considers the proof indisputable that the action of the body A is equal to that of B, and that their forces are properly measured 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 estimation 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 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 4 times as much labour 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 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