in progress, can be referred to existing
causes with the same certainty with which the
motions of the planets, and all their periodic and
secular variations, are referable to the law of gravitation.
The traces of extreme antiquity perpetually
occurring to the geologist give that information
as to the origin of things in vain looked
for in the other parts of the universe. They date
the beginning of time with regard to our system;
since there is ground to believe that the formation
of the earth was contemporaneous with that of the
rest of the planets; but they show that creation is
the work of Him with whom a thousand years are
as one day, and one day as a thousand years.
It thus appears that the theory of dynamics,
founded upon terrestrial phenomena, is indispensable
for acquiring a knowledge of the revolutions
of the celestial bodies and their reciprocal influences.
The motions of the satellites are affected
by the forms of their primaries, and the figures of
the planets themselves depend upon their rotations.
The symmetry of their internal structure
proves the stability of these rotatory motions,
and the immutability of the length of the day,
which furnishes an invariable standard of time;
and the actual size of the terrestrial spheroid
affords the means of ascertaining the dimensions
of the solar system, and provides an invariable
foundation for a system of weights and measurest.
The mutual attraction of the celestial
bodies disturbs the fluids at their surfaces, whence
the theory of the tides and the oscillations of the
atmosphere. The density and elasticity of the
air, varying with every alternation of temperature;
lead to the consideration of barometrical changes,
the measurement of heights, and capillary attraction;
and the doctrine of sound, including the
theory of music, is to be referred to the small undulations
of the aerial medium. A knowledge of the
action of matter upon light is requisite for tracing
the curved path of its rays through the atmosphere,
by which the true places of distant objects
are determined, whether in the heavens or on the
earth. By this we learn the nature and properties
of the sunbeam, the mode of its propagation
through the etherial fluid, or in the interior of
material bodies, and the origin of colour. By the
eclipises of Jupiter's satellites, the velocity of light
is ascertained, and that velocity, in the aberration
of the fixed stars, furnishes the only direct proof
of the real motion of the earth. The effects of
the invisible rays of light are immediately connected
with chemical action; and heat, forming
part of the solar ray, so essential to animated and
inanimated existence, whether considered as invisible
light or as a distinct quality, is too important
an agent in the economy of creation not to hold a
principal place in the order of physical science:
Whence follows its distribution over the surface
of the globe, its power on the geological
convulsions of our planet, its influence on the
atmosphere and on climate, and its effects on
vegetable and animal life, evinced in the localities
of organized beings on the earth, in the
waters, and in the air. The connexion of heat
with electrical phenomena, and the electricity
of the atmosphere, together with all its energetic
effects, its identity with magnetism and the phenomena
of terrestrial polarity, can only be understood
from the theories of these invisible agents,
and are probably principal causes of chemical
affinities. Innumerable instances might be given
in illustration of the immediate connexion of the
physical sciences, most of which are united still
more closely by the common bond of analysis
which is daily extending its empire, and will ultimately
embrace almost every subject in nature in
its formulæ.
These formulæ, emblematic of Omniscience, condense
into a few symbols the immutable laws of
the universe. This mighty instrument of human
power itself originates in the primitive constitution
of the human mind, and rests upon a few fundamental
axioms which have eternally existed in
Him who implanted them in the breast of man
when He created him after His own image.
EXPLANATION OF TERMS.
EXPLANATION OF TERMS.
Aberration.	An apparent annual motion in the fixed
stars, occasioned by the velocity of light combined
with the real velocity of the earth in its
orbit.
Absorbent media.	Substances either solid, liquid, or
fluid, which imbibe the rays of light or heat.
Accidental colours.	If the eye has been dazzled by
looking steadily at a bright colour, as, for example,
at a red wafer, upon turning it to a white
object a bluish-green image of the wafer will
appear. Bluish-green is therefore the accidental
colour of red, and vice versâ. Each tint
has its accidental colour. When the real and accidental
colours are of equal intensity, the one is
said to be the complementary colour of the other,
because the two taken together make white light.
Acceleration.	A secular variation in the mean motion
of the moon.
Aëriform.	having the form of air.
Aërolite.	A meteoric stone.
Aërostatic expedition.	Ascent in a balloon.
Affinity or cohesive force.	The force with which the
particles of bodies resist separation.
Algæ.	Sea weeds or marine plants.
Aliquot parts.	The parts into which a quantity is
divided when no remainder is left.
Altitude.	The height of an object above the horizon.
Analysis.	Mathematical reasoning conducted by
means of abstract symbols.
Analyzing plate.	A piece of glass or a slice of a,
crystal used for examining the properties of polarized
light.
Analytical formula or expression.	A combination
of symbols expressing a series of calculation, and
including every particular case that can arise
from a general law.
Angle of position of a double star.	The angle
which a line joining the two stars makes with
one parallel to the meridian.
Angular velocity.	The swiftness with which the
particles of a revolving body move. It is proportional
to the velocity of each particle divided
by its distance from the axis or centre of rotation.
Annual equation.	A periodical inequality in the
motion of the moon going through its changes in
a year.
