NormalizeHEADmain

8 files changed, 17 insertions, 6092 deletions

diff --git a/.gitattributes b/.gitattributes
new file mode 100644
index 0000000..d7b82bc
--- /dev/null
+++ b/.gitattributes
@@ -0,0 +1,4 @@
+*.txt text eol=lf
+*.htm text eol=lf
+*.html text eol=lf
+*.md text eol=lf
diff --git a/LICENSE.txt b/LICENSE.txt
new file mode 100644
index 0000000..6312041
--- /dev/null
+++ b/LICENSE.txt
@@ -0,0 +1,11 @@
+This eBook, including all associated images, markup, improvements,
+metadata, and any other content or labor, has been confirmed to be
+in the PUBLIC DOMAIN IN THE UNITED STATES.
+
+Procedures for determining public domain status are described in
+the "Copyright How-To" at https://www.gutenberg.org.
+
+No investigation has been made concerning possible copyrights in
+jurisdictions other than the United States. Anyone seeking to utilize
+this eBook outside of the United States should confirm copyright
+status under the laws that apply to them.
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..66faadf
--- /dev/null
+++ b/README.md
@@ -0,0 +1,2 @@
+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #67386 (https://www.gutenberg.org/ebooks/67386)
diff --git a/old/67386-0.txt b/old/67386-0.txt
deleted file mode 100644
index ddf4590..0000000
--- a/old/67386-0.txt
+++ /dev/null
@@ -1,2789 +0,0 @@
-The Project Gutenberg eBook of A Preliminary Dissertation on the
-Mechanisms of the Heavens, by Mary Somerville
-
-This eBook is for the use of anyone anywhere in the United States and
-most other parts of the world at no cost and with almost no restrictions
-whatsoever. You may copy it, give it away or re-use it under the terms
-of the Project Gutenberg License included with this eBook or online at
-www.gutenberg.org. If you are not located in the United States, you
-will have to check the laws of the country where you are located before
-using this eBook.
-
-Title: A Preliminary Dissertation on the Mechanisms of the Heavens
-
-Author: Mary Somerville
-
-Release Date: February 12, 2022 [eBook #67386]
-
-Language: English
-
-Produced by: Laura Natal Rodrigues (Images generously made available by
-             Hathi Trust Digital Library.)
-
-*** START OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON
-THE MECHANISMS OF THE HEAVENS ***
-
-
-A
-
-PRELIMINARY DISSERTATION
-
-ON THE
-
-MECHANISM OF THE HEAVENS.
-
-
-
-BY
-
-MRS. SOMMERVILLE
-
-
-
-
-PHILADELPHIA:
-CAREY & LEA
-
-1832
-
-
-
-
-In order to convey some idea of the object of this work, it may be
-useful to offer a few preliminary observations on the nature of the
-subject which it is intended to investigate, and of the means that have
-already been adopted with so much success to bring within the reach of
-our faculties, those truths which might seem to be placed so far beyond
-them.
-
-All the knowledge we possess of external objects is founded upon
-experience, which furnishes a knowledge of facts, and the comparison of
-these facts establishes relations, from which, induction, the intuitive
-belief that like causes will produce like effects, leads us to general
-laws. Thus, experience teaches that bodies fall at the surface of the
-earth with an accelerated velocity, and proportional to their masses.
-Newton proved, by comparison, 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 combined efforts of astronomers, from the earliest dawn of
-civilization, have been requisite 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 system of the world has been so completely
-explained, that 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 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
-limits. 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 us 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 which seem so mighty to us
-must 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 or creation.
-
-A complete acquaintance with Physical Astronomy can only be attained by
-those who are well versed in the higher branches of mathematical and
-mechanical science: such alone can appreciate the extreme beauty of
-the results, and of the means by which these results are obtained.
-Nevertheless 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 possibly overrating them by not making a
-sufficient 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 truth, whether it be
-in the discovery of a world, or of a new property of numbers.
-
-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 name manner as
-if its mass, 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 each other,
-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 ⅓, 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, 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 her 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; but as experience shows that the action and reaction 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 be supposed
-to be 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
-reaction, each body is itself the centre of an attractive force
-extending indefinitely in space, whence proceed all the mutual
-disturbances that 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 taken in mass; 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
-in other respects they also would 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, which is impossible.
-
-The form of the planets results 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 when these two forces are balanced by an increase of
-gravity; therefore, as the attractive force is the same on 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. 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, differs but little from a
-sphere. Although the planets attract each other as if they were spheres
-on account of their immense 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 nutation 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 receives 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 give it 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 progression,
-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 that
-would in no way interfere with their relative motions; for, in
-consequence of our experience 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 the rotation and translation of the planets are
-independent of each other, though probably communicated by the same
-impulse, they form separate subjects of investigation.
-
-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 a planet is in its aphelion or at the
-point where the orbit is farthest from the sun, his action overcomes its
-velocity, and brings it towards him with such an accelerated motion,
-that it at last overcomes the sun's attraction, and shoots past him;
-then, gradually decreasing in velocity, 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 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
-immensely 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, and 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 the existence of disturbing forces.
-
-To determine 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 arises the celebrated
-problem of the three bodies, which originally was that of 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 position at any given instant.
-
-By this problem the motions of translation of all the celestial bodies
-are determined. It is one of extreme difficulty, and would be of
-infinitely greater difficulty, 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 on 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
-on 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 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 immensely
-greater than those of the planets; and as their inequalities bear 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.
-
-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 it 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 the orbit intersects the
-plane of the ecliptic are its nodes.
-
-The orbits of the recently discovered planets deviate more from the
-ecliptic: that of Pallas has an inclination of 35° to it: on that
-account it will be 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.
-
-The planets are subject to disturbances of two distinct 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 troubled 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 on 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 disturbances of this kind, the apsides, or extremities
-of the major axes of all the orbits, have a direct, but variable motion
-in space, excepting those of Venus, which are retrograde; and the lines
-of the nodes move with a variable velocity in the contrary direction.
-The motions of both are extremely slow; it requires more than 109770
-years for the major axis of the earth's orbit to accomplish a sidereal
-revolution, and 20935 years to complete its tropical motion. The major
-axis of Jupiter's orbit requires no less than 197561 years to perform
-its revolution from the disturbing action of Saturn alone. The periods
-in which the nodes revolve are also very great. Beside 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 six minutes less now than it was in the age of Ptolemy. The
-terrestrial eccentricity is decreasing at the rate of 3914 miles in a
-century; and if it were to decrease equably, it would be 36300 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 is in a state of perpetual change.
-Minute as these changes are, they might be supposed liable 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. The
-consequences being so dreadful, it is natural to inquire, what proof
-exists that creation will be preserved from such a catastrophe? For
-nothing can be known from observation, since the existence of the human
-race has occupied 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, as well secular as periodic, are
-expressed analytically by the sines and cosines of circular arcs, which
-increase with the time; and as a sine or cosine never can 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 then
-begin a new course, thus for ever oscillating about a mean value. This,
-however, would not be the case 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. But if the planets do move in an ethereal medium,
-it must be of extreme rarity, since its resistance has hitherto been
-quite insensible.
-
-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 revolution of all the bodies,
-as well planets as satellites, in the same direction. These, however,
-are not necessary conditions: the periodicity of the terms in which the
-inequalities are expressed is sufficient 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 52"·109, occasioned by the reciprocal action
-of the planets; but as this is also periodical, the terrestrial equator,
-which is inclined to it at an angle of about 23° 28', 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 untroubled by foreign causes.
-
-
-                   Yonder starry sphere
-     Of planets, and of fix'd, in all her wheels
-     Resembles nearest, mazes intricate,
-     Eccentric, intervolv'd, 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
-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. This difficulty is obviated by La Place, who has shown
-that whatever changes time may induce either in the orbits themselves,
-or in the plane of the ecliptic, there exists an invariable plane
-passing through the centre of gravity of the sun, about which the whole
-system oscillates within narrow limits, and which is determined by this
-property; that if every body in the system be projected on it, and if
-the mass of each be multiplied by the area described in a given time by
-its projection on this plane, the sum of all these products will be a
-maximum. 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 remains parallel to itself, and
-maintains a fixed position, whence the oscillations of the system may be
-estimated through unlimited time. It is situate nearly half way between
-the orbits of Jupiter and Saturn, and is inclined to the ecliptic at an
-angle of about 1° 35' 31".
-
-All the periodic and secular inequalities deduced from the law of
-gravitation are so perfectly confirmed by observations, 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 great inequalities of very long periods, forming
-what appeared an 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 inequality in the mean
-motion of each of these planets, which completes its period in nearly
-929 Julian years, the one being retarded, while the other is
-accelerated. These inequalities are strictly periodical, since they
-depend on 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 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 those bodies were united in their common centre
-of gravity; the action of the sun however disturbs in some degree the
-motion of the satellites about their primary.
-
-The changes that take place in the planetary system are exhibited on a
-small 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
-centuries. 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 further 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 motion of the nodes of these little bodies is so much more rapid
-than those of the planet. The nodes of the fourth satellite accomplish a
-revolution in 520 years, while those of Jupiter's orbit require no less
-than 50673 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
-further the satellite is removed, a circumstance entirely owing to the
-influence of Jupiter's compression.
-
-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. 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 planet. 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 or a discovery, which, though not so immediately
-applicable to the wants of man, unfolds a property 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 16' 26" 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 192
-millions of miles; whence it is estimated, that light travels at the
-rate of 192000 miles in one second. Such is its velocity, that the
-earth, moving at the rate of nineteen 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 that 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, when Jupiter is in conjunction, we
-see him by means of rays that left him 16' 26" before; but during that
-time we have changed our position, in consequence of the motion of the
-earth in its orbit; we therefore 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 192000 to 19. In consequence of
-aberration, none of the heavenly bodies are in the place in which they
-seem to be. 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 be 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 never
-exceeds twenty seconds, 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 apparently the most unpromising and dissimilar
-circumstances, occur in 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, which hypothesis 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 its compression. The orbits of its satellites are nearly
-perpendicular to the plane of the ecliptic.
-
-Our constant companion the moon next claims 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. Neither the
-eccentricity of the lunar orbit, nor its inclination to the plane of the
-ecliptic, have experienced any changes from secular inequalities; but
-the mean motion, the nodes, and the perigee, are subject to very
-remarkable variations.
-
-From an eclipse observed at Babylon by the Chaldeans, 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 back 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 the 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, and it was at one time attributed to the
-resistance of an ethereal medium pervading space; 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 latter from such a cause being
-inseparably connected with variations in the two former of these
-elements. That great mathematician, however, in studying the theory of
-Jupiter's satellites, perceived that the secular variations in the
-elements of Jupiter's orbit, from the action of the planets, occasion
-corresponding changes in the motions of the satellites: this led him to
-suspect that the acceleration in the mean motion of the moon might be
-connected with the secular variation in the eccentricity of the
-terrestrial orbit; and analysis has proved that he assigned the true
-cause.
-
-If the eccentricity 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; but it would be periodic,
-since it would be the same as often as the sun, the earth, and the moon
-returned to the same relative positions: on account however of the slow
-and incessant diminution in the eccentricity 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 which is
-very 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
-eccentricity diminishes, the moon's mean motion will be accelerated; but
-when the eccentricity 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 10", 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 eccentricity, 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 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; the former, though they recede during
-the greater part of the moon's revolution, and advance during the
-smaller, perform their sidereal revolutions in 6793^days.4212, and the
-latter, though its motion is sometimes retrograde and sometimes direct,
-in 3232^days.5807, or a little more than nine years: 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 109770 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 motion of 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 eccentricity
-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 latitude; and, 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 diameter to the diameter
-of the equator is 1/305.05. 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, it would assume the form of a spheroid, whose compression is
-1/230. Whence it appears, that the earth is not homogeneous, but 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 Jupiter's
-satellites prove that his mass is not homogeneous, and that his
-compression is 1/13·8.
-
-The motions of the moon have now become of more importance to the
-navigator and geographer than those of any other body, from the
-precision with which the longitude is determined by the occultations of
-stars and lunar distances. The lunar theory is brought to such
-perfection, that the times of these phenomena, observed under any
-meridian, when compared with that computed for Greenwich in the Nautical
-Almanack, gives 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 distance of the sun and
-moon from the earth is obtained: whence it appears that the sun's
-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
-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 be very great
-indeed, to be visible at all from the celestial bodies. But the globe
-itself whose dimensions are ascertained by actual admeasurement,
-furnishes a standard of measures, with which we compare the distances,
-masses, densities, and volumes of the sun and planets.
-
-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, at any rate, quite 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 gravity, 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 contemporaneously the same noon. 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; a comparison of the length of
-the degrees in different parts of the earth's surface will therefore
-determine its size and form.
-
-An arc 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 inequalities 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 is spherical, they
-require a correction to reduce them from plane to spherical triangles.
-
-Arcs of the meridian have been measured in a variety of latitudes, both
-north and south, as well as arcs perpendicular to the meridian. From
-these measurements it appears that the length of the degrees increase
-from the equator to the poles, nearly as the square of the sine of the
-latitude; consequently, the convexity of the earth diminishes from the
-equator to the poles. Many discrepancies occur, but the figure that most
-nearly follows this law is an ellipsoid of revolution, whose equatorial
-radius is 3962.6 miles, and the polar radius 3949.7; the difference, or
-12.9 miles, divided by the equatorial radius, is 1/308·7, or 1/309
-nearly; 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 1/22 British miles; therefore
-360 degrees, or the whole circumference of the globe is 24856, and the
-diameter, which is something less than a third of the circumference, is
-7916 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 mensuration of an arc between Alexandria and Syene.
-
-But there is another method of finding the figure of the earth, 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, the force of gravity
-theoretically ought to increase, from the equator to the pole as the
-square of the sine of the latitude; but for a spheroid in rotation, by
-the laws of mechanics the centrifugal force varies 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 effects 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 in going 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 that they may
-always be performed in the same time, the length of the pendulum must
-be altered. Now, by numerous and very careful experiments, it is proved
-that a pendulum, which makes 86400 oscillations in a mean day at the
-equator, will do the same at every point of the earth's surface, if
-its length be increased in going to the pole, as the square of the
-sine of the latitude. From the mean of these it appears that the
-compression of the terrestrial spheroid is about 1/342, which does not
-differ much from that given by the lunar inequalities, and from the arcs
-of the meridian. 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 nutation 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 1/578.
-
-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 such discrepancies 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 1/320; that given by the lunar theory has the advantage
-of being independent of the irregularities at the earth's surface,
-and of local attractions. 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.
-
-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 that, when the moon is in the horizon at the
-instant of rising or setting, lines were 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 distances 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 3454"·2; whence the mean distance
-of the moon is about sixty times the mean terrestrial radius, or 240000
-miles nearly. Since the parallax is equal to the radius of the earth
-divided by the distance of the moon; under the same parallel of latitude
-it varies with the distance of the moon from the earth, and proves the
-ellipticity of the lunar orbit; and 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 so 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 by the transits of Venus that difficulty
-is obviated. 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 block 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 sun is not so remote but that
-the semidiameter of the earth has a sensible magnitude when viewed from
-his centre, 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 being the object of Cook's first voyage. The
-transit lasted about six hours at Otaheite, and the difference in the
-duration at these two stations was eight minutes; whence the sun's
-parallax was found to be 8"·72; but by other considerations it has
-subsequently been reduced to 8"·575; from which the mean distance of
-the sun appears to be about 95996000, or ninety-six millions of miles
-nearly. This is confirmed by an inequality in the motion of the moon,
-which depends on 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. 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 1843 millions of
-miles from the luminary that warms and enlivens the world; to it,
-situate on the verge of the system, the sun must appear 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 the most perfect 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
-20500000 millions of miles. At such a distance not only the terrestrial
-orbit shrinks to a point, but, where the whole solar system, when
-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 rationally be supposed to be
-situated many thousand times further 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.'
-
-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 greater than 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 1070.5 times less than the sun. The mass of the moon is
-determined from four different sources,--from her action on the
-terrestrial equator, which occasions the rotation 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 titles. 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 very much from each
-other; but, from her action in raising  the tides, which furnishes
-the fourth method, 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 diameter of a planet is to the real diameter of
-the earth, or 8000 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 1920", and with the solar parallax 8"·65, it will be found that
-the diameter of the sun is about 888000 miles; therefore, 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 240000 miles; so that twice the distance of
-the moon is 480000 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
-88000 miles is incomparably less than that of the sun The diameter of
-Pallas does not much exceed 71 miles, so that an inhabitant of that
-planet, in one of our steam-carriages, might go round his world in five
-or six hours.
-
-The oblate form of the celestial bodies indicates rotatory motion, and
-this has been confirmed, in most cases, by tracing spots on their
-surfaces, whence 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 ten hours, about an axis that is directed
-towards a point half way between the pole star and Lyra, the plane of
-rotation being inclined a little more than 70° to that on which the
-earth revolves. 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 as yet 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 about 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 from the primitive causes which have
-determined the planetary motions.
