VOL. IV.] PHILOSOPHICAL TRANSACTIONS. 33/ 



laid before the Society, but that both of them by their own ingenuity produced 

 beautiful originals. 



It is indeed true that M. Huygens, when he was at London some years ago, 

 resolved some of those cases on motion that were proposed to him ; by which 

 it plainly appears that he was then master of those rules by which he gave 

 those solutions. But he himself must own that he did not communicate the 

 least hint of his theory to any of the English, though he was often solicited to 

 it, till very lately. 



After having said so much in favour of truth and justice, we shall now deliver 

 M. Huygens'^ rules. 



Rules concerning tJie Motion of Bodies after mutual Impulse. 



1. If a hard* body strike against another and equal hard body, at rest ; after 

 impact the former will rest, and the latter will acquire a velocity equal to that of 

 the moving body. 



2. But if the second body be likewise in motion, and moving in the same 

 right line, after contact, the bodies will move with interchanged velocities. 



3. Any body ever so great may be moved by a body however small, that 

 strikes it \tith any velocity whatsoever. 



4. The general rule for determining the motion of hard bodies arising from 

 their direct impulse is this, viz. 



Let A and B, fig. 4, pi. Q, be two bodies, of which A is moved with the 

 velocity AD; and let B meet it, or let it move the same way with the velocity 

 BD, or lastly, let it be at rest, that is, in this case, let the point D coincide 

 with B. Dividing the line AB in C, the centre of gravity of the bodies A and 

 B, let CE be taken equal to CD. I say, E A will be the velocity of the body A 

 after the stroke; and EB of the body B; and each will move in that way, 

 which is shown by the order of the points EA, EB. But if E coincide either 

 with A or B, the body A or B will remain at rest. 



5. The quantity of motion of two bodies may be either increased or dimi- 

 nished by their shock ; but the same quantity, towards the same part, remains, 

 after subtracting the quantity of the contrary motion. 



6. The sum of the products arising from multiplying the mass of each hard 

 body into the square of its velocity, is the same both before and after the stroke. 



7. A hard body at rest will receive a greater quantity of motion from another 

 hard body, either greater or less than itself, by the interposition of any third 



* The term hard is not here used in its more modem acceptation, but it means elastic; tlie rules 

 here delivered, being those that relate to tlie collision of elastic bodies. 



VOL. I. U U 