Annual parallax.	See Parallax.
Antimony.	A metal.
Antennæ.	The thread-like horns on the heads of
insects.
Aphelion.	The point in which a planet is at
greatest distance from the sun—the point A in
fig. 8, S being the sun.
Apogee.	The point in which the sun or moon is
farthest from the earth.
Apparent motion.	The motion of the celestial bodies
as viewed from the earth.
Apparent diameter.	See Diameter.
Apparent time.	See Time.
Apsides.	The extremities A and P, fig. 8, of the major
axis of an orbit, or the points in which a planet
Is at its greatest and least distances from S the
sun; also those in which a satellite is at its
greatest and least distances from its planet.
Arc of the meridian.	Part of a plane curve passing
through the poles of the earth, and along its
surface.
Areas.	Superficial extent. In astronomy, they are
the spaces passed over by the radius vector of a
celestial body.
Arithmetical progression.	A series of quantities or
numbers continually increasing or diminishing
by the same quantity ; as, for example, the natural
numbers 0, 1, 2, 3, 4, &c., which continually
increase by one.
Armature.	A piece of soft iron connecting the poles
of a horse-shoe magnet.
Astronomical or solar day.	The time between two
consecutive true noons or midnights.
Atmospheric refraction.	See Refraction.
Aurora.	A luminous appearance in the heavens,
frequently seen in high northern and southern
latitudes.
Axis of rotation.	The line, real or imaginary, about
which a body, revolves. The imaginary line
passing through both poles and the centre of
the earth is the axis of the earth's rotation.
Axis of a prism.	The line a b, fig. 11, passing
through the centre of a prism parallel to its sides.
Axis of a telescope.	An imaginary line passing
through the centre of the tube.
Axis of an ellipse.	See Ellipse, line A B fig 2.
Base.	In surveying, a base is a line measured on the
surface of the earth, and assumed as an origin
from whence the angular and linear distances of
remote objects may be determined.
Binary system of stars.	Two stars revolving about
each other.
Bisextile.	Leap year, every fourth year.
Caloric.	The material of heat; heat being the sensation.

Centre of gravity.	A point in a body, which, if supported,
the body will remain at rest.
Capillary attraction.	The attraction of tubes with a
very minute bore, such as thermometer tubes,
which causes liquids to ascend and remain suspended
within them.
Centrifugal force.	The force with which a revolving
body tends to fly from the centre of motion.
The direction of this force is in, the tangent to
the path the body describes.
Circumference.	The boundary of a circle.
Civil day	The time comprised between two consecutive
returns of the sun to the same meridian.
Civil or tropical year.	The time comprised between
two consecutive returns of the sun to the same
solstice or equinox.
Chemical rays.	The rays of the solar spectrum
which do not produce light but destroy vegetable
colours.
Chronometer.	A watch which measures time more
accurately than those in common use.
Coal measures	The strata which contains beds of
coal.
Cobalt.	A metal.
Cohesion.	The force with which the parts of bodies
resist any endeavour to separate them. Hardness,
softness, tenacity, fluidity, and ductility,
are modifications of cohesion.
Collecting wires, or Collectors.	Wires for collecting
and conveying electricity.
Complementary colours.	See Accidental colours.
Compression of a spheroid.	Flattening at the poles.
It is equal to the difference between the greatest
and least diameters divided by the greatest.
Concave mirror.	A polished curved surface which,
being holIow, reflects parallel rays of light so as
to make,them tend to meet.
Concentric.	Having the same centre.
Conductor.	A substance which conducts the electric
fluid.
Cone.	A solid figure A B C,
like a sugar-loaf, of
which A is the apex, A D
the axis, and the plane
c the base. The axis
may or may not be at
tight angles to the base,
and the base may be a
circle, an ellipse, or any
other line. When the axis is at right angles to
the base, the figure is a right cone.
Conic sections.	Lines formed by a plane cutting a
cone, of which there are five. If a right cone
with a circular base, be cut at right angles to
the base by a plane passing through the apex;
the section will be a triangle. If the cone be
cut through both sides by a plane parallel to the
base, the section will be a circle. If the cone be
cut slanting quite through both sides, the section
will be an ellipse, B a A b, fig. 2. If the cone be
cut parallel to one of its sloping sides, the section
will be a parabola, D A B, fig. 3; and if the section
cut only one side of the cone, and be not parallel
to the other, it will be a hyperbola, D A B, fig. 4.
Configuration.	The position of bodies with regard
to one another.
Conjunction.	A planet is said to be in conjunction
when it has the same longitude with the sun.
Constellations.	Groups of stars to which the names
of men and animals have anciently been given.
The whole starry firmament is divided into such
groups.
Contrasted colours.	See Accidental colours.
Converging.	Tending to the same point.
Convex mirror.	A polished curved surface which,
being protuberant, reflects parallel rays of light,
so as to make them diverge.
Cosine of an arc or angle.	In fig. 5, A D is the cosine
of the arc C B, and of the angle B A C.
Crystal.	A chemical or mineral substance having a
regular form.