-
-The larger planets rotate in shorter periods than the smaller planets
-and the earth; their compression is consequently greater, and the action
-of the sun and of their satellites occasions a nutation 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. 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 surrounded by a ring even brighter than himself, which always remains
-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. 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 10 1/2 hours, 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 31°; and in consequence
-of this obliquity of position they always appear elliptical to us, but
-with an eccentricity so variable as even to be occasionally like a
-straight line drawn across the planet. At present the apparent axes of
-the rings are as 1000 to 160; and on the 29th of September, 1832,
-the plane of the rings will pass through the centre of the earth
-when they will be visible only with superior instruments, and will
-appear like a fine line across the disc of Saturn. On the 1st of
-December in the same year, the plane of the rings will pass through
-the centre of the sun.
-
-It is a singular result of the theory, that the rings could not maintain
-their stability of rotation if they were everywhere 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 the 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 eccentricity 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 the 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 other 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 the poles from her centrifugal
-force, therefore her polar axis is 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 earth and moon; so that it would vibrate 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 earthy it would
-have rendered the libration sensible. A similar libration exists in the
-motions of Jupiter's satellites; but although the comet of 1767 and 1779
-passed through the midst of them, their libration still remains
-insensible. It is true, the moon is liable to librations depending on
-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 moon exhibiting a surface thirteen times
-larger than ours, 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 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 that prevail throughout creation, the period of
-the earth's diurnal rotation is immutable. A fluid, as Mr. Babbage
-observes, in 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
-its 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 again by removing matter to a greater distance from the centre,
-destroy the velocity generated by its previous approach; so that the
-descent of the rivers does not affect the earth's rotation. Enormous
-masses projected by volcanoes from the equator to the poles, and the
-contrary, would indeed affect 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 an
-external 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 nature of fossil
-remains, that the mean temperature of the globe is decreasing.
-
-The high temperature of mines, hot springs, and above all, the internal
-fires that have produced, and do still occasion such devastation on our
-planet, indicate an augmentation of heat towards its centre the increase
-of density in the strata 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, 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. But even if this cause be
-sufficient to produce the observed effects, 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 hundredth 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 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 indication of the
-primitive fluidity of the earth, as there is no direct proof, it can
-only be regarded as a very probable hypothesis; but one of the most
-profound philosophers and elegant writers of modern times has found, in
-the secular variation of the eccentricity 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 8 higher degree than it
-would have were the sun extinguished, must 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, _cœteris 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 eccentricity 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 the other 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 of
-its orbit, which accomplishes a tropical revolution in 20935 years. In
-the year 1250 of our era, and 29653 years before it, the perigee
-coincided with the summer 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 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 ending to the new equator would leave some portions
-of the globe, and overwhelm others.
-
-But theory 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 some foreign
-cause, as the collision of a comet which may have happened in the
-immensity of time. Then indeed, the equilibrium could only have been
-restored by the rushing of the seas to the new equator, which they would
-continue to do, till the surface was every where 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
-even of the Pacific ocean is not more than four miles, whereas the
-equatorial radius of the earth exceeds the polar radius by twenty-five
-or thirty miles; consequently the influence of the sea on the direction
-of gravity is very small; and as it appears that a great change in the
-position of the axes is incompatible with the law of equilibrium, the
-geological phenomena must be ascribed to an internal cause. 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 axis on
-its surface, have undergone but slight variations.
-
-It is beyond a doubt that the strata increase in density from the
-surface of the earth to its centre, which is even proved by the lunar
-inequalities; and it is manifest from the mensuration of arcs of the
-meridian and the lengths of the seconds pendulum that the strata are
-elliptical and concentric. This certainly would 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
-these phenomena. 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
-4000 miles, the condensation of ordinary materials would surpass the
-utmost powers of conception. But a density so extreme is not borne out
-by astronomical observation. It might seem therefore to follow, 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. 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; but, from the experiments of Mr.
-Perkins, they appear to be capable of a greater degree of compression
-than has generally been imagined.
-
-It appears then, that the axis of rotation is invariable on the surface
-of the earth, and observation shows, 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 exterior 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 situated 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 about 23° 28', and the inclination of the lunar orbit on the
-same is nearly 5°; 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 about 50"·412 annually. The direct tendency of this action
-would be to make the planes of the equator and ecliptic coincide; but in
-consequence of the rotation of the earth, the inclination of the two
-planes remains constant, as a top in 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
-to the same points of the ecliptic, at least as far as this kind of
-action is concerned. But another and totally different cause operates on
-this motion, which 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 on
-the plane of the equator, and gives the equinoctial points a slow but
-direct motion on the ecliptic of 0"·312 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,
-but 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"·1 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 then 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"·1 annually, the equinoctial points will
-accomplish a revolution in 25868 years; but as the precession varies in
-different centuries, the extent of this period will be 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
-365.242264 days must be increased by the time he takes to move through
-an arc of 50"·1, in order to have the length of the sidereal year. By
-simple proportion it is the 0.014119th part of a day, so that the
-sidereal year is 365.256383.
-
-The mean annual precession is subject to a secular variation; for
-although the change in the plane of the ecliptic which is the orbit of
-the sun, 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 lime of Hipparchus; consequently the
-actual length of the tropical year is about 4"·154 shorter than it was
-at that time. The utmost change that it can experience from this cause
-amounts to 43".
-
-Such is the secular motion of the equinoxes, but it is sometimes
-increased and sometimes diminished by periodic variations, whose periods
-depend on the relative positions of the sun and moon with regard to the
-earth, and 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
-nineteen 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
-oblique of the ecliptic is annually diminished by 0"·52109. With
-regard to the fixed stars, this variation in the course of ages may
-amount to tea or eleven degrees; but the obliquity of the ecliptic to
-the equator can never vary more than two or three degrees, 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" and
-17"·08, and the mass of the earth is the 1/354936th 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 450 feet
-in a second; consequently if he were even habitable by human beings,
-they would be unable to move, since their weight would be thirty
-times as great as it is here. A moderate sized man would weigh about
-two tons at the surface of the sun. On the contrary, at the surface
-of the four new planets we should be so light, that it would be
-impossible to stand from the excess of our muscular force, for a man
-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; and
-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.
-
-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 to compare all great periods of
-time; 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 same 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 the meridian, or of
-one which is supposed to move in the equator, is denominated mean solar
-time, such as is given by clocks and watches in common life: when it is
-reckoned by the arrival of the real sun at the meridian, it is apparent
-time, such as is given by dials. The difference between the time shown
-by a clock and a dial is the equation of time given in the Nautical
-Almanac, and sometimes amounts to as much as sixteen minutes. The
-apparent and mean time coincide four times in the year.
-
-Astronomers begin the day at noon, but in common reckoning the day
-begins at midnight. In England it is divided into twenty-four hours,
-which are counted by twelve and twelve; but in France, astronomers
-adopting decimal division, divide the day into ten hours, the hour into
-one hundred minutes, and the minute into a hundred seconds, because of
-the facility in computation, and in conformity with their system of
-weights and measures. This subdivision is not used in common life, nor
-has it been adopted in any other country, though their scientific
-writers still employ that division of time. The mean length of the day,
-though accurately determined, is not sufficient for the purposes either
-of astronomy or civil life. The length of the year is pointed out by
-nature as a measure of long periods; but the incommensurability that
-exists between the lengths of the day, and the revolutions of the sun,
-renders it difficult to adjust the estimation of both in whole numbers.
-If the revolution of the sun were accomplished in 365 days, all the
-years would be of precisely the same number of days, and would begin and
-end with the sun at the same point of the ecliptic; but as the sun's
-revolution includes the fraction of a day, a civil year and a revolution
-of the sun have not the same duration. Since the fraction is nearly the
-fourth of a day, four years are nearly equal to four revolutions of the
-sun, so that the addition of a supernumerary day every fourth year
-nearly compensates the difference; but in process of time further
-correction will be necessary, because the fraction is less than the
-fourth of a day. 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 Cæsar; the
-25th of December in his 45th year, is considered as the date of Christ's
-nativity; and Cæsar's 46th 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 actually elapsed
-since that time.
-
-Some remarkable astronomical eras are determined by the position of the
-major axis of the solar ellipse. Moving at the rate of 61"·906
-annually, it accomplishes a tropical revolution in 20935 years. It
-coincided with the line of the equinoxes 4000 or 4089 years before the
-Christian era, much about the time chronologists assign for the creation
-of man. In 6485 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 1250 the major axis was perpendicular to the line
-of the equinoxes, and then the solar perigee coincided with the solstice
-of winter, and the apogee with the solstice of summer. On that account
-La Place proposed the year 1250 as a universal epoch, and that the
-vernal equinox of that year should be the first day of the first year.
-
-The variations in the positions of the solar ellipse occasion
-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 about seven days. These intervals will be
-equal towards the year 6485, when the perigee comes to the equinox of
-spring. Were the earth's orbit circular, the seasons would be equal;
-their differences arise from the eccentricity of the earth's orbit,
-small as it is; but the changes are so gradual 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 language, arts and
-sciences, leaving but confused masses of ruin 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 period 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 show to how many centuries they may be extended,
-without the fear of error. A few examples will show the importance of
-this 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 style 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 in the obliquity is known, both the time
-and place of the observations have been verified by computation from
-modern tables. Thus the Chinese had made some advances in the science of
-astronomy at that early period; the whole chronology of the Chinese is
-founded on the observations 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 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. 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 menu motion of Saturn was at the slowest, and that of Jupiter
-the most rapid. The periods in which that happened were 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 from computation it
-appears that  _χ_ Draconis was not very far from that place about 3000
-years ago; but as Eudoxus lived only about 2150 years ago, he must have
-described an anterior state of the heavens, supposed to be the same that
-was determined 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.
-
-A knowledge of astronomy leads to the interpretation of hieroglyphical
-characters, since astronomical signs are often found on the ancient
-Egyptian monuments, which were probably employed by the priests to
-record dates. On the ceiling of the portico of a temple among the ruins
-of Tentyris, there is a long row of figures of men and animals,
-following each other in the some direction among these are the twelve
-signs of the zodiac, placed according to the motion of the sun: it is
-probable that the first figure in the procession represents the
-beginning of the year. Now the first is the Lion as if coming out of the
-temple; and as it is well known that the agricultural year of the
-Egyptians commenced at the solstice of summer, the epoch of the
-inundations of the Nile, if the preceding hypothesis be true, the
-solstice at the time the temple was built must have happened in the
-constellation of the lion; but as the solstice now happens 21° 6' north
-of the constellation of the Twins, it is easy to compute that the zodiac
-of Tentyris must have been made 4000 years ago.
-
-The author had occasion to witness an instance of this most interesting
-application of astronomy, in ascertaining the dale 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 not only
-to his country, but 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 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, in parts of the imperial standard yard,
-to be 39.1387 inches. The weight of a cubic inch of water at the
-temperature of 62° Fahrenheit, barometer 30, 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 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 vicissitudes 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 subdivision in taking its ten millionth part. The
-French have adopted the decimal division not only in time, but in their
-degrees, weights, and measures, which affords very great facility 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 the 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 Yunus made
-his observations at Cairo, about the year 1000, the Arabians were in the
-habit of employing the vibrations of the pendulum in their astronomical
-observations.
-
-One of the most immediate and striking 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 24^h 50^m 48^s of mean solar
-time. As it depends on the action of the sun and moon, it is classed
-among astronomical problems, of which it is by far the most difficult
-and 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 mechanical
-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, 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 on the motion of the
-disturbing body in its orbit, they are of long periods. The second kind
-of oscillations depends on the rotation of the earth, therefore their
-period is nearly a day: and the oscillations of the third kind depend on
-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 on the second. At the time of the solstices,
-this difference which, according to Newton's theory, ought to be very
-great, 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, were it
-not for 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 in the earth's axis, are the same as if the
-sea formed one solid mass with the earth.
-
-The third kind of oscillations are the semidiurnal 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, in 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 this tendency diminishes. 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 this tendency again diminishes. 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 above the
-surface of equilibrium of nearly the same height; 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 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 really 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 instantly assuming the form of equilibrium, 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 on 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 the meridian at 90° distant,
-it is everywhere low water. It is evident that these tides must happen
-twice in a day, since in that time the rotation of the earth brings the
-same point twice under the meridian of the moon, once under the superior
-and once under the inferior meridian.
-
-In the semidiurnal tides there are two phenomena particularly to be
-distinguished, one that happens 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 the
-full tide, the lower it is in the ebb. The neap tides lake 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. It is evident that the spring tides must happen twice 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° 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. Beside these remarkable variations, there are
-others arising from the declination of the moon, which has a great
-influence on the ebb and flow of the waters.
-
-Both the height and time of high water are thus perpetually changing;
-therefore, in solving the problem, it is required to determine the
-heights to which they rise, the times at which they happen, and the
-daily variations.
-
-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, 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, the resistance the waters meet with, all of
-them causes which 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 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 funeral phenomena which ought to
-result from the attraction of the sun and moon, but these must be
-corrected in each particular case by those local observations which are
-modified by the extent and depth of the sea, and the peculiar
-circumstances of the port.
-
-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, and from that 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 great combined wave, reflected by the shores of the
-Atlantic, extending nearly from pole to pole, still coming northward,
-occurs through the Irish and British channels into the North sea, so
-that the tides in our ports are modified by those of another hemisphere.
-Thus 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. 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 one. 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 commotions in the waters of the ocean are occasioned by
-forces that bear a very small proportion to terrestrial gravitation: the
-sun's action in raising the ocean is only the 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. From this
-ratio the mass of the moon is found to be only 1/15 part of that of the
-earth. 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, 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.
-
-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 the particles of matter 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. Now at the
-temperature of melting ice, the density of mercury is to that of air as
-10320 to 1; and as the mean height of the barometer is 29.528 inches,
-the height of the atmosphere by simple proportion is 30407 feet, at the
-mean temperature of 62°, or 34153 feet, which is 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 occasion periodic variations in the
-heights of the barometer. These, however, are so extremely small, that
-their existence in latitudes so far removed from the equator is
-doubtful; a series of observations within the tropics can alone decide
-this delicate point. 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 currents in the direction of the meridian. But the
-rotatory velocity of the air corresponding to its geographical situation
-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 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.
-
-The sun and most of the planets appear to be surrounded with atmospheres
-of considerable density. The attraction of the earth has probably
-deprived the moon of hers, for the refraction of the air at the surface
-of the earth is at least a thousand times as great as at 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.
-
-Many philosophers of the highest authority concur in the belief that
-light consists in the undulations of a highly elastic ethereal medium
-pervading space, which, communicated to the optic nerves produce the
-phenomena of vision. The experiments of our illustrious countryman, Dr.
-Thomas Young, and those of the celebrated Fresnel, show that this theory
-accords better with all the observed phenomena than that of the emission
-of particles from the luminous body. As sound is propagated by the
-undulations of the air, its theory is in a great many respects similar
-to that of light. 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 notes of the organ to the
-highest known cry of insects, as of the cricket, includes about nine
-octaves.
-
-The undulations of light are much more rapid than those of sound, but
-they are analogous in this respect, that as the frequency of the
-pulsations in sound increases from the low tones to the higher, so those
-of light augment in frequency, from the red rays of the solar spectrum
-to the extreme violet. By the experiments of Sir William Herschel, it
-appears that the heat communicated by the spectrum increases from the
-violet to the red rays; but that the maximum of the hot invisible rays
-is beyond the extreme red. Heat in all probability consists, like light
-and sound, 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 by 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
-undulating theories are perfectly similar. If, therefore, we may judge
-from analogy, the undulations 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 requires a much denser medium than that of
-either 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.
-
-What the body of the sun may be, it is impossible to conjecture; but he
-seems to be surrounded by an ocean of flame through which his dark
-nucleus appears like black spots, often of enormous size. The solar
-rays, which probably arise from the 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 where such combustion is going on, as
-the intensity both of his light and heat diminishes with the square of
-the distance, his kindly influence can hardly be felt at the boundaries
-of our system. Much depends on the manner in which the rays fall, as we
-readily perceive from the different climates on our globe. In winter the
-earth is nearer the sun by 1/30th 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; that is however 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, unless indeed the
-ether has a temperature. 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 quick-silver, 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 a 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 imparts no heat, even when brought to a focus by a mirror.
