on the Force of Percussion. 15 
considers the proof indisputable that the action of the body A 
is equal to that of B, and that their forces are properly mea- 
sured by their momenta, which are equal, because their 
velocities are in the simple inverse ratio of the bodies. Their 
opponents think it equally proved by the unequal depths to 
which the pegs have penetrated, that the causes of these 
effects are unequal, as they find to be the case in their esti- 
mation of the forces by the squares of the velocities. 
One party is satisfied that equal momenta can resist equal 
pressures during the same time ; the other party attend to 
the spaces through which the same moving force is exerted, 
and finding them in the proportion of 2 to 1, are convinced 
that the vis viva of a body in motion is justly estimated by its 
magnitude and the square of its velocity jointly. 
The former conception of a quantity dependent on the 
continuance of a given vis matrix for a certain time may have its 
use, when correctly applied, in certain philosophical considera- 
tions ; but the latter idea of a quantity resulting from the 
same force exerted through a determinate space is of greater 
practical utility, as it occurs daily in the usual occupations of 
men ; since any quantity of w T ork performed is always appre- 
ciated by the extent of effect resulting from their exertions ; 
for it is well known, that the raising any great weight 40 
feet would require 4 times as much labour as would be requi- 
site to raise an equal weight to the height of 10 feet, and that 
in its slow descent the former would produce 4 times the 
effect of the latter in continuing the motion of any kind of 
machine. Moreover, if the weights so raised were suffered 
to fall freely through the heights that have been ascended by 
means of 4 and of 1 minute's labour, the velocities acquired 
