Ou the Force of Percussion. 231 
One side observing that the ball of clay remains unmoved, 
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 ve- 
locities 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 ime; 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, and 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 motrix for a certain time may 
have its use, when correctly applied, in certain philosophical 
considerations; 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 work performed 
is always appreciated by the extent of effect resulting from 
their exertions ; for it is well known that the raising any 
great weight 40 feet would require four times as much Ja- 
bour as would be requisite to raise an equal weight to the 
height of 10 feet, and that in its slow descent the former 
would produce four times the effect of the latter in conti- 
nuing 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 four and of 
one minute’s labour, the velocities acquired would be in the 
ratio of 2 to 1, and the squares of the velocities in propor- 
tion to the quanuties of labour from which they originated, 
or as 4 to 1; and if the forces acquired by their descent were 
employed in driving piles, their more sudden effects pro- 
duced would be found to be in that same ratio. 
This species of force has been, first by Bernoulli and after- 
P4 wards 
