Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/80

36 ; I mut add, that the experiments we have been decribing, by no means depending upon that quality of hardnes, do ucceed as well in oft as in hard bodies. For if the rule is to be tried in bodies not perfectly hard, we are only to diminih the reflexion uch a certain proportion as the quantity of the elatic force requires. By the theory of Wren and Huygens, bodies abolutely hard return one from another with the ame velocity with which they meet. But this may be affirmed with more certainty of bodies perfectly elatic. In bodies imperfectly elatic the velocity of the return is to be diminihed together with the elatic force; becaue that force (except when the parts of bodies are bruied by their congres, or uffer ome uch extenion as happens under the trokes of a hammer) is (as far as I can perceive) certain and determined, and makes the bodies to return one from the other with a relative velocity, which is in a given ratio to that relative velocity with which they met. This I tried in balls of wool, made up tightly, and trongly compreed. For, firt, by letting go the pendulous bodies, and meauring their reflexion, I determined the quantity of their elatic force; and then, according to this force, etimated the reflexions that ought to happen in other caes of congres. And with this computation other experiments made afterwards did accordingly agree; the balls always receding one from the other with a relative velocity, which was to the relative velocity with which they met as about 5 to 9. Balls of teel returned with almot the ame velocity: thoe of cork with a velocity omething les; but in balls of glas the proportion was as about 15 to 16. And thus the third Law, o far as it regards percuions and reflexions, is proved by a theory exactly agreeing with experience. Rh