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

ture; I muſt add, that the experiments we have been deſcribing, by no means depending upon that quality of hardneſs, do ſucceed as well in ſoft as in hard bodies. For if the rule is to be tried in bodies not perfectly hard, we are only to diminiſh the reflexion ſuch a certain proportion as the quantity of the elaſtic force requires. By the theory of Wren and Huygens, bodies abſolutely hard return one from another with the ſame velocity with which they meet. But this may be affirmed with more certainty of bodies perfectly elaſtic. In bodies imperfectly elaſtic the velocity of the return is to be diminiſhed together with the elaſtic force; becauſe that force (except when the parts of bodies are bruiſed by their congreſs, or ſuffer ſome ſuch extenſion as happens under the ſtrokes 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 ſtrongly compreſſed. For, firſt, by letting go the pendulous bodies, and meaſuring their reflexion, I determined the quantity of their elaſtic force; and then, according to this force, eſtimated the reflexions that ought to happen in other caſes of congreſs. 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 ſteel returned with almoſt the ſame velocity: thoſe of cork with a velocity ſomething leſs; but in balls of glaſs the proportion was as about 15 to 16. And thus the third Law, ſo far as it regards percuſſions and reflexions, is proved by a theory exactly agreeing with experience.