-
-In adverting to the peculiarities in the form and nature of the earth
-and planets, it is impossible to pass in silence the magnetism of the
-earth, the director of the mariner's compass, and his guide through the
-ocean. This property probably arises from metallic iron in the interior
-of the earth, or from the circulation of currents of electricity round
-it: its influence extends over every part of its surface, but its
-accumulation and deficiency determine the two poles of this great
-magnet, which are by no means the same as 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 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. In the year 1819, Captain Parry, in his voyage to
-discover the north-west passage round America, sailed directly over the
-magnetic pole; and in 1824, Captain Lyon, when on en expedition for the
-same purpose, found that the variation of the compass was 37° 30'
-west, and that the magnetic pole was then situate in 63° 26' 51"
-north latitude, and in 80° 51' 25" west longitude. It appears
-however from later researches that the law of terrestrial magnetism is
-of considerable complication, and the existence of more than one
-magnetic pole in either hemisphere has been rendered highly probable.
-The needle is also subject to diurnal variations; in our latitudes it
-moves slowly westward from about three in the morning till two, and
-returns to its former position in the evening.
-
-A needle suspended so as only to be moveable in the vertical plane, dips
-or become more and more inclined to the horizon the nearer it is brought
-to the magnetic pole. Captain Lyon found that the dip in the latitude
-and longitude mentioned was 86° 32'. What properties the planets may
-have in this respect, it is impossible to know, but it is probable that
-the moon has become highly magnetic, in consequence of her proximity to
-the earth, and because her greatest diameter always points towards it.
-
-The passage of comets has never sensibly disturbed the stability of the
-solar system; their nucleus is 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 effect. The comet of 1770 passed
-within 80000 miles of the earth without even affecting our tides, and
-swept through the midst of Jupiter's satellites without deranging the
-motions of those little moons. Had the mass of that comet been equal to
-the mass of the earth, its disturbing action would have shortened the
-year by the ninth of a day; but, as Delambre's computations from the
-Greenwich observations of the sun, show that the length of the year has
-not been sensibly affected by the approach of the comet. La Place proved
-that its mass could not be so much as the 5000th part of that of the
-earth. The paths of comets have every possible inclination to the plane
-of the ecliptic, and unlike the planets, their motion is frequently
-retrograde. Comets 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 eccentric ellipses, although, in most cases, the
-parabolic curve coincides most nearly with their observed motions. Even
-if the orbit be determined with all the accuracy that 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 and Clairaut predicted that, in consequence of the
-attraction of Jupiter and Saturn, the return of the comet of 1759 would
-be retarded 618 days, which was verified by the event as nearly as could
-be expected.
-
-The nebulous appearance of comets is perhaps occasioned by the vapours
-which the solar heat raises at their surfaces in their passage at the
-perihelia, and which are again condensed as they recede from the sun.
-The comet of 1680 when in its perihelion was only at the distance of
-one-sixth of the sun's diameter, or about 148000 miles from its surface;
-it consequently would be exposed to a heat 27500 times greater than that
-received by the earth. As the sun's heat is supposed to be in proportion
-to the intensity of his height, 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.
-
-In those positions of comets where only half of their enlightened
-hemisphere ought to be seen, they exhibit no phases even when viewed
-with high magnifying powers. Some slight indications however were once
-observed by Hevelius and La Hire in 1682; and in 1811 Sir William
-Herschel discovered a small luminous point, which he concluded to be the
-disc of the comet. In general their masses are so minute, that they have
-no sensible diameters, the nucleus being principally formed of denser
-strata of the nebulous matter, but so rare that stars have been seen
-through them. The transit of a comet over the sun's disc would afford
-the best information on this point. It was computed that such an event
-was to take place in the year 1627; unfortunately the sun was hid by
-clouds in this country, but it was observed at Viviers and at Marseilles
-at the time the comet must have been on it, but no spot was seen. The
-tails are often of very great length, and are generally situate in the
-planes of their orbits; they follow them in their descent towards the
-sun, but precede them in their return, with a small degree of curvature;
-but their extent and form must vary in appearance, according to the
-position of their orbits with regard to the ecliptic. The tail of the
-comet of 1680 appeared, at Paris, to extend over sixty-two degrees. The
-matter of which the tail is composed must be extremely buoyant to
-precede a body moving with such velocity; indeed the rapidity of its
-ascent cannot be accounted for. 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 in 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 wilt disappear for ever. Possibly comets
-may have vanished from our view sooner than they otherwise would have
-done from this cause. Of about six hundred comets that have been seen at
-different times, three are now perfectly ascertained to form part of our
-system; that is to say, they return to the sun at intervals of 76, 6 1/3,
-and 3 1/4 years nearly.
-
-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 that range within the earth's
-orbit must be 1400; but Uranus being twenty times more distant, there
-may be no less than 11,200,000 comets that come within the known extent
-of our system. In such a multitude of wandering bodies it is just
-possible that one of them may come in collision with the earth; but even
-if it should, the mischief would be local, and the equilibrium soon
-restored. It is however more probable that the earth would only be
-deflected a little from its course by the near approach of the comet,
-without being touched. 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 quarter of an hour Sir
-William Herschel estimated that 116000 stars passed through the field of
-his telescope, which subtended an angle of 15'. This however was
-stated as a specimen of extraordinary crowding; but at an average the
-whole expanse of the heavens must exhibit about a hundred millions of
-fixed stars that come within the reach of telescopic vision.
-
-Many of the stars have a very small progressive motion, especially _μ_
-Cassiopeia and 61 Cygni, both small stars; and, as the sun is decidedly
-a star, it is an additional reason for supposing the solar system to be
-in motion. The distance of the fixed stars is too great to admit of
-their exhibiting a sensible disc; but in all probability they are
-spherical, and must certainly be so, if gravitation pervades all space.
-With a fine telescope they appear like a point of light; their twinkling
-arises from sudden changes in the refractive power of the air, which
-would not be sensible if they had discs like the planets. Thus we can
-learn nothing of the relative distances of the stars from us and from
-one another, by their apparent diameters; but their annual parallax
-being insensible, shows that we must be one hundred millions of millions
-of miles from the nearest; many of them however must be vastly more
-remote, for of two stars that appear close together, one may be far
-beyond the other in the depth of space. The light of Sirius, according
-to the observations of Mr. Herschel, is 324 times greater than that of a
-star of the sixth magnitude; if we suppose the two to be really of the
-same size, their distances from us must be in the ratio of 57.3 to 1,
-because light diminishes as the square of the distance of the luminous
-body increases.
-
-Of the absolute magnitude of the stars, nothing is known, only that many
-of them must be much larger than the sun, from the quantity of light
-emitted by them. Dr. Wollaston determined the approximate ratio that the
-light of a wax candle bears to that of the sun, moon, and stars, by
-comparing their respective images reflected from small glass globes
-filled, with mercury, whence a comparison was established between the
-quantities of light emitted by the celestial bodies themselves. By this
-method he found that the light of the sun is about twenty millions of
-millions of times greater than that of Sirius, the brightest, 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
-immensely greater than Sirius. Sometimes stars have all at once
-appeared, shone with a brilliant light, and then vanished. 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 any thing
-more tremendous than a conflagration that could be visible at such a
-distance. Some stars are periodic, possibly from the intervention of
-opaque bodies revolving about them, or from extensive spots on their
-surfaces. 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 revolving about a common centre. These double 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 William Herschel, to whom astronomy is indebted for so many
-brilliant discoveries, and with whom originated the idea of their
-combination in binary and multiple systems, an idea which his own
-observations had completely established, but which has since received
-additional confirmation from those of his son and Sir James South, the
-former of whom, as well as Professor Struve of Dorpat, have added many
-thousands to their numbers. The motions of revolution round a common
-centre of many have been clearly established, and their periods
-determined with considerable accuracy. Some have already since their
-first discovery accomplished nearly a whole revolution, and one, if the
-latest observations can be depended on, is actually considerably
-advanced in its second period. These interesting systems thus present a
-species of sidereal chronometer, by which the chronology 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.
-
-Possibly among the multitudes of small stars, whether double or
-insulated, some may be found near enough to exhibit distinct parallactic
-motions, or perhaps something approaching to planetary motion, which may
-prove that solar attraction is not confined to our system, or may lead
-to the discovery of the proper motion of the sun. 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
-of a full ruby red, or almost blood colour, and the small one a fine
-green, the latter lost its colour when the former was 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. Mr. Herschel
-observes in one of his papers in the _Philosophical Transactions_, as a
-very remarkable fact, that although red single stars are common enough,
-no example of an insulated blue, green, or purple one has as yet been
-produced.
-
-In some parts of the heavens, the stars are so near together as to form
-clusters, which to the unassisted eye appear like thin white clouds;
-such is the milky way, which has its brightness from the diffused light
-of myriads of stars. Many of these clouds, however, are never resolved
-into separate stars, even by the highest magnifying powers. This
-nebulous matter exists in vast abundance in space. No fewer than 2500
-nebulæ 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 celebrated for astronomical knowledge and
-discovery. 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 rudiments of future systems. With this view, Mr. Herschel is now
-engaged in the difficult and laborious investigation, which is
-understood to be nearly approaching its completion, and the results of
-which we may therefore hope ere long to see made public. The most
-conspicuous of these appearances are found in Orion, and in the girdle
-of Andromeda. It is probable that light must be millions of years
-travelling to the earth from some of the nebulæ.
-
-So numerous are the objects which meet our view in the heavens, that we
-cannot imagine a part of space where some light would not strike the
-eye: but as the fixed stars would not be visible at such distances, if
-they did not shine by their own light, it is reasonable to infer that
-they are suns; and if so, they are in all probability attended by
-systems of opaque bodies, revolving about them as the planets do about
-ours. But although there be no proof that planets not seen by us revolve
-about these remote suns, certain it is, that there are many invisible
-bodies wandering in space, which, occasionally coming 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 obliquity of the descent of meteorites, the peculiar
-matter of which they are composed, and the explosion with which their
-fall is invariably accompanied, show that they are foreign to our
-planet. Luminous spots altogether independent of the phases have
-occasionally appeared on the dark part of the moon, which have been
-ascribed to the light arising from the eruption of volcanoes; 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, and with an
-initial velocity of 10992 feet in a second, which is 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.
-
-The known quantity of matter bears a very small proportion to the
-immensity of space. Large as the bodies are, the distances that 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 void, when it is traversed in
-all directions by light, heat, gravitation, and possibly by influences
-of which we can form no idea; but whether it be replete with an ethereal
-medium, time alone will show.
-
-Though totally ignorant of the laws which obtain in the more distant
-regions of creation, we are assured, that one alone regulates the
-motions of our own system; and as general laws form the ultimate object
-of philosophical research, we cannot conclude these remarks without
-considering the nature of 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 gravitating 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 analytical expression for the gravitating force is a straight line;
-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 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 other laws,
-its 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 in the solar system, their mutual distances, and their
-velocities, were to diminish proportionally, they would describe curves
-in all respect 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. Experience shows 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 attractions, 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 at the immense distance of the fixed stars. 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 impeded by the intervention
-even of the densest substances. If the attraction of the sun for the
-centre of the earthy and for the hemisphere diametrically opposite to
-him, was 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 on the earth differed by a millionth part
-from his action on the moon, the difference would occasion a variation
-in the sun's parallax amounting to several seconds, which is 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 goes, 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, and magnetic fluids are
-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 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 which we in vain look for in the
-other parts of the universe. They date the beginning of time; since
-there is every reason 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.'
-
-*** END OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON
-THE MECHANISMS OF THE HEAVENS ***
-
-Updated editions will replace the previous one--the old editions will
-be renamed.
-
-Creating the works from print editions not protected by U.S. copyright
-law means that no one owns a United States copyright in these works,
-so the Foundation (and you!) can copy and distribute it in the
-United States without permission and without paying copyright
-royalties. Special rules, set forth in the General Terms of Use part
-of this license, apply to copying and distributing Project
-Gutenberg-tm electronic works to protect the PROJECT GUTENBERG-tm
-concept and trademark. Project Gutenberg is a registered trademark,
-and may not be used if you charge for an eBook, except by following
-the terms of the trademark license, including paying royalties for use
-of the Project Gutenberg trademark. If you do not charge anything for
-copies of this eBook, complying with the trademark license is very
-easy. You may use this eBook for nearly any purpose such as creation
-of derivative works, reports, performances and research. Project
-Gutenberg eBooks may be modified and printed and given away--you may
-do practically ANYTHING in the United States with eBooks not protected
-by U.S. copyright law. Redistribution is subject to the trademark
-license, especially commercial redistribution.
-
-START: FULL LICENSE
-
-THE FULL PROJECT GUTENBERG LICENSE
-PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK
-
-To protect the Project Gutenberg-tm mission of promoting the free
-distribution of electronic works, by using or distributing this work
-(or any other work associated in any way with the phrase "Project
-Gutenberg"), you agree to comply with all the terms of the Full
-Project Gutenberg-tm License available with this file or online at
-www.gutenberg.org/license.
-
-Section 1. General Terms of Use and Redistributing Project
-Gutenberg-tm electronic works
-
-1.A. By reading or using any part of this Project Gutenberg-tm
-electronic work, you indicate that you have read, understand, agree to
-and accept all the terms of this license and intellectual property
-(trademark/copyright) agreement. If you do not agree to abide by all
-the terms of this agreement, you must cease using and return or
-destroy all copies of Project Gutenberg-tm electronic works in your
-possession. If you paid a fee for obtaining a copy of or access to a
-Project Gutenberg-tm electronic work and you do not agree to be bound
-by the terms of this agreement, you may obtain a refund from the
-person or entity to whom you paid the fee as set forth in paragraph
-1.E.8.
-
-1.B. "Project Gutenberg" is a registered trademark. It may only be
-used on or associated in any way with an electronic work by people who
-agree to be bound by the terms of this agreement. There are a few
-things that you can do with most Project Gutenberg-tm electronic works
-even without complying with the full terms of this agreement. See
-paragraph 1.C below. There are a lot of things you can do with Project
-Gutenberg-tm electronic works if you follow the terms of this
-agreement and help preserve free future access to Project Gutenberg-tm
-electronic works. See paragraph 1.E below.
-
-1.C. The Project Gutenberg Literary Archive Foundation ("the
-Foundation" or PGLAF), owns a compilation copyright in the collection
-of Project Gutenberg-tm electronic works. Nearly all the individual
-works in the collection are in the public domain in the United
-States. If an individual work is unprotected by copyright law in the
-United States and you are located in the United States, we do not
-claim a right to prevent you from copying, distributing, performing,
-displaying or creating derivative works based on the work as long as
-all references to Project Gutenberg are removed. Of course, we hope
-that you will support the Project Gutenberg-tm mission of promoting
-free access to electronic works by freely sharing Project Gutenberg-tm
-works in compliance with the terms of this agreement for keeping the
-Project Gutenberg-tm name associated with the work. You can easily
-comply with the terms of this agreement by keeping this work in the
-same format with its attached full Project Gutenberg-tm License when
-you share it without charge with others.
-
-1.D. The copyright laws of the place where you are located also govern
-what you can do with this work. Copyright laws in most countries are
-in a constant state of change. If you are outside the United States,
-check the laws of your country in addition to the terms of this
-agreement before downloading, copying, displaying, performing,
-distributing or creating derivative works based on this work or any
-other Project Gutenberg-tm work. The Foundation makes no
-representations concerning the copyright status of any work in any
-country other than the United States.
-
-1.E. Unless you have removed all references to Project Gutenberg:
-
-1.E.1. The following sentence, with active links to, or other
-immediate access to, the full Project Gutenberg-tm License must appear
-prominently whenever any copy of a Project Gutenberg-tm work (any work
-on which the phrase "Project Gutenberg" appears, or with which the
-phrase "Project Gutenberg" is associated) is accessed, displayed,
-performed, viewed, copied or distributed:
-
-  This eBook is for the use of anyone anywhere in the United States and
-  most other parts of the world at no cost and with almost no
-  restrictions whatsoever. You may copy it, give it away or re-use it
-  under the terms of the Project Gutenberg License included with this
-  eBook or online at www.gutenberg.org. If you are not located in the
-  United States, you will have to check the laws of the country where
-  you are located before using this eBook.
-
-1.E.2. If an individual Project Gutenberg-tm electronic work is
-derived from texts not protected by U.S. copyright law (does not
-contain a notice indicating that it is posted with permission of the
-copyright holder), the work can be copied and distributed to anyone in
-the United States without paying any fees or charges. If you are
-redistributing or providing access to a work with the phrase "Project
-Gutenberg" associated with or appearing on the work, you must comply
-either with the requirements of paragraphs 1.E.1 through 1.E.7 or
-obtain permission for the use of the work and the Project Gutenberg-tm
-trademark as set forth in paragraphs 1.E.8 or 1.E.9.
-
-1.E.3. If an individual Project Gutenberg-tm electronic work is posted
-with the permission of the copyright holder, your use and distribution
-must comply with both paragraphs 1.E.1 through 1.E.7 and any
-additional terms imposed by the copyright holder. Additional terms
-will be linked to the Project Gutenberg-tm License for all works
-posted with the permission of the copyright holder found at the
-beginning of this work.
