74. SIR ~ISAAC NEWTON~ has described these experiments; and has shewn how to improve them to a greater exactness by making allowance for the resistance, which the air gives to the motion of the balls[67]. But as this resistance is exceeding small, and the manner of allowing for it is delivered by himself in very plain terms, I need not enlarge upon it here. I shall rather speak to a discovery, which he made by these experiments upon the elasticity of bodies. It has been explained above[68], that when two bodies strike, if they be not elastic, they remain contiguous after the stroke; but that if they are elastic, they separate, and that the degree of their elasticity determines the proportion between the celerity wherewith they separate, and the celerity wherewith they meet. Now our author found, that the degree of elasticity appeared in the same bodies always the same, with whatever degree of force they struck; that is, the celerity wherewith they separated, always bore the same proportion to the celerity wherewith they met: so that the elastic power in all the bodies, he made trial upon, exerted it self in one constant proportion to the compressing force. Our author made trial with balls of wool bound up very compact, and found the celerity with which they receded, to bear about the proportion of 5 to 9 to the celerity wherewith they met; and in steel he found nearly the same proportion; in cork the elasticity was something less; but in glass much greater; for the celerity, wherewith balls of that material separated after percussion, he found to bear the proportion of 15 to 16 to the celerity wherewith they met[69].
75. I SHALL finish my discourse on pendulums, with this farther observation only, that the center of oscillation is also the center of another force. If a body be fixed to any point, and being put in motion turns round it; the body, if uninterrupted by the power of gravity or any other means, will continue perpetually to move about with the same equable motion. Now the force, with which such a body moves, is all united in the point, which in relation to the power of gravity is called the center of oscillation. Let the cylinder A B C D (in fig. 60.) whose axis is E F, be fixed to the point E. And supposing the point E to be that on which the cylinder is suspended, let the center of oscillation be found in the axis E F, as has been explained above[70]. Let G be that center: then I say, that the force, wherewith this cylinder turns round the point E, is so united in the point G, that a sufficient force applied in that point shall stop the motion of the cylinder, in such a manner, that the cylinder should immediately remain without motion, though it were to be loosened from the point E at the same instant, that the impediment was applied to G: whereas, if this impediment had been applied to any other point of the axis, the cylinder would turn upon the point, where the impediment was applied. If the impediment had been applied between E and G, the cylinder would so turn on the point, where the impediment was applied, that the end B C would continue to move on the same way it moved before along with the whole cylinder; but if the impediment were applied to the axis farther off from E than G, the end A D of the cylinder would start out of its present place that way in which the cylinder moved. From this property of the center of oscillation, it is also called the center of percussion. That excellent mathematician, Dr. BROOK TAYLOR, has farther improved this doctrine concerning the center of percussion, by shewing, that if through this point G a line, as G H I, be drawn perpendicular to E F, and lying in the course of the body’s motion; a sufficient power applied to any point of this line will have the same effect, as the like power applied to G[71]: so that as we before shewed the center of percussion within the body on its axis; by this means we may find this center on the surface of the body also, for it will be where this line H I crosses that surface.