306 Notices resjjecting New Books. 



memoirs, aud has had to study compression in ever}^ possible way. 

 In some cases the results of an extensive investigation are stated 

 in a short article; in others important theoren)s are given in the 

 form of examples, the reasoning by which their truth is established 

 being left to be made out by the student with little or no assistance. 

 Thus, on p, 139 Mr. Eouth gives as an example M. Morin's ex- 

 perimental proof that impulsive friction obeys the laws of ordinary 

 friction; in Art. 151 he gives (with certain variations), the sub- 

 stance of M. Morin's investigation of the friction of carriage- 

 wheels ; in Art. 224, nuder the head of an example he gives four 

 of the principal theorems of Mr. Ball's Theory of Screws ; and 

 similar cases are to be found elsewhere — e. q. Ex. 2 p. 312, Ex. 1 

 p. 366, Ex. 1, 2 p. 371, Ex. 4 p. 498, &c. All these are, we believe, 

 additious made to the present edition. 



In other cases the additions are supplementary to articles that 

 occurred in former editions. Thus, in Chap. IX. (on the motion 

 of a body under the action of no forces), in this and in former 

 editions, the determination of the angular velocities round the 

 principal axes is shown to depend on a differential equation, the 

 integration of which can be made without difficulty to depend on 

 an elliptic Integral. In the present edition the solution is actu- 

 ally eifected by means of elliptic functions, according to a method 

 due to Kirchhoff. 



In a case where the matter of a book is very closely packed, and 

 where a good deal of detail is left to be made out by the reader, 

 there is of course considerable dauger of needful explanation being 

 altogether withheld, or given with so much brevity as to be insuffi- 

 cieut for the wants of many of the readers. Although Mr. Eouth's 

 explanations are for the most part sufficient, and in many cases 

 singularly clear, yet we cannot help thinking that occasionally his 

 text might be expanded with advantage. We will give an example 

 of what we mean. On p. 411, in the chapter on the motion of a 

 body under the action of no forces, after defining the polhode, and 

 showing that its equations are 



A^,^+By+c^-=^, 



Aa7^+B3/HCr=Me^ 



our author goes on thus : — 



" Eliminating y, we have 



A(A-B).rHC(C-B);3^=(^|'-B)Me*. 



"Hence if B be the axis of greatest or least moment of inertia, 

 the signs of the coefficients of .r^ and z~ w'Al be the same, and the 

 projection of the polhode will be an ellipse. But if B be the axis 

 of mean moment of iuertia, the projection is an hyperbola. 



" A polhode is therefore a closed curve drawn round the axis of 

 greatest or least moment, and the concavity is turned towards the 

 axis of greatest or least moment, according as G-'-^T is greater or 

 less than the mean moment of iuertia." 



