282 Theorems and Problems 
directions GP and GQ thereby giving to each 
body equal quantities of motion in opposite. 
directions... In this, imaginary case, then, the. 
whole force of APE, and BQE acts in. the, 
character of momentum ; consequently ; the 
vires, vive of bodies. arise from the. soft, 
and pliant, texture of all. substances with, 
which men are acquainted. ‘This observation 
affords a. clear distinction of momentum, and. 
vis viva: the former is a force, which. one 
body. exerts on another to change its motion, 
in absolute space; but, the latter is employed 
in overcoming the continued reaction of resist, 
ing mediums, and in Lage the Pana of 
soft and elastic bodies. ; 
Cor. 3. Let P, Q, R, sci (plate 4, fig. A) 
be the centres of gravity of three . or, more 
bodies situated in the right line PR ;,im which. 
some or all of them move so as to bring all of 
them. into contact ; moreover let a, b, d,, &e. 
be the masses of P, Q, R, &c; &. the relative 
velocity of P and Q;' + that.of P and R; 
n that of Q and R; é= the. mass. of the sys- 
tem =at+b+i, &c: LI say the quantity of vis 
viva exerted on the system to change its figure, 
is as the sum of the rectangles of each.pair of 
bodies drawn into the square of their relative. 
velocity directly, and.inversely as the mass ¢5 
or it isas S004 ae" x ee bdn*. For let u,V, v; 
t 
