REVIEWS 471 



fun at " Mathematical Tripos Mathematics," and to wish that the author, 

 instead of consulting Examination Papers set at Oxford, Cambridge, London, 

 and elsewhere, had spent the time in reading " memoirs published mostly 

 elsewhere." It is to be feared that the publication of the Integral Calculus 

 will merely convince the mathematical world of the justice of this gibe. 

 Problems there are in plenty, a magnificent collection, each with its source 

 duly acknowledged (including one by " Asparagus " of the Educational 

 Times), but the general theory is sadly deficient. It seems as if the author 

 fell asleep some thirty or forty years ago, and is not in the least aware of 

 any recent work. He acknowledges in the Preface indebtedness to the works 

 of Hobson and Forsjrth, but shows no sign of having read them. There are 

 references to Hobson, it is true, as well as many to Bertrand and Serret 

 and Williamson, but they are to the Trigonometry and not to the Functions, 

 as one would have expected. On page 76 reference is made to the ordinary 

 notation for the hyperbolic functions as being " now commonly adopted by 

 modern writers," and the book quoted was published in 1888. Following 

 this it is rather a shock to find mention of tables of these functions published 

 in 1914. 



Earlier reviewers tried to acquaint Mr. Edwards with the idea of uniform 

 convergence, but in vain, as is evidenced by his curious proposition, curiously 

 proved, on p. 44, on the integration of series. 



The proportions of the book are so astonishing, too. After long and, 

 in many cases, far too complicated investigations of standard forms and 

 reduction formulae (for which the student would be much better advised to 

 consult Bromwich's shilling tract. Elementary Integrals) we get 120 pages 

 on Quadratures, and 150 pages on Rectification. These include, it is true, 

 such notice as the author deigns to give (six pages in all) to Stokes's Theorem 

 and double integrals, but there are pages and pages on pedals, lemniscates, 

 Cassini's ovals, bipolar curves, biangular co-ordinates, areas and arcs in 

 terms of trilinear co-ordinates, etc., etc. 



The book is, in fact, a hotch-potch of curious and disconnected mathe- 

 matical puzzles. 



F. P. W. 



Calculus for Beginners. By H. Sydney Jones, M.A. [Pp. ix + 300.] 

 (London: Macmillan & Co., 1921. Price 6s. net.) 



This book is yet another attempt to write an introduction to the Calculus 

 " sufficient for practical applications," without any mention of the word 

 " limit." The necessary consequence is vagueness, and the use of phrases 

 such as " when Q is verj'- very small, AC becomes equal to AC" (p. 60)," 

 " when Q is exceedingly close to P " (p. 212), " suppose x very very great " 

 (p. 109). Series are of course mentioned without reference to convergence, 

 except that "to be of service in computation the individual terms must 

 be getting smaller and smaller." 



The author is strangely inconsistent in his notation ; the exponential 

 number is denoted by the Greek e on p. 259, although elsewhere the usual 

 convention is adopted ; and the treatment of the Leibniz theorem (of 

 course spelt Leibnitz), unnecessarily heavy as it is, is made still more 

 clumsy by the use, just here, of the old factorial notation instead of the 

 modern n ! 



There is a wonderful picture of a staircase on p. 105. 



Altogether it is difficult to see the need of the book, when excellent ones 

 {e.g. Gibson) covering much the same ground, so very much better, already 

 exist. 



F. C. W. 