Curves of double curvature.	Lines curved in two
directions, so that no two of their indefinitely
small parts lie in the same plane, as a corkscrew
or a line drawn obliquely on the side of a
cylinder which has its own curvature, at the same
time that it partakes of the curvature of the
surface on which it is drawn.
Curves of the second order.	The conic. sections. In
a circle, the relation of the part A D, fig. 5, of the
diameter to the perpendicular D C, is the same.
for every point in the circumference. The two
lines A D, D C are called co-ordinates. The relation
of these co-ordinates to one another is different
in different curves, but remains invariable
in any one curve; and lines are said to be of
the first or second order, according as this relation
can be expressed by the simple lines themselves,
or by their squares and products.
Cylinder.	A solid A B,
fig. 6, formed by the
revolution of a parallelogram
about one of
its sides.
Declination.	The angular distance of a celestial object
from the celestial equator.
Density.	The quantity of matter in a given bulk.
Diagonal.	A line drawn from angle to angle of a
four sided figure, as C D, fig. 10.
Diameter.	A straight line, E B, fig. 5, passing
through the centre, and terminated both ways,
by the sides or surface of a figure.
Diameter, apparent	The diameter of a body as seen
from the earth.
Diaphanous.	Transparent.
Dicotyledonous plants.	Such as have seeds containing
two lobes.
Dip.	The angle formed by the direction of the magnetic
force of the earth with the plumb-line.
Dipping needle.	An instrument for measuring the
dip of a magnetized needle.
Direct motion of a celestial body.	Motion from west
to east, according to the order of the signs of
the zodiac.
Disc.	The apparent surface of a heavenly body.
Disintegration.	Mouldering down, separating into
parts.
Distance, mean.	See Mean distance.
7
Distance, true.	See True distance.
Distance, Perihelion.	See Perihelion distance
Diverging.	Tending from a point.
Double refraction.	The power which some substances
possess of refracting or transmitting a
ray of light in two pencils instead of one. If S I,
fig. 13, be a ray of light, falling upon a doubly
refracting surface G g,will be transmitted
in two pencils I O, I E, so that the luminous
point s will appear double, if viewed through
the substance G g ; whereas if G g were of glass
or water, the ray S I would be transmitted in a
single pencil, I O, and only one image of s would
be seen.
Dynamics.	The science of force and motion.
Ecliptic. The great circle traced in the starry heavens
by the plane of the ecliptic.
Ecliptic, plane of.	An imaginary plane passing
through the earth's orbit, and extending to the
starry heavens.
Elasticity.	The property bodies possess of resuming
their original form, when pressure is removed.

Elastic media.	Atmospheric air, gas, ether, &c.,
which are highly compressible, and instantly
resume their volume or bulk, when pressure is
removed.
Electrics.	Substances in which electricity may be
excited, but which are incapable of conducting it.
Electric induction.	The effect of electrified
bodies to produce an electric state opposite to
their own, in all bodies near them capable of receiving
it.
Electromagnetism.	The science which determines
the reciprocal action of electricity and magnetism.

Electro-magnets.	Cylinders which have all the properties
of magnets when a stream of electricity
is passing through them.
Electrodynamics.	The science of the motion and
reciprocal action of electric currents.
Electro-dynamic-cylinder.	A hollow coil of copper
wire, (fig. 7,) in the form of a corkscrew, the
extreme parts of the wires of which are passed
back through the centre of the coil, and being
bent at right angles are brought out through
its middle. There are several forms of this
instrument, all of which have the same properties
as magnets, when a galvanic current is passing
through them.
Elements of an orbit.	In an elliptical orbit there are
six elements. Let P n A N (fig. 8) be the orbit
of a planet, s the Sun, C N E n the plane of the
ecliptic, and cr the first point of Aries, then the six
elements are the major ,axis P A, the excentricity
s o, the longitude Y S P the perihelion, the
longitude Y S N of N, the ascending node, the
inclination of the orbit n A N on the plane of the
ecliptic n E N,and Ys m the longitude of the body
m, at any given instant called the longitude of
the epoch. In a parabolic orbit, there are only
five elements, since the major axis is infinite.
Ellipse.	One of the conic sections. An ellipse may
be drawn, by fixing the ends of a string to two
points, F and f (fig. 2.) in a sheet of paper and
then carrying the point of a pencil round in the
loop of the string kept stretched, the length of
the string being greater than the distance between
the two points. The points Fand f are
called the foci, and the distance F C is the excentricity,
c being the centre of the ellipse; it
is evident that the less F C is, the nearer does
the ellipse approach the form of a circle. A B is
the major axis, a b the minor axis, and F A the
focal distance. From the construction, the length
of the string, F m f, is equal to the major axis.
If T t be a tangent to any point m, and F m, f m
lines from the foci, the angle F m T is equal to
the angle f m t; and as this is true for every
point of the ellipse, it follows that, in an elliptical
reflecting surface, rays of light or sound coming
from the focus F will be reflected by the surface
to the other focus f, since the angle of incidence
is equal to the angle of reflection, by the theory
of optics and acoustics.
