Manchester Memoirs, Vol. xlvi. (1902), No. 10. 15 



sometime professor of natural philosophy at London 

 University College, are remarkable as the logical outcome 

 of measuring the quantity of motion of a moving body by 

 its mass and velocity conjointly. " It appears, therefore, 

 that the velocity or force with which a falling body 

 strikes the ground increases in much less proportion than 

 the height from which it falls. If the height be augmented 

 in a fourfold proportion, the force of the fall will only be 

 augmented in a twofold proportion. This explains a fact 

 of not unfrequent occurrence, and which sometimes pro- 

 duces surprise. Persons sometimes fall or leap from such 

 heights as would seem to render their destruction 

 inevitable, yet they are frequently found to escape 

 without considerable injury. This is explained by the 

 fact that the momentum, or shock produced by the fall, 

 increases in a proportion so very much less than the 

 height." And again, " the force with which a ball weigh- 

 ing an ounce and moving at ten feet per second will strike 

 any object, will be exactly ten times the force with which 

 the same ball moving at one foot per second would strike 

 such an object." He adds that " These fundamental 

 principles are so obviously consistent with universal 

 experience that they can scarcely be said to require 

 proof." The simple dogmatism of this last statement 

 still finds expression in classical text-books on the laws 

 of motion of the present day. 



Metaphysicians and men of letters, as I have said, have 

 been peculiarly unfortunate in their attitude towards the 

 Leibnitzian measure of moving force. Schopenhauer, 

 in Haldane and Kemp's translation of his work 

 entitled The World as Will and Idea,"^ supports the 

 Cartesian measure by the following illustration. " A 

 hammer weighing six pounds with a velocity = 6, in 



* Note to Pradicabilia a priori of Matter. (Vol. 2, pp. 226-227). 



