292 Theorems and Problems, sc. 
Examrre. Let A and B be two wires, 
the first 5, and the latter 3 inches long; and 
let A be drawn to one tenth, and B to one 
fourth of its original diameter; and we have 
Fi: f'::99X5:15x3::11: 1. 
Prospitem VII. If a brittle ball A be 
broken by falling with the velocity uv, on a 
‘Jarger ball B of the same matter; with what 
velocity v, must B strike another ball C 
larger than itself, to be broken in like man- 
ner ? 
Sotvution. Put a, 6 and c= the masses 
of A, B and C; then a= the vis viva 
exerted to change the figure of the system 
A and B, by theor. 6; and the quantity 
bar pity to change the figure of it is as 
aes = by cor. 1, theor. 6, and theor. 3; for 
a 
the same reason, the force employed to change 
the figure of B when -it falls upon C, is as 
b c? vo? 
(b-+-¢)? 
and B must be equal; because they produce 
equal effects ; but the intensity is.as the vis viva 
directly and mass ce by cor: 1, theor.7; 
therefore apache 3 hence as c. (atb) 
(@Fb* ora 
1b. (b+e) ::u:v. Q.EI 
Cor. If € be iudedinitely great, it will 
beasatd:b::u:v 
: now the intensities of these forces in A 
