On the Vis viva. 279 
until a quantity of resistance has been sur- 
mounted equivalent to the excess in question, 
by axiom 4,; at which time the figure of the 
system will become permanent by the last 
corollary; if no new disturbing force inter- 
vene. 
Cor. 3. The excess of vis viva, pointed out 
above, is exerted altogether in the relative 
space PQR ; consequently the mutual reaction 
of the parts of a system can not alter the vis 
viva of its centre of gravity ; therefore the 
same cause does not change the momentum 
of this point by cor. 4. theor. 3 ; which agrees 
perfectly with the common dynamics. 
Scuorium. In estimating the change of 
figure, produced in a system by the reaction of 
its parts, we may consider the centre of gravity 
to be at rest, and take notice only of the velo- 
cities of the constituent parts relative to the 
centre of gravity; in which case we shall 
have, au4bV+dv=o. 
Turorem VI. Let APE, BQH, (plate 
4, fig. 3) be two bodies, which meet in E; 
put k= their relative velocity, and a, 6 for the 
masses of APE, BQE respectively ; and the 
quantity of vis viva exerted on the system 
APQB, to change its figure, will be as - - . 
a 
For let G be the centre of gravity of the 
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