Ellipsoid of revolution.	A solid formed by the revolution
of an ellipse about its axis. If theellipse
revolves about its minor axis, the ellipsoidwill
be oblate, or flattened at the poles, like an
orange: if the revolution be about the major
axis, the ellipsoid will be drawn out at the poles,
or prolate, like an egg.
Ellipticity.	Excentricity, or, deviation fromthe circular
or spherical form.
Elongation.	The angular distance, of a celestial
body from the sun, as it would be seen from the
centre of the earth.
Epoch.	The assumed instant from whence all the
subsequent and antecedent periods of a celestial
body are estimated.
Equation of time.	The difference between the time
shown by a watch, and that given by a dial,
or the difference of mean and true time.
Equation of tide centre.	The difference between the
true and mean motion of a planet or satellite. At
its maximum, it is equal to the excentricity of
the orbit, since it is the difference of the motion
of a body in an ellipse, and in a circle whose
diameter is equal to the major axis of the ellipse.
Equator.	The terrestrial equator is the equinoctial
line. The celestial equator is the great circle
traced in the starry heavens by the imaginary
extension of the plane of the terrestrial equator.
Equinoxes.	The vernal and autumnal equinoxes
are two points in the heavens diametrically opposite
one another, that is 180° apart. The
line in which the planes of the equator and
ecliptic intersect passes through them. The
vernal equinox is the point from whence the
longitudes or angular distances of the celestial
bodies are estimated; it is generally called the
first point of Aries, though these two points have
not coincided since the early ages of astronomy,
about two thousand two hundred and thirty-two
years ago, on account of the precession or retrograde
motion of the equinoctial points.
Etherial medium.	The ether or highly elastic fluid
with which space is filled.
Evection.	A certain periodic inequality in the motion
of the moon.
Excentricity.	The distances between the centre and
focus of an ellipse, or c F, (fig. 2.)
Extraordinary refraction.	See Refraction.
Extraordinary ray.	See Refraction.
Focus.	A point where converging rays or lines meet.
Focal distance.	The line F A in the conic sections,
(fig. 2, 3, and 4.)
Foci of an ellipse. Two points F and f (fig. 2.) in
the major axis, such, that the sum of the two
lines drawn from them to any point m in the
ellipse is equal to the major axis A B.
Fossils, organic.	The remains of ancient animals
and plants embodied in the strata of the earth.
Fundamental note.	The natural note of any sonorous
body, as of a string or organ-pipe.
Galvanism.	Electricity perpetually in motion, and
produced by chemical action.
Galvanic battery.	An instrument for producing
galvanic electricity, constructed of alternate
layers of two metals and a fluid.
Galvanic circuit.	Three substances in contact,
generating a stream of electricity, which flows in
a perpetual circuit through them.
Galvanometer.	An instrument for measuring the
intensity of the galvanic force.
Genera of plants.	The divisions of plants into families,
each of which contains a variety of species.
General analytical expression.	The representation
in symbols of a series of reasoning, including
every particular case of the subject in question.
Geometrical progression.	A series of quantities increasing
or diminishing by a continual multiplication
or division by the same quantity, as the
numbers 1, 2, 4, 8, 16, &c., which are constantly
multiplied by 2, or the series 1, 1/2, 1/4, 1/8, &c.,
which decreases by the continual division by 2.
Graphical construction of an orbit.	The drawing
of an orbit by ruler and compass from given observations.

Gravity.	The attraction of matter, weight.
Gravitating force.	The force with which matter
attracts; its intensity varies inversely as the
square of the distance; that is, the weight of a
body decreases in proportion as the square of
its distance from the centre of the earth increases,
and vice versa. But if the body be
within the surface of the earth, the force varies
inversely as the distance from the centre.
Gravitation.	Sensible gravity.
Grylli.	Grasshoppers, crickets, locusts, &c.
Harmonics.	The doctrine of musical sound.
Harmonic sounds.	The sympathetic notes heard
along with the principal note of a musical string,
or other sonorous body.
Harmonic divisions.	The parts into which a vibrating
musical string spontaneously divides itself,
each of which gives a distinct note, besides the
principal note arising from the vibration of the
whole string.
Harmonic colours.	Tints which become visible upon
looking steadfastly at a bright coloured light,
supposed to be analogous to the sympathetic
notes of a musical string.
Helix.	A. curve like a corkscrew, whose turnings
may either be circular or elliptical.
Homogeneous light.	Rays of the same colour.
Homogeneous spheroid.	A spheriod of uniform
density.
Horizontal plane.	An imaginary plane touching
the surface of the earth in one point, and terminating
on all sides in the horizon.
Horoscope.	The relative positions of the planets at
the time of a person's birth.
Hyperbola.	One of the conic sections. An open
curve, having two infinite branches, A B, A D,
(fig. 4.) and a focus F, to which every point in
the curve has a fixed relation.
Hypothesis.	A system upon supposition. An assumption.

