Page:Proceedings of the Royal Society of London Vol 1.djvu/233

Rh which is found in the lengths of various muscles that act together ;' as by that means organs of velocity are joined with those of power.

The force of percussion is a subject, respecting the estimation of which a controversy has subsisted for more than a century past be- tween different classes of philosophers. For although it is agreed that when unequal bodies move with the same velocity, the forces are as their quantities of matter; yet when equal bodies move with unequal velociti, there are two methods of estimating the compa- rative forces of such bodies. Leibnitz and his followers conceive the forces to vary as the squares of the velocities; while their Opponents maintain that the forces are in the simple ratio of the velocities of the bodies respectively. The latter have been considered as New- tonians; but Dr. Wollaston endeavours to show that they can derive no support from any expressions of Newton.

In order to explain the grounds for each opinion, the author pro- poses the following experiment.

He supposes a ball of clay to be suspended at rest, having two similar and equal pegs slightly inserted into its opposite sides; and he supposes two other bodies, A and B, which are to each other in the proportion of 2 to l, to strike at the same instant against the opposite pegs, with velocities which are in the proportion of l to 2. In this case, the ball of clay would not be moved from its place to either side; nevertheless, the peg impelled by the smaller body B, which has the double velocity, would be found to have penetrated twice as far into the clay as the peg impelled by the larger body A.

It is, Dr. Wollaston says, unnecessary to make the above experi- ment precisely as it is here stated, because the results are admitted as facts by both parties ; but upon these facts they reason differently. One party. observing that the ball of clay remains unmoved, considers the proof indisputable, that the action of the body A is equal to that of the body B, as they would be led to expect, because their momenta are equal. 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 would have expected, from considering the forces as proportional to the squares of the velocities.

The former party observe, in this experiment, that equal momenta can resist equal pressures during the same time,- the other party at tend to the spaces throngh which the same moving force is exerted, and ﬁnding them to be in the proportion of 2 to l, observe that the vis viva of a body in motion is justly estimated by the magnitude and the square of the velocity jointly,—a multiple to which Dr. Wollaston has thought it convenient to give the name of Impetus.

This latter conception, of a quantity of force as a vis motrix extended through space, rather than continued for a. certain time, is an