S-l" Rev. W. Whewell on the principles of Dynamics, 



AB, BD, act at the same point of time.* We resolve the ve- 

 locity AB, as it were, into the force which may have produced 

 it at a former period. Now, it seems hardly self-evident, that, 

 assuming a pressure of ten pounds, or a blow of a certain mo- 

 mentum, to have produced this velocity, we may at any fu- 

 ture period substitute this pressure for the velocity. It is true, 

 it may be said that it makes no difference at what interval 

 of time we suppose these forces to act, and that therefore 

 we may first suppose the force AB to act, and then BD at an 

 indefinitely short distance of time, which comes to the same 

 thing, supposing them to act simultaneously. But when we 

 are requiring the strictness of demonstration, it may still I think 

 be replied, that there may be an essential difference between 

 the successive and the simultaneous action of forces ; and that 

 it is by no means clear that their action, one after the other, 

 however small the interval may be, is the same thing as their 

 acting together. I would even ask any one whether this is 

 manifestly clear in the case of the real physical impact of two 

 balls upon a third. At any rate, it can hardly be said to be 

 self-evident, and therefore ought not to be assumed in a de- 

 monstration of the nature of that which we are now consider- 



If these objections to the deduction of the second law of 

 motion from the third are well-founded, it will appear that 

 the proper and philosophical method is to deduce the second 

 independently from observation, as English writers are in the 

 habit of doing. 



It may here be remarked, that if the second and third laws 

 were connected in the way which some .have supposed, either 

 of them might be made the fundamental one, and the other 

 might be deduced from it. Thus assuming the second law, 

 we might, by the same kind of reasoning as that which we 

 have been discussing, prove the truth of the third. 



• Poisson, torn. i. p. 309. Le point se mouvra uniformeraent sur la 

 diagonale, &c. 



En chaque point de cette droits le mobile sera dans le meme etat que si 

 la force R agissait actuellement sur lui et lui imprimait la vitesse mc. 



If the velocity has been produced by a force which acted during a finite 

 portion of time, however small, the replacement of the velocity by the force 

 i%,a supposition attended with still more embarrassing difficulties. 