-
-1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm
-License terms from this work, or any files containing a part of this
-work or any other work associated with Project Gutenberg-tm.
-
-1.E.5. Do not copy, display, perform, distribute or redistribute this
-electronic work, or any part of this electronic work, without
-prominently displaying the sentence set forth in paragraph 1.E.1 with
-active links or immediate access to the full terms of the Project
-Gutenberg-tm License.
-
-1.E.6. You may convert to and distribute this work in any binary,
-compressed, marked up, nonproprietary or proprietary form, including
-any word processing or hypertext form. However, if you provide access
-to or distribute copies of a Project Gutenberg-tm work in a format
-other than "Plain Vanilla ASCII" or other format used in the official
-version posted on the official Project Gutenberg-tm website
-(www.gutenberg.org), you must, at no additional cost, fee or expense
-to the user, provide a copy, a means of exporting a copy, or a means
-of obtaining a copy upon request, of the work in its original "Plain
-Vanilla ASCII" or other form. Any alternate format must include the
-full Project Gutenberg-tm License as specified in paragraph 1.E.1.
-
-1.E.7. Do not charge a fee for access to, viewing, displaying,
-performing, copying or distributing any Project Gutenberg-tm works
-unless you comply with paragraph 1.E.8 or 1.E.9.
-
-1.E.8. You may charge a reasonable fee for copies of or providing
-access to or distributing Project Gutenberg-tm electronic works
-provided that:
-
-* You pay a royalty fee of 20% of the gross profits you derive from
-  the use of Project Gutenberg-tm works calculated using the method
-  you already use to calculate your applicable taxes. The fee is owed
-  to the owner of the Project Gutenberg-tm trademark, but he has
-  agreed to donate royalties under this paragraph to the Project
-  Gutenberg Literary Archive Foundation. Royalty payments must be paid
-  within 60 days following each date on which you prepare (or are
-  legally required to prepare) your periodic tax returns. Royalty
-  payments should be clearly marked as such and sent to the Project
-  Gutenberg Literary Archive Foundation at the address specified in
-  Section 4, "Information about donations to the Project Gutenberg
-  Literary Archive Foundation."
-
-* You provide a full refund of any money paid by a user who notifies
-  you in writing (or by e-mail) within 30 days of receipt that s/he
-  does not agree to the terms of the full Project Gutenberg-tm
-  License. You must require such a user to return or destroy all
-  copies of the works possessed in a physical medium and discontinue
-  all use of and all access to other copies of Project Gutenberg-tm
-  works.
-
-* You provide, in accordance with paragraph 1.F.3, a full refund of
-  any money paid for a work or a replacement copy, if a defect in the
-  electronic work is discovered and reported to you within 90 days of
-  receipt of the work.
-
-* You comply with all other terms of this agreement for free
-  distribution of Project Gutenberg-tm works.
-
-1.E.9. If you wish to charge a fee or distribute a Project
-Gutenberg-tm electronic work or group of works on different terms than
-are set forth in this agreement, you must obtain permission in writing
-from the Project Gutenberg Literary Archive Foundation, the manager of
-the Project Gutenberg-tm trademark. Contact the Foundation as set
-forth in Section 3 below.
-
-1.F.
-
-1.F.1. Project Gutenberg volunteers and employees expend considerable
-effort to identify, do copyright research on, transcribe and proofread
-works not protected by U.S. copyright law in creating the Project
-Gutenberg-tm collection. Despite these efforts, Project Gutenberg-tm
-electronic works, and the medium on which they may be stored, may
-contain "Defects," such as, but not limited to, incomplete, inaccurate
-or corrupt data, transcription errors, a copyright or other
-intellectual property infringement, a defective or damaged disk or
-other medium, a computer virus, or computer codes that damage or
-cannot be read by your equipment.
-
-1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right
-of Replacement or Refund" described in paragraph 1.F.3, the Project
-Gutenberg Literary Archive Foundation, the owner of the Project
-Gutenberg-tm trademark, and any other party distributing a Project
-Gutenberg-tm electronic work under this agreement, disclaim all
-liability to you for damages, costs and expenses, including legal
-fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
-LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE
-PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE
-TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE
-LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR
-INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH
-DAMAGE.
-
-1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a
-defect in this electronic work within 90 days of receiving it, you can
-receive a refund of the money (if any) you paid for it by sending a
-written explanation to the person you received the work from. If you
-received the work on a physical medium, you must return the medium
-with your written explanation. The person or entity that provided you
-with the defective work may elect to provide a replacement copy in
-lieu of a refund. If you received the work electronically, the person
-or entity providing it to you may choose to give you a second
-opportunity to receive the work electronically in lieu of a refund. If
-the second copy is also defective, you may demand a refund in writing
-without further opportunities to fix the problem.
-
-1.F.4. Except for the limited right of replacement or refund set forth
-in paragraph 1.F.3, this work is provided to you 'AS-IS', WITH NO
-OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
-LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE.
-
-1.F.5. Some states do not allow disclaimers of certain implied
-warranties or the exclusion or limitation of certain types of
-damages. If any disclaimer or limitation set forth in this agreement
-violates the law of the state applicable to this agreement, the
-agreement shall be interpreted to make the maximum disclaimer or
-limitation permitted by the applicable state law. The invalidity or
-unenforceability of any provision of this agreement shall not void the
-remaining provisions.
-
-1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
-trademark owner, any agent or employee of the Foundation, anyone
-providing copies of Project Gutenberg-tm electronic works in
-accordance with this agreement, and any volunteers associated with the
-production, promotion and distribution of Project Gutenberg-tm
-electronic works, harmless from all liability, costs and expenses,
-including legal fees, that arise directly or indirectly from any of
-the following which you do or cause to occur: (a) distribution of this
-or any Project Gutenberg-tm work, (b) alteration, modification, or
-additions or deletions to any Project Gutenberg-tm work, and (c) any
-Defect you cause.
-
-Section 2. Information about the Mission of Project Gutenberg-tm
-
-Project Gutenberg-tm is synonymous with the free distribution of
-electronic works in formats readable by the widest variety of
-computers including obsolete, old, middle-aged and new computers. It
-exists because of the efforts of hundreds of volunteers and donations
-from people in all walks of life.
-
-Volunteers and financial support to provide volunteers with the
-assistance they need are critical to reaching Project Gutenberg-tm's
-goals and ensuring that the Project Gutenberg-tm collection will
-remain freely available for generations to come. In 2001, the Project
-Gutenberg Literary Archive Foundation was created to provide a secure
-and permanent future for Project Gutenberg-tm and future
-generations. To learn more about the Project Gutenberg Literary
-Archive Foundation and how your efforts and donations can help, see
-Sections 3 and 4 and the Foundation information page at
-www.gutenberg.org
-
-Section 3. Information about the Project Gutenberg Literary
-Archive Foundation
-
-The Project Gutenberg Literary Archive Foundation is a non-profit
-501(c)(3) educational corporation organized under the laws of the
-state of Mississippi and granted tax exempt status by the Internal
-Revenue Service. The Foundation's EIN or federal tax identification
-number is 64-6221541. Contributions to the Project Gutenberg Literary
-Archive Foundation are tax deductible to the full extent permitted by
-U.S. federal laws and your state's laws.
-
-The Foundation's business office is located at 809 North 1500 West,
-Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up
-to date contact information can be found at the Foundation's website
-and official page at www.gutenberg.org/contact
-
-Section 4. Information about Donations to the Project Gutenberg
-Literary Archive Foundation
-
-Project Gutenberg-tm depends upon and cannot survive without
-widespread public support and donations to carry out its mission of
-increasing the number of public domain and licensed works that can be
-freely distributed in machine-readable form accessible by the widest
-array of equipment including outdated equipment. Many small donations
-($1 to $5,000) are particularly important to maintaining tax exempt
-status with the IRS.
-
-The Foundation is committed to complying with the laws regulating
-charities and charitable donations in all 50 states of the United
-States. Compliance requirements are not uniform and it takes a
-considerable effort, much paperwork and many fees to meet and keep up
-with these requirements. We do not solicit donations in locations
-where we have not received written confirmation of compliance. To SEND
-DONATIONS or determine the status of compliance for any particular
-state visit www.gutenberg.org/donate
-
-While we cannot and do not solicit contributions from states where we
-have not met the solicitation requirements, we know of no prohibition
-against accepting unsolicited donations from donors in such states who
-approach us with offers to donate.
-
-International donations are gratefully accepted, but we cannot make
-any statements concerning tax treatment of donations received from
-outside the United States. U.S. laws alone swamp our small staff.
-
-Please check the Project Gutenberg web pages for current donation
-methods and addresses. Donations are accepted in a number of other
-ways including checks, online payments and credit card donations. To
-donate, please visit: www.gutenberg.org/donate
-
-Section 5. General Information About Project Gutenberg-tm electronic works
-
-Professor Michael S. Hart was the originator of the Project
-Gutenberg-tm concept of a library of electronic works that could be
-freely shared with anyone. For forty years, he produced and
-distributed Project Gutenberg-tm eBooks with only a loose network of
-volunteer support.
-
-Project Gutenberg-tm eBooks are often created from several printed
-editions, all of which are confirmed as not protected by copyright in
-the U.S. unless a copyright notice is included. Thus, we do not
-necessarily keep eBooks in compliance with any particular paper
-edition.
-
-Most people start at our website which has the main PG search
-facility: www.gutenberg.org
-
-This website includes information about Project Gutenberg-tm,
-including how to make donations to the Project Gutenberg Literary
-Archive Foundation, how to help produce our new eBooks, and how to
-subscribe to our email newsletter to hear about new eBooks.
diff --git a/old/67386-0.zip b/old/67386-0.zip
deleted file mode 100644
index 812682c..0000000
--- a/old/67386-0.zip
+++ /dev/null
diff --git a/old/67386-h.zip b/old/67386-h.zip
deleted file mode 100644
index f9c27bc..0000000
--- a/old/67386-h.zip
+++ /dev/null
diff --git a/old/67386-h/67386-h.htm b/old/67386-h/67386-h.htm
deleted file mode 100644
index 05b9fd3..0000000
--- a/old/67386-h/67386-h.htm
+++ /dev/null
@@ -1,3303 +0,0 @@
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
-    "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
-<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
-  <head>
-    <meta http-equiv="content-type" content="text/html; charset=utf-8" />
-    <meta http-equiv="Content-Style-Type" content="text/css" />
-    <title>
-      The Project Gutenberg eBook of A Preliminary Dissertation on the
-      Mechanisms of the Heavens, by Mary Somerville.
-    </title>
-    <style type="text/css">
-
-body {
-    margin-left: 10%;
-    margin-right: 10%;
-}
-
-    h1,h2,h3,h4,h5,h6 {
-    text-align: center; /* all headings centered */
-    clear: both;
-}
-
-p {
-    margin-top: .51em;
-    text-align: justify;
-    margin-bottom: .49em;
-    text-indent:4%;
-}
-
-sup {
-  vertical-align: super;
-  font-size: smaller;
-}
-
-sub {
-  vertical-align: sub;
-  font-size: smaller;
-}
-
-.p2       {margin-top: 2em;}
-.p4       {margin-top: 4em;}
-.p6       {margin-top: 6em;}
-
-.nind {text-indent:0%;}
-
-hr {
-    width: 33%;
-    margin-top: 2em;
-    margin-bottom: 2em;
-    margin-left: auto;
-    margin-right: auto;
-    clear: both;
-}
-
-hr.tb   {width: 45%;}
-hr.chap {width: 65%}
-hr.full {width: 95%;}
-
-hr.r5  {width: 5%; margin-top: 1em; margin-bottom: 1em;}
-hr.r65 {width: 65%; margin-top: 3em; margin-bottom: 3em;}
-
-ul.index { list-style-type: none; }
-li.ifrst { margin-top: 1em; }
-li.indx { margin-top: .5em; }
-li.isub1 {text-indent: 1em;}
-li.isub2 {text-indent: 2em;}
-li.isub3 {text-indent: 3em;}
-
-table {
-    margin-left: auto;
-    margin-right: auto;
-}
-
-    .tdl      {text-align: left;}
-    .tdr      {text-align: right;}
-    .tdc      {text-align: center;}
-
-.blockquot {
-    margin-left: 5%;
-    margin-right: 10%;
-}
-
-
-.bb       {border-bottom: solid 2px;}
-
-.bl       {border-left: solid 2px;}
-
-.bt       {border-top: solid 2px;}
-
-.br       {border-right: solid 2px;}
-
-.bbox     {border: solid 2px;}
-
-.center   {text-align: center;}
-
-.right   {text-align: right;}
-
-.smcap    {font-variant: small-caps;}
-
-.u        {text-decoration: underline;}
-
-.tb {
-    text-align: center;
-    padding-top: .76em;
-    padding-bottom: .24em;
-    letter-spacing: 1.5em;
-    margin-right: -1.5em;
-}
-
-
-/* Images */
-.figcenter   {
-    margin: auto;
-    text-align: center;
-}
-
-/* Poetry */
-.poem {
-    margin-left:10%;
-    margin-right:10%;
-    text-align: left;
-}
-
-.poem br {display: none;}
-.poetry-container { text-align: center; }
-.poem { display: inline-block; text-align: left; }
-.poem .stanza {margin: 1em 0em 1em 0em;}
-.poem span.i2  {display: block; margin-left: 1em; padding-left:   3em; text-indent: -3em;}
-.poem span.i12 {display: block; margin-left: 6em; padding-left:   3em; text-indent: -3em;}
-
-
-    </style>
-  </head>
-<body>
-<p style='text-align:center; font-size:1.2em; font-weight:bold'>The Project Gutenberg eBook of A Preliminary Dissertation on the Mechanisms of the Heavens, by Mary Somerville</p>
-<div style='display:block; margin:1em 0'>
-This eBook is for the use of anyone anywhere in the United States and
-most other parts of the world at no cost and with almost no restrictions
-whatsoever. You may copy it, give it away or re-use it under the terms
-of the Project Gutenberg License included with this eBook or online
-at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you
-are not located in the United States, you will have to check the laws of the
-country where you are located before using this eBook.
-</div>
-
-<p style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Title: A Preliminary Dissertation on the Mechanisms of the Heavens</p>
-<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Author: Mary Somerville</p>
-<p style='display:block; text-indent:0; margin:1em 0'>Release Date: February 12, 2022 [eBook #67386]</p>
-<p style='display:block; text-indent:0; margin:1em 0'>Language: English</p>
-  <p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em; text-align:left'>Produced by: Laura Natal Rodrigues (Images generously made available by Hathi Trust Digital Library.)</p>
-<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON THE MECHANISMS OF THE HEAVENS ***</div>
-
-<div class="figcenter" style="width: 500px;">
-<img src="images/dissertation_cover.jpg" width="500" alt="" />
-</div>
-
-
-
-<h1>A
-<br />
-PRELIMINARY DISSERTATION
-<br />
-ON THE
-<br />
-MECHANISM OF THE HEAVENS.</h1>
-
-<p><br /></p>
-
-<h5>BY</h5>
-
-<h2>MRS. SOMMERVILLE</h2>
-
-<p><br /></p>
-
-<h4>PHILADELPHIA:</h4>
-
-<h3>CAREY &amp; LEA</h3>
-
-<h5>1832</h5>
-
-<p><br /><br /><br /></p>
-
-<p>
-In order to convey some idea of the object of this work, it may be
-useful to offer a few preliminary observations on the nature of the
-subject which it is intended to investigate, and of the means that have
-already been adopted with so much success to bring within the reach of
-our faculties, those truths which might seem to be placed so far beyond
-them.
-</p>
-
-<p>
-All the knowledge we possess of external objects is founded upon
-experience, which furnishes a knowledge of facts, and the comparison of
-these facts establishes relations, from which, induction, the intuitive
-belief that like causes will produce like effects, leads us to general
-laws. Thus, experience teaches that bodies fall at the surface of the
-earth with an accelerated velocity, and proportional to their masses.
-Newton proved, by comparison, 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.
-</p>
-
-<p>
-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.
-</p>
-
-<p>
-The combined efforts of astronomers, from the earliest dawn of
-civilization, have been requisite 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 system of the world has been so completely
-explained, that no astronomical phenomenon can now be transmitted to
-posterity of which the laws have not been determined.
-</p>
-
-<p>
-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 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.
-</p>
-
-<p>
-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
-limits. 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 us 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 which seem so mighty to us
-must 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 or creation.
-</p>
-
-<p>
-A complete acquaintance with Physical Astronomy can only be attained by
-those who are well versed in the higher branches of mathematical and
-mechanical science: such alone can appreciate the extreme beauty of
-the results, and of the means by which these results are obtained.
-Nevertheless 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 possibly overrating them by not making a
-sufficient 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 truth, whether it be
-in the discovery of a world, or of a new property of numbers.
-</p>
-
-<p>
-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 name manner as
-if its mass, 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 each other,
-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.
