216 Dr. C. H. Lees on a Graphical Method of 
Case (1). Direct Impact. 
Let a smooth elastic sphere of mass m, moving ina straight 
line with velocity v,; impinge on another of mass my moving 
in the same straight line with velocity vs. 
Calculate mv, and mv, the momenta of the two spheres. 
From some point A, (figs. 1 and 2) draw A,B in direction 
and magnitude equal to m,v, the momentum of the mass m,. 
Fie. 1, 
From B draw BA, equal in direction and magnitude to mv, 
the momentum of the mass mj. From A, and A, draw on 
opposite sides of A,A, two perpendiculars to A,A, and 
measure off AyN,=m,, and A,No2=m,. Join NN, and let it 
cut A,A,inC. Then, since ae 
sat, A Cis themomentum 
of m and CA, that of mz, at the end of the first portion of 
