treating the Impact of Smooth Elastic Spheres. 217 
the impact, when the spheres are moving with the same 
velocity. 
To find the momenta after separation of the spheres, since 
the change of momenta during the second portion of the 
impact is e times that during the first portion, e being the 
coefficient of restitution, measure off from C along N,N, in 
the direction of B a length CF=1 on any convenient scale, 
and in the opposite direction a length CH=e. Join BF and 
draw through EH, ED parallel to BF cutting A,A, in D. 
Then, since CD=eBC, A,D is the momentum of m,, and 
DA, that of m, after impact. 
The velocities after impact may be found from these 
momenta by dividing by the masses. 
Case (2). Oblique Impact. 
If the impact is oblique, then, since the components of the 
momenta perpendicular to the line of centres are unaffected 
by the impact, while the components of the momenta along 
the line of centres are affected, the latter are determined and 
treated as in the previous case. 
Fig. 3. 
Nv, 
Let M,B represent in magnitude and direction the momen- 
tum m,v,, BM, the other m,v.. Draw through B a line 
parallel to the line of centres and let the perpendiculars on 