-</p>
-
-<p>
-The attraction of the earth on bodies at its surface in that latitude,
-the square of whose sine is ⅓, 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, 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 her 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; but as experience shows that the action and reaction of matter are
-equal and contrary, the moon must attract the earth with an equal and
-contrary force.
-</p>
-
-<p>
-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.
-</p>
-
-<p>
-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 be supposed
-to be 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
-reaction, each body is itself the centre of an attractive force
-extending indefinitely in space, whence proceed all the mutual
-disturbances that render the celestial motions so complicated, and their
-investigation so difficult.
-</p>
-
-<p>
-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 taken in mass; 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
-in other respects they also would 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, which is impossible.
-</p>
-
-<p>
-The form of the planets results 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 when these two forces are balanced by an increase of
-gravity; therefore, as the attractive force is the same on 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. 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, differs but little from a
-sphere. Although the planets attract each other as if they were spheres
-on account of their immense 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 nutation 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.
-</p>
-
-<p>
-If a sphere at rest in space receives 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 give it 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 progression,
-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 that
-would in no way interfere with their relative motions; for, in
-consequence of our experience 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.
-</p>
-
-<p>
-Since the motions of the rotation and translation of the planets are
-independent of each other, though probably communicated by the same
-impulse, they form separate subjects of investigation.
-</p>
-
-<p>
-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 a planet is in its aphelion or at the
-point where the orbit is farthest from the sun, his action overcomes its
-velocity, and brings it towards him with such an accelerated motion,
-that it at last overcomes the sun's attraction, and shoots past him;
-then, gradually decreasing in velocity, 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 planets, pass over
-equal areas in equal times.
-</p>
-
-<p>
-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
-immensely 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, and 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 the existence of disturbing forces.
-</p>
-
-<p>
-To determine 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 arises the celebrated
-problem of the three bodies, which originally was that of the moon, the
-earth, and the sun, namely,&mdash;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 position at any given instant.
-</p>
-
-<p>
-By this problem the motions of translation of all the celestial bodies
-are determined. It is one of extreme difficulty, and would be of
-infinitely greater difficulty, 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.
-</p>
-
-<p>
-On account of the reciprocal action of matter, the stability of the
-system depends on 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
-on 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 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 immensely
-greater than those of the planets; and as their inequalities bear 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.
-</p>
-
-<p>
-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 it 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 the orbit intersects the
-plane of the ecliptic are its nodes.
-</p>
-
-<p>
-The orbits of the recently discovered planets deviate more from the
-ecliptic: that of Pallas has an inclination of 35° to it: on that
-account it will be 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.
-</p>
-
-<p>
-The planets are subject to disturbances of two distinct 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 troubled 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.
-</p>
-
-<p>
-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 on 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.
-</p>
-
-<p>
-In consequence of disturbances of this kind, the apsides, or extremities
-of the major axes of all the orbits, have a direct, but variable motion
-in space, excepting those of Venus, which are retrograde; and the lines
-of the nodes move with a variable velocity in the contrary direction.
-The motions of both are extremely slow; it requires more than 109770
-years for the major axis of the earth's orbit to accomplish a sidereal
-revolution, and 20935 years to complete its tropical motion. The major
-axis of Jupiter's orbit requires no less than 197561 years to perform
-its revolution from the disturbing action of Saturn alone. The periods
-in which the nodes revolve are also very great. Beside 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 six minutes less now than it was in the age of Ptolemy. The
-terrestrial eccentricity is decreasing at the rate of 3914 miles in a
-century; and if it were to decrease equably, it would be 36300 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.
-</p>
-
-<p>
-With the exception of these two elements, it appears, that all the
-bodies are in motion, and every orbit is in a state of perpetual change.
-Minute as these changes are, they might be supposed liable 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. The
-consequences being so dreadful, it is natural to inquire, what proof
-exists that creation will be preserved from such a catastrophe? For
-nothing can be known from observation, since the existence of the human
-race has occupied 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, as well secular as periodic, are
-expressed analytically by the sines and cosines of circular arcs, which
-increase with the time; and as a sine or cosine never can 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 then
-begin a new course, thus for ever oscillating about a mean value. This,
-however, would not be the case 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. But if the planets do move in an ethereal medium,
-it must be of extreme rarity, since its resistance has hitherto been
-quite insensible.
-</p>
-
-<p>
-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 revolution of all the bodies,
-as well planets as satellites, in the same direction. These, however,
-are not necessary conditions: the periodicity of the terms in which the
-inequalities are expressed is sufficient 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.
-</p>
-
-<p>
-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 52"·109, occasioned by the reciprocal action
-of the planets; but as this is also periodical, the terrestrial equator,
-which is inclined to it at an angle of about 23° 28', will never
-coincide with the plane of the ecliptic; so there never can be perpetual
-spring.
-</p>
-
-<p>
-The rotation of the earth is uniform; therefore day and night, summer
-and winter, will continue their vicissitudes while the system endures,
-or is untroubled by foreign causes.
-</p>
-
-<div class="poem"><div class="stanza">
-<span class="i12">Yonder starry sphere</span><br />
-<span class="i2">Of planets, and of fix'd, in all her wheels</span><br />
-<span class="i2">Resembles nearest, mazes intricate,</span><br />
-<span class="i2">Eccentric, intervolv'd, yet regular</span><br />
-<span class="i2">Then most, when most irregular they seem.</span>
-</div></div>
-
-<p>
-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
-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.'
-</p>
-
-<p>
-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. This difficulty is obviated by La Place, who has shown
-that whatever changes time may induce either in the orbits themselves,
-or in the plane of the ecliptic, there exists an invariable plane
-passing through the centre of gravity of the sun, about which the whole
-system oscillates within narrow limits, and which is determined by this
-property; that if every body in the system be projected on it, and if
-the mass of each be multiplied by the area described in a given time by
-its projection on this plane, the sum of all these products will be a
-maximum. 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 remains parallel to itself, and
-maintains a fixed position, whence the oscillations of the system may be
-estimated through unlimited time. It is situate nearly half way between
-the orbits of Jupiter and Saturn, and is inclined to the ecliptic at an
-angle of about 1° 35' 31".
-</p>
-
-<p>
-All the periodic and secular inequalities deduced from the law of
-gravitation are so perfectly confirmed by observations, 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 great inequalities of very long periods, forming
-what appeared an 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 inequality in the mean
-motion of each of these planets, which completes its period in nearly
-929 Julian years, the one being retarded, while the other is
-accelerated. These inequalities are strictly periodical, since they
-depend on 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 3° 23',
-and Saturn's retarded by 5° 13'.
-</p>
-
-<p>
-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 those bodies were united in their common centre
-of gravity; the action of the sun however disturbs in some degree the
-motion of the satellites about their primary.
-</p>
-
-<p>
-The changes that take place in the planetary system are exhibited on a
-small 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
-centuries. 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 further 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 motion of the nodes of these little bodies is so much more rapid
-than those of the planet. The nodes of the fourth satellite accomplish a
-revolution in 520 years, while those of Jupiter's orbit require no less
-than 50673 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.
-</p>
-
-<p>
-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
-further the satellite is removed, a circumstance entirely owing to the
-influence of Jupiter's compression.
-</p>
-
-<p>
-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. 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 planet. 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 or a discovery, which, though not so immediately
-applicable to the wants of man, unfolds a property 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 16' 26" 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 192
-millions of miles; whence it is estimated, that light travels at the
-rate of 192000 miles in one second. Such is its velocity, that the
-earth, moving at the rate of nineteen 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.
-</p>
-
-<p>
-Objects appear to be situate in the direction of the rays that 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, when Jupiter is in conjunction, we
-see him by means of rays that left him 16' 26" before; but during that
-time we have changed our position, in consequence of the motion of the
-earth in its orbit; we therefore 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 192000 to 19. In consequence of
-aberration, none of the heavenly bodies are in the place in which they
-seem to be. 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 be 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 never
-exceeds twenty seconds, in ordinary cases.
-</p>
-
-<p>
-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 apparently the most unpromising and dissimilar
-circumstances, occur in 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, which hypothesis 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."
-</p>
-
-<p>
-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.
-</p>
-
-<p>
-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 its compression. The orbits of its satellites are nearly
-perpendicular to the plane of the ecliptic.
-</p>
-
-<p>
-Our constant companion the moon next claims 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. Neither the
-eccentricity of the lunar orbit, nor its inclination to the plane of the
-ecliptic, have experienced any changes from secular inequalities; but
-the mean motion, the nodes, and the perigee, are subject to very
-remarkable variations.
-</p>
-
-<p>
-From an eclipse observed at Babylon by the Chaldeans, 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 back 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 the 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, and it was at one time attributed to the
-resistance of an ethereal medium pervading space; 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 latter from such a cause being
-inseparably connected with variations in the two former of these
-elements. That great mathematician, however, in studying the theory of
-Jupiter's satellites, perceived that the secular variations in the
-elements of Jupiter's orbit, from the action of the planets, occasion
-corresponding changes in the motions of the satellites: this led him to
-suspect that the acceleration in the mean motion of the moon might be
-connected with the secular variation in the eccentricity of the
-terrestrial orbit; and analysis has proved that he assigned the true
-cause.
-</p>
-
-<p>
-If the eccentricity 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; but it would be periodic,
-since it would be the same as often as the sun, the earth, and the moon
-returned to the same relative positions: on account however of the slow
-and incessant diminution in the eccentricity 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 which is
-very 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
-eccentricity diminishes, the moon's mean motion will be accelerated; but
-when the eccentricity 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 10", 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 eccentricity, 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 1° 48' in the moon's longitude,
-and of 7° 12' in her mean anomaly.
-</p>
-
-<p>
-The action of the sun occasions a rapid but variable motion in the nodes
-and perigee of the lunar orbit; the former, though they recede during
-the greater part of the moon's revolution, and advance during the smaller,
-perform their sidereal revolutions in 6793<sup>days</sup>.4212, and the
-latter, though its motion is sometimes retrograde and sometimes direct,
-in 3232<sup>days</sup>.5807, or a little more than nine years: 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 109770 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 motion of 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 eccentricity
-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.
-</p>
-
-<p>
-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.'
-</p>
-
-<p>
-The moon is so near, that the excess of matter at the earth's equator
-occasions periodic variations in her longitude and latitude; and, 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 diameter to the diameter
-of the equator is ¹⁄₃₀₅.₀₅ 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, it would assume the form of a spheroid, whose compression is
-¹⁄₂₃₀. Whence it appears, that the earth is not homogeneous, but 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 Jupiter's
-satellites prove that his mass is not homogeneous, and that his
-compression is ¹⁄₁₃.₈.
-</p>
-
-<p>
-The motions of the moon have now become of more importance to the
-navigator and geographer than those of any other body, from the
-precision with which the longitude is determined by the occultations of
-stars and lunar distances. The lunar theory is brought to such
-perfection, that the times of these phenomena, observed under any
-meridian, when compared with that computed for Greenwich in the Nautical
-Almanack, gives 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.
-</p>
-
-<p>
-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 distance of the sun and
-moon from the earth is obtained: whence it appears that the sun's
-distance from the earth is nearly 396 times greater than that of the
-moon.
-</p>
-
-<p>
-The method however of finding the absolute distances of the celestial
-bodies in miles, is in fact the same with that employed in measuring
-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 be very great
-indeed, to be visible at all from the celestial bodies. But the globe
-itself whose dimensions are ascertained by actual admeasurement,
-furnishes a standard of measures, with which we compare the distances,
-masses, densities, and volumes of the sun and planets.
-</p>
-
-<p>
-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, at any rate, quite 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 gravity, 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:&mdash;
-</p>
-
-<p>
-A terrestrial meridian is a line passing through both poles, all the
-points of which have contemporaneously the same noon. 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; a comparison of the length of
-the degrees in different parts of the earth's surface will therefore
-determine its size and form.
-</p>
-
-<p>
-An arc 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 inequalities 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 is spherical, they
-require a correction to reduce them from plane to spherical triangles.
-</p>
-
-<p>
-Arcs of the meridian have been measured in a variety of latitudes, both
-north and south, as well as arcs perpendicular to the meridian. From
-these measurements it appears that the length of the degrees increase
-from the equator to the poles, nearly as the square of the sine of the
-latitude; consequently, the convexity of the earth diminishes from the
-equator to the poles. Many discrepancies occur, but the figure that most
-nearly follows this law is an ellipsoid of revolution, whose equatorial
-radius is 3962.6 miles, and the polar radius 3949.7; the difference, or
-12.9 miles, divided by the equatorial radius, is ¹⁄₃₀₈.₇, or ¹⁄₃₀₉
-nearly; 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 ¹⁄₂₂ British miles; therefore
-360 degrees, or the whole circumference of the globe is 24856, and the
-diameter, which is something less than a third of the circumference, is
-7916 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 mensuration of an arc between Alexandria and Syene.
-</p>
-
-<p>
-But there is another method of finding the figure of the earth, 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, the force of gravity
-theoretically ought to increase, from the equator to the pole as the
-square of the sine of the latitude; but for a spheroid in rotation, by
-the laws of mechanics the centrifugal force varies 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 effects 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 in going 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 that they may
-always be performed in the same time, the length of the pendulum must
-be altered. Now, by numerous and very careful experiments, it is proved
-that a pendulum, which makes 86400 oscillations in a mean day at the
-equator, will do the same at every point of the earth's surface, if
-its length be increased in going to the pole, as the square of the
-sine of the latitude. From the mean of these it appears that the
-compression of the terrestrial spheroid is about ¹⁄₃₄₂, which does not
-differ much from that given by the lunar inequalities, and from the arcs
-of the meridian. 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 nutation 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 ¹⁄₅₇₈.
-</p>
-
-<p>
-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 such discrepancies 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 ¹⁄₅₇₈; that given by the lunar theory has the advantage
-of being independent of the irregularities at the earth's surface,
-and of local attractions. 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.
-</p>
-
-<p>
-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 that, when the moon is in the horizon at the
-instant of rising or setting, lines were 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 distances 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 3454"·2; whence the mean distance
-of the moon is about sixty times the mean terrestrial radius, or 240000
-miles nearly. Since the parallax is equal to the radius of the earth
-divided by the distance of the moon; under the same parallel of latitude
-it varies with the distance of the moon from the earth, and proves the
-ellipticity of the lunar orbit; and when the moon is at her mean
-distance, it varies with the terrestrial radii, thus showing that the
-earth is not a sphere.
-</p>
-
-<p>
-Although the method described is sufficiently accurate for finding the
-parallax of an object so 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 by the transits of Venus that difficulty
-is obviated. When that planet is in her nodes, or within 1 ¼° of them,
-that is, in, or nearly in the plane of the ecliptic, she is occasionally
-seen to pass over the sun like a block 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 sun is not so remote but that
-the semidiameter of the earth has a sensible magnitude when viewed from
-his centre, 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 being the object of Cook's first voyage. The
-transit lasted about six hours at Otaheite, and the difference in the
-duration at these two stations was eight minutes; whence the sun's
-parallax was found to be 8"·72; but by other considerations it has
-subsequently been reduced to 8"·575; from which the mean distance of
-the sun appears to be about 95996000, or ninety-six millions of miles
-nearly. This is confirmed by an inequality in the motion of the moon,
-which depends on the parallax of the sun, and which when compared
-with observation gives 8"·6 for the sun's parallax.
-</p>
-
-<p>
-The parallax of Venus is determined by her transits, that of Mars
-by direct observation. 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.
-</p>
-
-<p>
-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 1843 millions of
-miles from the luminary that warms and enlivens the world; to it,
-situate on the verge of the system, the sun must appear 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.
-</p>
-
-<p>
-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 the most perfect 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
-20500000 millions of miles. At such a distance not only the terrestrial
-orbit shrinks to a point, but, where the whole solar system, when
-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 rationally be supposed to be
-situated many thousand times further 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.'
-</p>
-
-<p>
-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 greater than 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 1070.5 times less than the sun. The mass of the moon is
-determined from four different sources,&mdash;from her action on the
-terrestrial equator, which occasions the rotation 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 titles. 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 very much from each
-other; but, from her action in raising  the tides, which furnishes
-the fourth method, her mass appears to be about the seventy-fifth part
-of that of the earth, a value that cannot differ much from the truth.
-</p>
-
-<p>
-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 diameter of a planet is to the real diameter of
-the earth, or 8000 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 1920", and with the solar parallax 8"·65, it will be found that
-the diameter of the sun is about 888000 miles; therefore, 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 240000 miles; so that twice the distance of
-the moon is 480000 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.
-</p>
-
-<p>
-The diameter of the moon is only 2160 miles; and Jupiter's diameter of
-88000 miles is incomparably less than that of the sun The diameter of
-Pallas does not much exceed 71 miles, so that an inhabitant of that
-planet, in one of our steam-carriages, might go round his world in five
-or six hours.
