36 Rev. W. Wliewell ow the pri^iciples of Dynamics^ 



it is struck. And this proves ihe Jbrmer of the two cases just 

 mentioned. For if the body be moving from west to east, and 

 is struck from north to south, it moves exactly southwards ; 

 showing that the velocity compounded with its former motion 

 (arising from the earth's motion) is parallel to the force impress- 

 ed. But this parallelism might have occurred, had the velocity 

 impressed in the south direction been of any magnitude what- 

 ever, and depended in any manner whatever upon the force 

 impressed. And again, though the above rule for compound- 

 ing the velocity impressed with the previous velocity had not 

 been true when a force acts obliquely to the motion of the 

 body, it might still have been true that in forces or pressures 

 acting directly the velocity impressed is as the force. And, on 

 this supposition, a body partaking of the earth's motion, and 

 struck eastwards or westwards, would have the same relative 

 motion communicated to it as if it had been at rest, and had 

 received the same impulse. 



I shall conclude by stating the difference of the two laws 

 which I have considered briefly thus : Suppose that in a ship 

 in motion a ball were made to impinge directly upon an equal 

 ball, (in a direction different from that of the ship's motion) so 

 that they should move on together. Then, if the second law 

 of motion were false, they would move in a direction different 

 from that of the impact ; and if the third law were false, they 

 would move with a velocity different from half the original ve- 

 locity. 



These and the foregoing reflections seem to show the pro- 

 priety of keeping distinct the second and third laws of motion. 

 Others may view the subject in a different manner, and be of 

 another opinion ; but at any rate it is desirable to bring the 

 question under the consideration of mathematicians, that it 

 may receive that degree of thought which is requisite for its 

 final decision. 



Notes. 



(A.) Laplace, torn i. p. 18. Voila done deua; loix du 



mouvement, savoir, la loi d'inertie, et celle de la force propor- 



tionelle a la vitesse, qui sont donnes par I'observation. EUes 



lont les plus natu relies que Ton puisse imaginer, et sans doute 



