284 Theorems and Problems 
the force remains accumulated in the matter, 
constantly ready to restore its original shape ; 
that is, the vis viva infused into a body of this 
description acts on the cohesion of its consti- 
tuent particles. Let g= the vis viva thus 
infused ; d= the mass, which receives it; t= 
the intensity of its action or its effect ona 
given part of d; and ¢ is as 43 and g as td. 
Cor. 2. We have, by the theorem, as 
Fif::b:a; but by cor. 1. as Fi f::aT 
;bt; hence as 7’: 1::b* : a*; that is, the 
intensity of the vis viva accumulated, by 
collision, in APE, is to the same power in 
BQE; asthe square of the mass of BQE, 
to the square of the mass of APE, hence it 
happens, that when two homogeneous elastic 
bodies of very different magnitudes strike each 
other, the Jess is broken while the greater 
remains uninjured: because the smaller body 
receives the greater quantity of vis viva in a 
less portion of matter. 
Cor. 3. The theorem is equally applicable 
to homogeneous bodies which are soft and 
ductile; now by the demonstration of the 
theorem, as F: f::Pp:Qq; that is, the 
vis viva exerted to change the figure of a body 
is as the space through which its centre of 
gravity is compelled to move by that effort. 
