213 



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 Bakerian Lecture on the Force of Percussion. By William Hyde 

 Wollaston, M.D. Sec. R.S. Read November 14, 1805. {Phil. 

 Trans, 1806,^. 13.] 



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 velocities, 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 1, to strike at the same instant against the 

 opposite pegs, with velocities which are in the proportion of 1 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 through which the same moving force is exerted, 

 and finding them to be in the proportion of 2 to 1, 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 ex- 

 tended through space, rather than continued for a certain time, is an 



