96 



these from the fundamental principles of matter, following 

 in the order of development that usually pursued by writers 

 on mechanics. The first law of motion is, that it must be 

 uniform and rectilinear. If the two simple activities are 

 equal in power, they must hold each other in equilibrium ; 

 but if one be stronger than the other, then there must be 

 motion in the direction of the stronger, and in proportion 

 to the surplus. We ask special attention to the conclusion 

 established here. In order that there should be a uniform 

 and rectilinear motion of a point, there is required the .con- 

 stant and unceasing action of a stronger energy. How is 

 it then that on the very next page (p. 122), in speaking of 

 impulsive force, he can assume, that after an impulse a body 

 consisting of balanced antagonisms will continue to move 

 uniformly ? If in the former case constant urging was re- 

 quired to produce uniform motion, how is it that an impulse, 

 which acts for an instant and then ceases, can produce ex- 

 actly the same thing? We shall have occasion to refer to 

 this point again, when we come to speak of the author's 

 account of falling bodies. 



The second law of motion he expresses thus : e< That motion 

 which any superinduced force would give, must be compounded 

 with the motion which the force already has" His demonstra- 

 tion of this law is purely one which might have been given 

 on any other conception of matter quite as well as this one. 

 Except that he uses no diagrams, and commits thereby some 

 blunders which we shall presently point out, his demonstra- 

 tion is really geometrical. The law does not seem to be at 

 all involved in the author's principles of activities, and his 

 demonstration does not depend upon them. He points out 

 justly enough, that when a point entertains two motions in 

 different directions at the same time, the point will move 

 in neither of the impressed directions, but in the one which 

 divides the angle made by the two. 



And here we beg the mathematician to observe to what 

 accurate and reliable results the rational insight will lead 



