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which has still the distant appearance of a uniform light and of a continuous [210] surface; and there seems no reason to doubt the possibility of the propagation of an undulation through the Newtonian medium with the actual velocity of light. It must be remembered that the difference of its pressure is not to be estimated from the actual bulk of the earth or any planet alone, but from the effect of the sphere of repulsion of which that planet is the center ; and we may then deduce the force of gravitation from a medium of no very enormous elasticity.

      1  Posthumous Works of Robert Hooke, edited by Richard Waller. London, 1705, pp. xiv, and 184.

      2  History of the Royal Society of London, by Thomas Birch, 1757, 4 vols, quarto, vol. iii, pp. 249–251.

      3  Philosophical Transactions of the Royal Society ; November 18, 1672. No. 88, vol. vii, p. 5088.

      4  Newton's Optics. Second edition, 1777. Book iii, appendix. Query 13.

      5  The Works of Isaac Newton, edited by Samuel Horsley : In 5 vols., quarto. Vol. iv, pp. 335–394.

      6  Works, edited by Horsley, vol. iv, p. 437.

      7  Works, ut supr., vol. iv, p. 438.

      8  Optics, book iii, appendix. Query 21.

      9  Loco citat. Query 28.

      10  Loco citat. Query 31.

      11  Lectures on Natural Philosophy. Ib07, 2 vols, quarto. Lect. xlix, vol. i, pp. 616, 617.

      12  Loco citat. Lecture 50, p. 6110.

      13  Philosophical Transactions of the Royal Society, 1802, vol. xcii, p. 21, and Young's Lectures on Natural Philosophy, vol. ii, p. 618.

      Conditions of the Problem

       Table of Contents

      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

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