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the effects of the resistance of an ether diffused through space, he found that the diminution in the periodic time, and on the eccentricity arising from the ether, supposing it to exist, corresponds exactly with observation. This coincidence is very remarkable, because ignorance of the nature of the medium in question imposes the necessity of forming an hypothesis of the law of its resistance. Future returns of this comet will furnish the best proof of the existence of an ether, which, by the computation of Mazotti, must be 360,000 millions of times more rare than atmospheric air, in order to produce the observed retardation. The existence of an ethereal medium, if established, would not only be highly important in astronomy, but also from the confirmation it would afford of the undulating theory of light; among whose chief supporters we have to number Huygens, Descartes, Hooke, Euler, and, in later times, the illustrious names of Young and Fresnel, who have applied it with singular success and ingenuity to the explanation of those classes of phenomena which present the greatest difficulties to the corpuscular doctrine.
793. La Place employs the same analysis to determine the effects that the resistance of light has on the motions of the bodies of the solar system, whether considered as propagated by the undulations of a very rare medium as ether, or emanating from the sun. He finds that it has no effect whatever on the motion of the perigee, either of the sun or moon; that its action on the mean motions of the earth and moon is quite insensible; but that the action of light, on the mean motion of the moon, in the corpuscular hypothesis, is to that in the undulating system as 1 to 0.01345.
794. If gravitation be produced by the impulse of a fluid towards the centre of the attracting body, the same analysis will give the secular equation due to the successive transmission of the attractive force. The result is, that if g be the attraction of any body as the earth; G the ratio of the velocity of the fluid which causes gravitation to that of the moon, at her mean distance, and t any finite time, the secular equation of the mean motion of the moon from the transmission of the attractive force is gt2
The gravity of a body moving in its orbit is equal to its centrifugal force; and the latter is equal to the square of the velocity
divided by the radius vector; and as the square of the moon's velocity is a2(27.32166) its centrifugal force is (27.32166)2,
Since G is the ratio of the velocity of the fluid in question to the
hence the velocity of the fluid is (27.32166)aG.
then the velocity of the gravitating fluid is equal to L velocity of light; whence L. vel. light = = (27.32166)aG; but by Bradley's theory, the velocity of light is
a' being the mean distance of the earth from the sun; whence
And the secular equation of the moon from the successive transmission of gravity becomes
Now, if the acceleration in the moon's mean motion arises from the successive transmission of gravity, and not from the secular variation in the earth's eccentricity, the preceding expression would be equal to 10".1816213, the acceleration in 100 Julian years. Therefore, making t = 100,
a (27.32166) 10000 tan 20".25
L = 3
thus the velocity with which gravity is transmitted must be more than forty-two million times greater than the velocity of light:
the velocity of light: hence we must suppose the velocity of the moon to be many a hundred million times greater than that of light to preserve her from being drawn to the earth, if her acceleration be Owing to the successive transmission of gravity. The action of gravity may therefore be regarded as instantaneous.
795. These investigations are general, though they have only been applied to the earth and moon; and, as the influence of the ethereal media and of the transmission of gravity on the moon is quite insensible, though greater than on the earth, it may be concluded, that they have no sensible effect on the motions of the solar system; but as they do not affect the motions of the lunar perigee and the perihelia of the earth and planets at all, these motions afford a more conclusive proof of the law of gravitation, than any other circumstance in the system of the world. The length of the day is proved to be constant by the secular equation of the moon. For if the day were longer now than in the time of Hipparchus by the 0.00324th of a second, the century would be 118".341 longer than at that period. In this interval, the moon would describe an arc of 173".2, and her actual mean secular motion would appear to be augmented by that quantity; so that her acceleration, which is 10".206 for the first century, beginning from 1801, would be increased by 4".377; but observations do not admit of so great an increase. It is therefore certain, that the length of the day has not varied the 0.00324th of a second since the time of Hipparchus.
796. It is evident then, that the lunar motions can be attributed to no other cause than the gravitation of matter of which the concurring proofs are the motion of the lunar perigee and nodes; the mass of the moon; the magnitude and compression of the earth; the parallax of the sun and moon, and consequently the magnitude of the system; the ratio of the sun's action to that of the moon, and the various secular and periodic inequalities in the moon's motions, every one of which is determined by analysis on the hypothesis of matter attracting inversely as the square of the distance; and the results thus obtained, corroborated by observation, leave not a doubt that the whole obey the law of gravitation. Thus the moon is, of all the heavenly bodies, the best adapted to establish the universal influence of this law of nature; and, from the intricacy of her motions, we may form some idea of the powers of analysis, that mar
If be the osculating radius of the orbit, the expression of the radius of curvature, in article 83, will give, when substitution is made for x, y, z, in supposing du constant,
Hence the square of the moon's velocity, divided by the radius of
By the theorems of Huygens, this expression must be equal to the lunar force resolved in the radius of curvature, and directed towards the centre of curvature. Now, if the force
be resolved into two, one parallel to the element of the
curve, and the other directed to the centre of curvature, the latter
these two forces directed towards the centre of curvature is
If the square of this expression be made equal to that of (252), then
which is the same with the second of equations (202), when the inclination of the orbit is omitted.
The equation in latitude is not so easily found as the other two; but the method followed by Newton was to resolve the action of the sun on the moon into two, one in the direction of the radius vector of the lunar orbit, the other parallel to a line joining the centres of the sun and earth. The difference between the last force and the action of the sun on the earth, he saw to be the only force that could change the * 2 K 2