Iceland spar.	A transparent and colourless carbonate
of lime, consisting of fifty-six parts of lime, and
forty-four of carbonic acid. It splits or cleaves
into solids called rhombs (fig. 14.) which are
bounded by six similar surfaces, whose sides are
parallel, but the angles are not right angles:
it possesses the property of double refraction in an
eminent degree.
Impetus.	A force whose intensity is measured by
the mass of a body and the square of its velocity
conjointly.
Incidence of light.	The angle which rays make with
a perpendicular to the surface upon which they
fall. Let A B, fig. 9, be the reflecting surface,
then S I is the incident and I R the refracted ray,
the angle S I P being equal to the angle R I P.
Inclination of an orbit.	The angle in fig. 8.
which the plane of an orbit P n A N makes with
the plane of the ecliptic C N E n.
Indigenous.	Native to a particular spot or country.
Inertia.	The disposition of matter to remain in its
state of rest or motion.
Interference of undulations.	The combination of
two series of waves in a fluid so as to augment,
diminish, or destroy each other.
Isochronous.	In equal times.
Isothermal lines.	Imaginary lines passing through
such places as have the same mean annual temperature.

Isogeothermal lines.	Imaginary lines passing through
all those places within the surface of the earth,
where the mean internal temperature is the
same.
Kepler's laws.	Three laws in the planetary motions
discovered by Kepler, which furnish the data
from whence the principle of gravitation is established:
they are, First, that the radii vectores of
the planets and comets describe areas proportional
to the time: Second, that the orbits of the
planets and comets are conic sections, having
the sun in one of their foci; and third, that the
squares of the periodic times of the planets are
proportional to the cubes of their mean distances
from the sun. These laws extend also to the
satellites.
Latent heat.	Caloric existing in all bodies, which is
not sensible, and cannot be detected by the thermometer.

Latitude.	Terrestrial latitude is the angular distance
between the vertical or plumb-line at any place
and the plane of the equator. Celestial latitude
is the height of a heavenly body above or below
the plane of the ecliptic, as m s p, fig. 8; when
above, it has north, and when below that plane,
it has south latitude.
Length of a wave.	The distance between two particles
of an undulating fluid similarly displaced
and moving similarly, consequently the length is
the distance between two consecutive hollows or
elevations.
Lens.	A transparent substance with curved surfaces.
The glasses of a telescope and of spectacles are
lenses. A lens may be convex on both sides,
or it may have both sides concave; one side
may be convex and the other concave; one side
plane and the other convex; or lastly, one side
may be plane and the other concave.
Libration.	A balancing motion.
Lines of the second order.	The circle, ellipse, parabola,
hyperbola, and generally such as are expressed
algebraically by a quadratic equation.
See Curves of the second order.
Lines of no variation.	Imaginary lines passing
through all places where the needle of the mariner's
compass points to the true north, that is, to
the pole of the earth's rotation.
Lines of perpetual snow.	Imaginary lines passing
through the limits of perpetual snow from the
equator to the poles.
Longitude.	Terrestrial longitude is the angular distance
of a place from a Meridian arbitrarily
chosen, such as that of Greenwich.
Longitude of a heavenly body.	The true longitude
of a planet, as of m, fig 8. is its angular distance
Y s m from Y the vernal equinox, estimated on
its elliptical orbit; its mean longitude is its angular
distance from the same point, supposing
the planet to move equably in a circle whose
radius is equal to the mean distance of the body
from the sun. The difference between the two
is the equation of the centre.
Longitude of the perihelion. The angular distance
of the perihelion of an orbit from the vernal
equinox, as Y S P fig. 8.
Longitude of the node.	The angular distance of the
node of an orbit from the vernal equinox as, Y S N
fig. 8.
Longitude of the.epoch.	The angular distance of a
celestial body from the vernal equinox at the
instant assumed as the origin of time whence all
its subsequent and antecedent longitudes are
estimated.
Lunar distance.	The angular distance of the centre
of a celestial object from the centre of the moon.
Magnetic equator.	The imaginary line passing
through those places where there is no dip, that
is where the compass needle is horizontal. It
encircles the earth, but does not coincide with
the terrestrial equator.
Magnetic meridian.	The vertical plane passing
through the direction of the needle of the compass
at any place.
Magnetic poles.	Points of the earth where the intensity
of the magnetic force is greatest.
Magnetic induction.	The effect of magnets to
excite magnetism in bodies near them.
Magneto-electric induction.	The effect of galvanic
currents to produce magnetism in bodies
near them capable of receiving it.
Major axis or greatest diameter of an ellipse	See
Ellipse, A B, fig. 2.
Mass.	The quantity of matter in a body. it is proportional
to the density and volume conjointly.
Mathematics.	The science of number and quantity.
Mean distance.	The mean distance of a planet from
the sun, or of a satellite from its planet, is equal
to  half the major axis of its orbit.
Mean longitude.	See Longitude.
Mean motion.	Equable motion in a circular orbit at
the mean distance during the same time that
the body accomplishes a revolution in its elliptical
orbit.
Mean time.	The time shown by clocks and watches
well regulated.
Mechanics.	The science of the equilibrium and
motion of bodies.
Meridian.	A vertical plane passing through the
poles of the earth.
