Notices respecting New Books, 303 



mical questions may be judged of by the following indication. His 

 definition of velocity runs thus : — " The velocity of a body is deter- 

 mined by multiplying the weight of the body by the space passed 

 over in a given time " (p. 1). Now not only is there a want of pre- 

 cision in the statement (a serious fault in such a matter), but what is 

 determined in the way stated is not what is generally termed velo- 

 city. The author might possibly object that this is a question of 

 words ; yet it is a strange use of language which implies that the 

 velocity of a horse is many times greater than that of his rider ; and, 

 moreover, a few pages after, he expresses the velocities of bodies in 

 the usual way of so many feet per second (p. 7, p. 26, &c). 



A large portion of the volume is taken up by a statement of" the 

 laws which determine the results of collision ;" and these statements 

 are applied to what may in courtesy be called a criticism of Newton's 

 laws of motion. As a specimen of our author's laws, we will 

 quote the first in the book (p. 3) : A and B, it must be premised, 

 are two spherical bodies, the weight of A being less than, or equal 

 to, that of B. The former moving with a given velocity along the 

 line of centres impinges on the latter at rest, then: — "Law I. A 

 will be reflected back from the point of collision in the same line 

 that it moved in before collision. Both the velocity and momentum 

 of A, as compared with the velocity and momentum of A before 

 collision, will be proportional to the difference of the respective 

 weights of A and B." 



A good many points are suggested by this "law:" e.g. First, it is 

 assumed as an ultimate fact, without any reason assigned. Secondly, 

 it is not stated, though incidentally it is assumed, that the colliding 

 bodies are perfectly elastic (case 100, p. 10). Thirdly, the "law," 

 as it stands, means that 



constantXA's velocity of rebound = (B— A) x A's velocity of impact. 



As the constant must be finite, it follows that if a boy drops a marble 

 on a pavement it rebounds with an indefinitely great velocity. 

 Fourthly, the words of the " law," however, do not convey the 

 author's meaning ; that, as appears from his treatment of particular 

 cases (pp. 4, 5), seems to be, 



B x A's velocity of rebound= (B— A) x A's velocity of impact. 



This, however, does not much mend the matter, for it is not the 

 true law. It is not necessary to continue our remarks ; if it were, 

 they could be continued indefinitely. What we have said will show 

 the reader that to buy the book is waste of money, to read it waste 

 of time. 



