Kinetic Theories of Gravitation/Conditions of the Problem

It is well to bear in mind that every hypothesis directed to the explication of gravity, is required in limine to give a satisfactory account of the following six characteristics of this mysterious influence :

1st. Its direction is radial toward the acting mass, or rectilinear — indefinitely. This rectilinear traction is incapable of deflection by any intermediate force. It suffers neither disturbance nor interference from any multiplication of similar lines of action, and admits neither of reflection, refraction, nor of composition.

2d. Its quantity is exactly proportional to the acting mass — indefinitely. Corollary: hence,

2d b. Its integrity of action is complete with every accumulation of additional demand — indefinitely ; that is to say, no multiplication of duty in the slightest degree impairs its previous tensions.

3d. Its intensity is diminished by recession, in proportion to the square of the distance through which it acts — indefinitely ; in a manner somewhat analogous to — but (as modified by the second condition) radically different from — the action of light.

4th. Its time of action is instantaneous throughout all ascertained distances, and therefore presumably — indefinitely. Corollary : hence,

4th b. Its rate of action (if the expression may be tolerated) is precisely the same on bodies at all velocities — indefinitely. It no more lags on a comet approaching the sun at the inconceivable speed of two hundred miles in one second than on a body at the lowest rate of motion, or than on the same comet receding 'from the sun at the same velocity.

5th. Its quality is invariable under all circumstances — indefinitely. It is entirely unaffected by the interposition of any material screen, whatever its character or extent ; or in other words, it can neither be checked by any insulator not retarded by any obstruction.

6th, Its energy is unchangeable in time, certainly for the past two thousand years; presumably — indefinitely. Corollary: hence,

6th b. Its activity is incessant and inexhaustible — indefinitely; the ceaseless fall of planets from their tangential impulses involving no dynamic expenditure in the sun or in other known matter.

It is scarcely necessary to add, as the necessary outcome of the latter propositions, that gravitation is a property immutable and inconvertible. As in the 1st proposition, tivo terminal elements (m' and m") are necessarily assumed for determining the direction and measure of the radial straight line of action ; and as in the 2d proposition, " the acting mass" (m) is the product of these two elements, {m'.m",) — the action being reciprocal ; so in the 3d proposition, the measure of the diminution of intensity (d²) has reference to the same two elements, between whose dynamic centers the value of the distance d is taken. And the expression for these propositions considered collectively is m'm"/d² as the measure of the combined quantity and intensity of the traction between the two given elements. If we regard m" as incomparably smaller than m', (as [212] for example, a one-pound spherical iron shot thrown to a distance from our terrestrial globe,) its mass may be entirely neglected as a vanishing quantity, and we have the simpler expression m'/d² as indicating the amount of action exercised by our earth upon such a ball.

No hypothesis failing to embrace each of these six requirements deserves consideration ; and any hypothesis fully covering them all, might be expected to account equally for the quite incomparable actions of elasticity, magnetism, affinity, and cohesion, before being entitled lo acceptance as a just or comprehensive theory of molecular force.

As the projectors of kinetic systems of gravitation have almost invariably quite ignored the fourth of the above conditions, it is worth while here to dwell somewhat upon this point. Swift as the earth's orbital motion is, (upward of 18 miles in one second,) the velocity of light is about ten thousand times greater, being 185,000 miles per second. And yet the composition of these two velocities gives .a displacement or '.'aberration" of the heavenly bodies, as seen from our earth, of about 20" of angle for the observed direction of the visual ray. A luminous impulse emanating from the sun requires about 8 ¼ minutes to reach the earth. Were the gravitative influence supposed to be so much swifter than light as to require but a single minute to pass through this distance, there would still be a corresponding gravity "aberration" of 2.4" of angle. The effect of this slight obliquity of traction would be an acceleration of the earth's orbital velocity which would become measurable in a single year.

This is a subject which has been very fully and carefully investigated by astronomers; and the illustrious Laplace, when he found an unexplained minute acceleration in the moon's orbit, threw out the suggestion that if the velocity of transmission of gravitation did not exceed eight million times that of light, it would satisfactorily explain the lunar anomaly. It is scarcely necessary to say that when he subsequently discovered the secular diminution of eccentricity in the earth's orbit, at present continuing, (though slowly reaching its minimum, ) he recognized the true cause of the moon's irregularity, which no longer permitted even the unimaginable limit of possible velocity he had provisionally assigned for gravitative action.

Arago has remarked : " Now if we apply to the perturbation the maximum value which the observations allow, when they have been corrected for the known acceleration due to the variation of the eccentricity of the terrestrial orbit, we find the velocity of the attractive force to amount to fifty millions of times the velocity of light." [213]

If it is possible to represent in such terms the lowest assignable limit of transition, it is because we are furnished with a test of planetary movement of most marvelous delicacy in the record of eclipses occurring at a particular locality 2,000 years ago ; — fixing the relation of annual revolution to diurnal rotation with an almost absolute precision. Sir John Herschel remarks: "From such comparisons Laplace has concluded that the sidereal day has not changed by so much as one-hundredth of a second since the time of Hipparchus!" This implies the absence of even an infinitesimal "aberration" of the gravity radiant, or the negation of any assignable interval for its full and complete action. Hence the fourth category above stated.

The same consideration serves to show that the energy of gravity has undergone no abatement or change during the lapse of two thousand years. Hence the sixth category.

It is but just however, to notice here that a minute outstanding anomaly of the moon, detected in recent years, and still unexplained, detracts somewhat from the accuracy of the above infinitesimal measure ; though it does not impair the value of the general argument. Every investigation, every calculation, of the astronomer, assumes the action of gravity to be for all distances, — absolutely instantaneous.