Meteorites.	Stones which fall from the heavens.
Mica.	A certain mineral.
Minor axis.	See Ellipse.
Minus.	Less. The sign of Subtraction.
Molecules.	The indefinitely small or ultimate particles
of matter.
Momentum.	Force measured by the mass and
simple velocity conjointly.
Monocotyledonous plants.	Such as have seeds of
one lobe.
Moon's southing.	The time when the moon comes to
the meridian of any place, which happens, about
forty-eight minutes later each day.
Multiple systems of stars.	Three or more stars revolving
about their common centre of gravity.,
Nebulæ.	White misty appearance in the heavens
like the milky way; some of them, when viewed
with powerful telescopes, are found to be clusters
of stars, others always retain the cloudy form.
Nebulosity of comets.	The coma or misty appearance
which always surrounds their heads, and
of which their whole mass is often composed.
Nickel.	A metal.
Nodes.	The two opposite points N and n, fig. 8, in
which the orbit N A n P of a planet or comet
intersects the plane C N E n of the ecliptic. Part,
N A n, of the orbit lies above the plane of the
ecliptic, and part, n P N, below it. The ascending
node N is the point through which the body
passes in rising above the plane of the ecliptic,
and the descending node n is the point in which
the body sinks below it. The nodes of a satellite's
orbit are the points in which it intersects
the plane of the orbit of its primary.
Nodes, line of.	The intersection N n, fig. 8. of the
plane of the orbit of a planet or comet with the
plane of the ecliptic. It passes through S, the
centre of the sun.
Nodal points.	Points of a sonorous body which
remain at rest during its vibrations.
Nodal lines.	Lines of sonorous surfaces which remain
at rest during their vibrations.
Non-electric's.	Substances in which electricity cannot
be sensibly excited by friction.
Nucleus of a comet.	The part of its head which
appears to be dense. Frequently they have
none.
Nucleus of the earth.	The solid part.
Nutation.	A variation in the obliquity of the ecliptic
from the attraction of the sun and Moon on the
protuberant matter at the terrestrial equator.
Natation of the lunar orbit.	A variation in the
inclination of the lunar orbit from the action of
the matter at the earth's equator on the moon.
It is the reaction of terrestrial nutation.
Oasis.	A fertile spot in a desert.
Oblate spheroid.	A solid like an orange,which may
be formed by the rotation of an ellipse about its
minor axis, and is therefore flattened at the
poles.
Obliquity of the ecliptic.	The angle formed by the
plane of the terrestrial equator with the plane
of the ecliptic.
Oscillation.	A motion to and fro, like the pendulum
of a clock.
Occultation.	The eclipse of a star or planet by the
moon or by another planet.
Opposition.	A body is said to be in opposition when
its longitude differs from that of the sun by 180°.
Optics	The science of light and colours.
Optic axis of a crystal.	A ray of passing
through a doubly refracting crystal, such as Iceland
spar, is generally divided into two rays, but
in certain directions it is transmitted in one ray
only: these directions are called the optic axes of
a crystal.
Orbit.	The track or path of a celestial body in the
heavens.
Ordinary refraction.	See Refraction.
Ordinary ray.	See Refraction.
Parabola.	One of the conic sections. It is the line
described by a cannon ball, and has two infinite
branches; A B, A D, fig. 3. and there is a point F
within it called the focus, to which every point
in the curve bears a certain relation.
Parabolic elements.	See Elements of an orbit.
Parallax.	The angle under which we view an
object; it therefore diminishes as the distance
increases.
Parallax of a celestial object.	The angle which, the
radius of the earth would be seen under, if
viewed from that object.
Parallax, horizontal.	The parallax of a celestial
body when in the horizon. Parallax is then at
its maximum; it decreases as the height of the
by above the horizon increases.
Parallax, annual.	The angle which the diameter of
the earth's orbit would be seen under, if viewed
from a celestial body, as a fixed star.
Parallactic motion.	The motion of a body is said to
be parallactic when the space described by it
subtends or is seen under a sensible angle.
Parallelogram.	A four-sided plane figure, A B, fig.
10. whose opposite sides are parallel: the dia
meter is the straight line joining two of its
opposite angles.
Passage at the perihelion.	The passage of a body
through the point of its orbit that is nearest to
the sun.
Penumbra.	The shadow or imperfect darkness which
precedes and follows an eclipse.
Perigee.	The points in which the sun and moon
are nearest to the earth.
Perihelion.	The point P fig. 8. of an orbit which is
nearest to the sun.
Perihelion distance.	The shortest distance of a
planet or comet from the sun, P S, fig. 8.
Periodic inequality.	An irregularity in the motion
of a celestial body requiring a comparatively
short time for its accomplishment.
Periodic time.	The time in which a planet or comet
performs a revolution round the sun, or a satellite
about its primary.
Perturbations.	Irregularities in the motions of bodies
from some disturbing cause.
Phanerogamous plants.	Such as have apparent
flowers and seeds.
Phases of the moon.	The periodic changes in the
enlightened part of her disc from a crescent to a
circle, depending upon her position with regard
to the sun and earth.
