392 Notices respecting New Books. 



\ anced student. After two introductory chapters (one kinematical, 

 the other physical), there are chapters devoted to rectilinear and to 

 parabolic motion, to central orbits, to constrained motion and to 

 motion in a resisting medium : then follow a chapter of " General 

 Theorems," one on impact, and, finally, a chapter on the motion of 

 two or more particles. The last of these subjects is treated under 

 the two divisions of free motion and constrained motion. In the 

 second division no more than the case of two particles is considered. 

 The methods employed " are applicable to more complicated cases, 

 when more particles than two are involved ; but nothing would be 

 gained by such a proceeding, as D'Alembert's Principle supplies us 

 with a far simpler mode of investigating the motions of any system 

 of free or connected particles" (p. 370). In fact the only case dis- 

 cussed in detail is that in which two particles of unequal masses 

 " are attached to different points of an inextensible string, one of 

 whose extremities is fixed." The solution of this question is ob- 

 tained for small vibrations, in which case the integrations can be 

 effected in finite terms. There is added a discussion of the case in 

 which the mass of one particle is much greater than that of the 

 other, and the strings are not approximately equal. This appendix 

 is taken from a paper by Sir W. Thomson, " On the rate of a Clock 

 or Chronometer as influenced by the mode of Suspension." To each 

 chapter numerous examples are appended, which have been taken 

 for the most part from Cambridge Examination Papers ; many of 

 them would require for their solution an amount of ingenuity such 

 as but few students possess. 



Professor Tait gives by way of introduction a short history of the 

 book, from which it appears that Mr. Steele's share in the compo- 

 sition of the First Edition was not very large, and, in fact, that he 

 died before its final arrangement and revision. The Second Edition 

 was thoroughly revised and, indeed, recast by Professor Tait, who 

 thus appears to be the sole responsible author. The Third Edition 

 was revised by W. D. Niven, Esq., of Trinity. " The present 

 Edition has been thoroughly revised by Professor Greenhill, who 

 has not only at great labour verified and (where necessary) cor- 

 rected the examples, but has endeavoured to adapt the book to the 

 present requirement of the Tripos by the free introduction of Ellip- 

 tic Eunctions, &c, which, in my Cambridge days, were under the 

 ban of the Board of Mathematical Studies." In short, it will be 

 seen that no pains have been spared to render the work as complete 

 and trustworthy as possible. And yet the author does not seem 

 very well satisfied with his work. The fact is that the book w T as 

 written with a view to the requirements of the Mathematical 

 Tripos; and this circumstance seems to have imposed restraints at 

 which Professor Tait chafes. Thus we find him writing as fol- 

 lows : — Several of the examples " have defied all attempts at im- 

 provement, and now stand in their unintelligibility as a warning, to 

 the Candidate for Mathematical Honours, of the ordeal he may 

 have to pass through." Again, the text of the work is to a great 