-</p>
-
-<p>
-The oblate form of the celestial bodies indicates rotatory motion, and
-this has been confirmed, in most cases, by tracing spots on their
-surfaces, whence 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 ten hours, about an axis that is directed
-towards a point half way between the pole star and Lyra, the plane of
-rotation being inclined a little more than 70° to that on which the
-earth revolves. 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 as yet 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 about seven times the distance of
-the moon from the earth.
-</p>
-
-<p>
-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 from the primitive causes which have
-determined the planetary motions.
-</p>
-
-<p>
-The larger planets rotate in shorter periods than the smaller planets
-and the earth; their compression is consequently greater, and the action
-of the sun and of their satellites occasions a nutation 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. 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.
-</p>
-
-<p>
-The appearance of Saturn is unparalleled in the system of the world; he
-is surrounded by a ring even brighter than himself, which always remains
-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. 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 10 ½ hours, 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 31°; and in consequence
-of this obliquity of position they always appear elliptical to us, but
-with an eccentricity so variable as even to be occasionally like a
-straight line drawn across the planet. At present the apparent axes of
-the rings are as 1000 to 160; and on the 29th of September, 1832,
-the plane of the rings will pass through the centre of the earth
-when they will be visible only with superior instruments, and will
-appear like a fine line across the disc of Saturn. On the 1st of
-December in the same year, the plane of the rings will pass through
-the centre of the sun.
-</p>
-
-<p>
-It is a singular result of the theory, that the rings could not maintain
-their stability of rotation if they were everywhere 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 the different parts
-of the circumference, so that their centres of gravity do not coincide
-with the centres of their figures.
-</p>
-
-<p>
-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 eccentricity of the globe in the ring of
-0"·215.
-</p>
-
-<p>
-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.
-</p>
-
-<p>
-The periods of the 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 other 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 the poles from her centrifugal
-force, therefore her polar axis is 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 earth and moon; so that it would vibrate 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.
-</p>
-
-<p>
-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 earthy it would
-have rendered the libration sensible. A similar libration exists in the
-motions of Jupiter's satellites; but although the comet of 1767 and 1779
-passed through the midst of them, their libration still remains
-insensible. It is true, the moon is liable to librations depending on
-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 moon exhibiting a surface thirteen times
-larger than ours, 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.
-</p>
-
-<p>
-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.
-</p>
-
-<p>
-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.
-</p>
-
-<p>
-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 that prevail throughout creation, the period of
-the earth's diurnal rotation is immutable. A fluid, as Mr. Babbage
-observes, in 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
-its 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 again by removing matter to a greater distance from the centre,
-destroy the velocity generated by its previous approach; so that the
-descent of the rivers does not affect the earth's rotation. Enormous
-masses projected by volcanoes from the equator to the poles, and the
-contrary, would indeed affect 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 an
-external 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 nature of fossil
-remains, that the mean temperature of the globe is decreasing.
-</p>
-
-<p>
-The high temperature of mines, hot springs, and above all, the internal
-fires that have produced, and do still occasion such devastation on our
-planet, indicate an augmentation of heat towards its centre the increase
-of density in the strata 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, 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. But even if this cause be
-sufficient to produce the observed effects, 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 hundredth 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 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 indication of the
-primitive fluidity of the earth, as there is no direct proof, it can
-only be regarded as a very probable hypothesis; but one of the most
-profound philosophers and elegant writers of modern times has found, in
-the secular variation of the eccentricity of the terrestrial orbit, an
-evident cause of decreasing temperature. That accomplished author, in
-pointing out the mutual dependences of phenomena, says&mdash;'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 8 higher degree than it
-would have were the sun extinguished, must 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, <i>cœteris paribus</i>, 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 eccentricity 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 the other inhabitants
-of the torrid zone, it is impossible to say.
-</p>
-
-<p>
-The relative quantity of heat received by the earth at different moments
-during a single revolution, varies with the position of the perigee of
-its orbit, which accomplishes a tropical revolution in 20935 years. In
-the year 1250 of our era, and 29653 years before it, the perigee
-coincided with the summer 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.
-</p>
-
-<p>
-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 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 ending to the new equator would leave some portions
-of the globe, and overwhelm others.
-</p>
-
-<p>
-But theory 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 some foreign
-cause, as the collision of a comet which may have happened in the
-immensity of time. Then indeed, the equilibrium could only have been
-restored by the rushing of the seas to the new equator, which they would
-continue to do, till the surface was every where 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
-even of the Pacific ocean is not more than four miles, whereas the
-equatorial radius of the earth exceeds the polar radius by twenty-five
-or thirty miles; consequently the influence of the sea on the direction
-of gravity is very small; and as it appears that a great change in the
-position of the axes is incompatible with the law of equilibrium, the
-geological phenomena must be ascribed to an internal cause. 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 axis on
-its surface, have undergone but slight variations.
-</p>
-
-<p>
-It is beyond a doubt that the strata increase in density from the
-surface of the earth to its centre, which is even proved by the lunar
-inequalities; and it is manifest from the mensuration of arcs of the
-meridian and the lengths of the seconds pendulum that the strata are
-elliptical and concentric. This certainly would 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
-these phenomena. 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
-4000 miles, the condensation of ordinary materials would surpass the
-utmost powers of conception. But a density so extreme is not borne out
-by astronomical observation. It might seem therefore to follow, 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. 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; but, from the experiments of Mr.
-Perkins, they appear to be capable of a greater degree of compression
-than has generally been imagined.
-</p>
-
-<p>
-It appears then, that the axis of rotation is invariable on the surface
-of the earth, and observation shows, 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.
-</p>
-
-<p>
-The attraction of an exterior 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 situated in the prolongation of one of the axes of
-the spheroid.
-</p>
-
-<p>
-The plane of the equator is inclined to the plane of the ecliptic at an
-angle of about 23° 28', and the inclination of the lunar orbit on the
-same is nearly 5°; 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 about 50"·412 annually. The direct tendency of this action
-would be to make the planes of the equator and ecliptic coincide; but in
-consequence of the rotation of the earth, the inclination of the two
-planes remains constant, as a top in 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
-to the same points of the ecliptic, at least as far as this kind of
-action is concerned. But another and totally different cause operates on
-this motion, which 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 on
-the plane of the equator, and gives the equinoctial points a slow but
-direct motion on the ecliptic of 0"·312 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,
-but 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"·1 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 then 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"·1 annually, the equinoctial points will
-accomplish a revolution in 25868 years; but as the precession varies in
-different centuries, the extent of this period will be 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
-365.242264 days must be increased by the time he takes to move through
-an arc of 50"·1, in order to have the length of the sidereal year. By
-simple proportion it is the 0.014119th part of a day, so that the
-sidereal year is 365.256383.
-</p>
-
-<p>
-The mean annual precession is subject to a secular variation; for
-although the change in the plane of the ecliptic which is the orbit of
-the sun, 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 lime of Hipparchus; consequently the
-actual length of the tropical year is about 4"·154 shorter than it was
-at that time. The utmost change that it can experience from this cause
-amounts to 43".
-</p>
-
-<p>
-Such is the secular motion of the equinoxes, but it is sometimes
-increased and sometimes diminished by periodic variations, whose periods
-depend on the relative positions of the sun and moon with regard to the
-earth, and 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
-nineteen 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
-oblique of the ecliptic is annually diminished by 0"·52109. With
-regard to the fixed stars, this variation in the course of ages may
-amount to tea or eleven degrees; but the obliquity of the ecliptic to
-the equator can never vary more than two or three degrees, since the
-equator will follow in some measure the motion of the ecliptic.
-</p>
-
-<p>
-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.
-</p>
-
-<p>
-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" and
-17"·08, and the mass of the earth is the ¹⁄₃₅₄₉₃₆th 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 450 feet
-in a second; consequently if he were even habitable by human beings,
-they would be unable to move, since their weight would be thirty
-times as great as it is here. A moderate sized man would weigh about
-two tons at the surface of the sun. On the contrary, at the surface
-of the four new planets we should be so light, that it would be
-impossible to stand from the excess of our muscular force, for a man
-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; and
-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.
-</p>
-
-<p>
-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 to compare all great periods of
-time; 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.
-</p>
-
-<p>
-The returns of the sun to the same 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 the meridian, or of
-one which is supposed to move in the equator, is denominated mean solar
-time, such as is given by clocks and watches in common life: when it is
-reckoned by the arrival of the real sun at the meridian, it is apparent
-time, such as is given by dials. The difference between the time shown
-by a clock and a dial is the equation of time given in the Nautical
-Almanac, and sometimes amounts to as much as sixteen minutes. The
-apparent and mean time coincide four times in the year.
-</p>
-
-<p>
-Astronomers begin the day at noon, but in common reckoning the day
-begins at midnight. In England it is divided into twenty-four hours,
-which are counted by twelve and twelve; but in France, astronomers
-adopting decimal division, divide the day into ten hours, the hour into
-one hundred minutes, and the minute into a hundred seconds, because of
-the facility in computation, and in conformity with their system of
-weights and measures. This subdivision is not used in common life, nor
-has it been adopted in any other country, though their scientific
-writers still employ that division of time. The mean length of the day,
-though accurately determined, is not sufficient for the purposes either
-of astronomy or civil life. The length of the year is pointed out by
-nature as a measure of long periods; but the incommensurability that
-exists between the lengths of the day, and the revolutions of the sun,
-renders it difficult to adjust the estimation of both in whole numbers.
-If the revolution of the sun were accomplished in 365 days, all the
-years would be of precisely the same number of days, and would begin and
-end with the sun at the same point of the ecliptic; but as the sun's
-revolution includes the fraction of a day, a civil year and a revolution
-of the sun have not the same duration. Since the fraction is nearly the
-fourth of a day, four years are nearly equal to four revolutions of the
-sun, so that the addition of a supernumerary day every fourth year
-nearly compensates the difference; but in process of time further
-correction will be necessary, because the fraction is less than the
-fourth of a day. 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.
-</p>
-
-<p>
-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 Cæsar; the
-25th of December in his 45th year, is considered as the date of Christ's
-nativity; and Cæsar's 46th 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 actually elapsed
-since that time.
-</p>
-
-<p>
-Some remarkable astronomical eras are determined by the position of the
-major axis of the solar ellipse. Moving at the rate of 61"·906
-annually, it accomplishes a tropical revolution in 20935 years. It
-coincided with the line of the equinoxes 4000 or 4089 years before the
-Christian era, much about the time chronologists assign for the creation
-of man. In 6485 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 1250 the major axis was perpendicular to the line
-of the equinoxes, and then the solar perigee coincided with the solstice
-of winter, and the apogee with the solstice of summer. On that account
-La Place proposed the year 1250 as a universal epoch, and that the
-vernal equinox of that year should be the first day of the first year.
-</p>
-
-<p>
-The variations in the positions of the solar ellipse occasion
-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 about seven days. These intervals will be
-equal towards the year 6485, when the perigee comes to the equinox of
-spring. Were the earth's orbit circular, the seasons would be equal;
-their differences arise from the eccentricity of the earth's orbit,
-small as it is; but the changes are so gradual as to be imperceptible in
-the short space of human life.
-</p>
-
-<p>
-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 language, arts and
-sciences, leaving but confused masses of ruin 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 period they must have made
-considerable progress in science.'
-</p>
-
-<p>
-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 show to how many centuries they may be extended,
-without the fear of error. A few examples will show the importance of
-this subject.
-</p>
-
-<p>
-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 style 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 in the obliquity is known, both the time
-and place of the observations have been verified by computation from
-modern tables. Thus the Chinese had made some advances in the science of
-astronomy at that early period; the whole chronology of the Chinese is
-founded on the observations 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 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. 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 menu motion of Saturn was at the slowest, and that of Jupiter
-the most rapid. The periods in which that happened were 3102 years
-before the Christian era, and the year 1491 after it.
-</p>
-
-<p>
-The returns of comets to their perihelia may possibly mark the present
-state of astronomy to future ages.
-</p>
-
-<p>
-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 from computation it
-appears that  <i>χ</i> Draconis was not very far from that place about 3000
-years ago; but as Eudoxus lived only about 2150 years ago, he must have
-described an anterior state of the heavens, supposed to be the same that
-was determined 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.
-</p>
-
-<p>
-A knowledge of astronomy leads to the interpretation of hieroglyphical
-characters, since astronomical signs are often found on the ancient
-Egyptian monuments, which were probably employed by the priests to
-record dates. On the ceiling of the portico of a temple among the ruins
-of Tentyris, there is a long row of figures of men and animals,
-following each other in the some direction among these are the twelve
-signs of the zodiac, placed according to the motion of the sun: it is
-probable that the first figure in the procession represents the
-beginning of the year. Now the first is the Lion as if coming out of the
-temple; and as it is well known that the agricultural year of the
-Egyptians commenced at the solstice of summer, the epoch of the
-inundations of the Nile, if the preceding hypothesis be true, the
-solstice at the time the temple was built must have happened in the
-constellation of the lion; but as the solstice now happens 21° 6' north
-of the constellation of the Twins, it is easy to compute that the zodiac
-of Tentyris must have been made 4000 years ago.
-</p>
-
-<p>
-The author had occasion to witness an instance of this most interesting
-application of astronomy, in ascertaining the dale 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 not only
-to his country, but 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.
-</p>
-
-<p>
-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 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, in parts of the imperial standard yard,
-to be 39.1387 inches. The weight of a cubic inch of water at the
-temperature of 62° Fahrenheit, barometer 30, 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 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 vicissitudes 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 subdivision in taking its ten millionth part. The
-French have adopted the decimal division not only in time, but in their
-degrees, weights, and measures, which affords very great facility 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 the 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 Yunus made
-his observations at Cairo, about the year 1000, the Arabians were in the
-habit of employing the vibrations of the pendulum in their astronomical
-observations.
-</p>
-
-<p>
-One of the most immediate and striking 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
-24<sup>h</sup> 50<sup>m</sup> 48<sup>s</sup> of mean solar
-time. As it depends on the action of the sun and moon, it is classed
-among astronomical problems, of which it is by far the most difficult
-and 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.
-</p>
-
-<p>
-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.
-</p>
-
-<p>
-It is proved by daily experience, as well as by strict mechanical
-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, producing their
-effects independently of each other, which may therefore be estimated
-separately.
-</p>
-
-<p>
-The oscillations of the first kind which are very small, are independent
-of the rotation of the earth; and as they depend on the motion of the
-disturbing body in its orbit, they are of long periods. The second kind
-of oscillations depends on the rotation of the earth, therefore their
-period is nearly a day: and the oscillations of the third kind depend on
-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 on the second. At the time of the solstices,
-this difference which, according to Newton's theory, ought to be very
-great, 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, were it
-not for 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 in the earth's axis, are the same as if the
-sea formed one solid mass with the earth.
-</p>
-
-<p>
-The third kind of oscillations are the semidiurnal 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.
-</p>
-
-<p>
-The particles of water under the moon are more attracted than the centre
-of gravity of the earth, in 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 this tendency diminishes. 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 this tendency again diminishes. 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 above the
-surface of equilibrium of nearly the same height; 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 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 really 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 instantly assuming the form of equilibrium, 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 on 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 the meridian at 90° distant,
-it is everywhere low water. It is evident that these tides must happen
-twice in a day, since in that time the rotation of the earth brings the
-same point twice under the meridian of the moon, once under the superior
-and once under the inferior meridian.
-</p>
-
-<p>
-In the semidiurnal tides there are two phenomena particularly to be
-distinguished, one that happens twice in a month, and the other twice in
-a year.
-</p>
-
-<p>
-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 the
-full tide, the lower it is in the ebb. The neap tides lake 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. It is evident that the spring tides must happen twice a
-month, since in that time the moon is once new and once full.
-</p>
-
-<p>
-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° 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. Beside these remarkable variations, there are
-others arising from the declination of the moon, which has a great
-influence on the ebb and flow of the waters.
-</p>
-
-<p>
-Both the height and time of high water are thus perpetually changing;
-therefore, in solving the problem, it is required to determine the
-heights to which they rise, the times at which they happen, and the
-daily variations.
-</p>
-
-<p>
-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, 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, the resistance the waters meet with, all of
-them causes which 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 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 funeral phenomena which ought to
-result from the attraction of the sun and moon, but these must be
-corrected in each particular case by those local observations which are
-modified by the extent and depth of the sea, and the peculiar
-circumstances of the port.
-</p>
-
-<p>
-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, and from that 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 great combined wave, reflected by the shores of the
-Atlantic, extending nearly from pole to pole, still coming northward,
-occurs through the Irish and British channels into the North sea, so
-that the tides in our ports are modified by those of another hemisphere.
-Thus 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.
-</p>
-
-<p>
-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. 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 one. 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.
