VOL. III.] PHILOSOPHICAL TRANSACTIONS. SOJ) 



the celerity l^—C. For F : PC'/. mnF: mnPC \\ F-\-mnr=: 

 — - — F : — - — P C= — — P X T-T — ^- Consequently the impetus of 

 the preceding body will be -j-r"— P C, and that of the following or pursuing 



body - — — mP C. 



11. If bodies moving contrary ways strike each other directly, as for instance, 

 the body P, with the force F, and the celerity C, moving towards the right 

 hand, and the body m P, with the celerity n C, and consequently with the force 

 mnF, towards the left hand, then the celerity, impetus, and direction of both 

 of them, after the impact, will be thus determined. The body moved towards 

 the right would communicate to the other, supposing it were at rest, the ce- 

 lerity •— — C, and consequently the impetus mPC, towards the right; 



and itself would retain that same celerity, and consequently the impetus 



PC, towards the right, (by art. q). And, after the same manner^ the 

 body moved towards the left hand would communicate to the other body, sup- 

 posed at rest, the celerity C, and consequently the momentum — — — PC, 



towards the left hand; also itself would have that same celerity, and conse- 

 quently the impetus /"" 7« P C, towards the left. Since, therefore, motion 

 is made by both the bodies, the impetus of the body which at first moved to- 

 wards the right, will now be the aggregate of the impetus — - — P C towards 



the right hand, and P C towards the left ; consequently the motion will 



in reality be made either towards the "right or left, according as the one or other 

 of these is the greater, and with an impetus equal to the difference of the two; 

 that is, putting the sign -f for the right hand, and — for the left, the impetus 



will be -|--i-PC- -^^PC = — — PC, and the celerity V^<^ ; 

 which will be towards either right or left, according as 1 or w n is the greater. 

 In like manner, the impetus of the other body, which at first moved towards the 



left, will be + — i-mPC '^^-^mPC = —-—mPC, and its celerity 



— — — C; which will be towards the right or left, according as 1 or mn may be 

 the greater of the two. 



12. But if the bodies should neither move straight in the same direction, nor 

 in directly opposite directions, but impinge obliquely; then the foregoing cal- 

 culus is to be regulated according to the degree of obliquity : observing that the 

 impetus of a body impinging obliquely, is to that of its direct impulse, avteris 



