NATURE 



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THURSDAY, NOVEMBER 7, 1912. 



MATHEMA TICAL TEXT-BOOKS. 

 (i) .4 Treatise on Plane Trigonometry. By Prof. 

 E. W. Hobson, F.R.S. Third edition. Pp. 

 ^v + 383. (Cambridge University Press, 191 1.) 

 Price 125. net. 



(2) A Shorter Geometry. By C. Godfrey, M.V.O., 

 and A. W. Siddons. Pp. xxii + 301. (Cam- 

 bridg-e University Press, 1912.) Price 2s. 6d. 



(3) A New Geometry. Books i-iii. By W. M. 

 Baker and A. A. Bourne. Pp. xxii+ 122 + iii. 

 (London: G. Bell aircf Sons, Ltd., 1912.) Price 

 IS. 6d. 



(4) Lessons in Geometry. Part i. By Dr. Charles 

 McLeod. Pp. xii + 212. (Aberdeen University 

 Press, 1912.) Price 2s. 6d. net. 



(5) Examples in Arithmetic. Part i., with 

 answers. Taken from "A School Arithmetic." 

 By H. S. Hall and F. H. Stevens. Pp. ix + 

 115 + xxii. (London: Macmillan and Co., 

 Ltd., 191 1.) Price is. 6d. 



(6) Solutions of the Examples in Godfrey and 

 Siddons's "Solid Geometry." By C. L. Beaven. 

 Pp. 164. (Cambridge University Press, 1912.) 

 Price 55. net. 



(7) A B C of Hydrodynamics. By Lieut.-Cul. R. 

 de Villamil. Pp. xi+135. (London: E. and 

 F. N. Spon, Ltd. ; New York : Spon and 

 Chamberlain, 1912.) Price 6s. net. 



(8) A New Algebra. By S. Barnard and J. M. 

 Child. Volume ii. Containing Parts iv.-vi. 

 Pp. X + 301-731. (London: Macmillan and 

 Co., Ltd., 1912.) Price 4s. 



(9) A Treatise on the Analytical Geometry of Three 

 . Dimensions. By Dr. George Salmon, F.R.S. 



Revised by Reginald A. P. Rogers. Fifth edi- 

 . tion. In two volumes. Vol. i. Pp. xxii + 

 470. (London : Longmans, Green and Co. ; 

 Dublin : Hodges, Figgis and Co., 1912.) Price 

 gs. 

 10) Fergusson's Percentage Unit of Angular 

 • Measurement, with Logarithms ; also a Descrip- 

 tion of his Percentage Theodolite and Per- 

 centage Compass. For the use of Surveyors, 

 Navigating Officers, Civil and Military En- 

 gineers, Universities and Colleges. By John 

 Coleman Fergusson. Pp. Ixvii + 467. (London: 

 Longmans, Green and Co., 1912.) Price 3/. 3s. 

 net. 

 (i) An Elementary Treatise on Statics. By Prof. 

 S. L. Loney. Pp. viii + 393. (Cambridge Uni- 

 versity Press, 1912.) Price 12s. 

 (i) pROF. HOBSON'S treatise on plane 

 1 trigonometry has for many years 

 ,ieen regarded as the best work: on the subject 

 i NO. 2245, VOL. 90] 



available for English students. There is prob- 

 ably no lecturer at Oxford or Cambridge who does 

 not recommend his pupils to read it. In fact, 

 before it's publication it was necessary for those 

 who w^ished for a rigorous treatment of those 

 infinite series and products which occur in higher 

 trigonometry to have recourse to French or 

 German text-books. But recently much has been 

 done in England to remedy this deficiency. Mr. 

 Hardy's volume on "Pure Mathematics," Prof. 

 Bromwich's work on "Infinite Series," and Prof. 

 Hobson's "Theory of Functions of a Real 

 Variable " are noteworthy examples. These, how- 

 ever, deal with a wider field, and students will 

 still continue to gain their first insight into the 

 problems of higher analysis from this volume. 



The need of a third edition has given the author 

 an opportunity for a complete revision ;■ new 

 matter has also been inserted. The theory of 

 the measurement of circular arcs is discussed at 

 some length in the opening chapter. Those who 

 are interested in mathematical history will appre- 

 ciate the section on the quadrature of the circle, 

 in which is given a modified form of Gordon's 

 proof that ir is a transcendental number, thus 

 establishing the impossibility of constructing by 

 Euclidean methods a straight line bearing to a 

 given straight line the ratio tt. But the most 

 important changes in the work are those which 

 relate to the theory of series and products. Many 

 additions have been made, further examples are 

 given to illustrate the different cases that arise, 

 and a number of references are supplied for those 

 who wish to make a more thorough study of the 

 subject. We have no doubt that this volume will 

 retain its place as the standard text-book for 

 many years to come. 



(2) This volume is a carefully reasoned inter- 

 pretation of the Board of Education circular on 

 the teaching of geometry. The first stage aims 

 at illustrating the fundamental concepts, the 

 second leads to the discovery of the principal 

 theorems, and the third builds up on this basis 

 a deductive development of the subsequent pro- 

 positions. The authors feel that too much time 

 has in the past been devoted to purposeless draw- 

 ing, and have therefore omitted much of the 

 experimental work contained in their previous 

 treatise ; the number of theoretical exercises, on 

 the other hand, has been increased. We shall be 

 much surprised if this text-book is not w-idelv 

 used. 



(3) This is an abbreviated form of the text- 

 book on elementary geometry by the same authors 

 published nine years ago. The only important 

 change is the redistribution of the propositions in 

 Book i., those on congruent triangles being now 



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