-</p>
-
-<p>
-These perpetual commotions in the waters of the ocean are occasioned by
-forces that bear a very small proportion to terrestrial gravitation: the
-sun's action in raising the ocean is only the ¹⁄₃₈₄₄₈₀₀₀₀ 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. From this
-ratio the mass of the moon is found to be only ¹⁄₁₅ part of that of the
-earth. 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, 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.
-</p>
-
-<p>
-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 the particles of matter 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. Now at the
-temperature of melting ice, the density of mercury is to that of air as
-10320 to 1; and as the mean height of the barometer is 29.528 inches,
-the height of the atmosphere by simple proportion is 30407 feet, at the
-mean temperature of 62°, or 34153 feet, which is 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 occasion periodic variations in the
-heights of the barometer. These, however, are so extremely small, that
-their existence in latitudes so far removed from the equator is
-doubtful; a series of observations within the tropics can alone decide
-this delicate point. 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.
-</p>
-
-<p>
-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 currents in the direction of the meridian. But the
-rotatory velocity of the air corresponding to its geographical situation
-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 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.
-</p>
-
-<p>
-The sun and most of the planets appear to be surrounded with atmospheres
-of considerable density. The attraction of the earth has probably
-deprived the moon of hers, for the refraction of the air at the surface
-of the earth is at least a thousand times as great as at 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.
-</p>
-
-<p>
-Many philosophers of the highest authority concur in the belief that
-light consists in the undulations of a highly elastic ethereal medium
-pervading space, which, communicated to the optic nerves produce the
-phenomena of vision. The experiments of our illustrious countryman, Dr.
-Thomas Young, and those of the celebrated Fresnel, show that this theory
-accords better with all the observed phenomena than that of the emission
-of particles from the luminous body. As sound is propagated by the
-undulations of the air, its theory is in a great many respects similar
-to that of light. 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 notes of the organ to the
-highest known cry of insects, as of the cricket, includes about nine
-octaves.
-</p>
-
-<p>
-The undulations of light are much more rapid than those of sound, but
-they are analogous in this respect, that as the frequency of the
-pulsations in sound increases from the low tones to the higher, so those
-of light augment in frequency, from the red rays of the solar spectrum
-to the extreme violet. By the experiments of Sir William Herschel, it
-appears that the heat communicated by the spectrum increases from the
-violet to the red rays; but that the maximum of the hot invisible rays
-is beyond the extreme red. Heat in all probability consists, like light
-and sound, 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 by 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
-undulating theories are perfectly similar. If, therefore, we may judge
-from analogy, the undulations 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.
-</p>
-
-<p>
-The propagation of sound requires a much denser medium than that of
-either 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.
-</p>
-
-<p>
-What the body of the sun may be, it is impossible to conjecture; but he
-seems to be surrounded by an ocean of flame through which his dark
-nucleus appears like black spots, often of enormous size. The solar
-rays, which probably arise from the 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 where such combustion is going on, as
-the intensity both of his light and heat diminishes with the square of
-the distance, his kindly influence can hardly be felt at the boundaries
-of our system. Much depends on the manner in which the rays fall, as we
-readily perceive from the different climates on our globe. In winter the
-earth is nearer the sun by ¹⁄₃₀th 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; that is however 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, unless indeed the
-ether has a temperature. 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 quick-silver, 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.
-</p>
-
-<p>
-The direct light of the sun has been estimated to be equal to that of
-5563 wax candles of a 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 imparts no heat, even when brought to a focus by a mirror.
-</p>
-
-<p>
-In adverting to the peculiarities in the form and nature of the earth
-and planets, it is impossible to pass in silence the magnetism of the
-earth, the director of the mariner's compass, and his guide through the
-ocean. This property probably arises from metallic iron in the interior
-of the earth, or from the circulation of currents of electricity round
-it: its influence extends over every part of its surface, but its
-accumulation and deficiency determine the two poles of this great
-magnet, which are by no means the same as 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 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. In the year 1819, Captain Parry, in his voyage to
-discover the north-west passage round America, sailed directly over the
-magnetic pole; and in 1824, Captain Lyon, when on en expedition for the
-same purpose, found that the variation of the compass was 37° 30'
-west, and that the magnetic pole was then situate in 63° 26' 51"
-north latitude, and in 80° 51' 25" west longitude. It appears
-however from later researches that the law of terrestrial magnetism is
-of considerable complication, and the existence of more than one
-magnetic pole in either hemisphere has been rendered highly probable.
-The needle is also subject to diurnal variations; in our latitudes it
-moves slowly westward from about three in the morning till two, and
-returns to its former position in the evening.
-</p>
-
-<p>
-A needle suspended so as only to be moveable in the vertical plane, dips
-or become more and more inclined to the horizon the nearer it is brought
-to the magnetic pole. Captain Lyon found that the dip in the latitude
-and longitude mentioned was 86° 32'. What properties the planets may
-have in this respect, it is impossible to know, but it is probable that
-the moon has become highly magnetic, in consequence of her proximity to
-the earth, and because her greatest diameter always points towards it.
-</p>
-
-<p>
-The passage of comets has never sensibly disturbed the stability of the
-solar system; their nucleus is 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 effect. The comet of 1770 passed
-within 80000 miles of the earth without even affecting our tides, and
-swept through the midst of Jupiter's satellites without deranging the
-motions of those little moons. Had the mass of that comet been equal to
-the mass of the earth, its disturbing action would have shortened the
-year by the ninth of a day; but, as Delambre's computations from the
-Greenwich observations of the sun, show that the length of the year has
-not been sensibly affected by the approach of the comet. La Place proved
-that its mass could not be so much as the 5000th part of that of the
-earth. The paths of comets have every possible inclination to the plane
-of the ecliptic, and unlike the planets, their motion is frequently
-retrograde. Comets 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 eccentric ellipses, although, in most cases, the
-parabolic curve coincides most nearly with their observed motions. Even
-if the orbit be determined with all the accuracy that 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 and Clairaut predicted that, in consequence of the
-attraction of Jupiter and Saturn, the return of the comet of 1759 would
-be retarded 618 days, which was verified by the event as nearly as could
-be expected.
-</p>
-
-<p>
-The nebulous appearance of comets is perhaps occasioned by the vapours
-which the solar heat raises at their surfaces in their passage at the
-perihelia, and which are again condensed as they recede from the sun.
-The comet of 1680 when in its perihelion was only at the distance of
-one-sixth of the sun's diameter, or about 148000 miles from its surface;
-it consequently would be exposed to a heat 27500 times greater than that
-received by the earth. As the sun's heat is supposed to be in proportion
-to the intensity of his height, 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.
-</p>
-
-<p>
-In those positions of comets where only half of their enlightened
-hemisphere ought to be seen, they exhibit no phases even when viewed
-with high magnifying powers. Some slight indications however were once
-observed by Hevelius and La Hire in 1682; and in 1811 Sir William
-Herschel discovered a small luminous point, which he concluded to be the
-disc of the comet. In general their masses are so minute, that they have
-no sensible diameters, the nucleus being principally formed of denser
-strata of the nebulous matter, but so rare that stars have been seen
-through them. The transit of a comet over the sun's disc would afford
-the best information on this point. It was computed that such an event
-was to take place in the year 1627; unfortunately the sun was hid by
-clouds in this country, but it was observed at Viviers and at Marseilles
-at the time the comet must have been on it, but no spot was seen. The
-tails are often of very great length, and are generally situate in the
-planes of their orbits; they follow them in their descent towards the
-sun, but precede them in their return, with a small degree of curvature;
-but their extent and form must vary in appearance, according to the
-position of their orbits with regard to the ecliptic. The tail of the
-comet of 1680 appeared, at Paris, to extend over sixty-two degrees. The
-matter of which the tail is composed must be extremely buoyant to
-precede a body moving with such velocity; indeed the rapidity of its
-ascent cannot be accounted for. 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 in 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 wilt disappear for ever. Possibly comets
-may have vanished from our view sooner than they otherwise would have
-done from this cause. Of about six hundred comets that have been seen at
-different times, three are now perfectly ascertained to form part of our
-system; that is to say, they return to the sun at intervals of 76, 6 ⅓,
-and 3 ¼ years nearly.
-</p>
-
-<p>
-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 that range within the earth's
-orbit must be 1400; but Uranus being twenty times more distant, there
-may be no less than 11,200,000 comets that come within the known extent
-of our system. In such a multitude of wandering bodies it is just
-possible that one of them may come in collision with the earth; but even
-if it should, the mischief would be local, and the equilibrium soon
-restored. It is however more probable that the earth would only be
-deflected a little from its course by the near approach of the comet,
-without being touched. 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 quarter of an hour Sir
-William Herschel estimated that 116000 stars passed through the field of
-his telescope, which subtended an angle of 15'. This however was
-stated as a specimen of extraordinary crowding; but at an average the
-whole expanse of the heavens must exhibit about a hundred millions of
-fixed stars that come within the reach of telescopic vision.
-</p>
-
-<p>
-Many of the stars have a very small progressive motion, especially <i>μ</i>
-Cassiopeia and 61 Cygni, both small stars; and, as the sun is decidedly
-a star, it is an additional reason for supposing the solar system to be
-in motion. The distance of the fixed stars is too great to admit of
-their exhibiting a sensible disc; but in all probability they are
-spherical, and must certainly be so, if gravitation pervades all space.
-With a fine telescope they appear like a point of light; their twinkling
-arises from sudden changes in the refractive power of the air, which
-would not be sensible if they had discs like the planets. Thus we can
-learn nothing of the relative distances of the stars from us and from
-one another, by their apparent diameters; but their annual parallax
-being insensible, shows that we must be one hundred millions of millions
-of miles from the nearest; many of them however must be vastly more
-remote, for of two stars that appear close together, one may be far
-beyond the other in the depth of space. The light of Sirius, according
-to the observations of Mr. Herschel, is 324 times greater than that of a
-star of the sixth magnitude; if we suppose the two to be really of the
-same size, their distances from us must be in the ratio of 57.3 to 1,
-because light diminishes as the square of the distance of the luminous
-body increases.
-</p>
-
-<p>
-Of the absolute magnitude of the stars, nothing is known, only that many
-of them must be much larger than the sun, from the quantity of light
-emitted by them. Dr. Wollaston determined the approximate ratio that the
-light of a wax candle bears to that of the sun, moon, and stars, by
-comparing their respective images reflected from small glass globes
-filled, with mercury, whence a comparison was established between the
-quantities of light emitted by the celestial bodies themselves. By this
-method he found that the light of the sun is about twenty millions of
-millions of times greater than that of Sirius, the brightest, 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
-immensely greater than Sirius. Sometimes stars have all at once
-appeared, shone with a brilliant light, and then vanished. 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 any thing
-more tremendous than a conflagration that could be visible at such a
-distance. Some stars are periodic, possibly from the intervention of
-opaque bodies revolving about them, or from extensive spots on their
-surfaces. 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 revolving about a common centre. These double and multiple
-stars are extremely remote, requiring the most powerful telescopes to
-show them separately.
-</p>
-
-<p>
-The first catalogue of double stars in which their places and relative
-positions are determined, was accomplished by the talents and industry
-of Sir William Herschel, to whom astronomy is indebted for so many
-brilliant discoveries, and with whom originated the idea of their
-combination in binary and multiple systems, an idea which his own
-observations had completely established, but which has since received
-additional confirmation from those of his son and Sir James South, the
-former of whom, as well as Professor Struve of Dorpat, have added many
-thousands to their numbers. The motions of revolution round a common
-centre of many have been clearly established, and their periods
-determined with considerable accuracy. Some have already since their
-first discovery accomplished nearly a whole revolution, and one, if the
-latest observations can be depended on, is actually considerably
-advanced in its second period. These interesting systems thus present a
-species of sidereal chronometer, by which the chronology 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.
-</p>
-
-<p>
-Possibly among the multitudes of small stars, whether double or
-insulated, some may be found near enough to exhibit distinct parallactic
-motions, or perhaps something approaching to planetary motion, which may
-prove that solar attraction is not confined to our system, or may lead
-to the discovery of the proper motion of the sun. 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
-of a full ruby red, or almost blood colour, and the small one a fine
-green, the latter lost its colour when the former was 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. Mr. Herschel
-observes in one of his papers in the <i>Philosophical Transactions</i>, as
-a very remarkable fact, that although red single stars are common enough,
-no example of an insulated blue, green, or purple one has as yet been
-produced.
-</p>
-
-<p>
-In some parts of the heavens, the stars are so near together as to form
-clusters, which to the unassisted eye appear like thin white clouds;
-such is the milky way, which has its brightness from the diffused light
-of myriads of stars. Many of these clouds, however, are never resolved
-into separate stars, even by the highest magnifying powers. This
-nebulous matter exists in vast abundance in space. No fewer than 2500
-nebulæ 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 celebrated for astronomical knowledge and
-discovery. 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 rudiments of future systems. With this view, Mr. Herschel is now
-engaged in the difficult and laborious investigation, which is
-understood to be nearly approaching its completion, and the results of
-which we may therefore hope ere long to see made public. The most
-conspicuous of these appearances are found in Orion, and in the girdle
-of Andromeda. It is probable that light must be millions of years
-travelling to the earth from some of the nebulæ.
-</p>
-
-<p>
-So numerous are the objects which meet our view in the heavens, that we
-cannot imagine a part of space where some light would not strike the
-eye: but as the fixed stars would not be visible at such distances, if
-they did not shine by their own light, it is reasonable to infer that
-they are suns; and if so, they are in all probability attended by
-systems of opaque bodies, revolving about them as the planets do about
-ours. But although there be no proof that planets not seen by us revolve
-about these remote suns, certain it is, that there are many invisible
-bodies wandering in space, which, occasionally coming 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 obliquity of the descent of meteorites, the peculiar
-matter of which they are composed, and the explosion with which their
-fall is invariably accompanied, show that they are foreign to our
-planet. Luminous spots altogether independent of the phases have
-occasionally appeared on the dark part of the moon, which have been
-ascribed to the light arising from the eruption of volcanoes; 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, and with an
-initial velocity of 10992 feet in a second, which is 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.
-</p>
-
-<p>
-The known quantity of matter bears a very small proportion to the
-immensity of space. Large as the bodies are, the distances that 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 void, when it is traversed in
-all directions by light, heat, gravitation, and possibly by influences
-of which we can form no idea; but whether it be replete with an ethereal
-medium, time alone will show.
-</p>
-
-<p>
-Though totally ignorant of the laws which obtain in the more distant
-regions of creation, we are assured, that one alone regulates the
-motions of our own system; and as general laws form the ultimate object
-of philosophical research, we cannot conclude these remarks without
-considering the nature of 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 gravitating 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.
-</p>
-
-<p>
-The analytical expression for the gravitating force is a straight line;
-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 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 other laws,
-its being the most simple, and that which gives the greatest stability
-to the celestial motions.
-</p>
-
-<p>
-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 in the solar system, their mutual distances, and their
-velocities, were to diminish proportionally, they would describe curves
-in all respect 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. Experience shows 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 attractions, 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 at the immense distance of the fixed stars. 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.
-</p>
-
-<p>
-The action of the gravitating force is not impeded by the intervention
-even of the densest substances. If the attraction of the sun for the
-centre of the earthy and for the hemisphere diametrically opposite to
-him, was 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 on the earth differed by a millionth part
-from his action on the moon, the difference would occasion a variation
-in the sun's parallax amounting to several seconds, which is proved to
-be impossible by the agreement of theory with observation. Thus all
-matter is pervious to gravitation, and is equally attracted by it.
-</p>
-
-<p>
-As far as human knowledge goes, 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, and magnetic fluids are
-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 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 which we in vain look for in the
-other parts of the universe. They date the beginning of time; since
-there is every reason 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.'
-</p>
-
-<p><br /><br /><br /></p>
-
-<div style='display:block; margin-top:4em'>*** END OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON THE MECHANISMS OF THE HEAVENS ***</div>
-<div style='text-align:left'>
-
-<div style='display:block; margin:1em 0'>
-Updated editions will replace the previous one&#8212;the old editions will
-be renamed.
-</div>
-
-<div style='display:block; margin:1em 0'>
-Creating the works from print editions not protected by U.S. copyright
-law means that no one owns a United States copyright in these works,
-so the Foundation (and you!) can copy and distribute it in the United
-States without permission and without paying copyright
-royalties. Special rules, set forth in the General Terms of Use part
-of this license, apply to copying and distributing Project
-Gutenberg&#8482; electronic works to protect the PROJECT GUTENBERG&#8482;
-concept and trademark. Project Gutenberg is a registered trademark,
-and may not be used if you charge for an eBook, except by following
-the terms of the trademark license, including paying royalties for use
-of the Project Gutenberg trademark. If you do not charge anything for
-copies of this eBook, complying with the trademark license is very
-easy. You may use this eBook for nearly any purpose such as creation
-of derivative works, reports, performances and research. Project
-Gutenberg eBooks may be modified and printed and given away&#8212;you may
-do practically ANYTHING in the United States with eBooks not protected
-by U.S. copyright law. Redistribution is subject to the trademark
-license, especially commercial redistribution.
