V4+ - Sir I S AA'C N E W T O N’s Book II.

dulousffiody with'a cavity in it capable to receive another bodyof an equal weight, at the lowest point of its vibration ; andwhen the body was drop’d into it, he found, by the subsequentvibration, that the velocity of the double mass was preciselyone halt of what the velocity of the pendulum was before >from which it appears, that the fame force produces in a doublequantity of matter one half of the velocity only ; which isagreeable to the common doctrine, but directly repugnant tothe new one, concerning the forces of. bodies in motion.-Many ingenious pieces have been writ against this new doc-,trine by learned men, to which we refer die reader who desiresto fee more on the subject *. It is pretended, that by this newdoctrine we are enabled to resolve problems in an easy manner,which are otherwise of great difficulty ; but by the rejectinghard and inflexible bodies, there is more lost than gained in thisrespect, as we have shewn elsewhere, and as will appear after-wards, when we come to determine more particularly theeffects of the collisions of bodies.

28. It is because aSHon and rea&ion are always equal, that 5the mutual actions ot bodies upon one another have no effectupon the motion of the common centre of gravity of the systemto which they appertain. If there was any aSHon in the system,that had not a contrary and equal reaEiion always correspond-ing to it, it would affect the state of the centre of gravity ofthe system, and disturb its motion : and, conversely, if it beallowed that the state of the centre of gravity of a system is,not disturbed by the actions of bodies upon one another that are :its parts, we may, conclude that their actions are mutual, equal,and have contrary directions. It will therefore be found agree-

* As a piece of Mr. de Mairan , in the memoires de 1 * academie royale des sciences1728. Several pieces of Dr. Jurin> philosophical transactions, &c.

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