150 Notices respecting New Books. 



Elementary Algebra, with brief notices of its History. By Robert 



Potts, M.A., Trin. Coll. Camb. In twelve sections, demy 8vo, 



pp. 618. Messrs. Longman and Co. 



In this important treatise on Algebra Mr. Potts has bestowed 

 much thought, judgment, and research on a very instructive and 

 interesting History of the subject, in which he traces its rise, 

 growth, and progress from the time of Euclid and Diophantus to 

 the present time. The first twelve sections are entirely devoted 

 to it, and comprise references to the works of the most distin- 

 guished writers on Algebra in every country where the subject has 

 been encouraged. The various notes and quotations are skilfully 

 compressed ; and it may be conceded that Mr. Potts has earned the 

 gratitude of teachers who take more thau an ordinary interest in 

 this subject. 



The arrangement of the subsequent sections is excellent : clear 

 and copious explanations of principles, carefully selected exercises, 

 results, and hints — these form the order of the different sections. 

 The rule of signs is made perfectly plain ; and factorial expressions 

 are treated exhaustively. On turning to the section on Simple 

 Equations, w T e were glad to find that the traditionalist and post 

 questions have no place there. There are no " clock " questions 

 and others of a like class, all of which are more suitable to the 

 pages of an Arithmetic. But, on the other hand, we have an un- 

 usual number of problems which will exercise the reasoning faculty 

 of young pupils. The exercises generally, which are chiefly taken 

 from Cambridge Examination Papers, will prove a mine of wealth 

 for examination-purposes. 



The scope of .the book is somewhat greater than that of ordinary 

 text-books, as it includes (and concludes with) a section on Cubic 

 and Biquadratic Equations. It may be said that Mr. Potts has 

 now done for Algebra what he did for Greometry many years ago, 

 and in our opinion has done it much better. It is a sequel to his 

 work on Arithmetic ; and the two, together with the edition of 

 Euclid alluded to, form a complete and valuable repertoire of a 

 student's requirements in Elementary Mathematics. 



On the Motion of a Solid in a Fluid, and the Vibrations of Liquid 

 Spheroids. By Thomas Craig, Ph.D., Fellow in Physics in the 

 Johns Hopkins University, Baltimore, Ind. Van Nostrand's Science 

 Series. London : Triibner & Co. 



This small treatise is the 49th of a series of text-books on Science, 

 mostly on Mechanical and Civil Engineering and cognate subjects. 

 The differential equations of fluid-motion are simplified, in the 

 author's opinion, by the introduction of curvilinear in the place of 

 rectangular coordinates. This transformation being accomplished 

 he then proceeds to investigate the subject in question. Of the 

 seven sections into which the book is divided, section 3, " On the 

 flow of a fluid, through an orifice" is very ably written. Many 

 valuable references to the highest authorities on the subject are 



