Manchester Memoirs, V^ol. xlvi. (1902), No. 10. 13 



Leibnitzian measure of moving force were (i) that a body 

 with a double velocity will overcome the resistance of four 

 springs, one of which alone is equivalent to the force of 

 the same body moving with a velocity as one; (2) that a body 

 falling with a velocity of two will penetrate a soft body 

 four times the depth of the same body with a velocity as 

 one ; (3) that if a non-elastic body moving with a given 

 velocity strike another equal body at rest in free space, 

 they will move on together after impact with half the 

 velocity of the first body, while one-half the force of impact 

 is lost in producing change of figure. The first and 

 second instances were met by the opponents of the vis viva 

 measure affirming that the forces generated by the double 

 velocities were destroyed in a double time (notwithstand- 

 ing Newton's second law in which it is laid down that the 

 effect is independent of the time), while in the third 

 instance it was denied that there was any loss of molar 

 motion from change of figure, and that, as the two bodies 

 moved together with half the velocity, the quantity of 

 motion was the same as before collision, in accordance 

 with the definition of Descartes and of Newton. 



Maclaurin expresses this point of the controversy with 

 singular lucidity. — "Now the difficulty was, how to account 

 for the loss of one half of the force of the first body in the 

 stroke : for this purpose they [the Leibnitzians] advanced, 

 without any other proof, this new doctrine, that when the 

 parts of soft bodies yield without restoring themselves, 

 being void of elasticity, a certain quantity of force is lost 

 in the compression of their parts by the collision : whereas 

 we know no way by which force is lost in one body, but 

 by its being communicated to another. The parts of soft 

 bodies are indeed moved out of their places, in the collision, 

 and some motion is lost in the first body being communi- 

 cated, in this manner, to the parts of the second; but these 