Phases of an undulation.	Alternate changes in the
surface or density of a fluid. The fluid particles in
the tops or in the hollows of a series of waves are
in the same phases, because their displacement
and motion are equal and in the same direction;
whereas the fluid particles in the tops of a series
of waves are in different phases from those in
the hollows, because the displacement and motion
of the first are equal, but opposite to those of the
second. For example: in waves of water, the particles
in the tops have arrived at their greatest
elevation, and are beginning to sink down,
whereas those in the hollows have reached their
greatest depression, and are beginning to rise up.
Phenomena.	Appearances.
Physical.	Belonging to material nature.
Physico-mathematical sciences.	Sciences in which
natural phenomena are explained by mathematical
reasoning.
Pitch in music.	The depth or shrillness of a note.
It depends upon the number of vibrations the
sonorous body makes in a second. The more
rapid the vibration the higher the pitch.
Plane.	Length and breadth without thickness.
Plane of reflection.	The plane passing through the
incident and reflected rays of light or sound as
S I, I R, fig. 9. It is perpendicular to the reflecting
surface.
Plane of refraction.	The plane passing through the
incident and refracted rays of light S I and I O,
fig. 13. It is perpendicular to the refracting
surface.
Plane of polarization.	The plane passing through
the incident and polarized ray. It is at right
angles to the plane of reflection, but deviates
from the plane of ordinary refraction.
Plus.	More; the sign of addition.
Polarity.	The tendency of magnetized bodies to
point to the magnetic poles of the earth.
Polarized Light.	Light which by reflection or refraction
at a certain angle, or by refraction in certain
crystals, has acquired the property of exhibitingopposite
effects in planes at right angles to each
other. This property is explained on the undulatory
theory by supposing the particles of the
ether to vibrate in one plane.
Polarization, circular.	The property which light
acquires, by transmission through quartz and
certain liquids, of producing a succession of appearances
which follow each other in a circular
order, as the thickness of the medium is increased.
This property is explained on the undulatory
theory by supposing the particles of the ether to
vibrate in circles one after the other, the undulatin
going on in a circular helix like a corkscrew
penetrating a cork.
Polarization, elliptical.	The property which light
acquires, by reflection at the surfaces of metals
and in other ways, of producing appearances
partly analogous to those of circular polarization.
It is explained by supposing the undulation to
follow the course of an elliptical helix.
Poles.	The extremities of the axis about which a
body revolves.
Poles of the earth.	The extremities of the axis of
diurnal rotation.
Poles, magnetic.	Points in the earth where the intensity
of the magnetic force is a maximum. Of
these there are certainly three, probably four, all
of which differ from the poles of rotation.
Poles of a magnet.	Points in a magnet where the
intensity of the magnetic force is a maximum;
one of these attracts and another repels the same
pole of another magnet.
Poles of maximum cold.	Points in the surface of
the earth where the mean annual temperature is
a maximum. There are several, but none of
them coincide with the poles of rotation.
Precession of the equinoxes.	A retrograde motion of
the equinoctial points in consequence of the
action of the sun and moon upon the protuberant
matter at the earth's equator.
Primary.	In astronomy signifies the planet about
which a satellite revolves.
Prism.	A triangularly or polygonally shaped piece
of glass or other substance, like,a three or more
cornered stick, as fig. 11.
Prism, a doubly refracting.	A prism made of a
doubly refracting substance, as Iceland spar.
Prismatic colours.	The colours of the rainbow.
Projected.	Thrown; transferred by means of lines.
Projection.	A line or surface is said to be projected
upon a plane when parallel straight lines are
drawn from every point of them to the plane.
The projection of an orbit is therefore its daylight
shadow, since the sun's rays are sensibly
parallel.
Prolate spheroid.	A solid figure something like an
egg. See Ellipsoid.
Pulse.	A vibration.
Pyramid.	A solid bounded by a base having several
sides, and by a number of triangular planes whos
summits meet in one point called the apex, at
fig.12.
Pyrometer.	An instrument for measuring intensity
degrees of heat.
Quadrant.	Ninety degrees, the fourth part of a
circle.
Quadrature.	A celestial body is said to be in quadrature
when it is ninety degrees distant from
the sun.
Quartz.	Rock crystal; a siliceous mineral whose
primitive form is a rhomboid, fig. 14, but it is
generally crystallized in six-sided prisms terminated
by six-sided pyramids.
Radiation.	An emission of rays.
Radius, equatorial.	A line drawn from the centre
of a spheroid to its equator.
Radius, polar.	A line drawn from the centre of a
spheroid to its pole.
Radius of a sphere.	Any straight line drawn from
the centre of a sphere to its circumference.
Radius vector.	The imaginary line joining the
centre of the sun and the centre of a planet or
comet, or the centre of a planet and that of its
satellite, as s m, fig. 8.
Ratio.	A fraction expressing the relation which one
quantity bears to another. Proportion is the
equality of ratios.
Rectangle.	A four-sided plane figure, in which all
the angles are right angles, and its opposite sides
equal and parallel. When all the sides are
equal, it is a square.
