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The value of in equation (225) will be augmented by av, there
Consequently, when periodic quantities are omitted, =-3fadv.dR
Thus the mean motion is affected by a secular variation from the resistance of the ethereal medium; but it may easily be shown, from the value of R in article 788, that this medium has no effect whatever on the motion of the lunar nodes or perigee. However, in consequence of that action the second of equations (224), which is the coefficient of sin (cv), ought to be augmented by 6. e; hence, rejecting c2, do, and making c = 1 it gives
must be augmented by av, if the square of v be omitted,
Thus the eccentricity of the lunar orbit is affected by a secular inequality from the resistance of ether, but it is insensible when compared with the corresponding inequality in the mean motion.
It appears then that the mean motion of the moon is subject to a secular variation in consequence of the resistance of ether, which neither affects the motion of the perigee nor the position of the orbit; and, as the secular inequalities of the moon deduced theoretically
from the variation of the eccentricity of the earth's orbit are perfectly confirmed by the concurrence of ancient and modern observations, they cannot be ascribed to the resistance of an ethereal medium. 791. The action of the ether on the motions of the earth may be found by the preceding formula to be
when the eccentricity of the earth's orbit is omitted, so that
If (u') be a function of the distance of the earth from the moon, then must K' = H'. (u'), H' being a constant quantity depending on the mass and surface of the earth. Whence it may be found by the same method with that employed, that the resistance of ether in the mean motion of the earth would be
Whence it appears that the acceleration in the mean motion of the moon is to that in the mean motion of the earth as unity to
Now H' and H depend on the masses and surfaces of the earth and moon; and as the resistance is directly as the surface, and inversely as the mass, therefore
But by article 652, if the radius of the earth be unity, the moon's true diameter =
But as the terrestrial radius is assumed = 1, the earth's surface is
square horizontal parallax of moon
mass of earth square of moon's apparent diameter
From observation half the moon's apparent diameter is 943". 164, her horizontal parallax is 3454.16, and her mass is of that of the
earth, so = 0.17883; and as m =
it follows that the
acceleration in the mean motion of the earth from the resistance of ether is equal to the corresponding acceleration in the mean motion of the moon multiplied by 0.008942, or about a hundred times less than the acceleration of the moon from the resistance of ether. No such acceleration has been detected in the earth's motion, nor could it be expected, since it is insensible with regard to the moon.
In the preceding investigation, the resistance was assumed to be as the square of the velocity, but Mr. Lubbock has obtained general formula, which will give the variations in the elements, whatever the law of this resistance may be.
792. Although we have no reason to conclude that the sun is surrounded by ether, from any effects that can be ascribed to it in the motions of the moon and planets, the question of the existence of such a fluid has lately derived additional interest from the retardation that has been observed in the returns of Enke's comet at each revolution, which it is difficult to account for by any other supposition than this existence of such a medium.
Mr. Enke has proved that this retardation does not arise from the disturbing action of the planets. But on computing
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 exist ence 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 gt aG
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 a (27.32166) its centrifugal force is (27.32166),
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 trans
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,
thus the velocity with which gravity is transmitted must be more than forty-two million times greater than the velocity of light::