Principles of progrejfive and rotatory Motion. 571 
loft by p from fimple impadl ; hence if the bodies be 
elaftic, t> e the velocity loft by p if elaf- 
tic, and confequently the velocity of p after the ftroke 
_ TT 2 x Cgx V x CG _PxDC— QxGC 
~ V (gxGC + PxDC “ QxGC + PxBC * V * 
Cor. i. If the direction ad paffes through g, then 
2 py 
cg being equal to cd, we have — ^ = (g’s velocity, and 
v =: p’s velocity, which is well known from tha 
common principles of elaftic bodies. 
Cor. 2. If p x dc = egx gc, or p : eg: : gc : dc, then 
will the body p be at reft after the ftroke. 
Cor. 3. If q_ were infinitely great, the velocity of p 
after the ftroke would be = - v as it ought, for p would 
then ftrike againft an immoveable obftacle. 
Cor. 4. Whatever motion eggains from the action of 
p, it would lofe, if, inftead of fuppofing p to ftrike eg, 
eg were to move in an oppofite direction, and ftrike p at 
reft with the fame velocity with which p ftruck <g; in 
fuch cafe, therefore, the velocity of q_ after the ftroke 
would be v - 
zPxGCxV 
0.x GC +P xDC 
Cg- 2 P x GC + P x DC 
CgxGC + PxDC 
Cor. 5. Hence if p be infinitely great, or eg be fup- 
pofed to ftrike an immoveable object, its velocity after 
the ftroke will be = x v : hence when dc = 2GC, 
xJ L/ 
the body <g will have no progreflive motion after the 
Vol. LXX. 4 F ftroke, 