Reflection.	The bending back of rays of light or
sound from a surface. The angles made by the
rays with a perpendicular to the surface, in
coming and going, are equal. If the ray, S I
(fig. 9) be reflected by a surface A B, in the direction
I R, then the angle S I P is equal
to R I P.
Refraction.	The bending or breaking of a ray of
light in passing through media of different densities,
as in going from air into water or glass,
and the contrary. If G g (fig. 13.) be a refracting
medium, as a piece of glass, then S I is
the incident, and I O the refracting ray.
Refraction, ordinary.	Light is said to suffer ordinary
refraction, when both the incident and refracted
rays are in a plane at right angles to the refracting
surface. This plane is called the plane
of ordinary refraction, and the refracted ray is
named the ordinary ray.
Refraction, extraordinary.	Light is said to suffer
extraordinary refraction, when it is refracted in
a different plane from that of ordinary refraction.
The plane in question is called the plane of
extraordinary refraction, and the ray so refracted
is named the extraordinary ray. In Iceland
spar, and other doubly refracting substances,
with one optic axis, the incident ray is split into
two, one of which, suffers ordinary, and the other
extraordinary refraction, but in all doubly refracting
substances, having two optic axes, both
rays suffer extraordinary refraction.
Resulting force.	The force resulting from the joint
effects of a number of forces.
Retrograde Motion of a celestial body.	Its motion
from east to west, or contrary to the signs of the
zodiac.
Revolution of a planet.	Its motion round the sun.
Revolution, sidereal.	The consecutive returns of a
planet to the same star.
Revolution, tropical.	The consecutive returns of a
planet to the same tropic or equinox.
Rhomb.	A plane four-sided figure, whose opposite
sides are equal and parallel, but all its sides are
not equal, nor are its angles right angles,
Rhomboid or rhombohedron.	A solid formed by six
planes; the opposite planes being equal and
similar rhombs parallel to one another, but all the
planes are not necessarily equal nor similar, nor
are its angles right angles (Fig. 14.)
Rotation.	The motion of a body round an axis,
Sauri or Saurians.	Reptiles of the lizard kind, as
crocodiles.
Secular inequalities.	Variations in the motions of
the heavenly bodies, requiring many ages for
their accomplishment.
Sidereal day.	The time included between two consecutive
transits of the same star at the same
meridian.
Sidereal year.	The time included between two consecutive
returns of the sun to the same star.
Sine.	The perpendicular drawn from the extremity
of an arc to the diameter of a circle, C D, (fig. 5,)
is the sine of the arc C B.
Solstices.	The points in which the sun is farthest
from the equator.
Solar spectrum.	The coloured image of the sun
refracted through a prism.
Space.	The boundless region which contains all
creation.
Species of plants.	Plants of the same kind.
Sphere.	A solid formed by the rotation of a semicircle
about its diameter.
Spheroid of revolution, or Ellipsoid.	A solid formed
by the revolution of an ellipse about one of its
axes. The spheroid will be oblate or prolate, according
as the revolution is performed about the
minor or major axis of the ellipse. Spheroids
are sometimes irregular in their form.
Spiral.	A curve like a watch spring. It may be circular,
like a thread wound about a round rod; or
elliptical, like a thread winding about an oval
stick.
Stratum.	A layer.
Subtend.	To be opposite. In fig. 5, the arc C B
subtends the angle C A B.
Sulphate of lime.	A mineral capable of being split
into thin transparent plates: it consists of 32.7
of lime, 46.3 of sulphuric acid, and 21 of water.
Synodic revolution of the moon.	The time between
two consecutive new or full moons.
Syzygies.	The points in the moons orbit where she
is new or full.
Tangent.	A straight line touching a curve in one
point, as T t in fig. 2.
Tangential force.	A force in the direction of the
tangent.
Time, true.	Time shown by a dial, or apparent
time.
Time, mean.	Time shown by ordinary clocks and
watches.
Thermo-electric currents.	Streams of electricity, excited
by heat.
Transit.	The passage of a body across the meridian
of a place.
Transit of Venus and Mercury.	The apparent passage
of these planets across the sun's disc.
Trigonometrical measurements.	Mensuration of the
surface of the earth by a series of triangles.
Tropical year.	The period between the consecutive
returns of the sun to the same tropic or solstice.
True distance.	The actual distance of a body from
the sun, or of a satellite from its planet.
Undulation.	A wave.
Undulatory theory.	The mechanical principles of
the motion of waves.
Vapour.	Steam.
Variation.	A periodic inequality in the motion of
the moon.
Variation of the compass.	The deviation of the
compass needle from the true north.
Vertical.	The direction of the plumb-line.
Vertical plane.	A plane passing through the plumbline,
consequently at right angles to the horizon.
Vesicles.	Small hollow spheres of water.
Vibration.	A motion to and fro.
Visual ray.	A ray of light coming from any object
to the eye.
Volta-electric induction.	The disposition of electric
currents to produce similar currents in bodies
near them capable of receiving them.