-</div>
-
-<div style='margin:0.83em 0; font-size:1.1em; text-align:center'>START: FULL LICENSE<br />
-<span style='font-size:smaller'>THE FULL PROJECT GUTENBERG LICENSE<br />
-PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK</span>
-</div>
-
-<div style='display:block; margin:1em 0'>
-To protect the Project Gutenberg&#8482; mission of promoting the free
-distribution of electronic works, by using or distributing this work
-(or any other work associated in any way with the phrase &#8220;Project
-Gutenberg&#8221;), you agree to comply with all the terms of the Full
-Project Gutenberg&#8482; License available with this file or online at
-www.gutenberg.org/license.
-</div>
-
-<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
-Section 1. General Terms of Use and Redistributing Project Gutenberg&#8482; electronic works
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.A. By reading or using any part of this Project Gutenberg&#8482;
-electronic work, you indicate that you have read, understand, agree to
-and accept all the terms of this license and intellectual property
-(trademark/copyright) agreement. If you do not agree to abide by all
-the terms of this agreement, you must cease using and return or
-destroy all copies of Project Gutenberg&#8482; electronic works in your
-possession. If you paid a fee for obtaining a copy of or access to a
-Project Gutenberg&#8482; electronic work and you do not agree to be bound
-by the terms of this agreement, you may obtain a refund from the person
-or entity to whom you paid the fee as set forth in paragraph 1.E.8.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.B. &#8220;Project Gutenberg&#8221; is a registered trademark. It may only be
-used on or associated in any way with an electronic work by people who
-agree to be bound by the terms of this agreement. There are a few
-things that you can do with most Project Gutenberg&#8482; electronic works
-even without complying with the full terms of this agreement. See
-paragraph 1.C below. There are a lot of things you can do with Project
-Gutenberg&#8482; electronic works if you follow the terms of this
-agreement and help preserve free future access to Project Gutenberg&#8482;
-electronic works. See paragraph 1.E below.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.C. The Project Gutenberg Literary Archive Foundation (&#8220;the
-Foundation&#8221; or PGLAF), owns a compilation copyright in the collection
-of Project Gutenberg&#8482; electronic works. Nearly all the individual
-works in the collection are in the public domain in the United
-States. If an individual work is unprotected by copyright law in the
-United States and you are located in the United States, we do not
-claim a right to prevent you from copying, distributing, performing,
-displaying or creating derivative works based on the work as long as
-all references to Project Gutenberg are removed. Of course, we hope
-that you will support the Project Gutenberg&#8482; mission of promoting
-free access to electronic works by freely sharing Project Gutenberg&#8482;
-works in compliance with the terms of this agreement for keeping the
-Project Gutenberg&#8482; name associated with the work. You can easily
-comply with the terms of this agreement by keeping this work in the
-same format with its attached full Project Gutenberg&#8482; License when
-you share it without charge with others.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.D. The copyright laws of the place where you are located also govern
-what you can do with this work. Copyright laws in most countries are
-in a constant state of change. If you are outside the United States,
-check the laws of your country in addition to the terms of this
-agreement before downloading, copying, displaying, performing,
-distributing or creating derivative works based on this work or any
-other Project Gutenberg&#8482; work. The Foundation makes no
-representations concerning the copyright status of any work in any
-country other than the United States.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.E. Unless you have removed all references to Project Gutenberg:
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.E.1. The following sentence, with active links to, or other
-immediate access to, the full Project Gutenberg&#8482; License must appear
-prominently whenever any copy of a Project Gutenberg&#8482; work (any work
-on which the phrase &#8220;Project Gutenberg&#8221; appears, or with which the
-phrase &#8220;Project Gutenberg&#8221; is associated) is accessed, displayed,
-performed, viewed, copied or distributed:
-</div>
-
-<blockquote>
-  <div style='display:block; margin:1em 0'>
-    This eBook is for the use of anyone anywhere in the United States and most
-    other parts of the world at no cost and with almost no restrictions
-    whatsoever. You may copy it, give it away or re-use it under the terms
-    of the Project Gutenberg License included with this eBook or online
-    at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you
-    are not located in the United States, you will have to check the laws
-    of the country where you are located before using this eBook.
-  </div>
-</blockquote>
-
-<div style='display:block; margin:1em 0'>
-1.E.2. If an individual Project Gutenberg&#8482; electronic work is
-derived from texts not protected by U.S. copyright law (does not
-contain a notice indicating that it is posted with permission of the
-copyright holder), the work can be copied and distributed to anyone in
-the United States without paying any fees or charges. If you are
-redistributing or providing access to a work with the phrase &#8220;Project
-Gutenberg&#8221; associated with or appearing on the work, you must comply
-either with the requirements of paragraphs 1.E.1 through 1.E.7 or
-obtain permission for the use of the work and the Project Gutenberg&#8482;
-trademark as set forth in paragraphs 1.E.8 or 1.E.9.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.E.3. If an individual Project Gutenberg&#8482; electronic work is posted
-with the permission of the copyright holder, your use and distribution
-must comply with both paragraphs 1.E.1 through 1.E.7 and any
-additional terms imposed by the copyright holder. Additional terms
-will be linked to the Project Gutenberg&#8482; License for all works
-posted with the permission of the copyright holder found at the
-beginning of this work.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.E.4. Do not unlink or detach or remove the full Project Gutenberg&#8482;
-License terms from this work, or any files containing a part of this
-work or any other work associated with Project Gutenberg&#8482;.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.E.5. Do not copy, display, perform, distribute or redistribute this
-electronic work, or any part of this electronic work, without
-prominently displaying the sentence set forth in paragraph 1.E.1 with
-active links or immediate access to the full terms of the Project
-Gutenberg&#8482; License.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.E.6. You may convert to and distribute this work in any binary,
-compressed, marked up, nonproprietary or proprietary form, including
-any word processing or hypertext form. However, if you provide access
-to or distribute copies of a Project Gutenberg&#8482; work in a format
-other than &#8220;Plain Vanilla ASCII&#8221; or other format used in the official
-version posted on the official Project Gutenberg&#8482; website
-(www.gutenberg.org), you must, at no additional cost, fee or expense
-to the user, provide a copy, a means of exporting a copy, or a means
-of obtaining a copy upon request, of the work in its original &#8220;Plain
-Vanilla ASCII&#8221; or other form. Any alternate format must include the
-full Project Gutenberg&#8482; License as specified in paragraph 1.E.1.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.E.7. Do not charge a fee for access to, viewing, displaying,
-performing, copying or distributing any Project Gutenberg&#8482; works
-unless you comply with paragraph 1.E.8 or 1.E.9.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.E.8. You may charge a reasonable fee for copies of or providing
-access to or distributing Project Gutenberg&#8482; electronic works
-provided that:
-</div>
-
-<div style='margin-left:0.7em;'>
-    <div style='text-indent:-0.7em'>
-        &#8226; You pay a royalty fee of 20% of the gross profits you derive from
-        the use of Project Gutenberg&#8482; works calculated using the method
-        you already use to calculate your applicable taxes. The fee is owed
-        to the owner of the Project Gutenberg&#8482; trademark, but he has
-        agreed to donate royalties under this paragraph to the Project
-        Gutenberg Literary Archive Foundation. Royalty payments must be paid
-        within 60 days following each date on which you prepare (or are
-        legally required to prepare) your periodic tax returns. Royalty
-        payments should be clearly marked as such and sent to the Project
-        Gutenberg Literary Archive Foundation at the address specified in
-        Section 4, &#8220;Information about donations to the Project Gutenberg
-        Literary Archive Foundation.&#8221;
-    </div>
-
-    <div style='text-indent:-0.7em'>
-        &#8226; You provide a full refund of any money paid by a user who notifies
-        you in writing (or by e-mail) within 30 days of receipt that s/he
-        does not agree to the terms of the full Project Gutenberg&#8482;
-        License. You must require such a user to return or destroy all
-        copies of the works possessed in a physical medium and discontinue
-        all use of and all access to other copies of Project Gutenberg&#8482;
-        works.
-    </div>
-
-    <div style='text-indent:-0.7em'>
-        &#8226; You provide, in accordance with paragraph 1.F.3, a full refund of
-        any money paid for a work or a replacement copy, if a defect in the
-        electronic work is discovered and reported to you within 90 days of
-        receipt of the work.
-    </div>
-
-    <div style='text-indent:-0.7em'>
-        &#8226; You comply with all other terms of this agreement for free
-        distribution of Project Gutenberg&#8482; works.
-    </div>
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.E.9. If you wish to charge a fee or distribute a Project
-Gutenberg&#8482; electronic work or group of works on different terms than
-are set forth in this agreement, you must obtain permission in writing
-from the Project Gutenberg Literary Archive Foundation, the manager of
-the Project Gutenberg&#8482; trademark. Contact the Foundation as set
-forth in Section 3 below.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.F.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.F.1. Project Gutenberg volunteers and employees expend considerable
-effort to identify, do copyright research on, transcribe and proofread
-works not protected by U.S. copyright law in creating the Project
-Gutenberg&#8482; collection. Despite these efforts, Project Gutenberg&#8482;
-electronic works, and the medium on which they may be stored, may
-contain &#8220;Defects,&#8221; such as, but not limited to, incomplete, inaccurate
-or corrupt data, transcription errors, a copyright or other
-intellectual property infringement, a defective or damaged disk or
-other medium, a computer virus, or computer codes that damage or
-cannot be read by your equipment.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the &#8220;Right
-of Replacement or Refund&#8221; described in paragraph 1.F.3, the Project
-Gutenberg Literary Archive Foundation, the owner of the Project
-Gutenberg&#8482; trademark, and any other party distributing a Project
-Gutenberg&#8482; electronic work under this agreement, disclaim all
-liability to you for damages, costs and expenses, including legal
-fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
-LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE
-PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE
-TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE
-LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR
-INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH
-DAMAGE.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a
-defect in this electronic work within 90 days of receiving it, you can
-receive a refund of the money (if any) you paid for it by sending a
-written explanation to the person you received the work from. If you
-received the work on a physical medium, you must return the medium
-with your written explanation. The person or entity that provided you
-with the defective work may elect to provide a replacement copy in
-lieu of a refund. If you received the work electronically, the person
-or entity providing it to you may choose to give you a second
-opportunity to receive the work electronically in lieu of a refund. If
-the second copy is also defective, you may demand a refund in writing
-without further opportunities to fix the problem.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.F.4. Except for the limited right of replacement or refund set forth
-in paragraph 1.F.3, this work is provided to you &#8216;AS-IS&#8217;, WITH NO
-OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
-LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.F.5. Some states do not allow disclaimers of certain implied
-warranties or the exclusion or limitation of certain types of
-damages. If any disclaimer or limitation set forth in this agreement
-violates the law of the state applicable to this agreement, the
-agreement shall be interpreted to make the maximum disclaimer or
-limitation permitted by the applicable state law. The invalidity or
-unenforceability of any provision of this agreement shall not void the
-remaining provisions.
-</div>
-
-<div style='display:block; margin:1em 0'>
-1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
-trademark owner, any agent or employee of the Foundation, anyone
-providing copies of Project Gutenberg&#8482; electronic works in
-accordance with this agreement, and any volunteers associated with the
-production, promotion and distribution of Project Gutenberg&#8482;
-electronic works, harmless from all liability, costs and expenses,
-including legal fees, that arise directly or indirectly from any of
-the following which you do or cause to occur: (a) distribution of this
-or any Project Gutenberg&#8482; work, (b) alteration, modification, or
-additions or deletions to any Project Gutenberg&#8482; work, and (c) any
-Defect you cause.
-</div>
-
-<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
-Section 2. Information about the Mission of Project Gutenberg&#8482;
-</div>
-
-<div style='display:block; margin:1em 0'>
-Project Gutenberg&#8482; is synonymous with the free distribution of
-electronic works in formats readable by the widest variety of
-computers including obsolete, old, middle-aged and new computers. It
-exists because of the efforts of hundreds of volunteers and donations
-from people in all walks of life.
-</div>
-
-<div style='display:block; margin:1em 0'>
-Volunteers and financial support to provide volunteers with the
-assistance they need are critical to reaching Project Gutenberg&#8482;&#8217;s
-goals and ensuring that the Project Gutenberg&#8482; collection will
-remain freely available for generations to come. In 2001, the Project
-Gutenberg Literary Archive Foundation was created to provide a secure
-and permanent future for Project Gutenberg&#8482; and future
-generations. To learn more about the Project Gutenberg Literary
-Archive Foundation and how your efforts and donations can help, see
-Sections 3 and 4 and the Foundation information page at www.gutenberg.org.
-</div>
-
-<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
-Section 3. Information about the Project Gutenberg Literary Archive Foundation
-</div>
-
-<div style='display:block; margin:1em 0'>
-The Project Gutenberg Literary Archive Foundation is a non-profit
-501(c)(3) educational corporation organized under the laws of the
-state of Mississippi and granted tax exempt status by the Internal
-Revenue Service. The Foundation&#8217;s EIN or federal tax identification
-number is 64-6221541. Contributions to the Project Gutenberg Literary
-Archive Foundation are tax deductible to the full extent permitted by
-U.S. federal laws and your state&#8217;s laws.
-</div>
-
-<div style='display:block; margin:1em 0'>
-The Foundation&#8217;s business office is located at 809 North 1500 West,
-Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up
-to date contact information can be found at the Foundation&#8217;s website
-and official page at www.gutenberg.org/contact
-</div>
-
-<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
-Section 4. Information about Donations to the Project Gutenberg Literary Archive Foundation
-</div>
-
-<div style='display:block; margin:1em 0'>
-Project Gutenberg&#8482; depends upon and cannot survive without widespread
-public support and donations to carry out its mission of
-increasing the number of public domain and licensed works that can be
-freely distributed in machine-readable form accessible by the widest
-array of equipment including outdated equipment. Many small donations
-($1 to $5,000) are particularly important to maintaining tax exempt
-status with the IRS.
-</div>
-
-<div style='display:block; margin:1em 0'>
-The Foundation is committed to complying with the laws regulating
-charities and charitable donations in all 50 states of the United
-States. Compliance requirements are not uniform and it takes a
-considerable effort, much paperwork and many fees to meet and keep up
-with these requirements. We do not solicit donations in locations
-where we have not received written confirmation of compliance. To SEND
-DONATIONS or determine the status of compliance for any particular state
-visit <a href="https://www.gutenberg.org/donate/">www.gutenberg.org/donate</a>.
-</div>
-
-<div style='display:block; margin:1em 0'>
-While we cannot and do not solicit contributions from states where we
-have not met the solicitation requirements, we know of no prohibition
-against accepting unsolicited donations from donors in such states who
-approach us with offers to donate.
-</div>
-
-<div style='display:block; margin:1em 0'>
-International donations are gratefully accepted, but we cannot make
-any statements concerning tax treatment of donations received from
-outside the United States. U.S. laws alone swamp our small staff.
-</div>
-
-<div style='display:block; margin:1em 0'>
-Please check the Project Gutenberg web pages for current donation
-methods and addresses. Donations are accepted in a number of other
-ways including checks, online payments and credit card donations. To
-donate, please visit: www.gutenberg.org/donate
-</div>
-
-<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
-Section 5. General Information About Project Gutenberg&#8482; electronic works
-</div>
-
-<div style='display:block; margin:1em 0'>
-Professor Michael S. Hart was the originator of the Project
-Gutenberg&#8482; concept of a library of electronic works that could be
-freely shared with anyone. For forty years, he produced and
-distributed Project Gutenberg&#8482; eBooks with only a loose network of
-volunteer support.
-</div>
-
-<div style='display:block; margin:1em 0'>
-Project Gutenberg&#8482; eBooks are often created from several printed
-editions, all of which are confirmed as not protected by copyright in
-the U.S. unless a copyright notice is included. Thus, we do not
-necessarily keep eBooks in compliance with any particular paper
-edition.
-</div>
-
-<div style='display:block; margin:1em 0'>
-Most people start at our website which has the main PG search
-facility: <a href="https://www.gutenberg.org">www.gutenberg.org</a>.
-</div>
-
-<div style='display:block; margin:1em 0'>
-This website includes information about Project Gutenberg&#8482;,
-including how to make donations to the Project Gutenberg Literary
-Archive Foundation, how to help produce our new eBooks, and how to
-subscribe to our email newsletter to hear about new eBooks.
-</div>
-
-</div>
-</body>
-
-</html>
diff --git a/old/67386-h/images/dissertation_cover.jpg b/old/67386-h/images/dissertation_cover.jpg
deleted file mode 100644
index 7fbf71f..0000000
--- a/old/67386-h/images/dissertation_cover.jpg
+++ /dev/null