Notices respecting New Booh. 533 



integral of the third kind, viz. 



d6 1 



j; 



l+»(sin0)« v/l- c 2( sin6>) ^ 



from the general formula above given, always of course subject 

 to the condition that c is supposed indefinitely near to 1*. 

 K, Woolwich Common, 

 November 1860. 



LXXIIT. Notices respecting New Books. 



An Elementary Treatise on the Dynamics of a System of Rigid Bodies. 

 With numerous Examples. By Edward John Routh, M.A., 

 Fellow and Assistant Tutor of St. Peters College, Cambridge; Ex- 

 aminer in the University of London. Cambridge : Macmillan and 

 Co. 1860. 



MR. ROUTH was Senior Wrangler in 1854, and is already 

 known as the joint author with Lord Brougham, of ' The 

 Analytical View of Newton's Principia.' His present work is in- 

 tended as a text-book for students at Cambridge, and will no doubt 

 take its place as such. We notice in it several of the more recent 

 methods of investigation, and such novelties, for instance, as the 

 reference of the motion to ' moving axes/ which have not hitherto 

 been incorporated into elementary books. 



We should have been glad to have seen the analytical processes 

 applied to such questions as the motion of a locomotive, and other 

 practical problems, instead of the purely fictitious and useless cases 

 which seem to be the peculiar delight of Cambridge mathematicians ; 

 e.g., such as the following: — " A perfectly rough, circular, hori- 

 zontal board is capable of revolving freely round a vertical axis 

 through its centre. A man whose weight is equal to that of the 

 board walks on and round it at the edge : when he has completed 

 the circuit, what will be his position in space?" (P. 53.) We feel 

 tempted to parody this, and ask, " When the student has completed 

 his circuit round a hundred such questions as this, what will be his 

 position in science ?" We believe it is not long since the Board of 

 Mathematical Studies at Cambridge received some very strong hints 

 on this subject from one of the most distinguished men of science in 

 England, whose own mathematical attainments have always been 

 applied to objects of real use and practical importance, instead of 

 being frittered away in trifling ingenuity. 



* It seems to be expected of every pilgrim up the slopes of the mathe- 

 matical Parnassus, that he will at some point or other of his journey sit 

 down and invent a definite integral or two towards the increase of the com- 

 mon stock. The author of these notes has been somewhat late in acquit- 

 ting himself of this debt of honour, but ventures to hope that the principal 

 results contained in the text above may be thought not unworthy of a 

 place in some future edition of that noble and sumptuous monument of 

 Dutch learning, industry, and fine taste, the invaluable collection of defi- 

 nite integrals by M, Bierens de Haan. 



