October 16, 1914] 



SCIENCE 



561 



of its possible services is that of awakening in 

 the reader a desire to understand the ghostly 

 theory that lurks behind the practician's rules. 

 I shall never forget how unhappy I was made 

 when a boy by having to learn by heart and to 

 use the rule for computing the area of a tri- 

 angle in terms of its sides before looking into 

 a geometry and what a burden was rolled off 

 when in subsequent years I learned to deduce 

 the rule. Industrial folk will not find it easy 

 to circumvent the necessity of understanding 

 something of the science they would use. The 

 way of the transgressor is hard. 



Among the more notable features of Pro- 

 fessor Kenyon and Professor Ingold's " Trig- 

 onometry " are the prominence given to the 

 solution of triangles, first by geometric meth- 

 ods, then gradually by means of the trigo- 

 nometric functions and logarithms ; the use of 

 composition and resolution of forces to show 

 the significance of large angles and of addition 

 formulae; the hinging of the treatment on a 

 minimum of theoretical considerations; the 

 very large number and variety of exercises 

 and applications; the omission of DeMoivre's 

 theorem and of infinite series; the presence of 

 a rather extensive chapter on spherical trig- 

 onometry, and the inclusion of 124 pages of 

 convenient tables. 



The attractiveness of the admirable little 

 volume of Professors Anderegg and Roe is due 

 partly to its smallness. The smallness is due 

 in some measure to conciseness but mainly to 

 omission of tables, model arithmetical solu- 

 tions, a list of answers and an index. A large 

 part of the book deals with spherical trigo- 

 nometry. It is shown that plane trigonom- 

 etry is a special case of spherical. It is evi- 

 dent that the authors are fascinated with the 

 theory of the subject, and their treatment of 

 it looks up toward higher analysis rather than 

 merely down to practical uses and computa- 

 tion. 



As we open Professor Collins's " Advanced 

 Algebra " it is pleasant to be greeted by a 

 genial likeness of Sylvester and, as we pass on, 

 to encounter the pictures of Tartaglia, 

 Cauchy and Gauss, with brief accounts of them. 

 A first-year course is presupposed. The book 



falls into three parts, devoted respectively to 

 a review, to the remaining topics of elementary 

 algebra, and to such college topics as general 

 equation theory, probability, determinants and 

 infinite series. The author's aim has been to 

 equip the student to meet either of the two 

 algebra standards of the College Entrance 

 Board and to carry him well into college 

 topics. 



Many students of modern logic will wel- 

 come Miss Robinson's excellent English trans- 

 lation of Dr. Couturat's well-known " L'Alge- 

 bre de la logique." This edition is distinctly 

 enhanced by the preface prepared by Mr. Jour- 

 dain. Here and now are not the place and 

 time to review the content of a work of which 

 the original French edition was published in 

 1905. Suffice it to say that it consists of the 

 elements of the classic logic of exclusion and 

 inclusion presented in algebraic garb and that 

 the algebra of logic is not to be confounded 

 with what is known as the logic of mathe- 

 matics. 



From the mathematical public thanks are 

 due Professor Smith, Mr. Mikami and the 

 Open Court Publishing Company for their 

 " History of Japanese Mathematics." Owing 

 to the wellnigh complete insulation of the 

 Japanese until recently from the western 

 world, this first English account of their 

 mathematical work is a real romance in the 

 austere things of the human spirit — almost as 

 fascinating as would be a message from Mars. 

 We confess to having read every line of it with 

 eager and increasing interest. Not only will 

 all liberal students and teachers of mathe- 

 matics wish to read it but it is rich in mater- 

 ial for psychologists, historians and other sci- 

 entific students. In particular may anthro- 

 pologists find in it evidence both for and 

 against the thesis that similarity or dissimi- 

 larity of circumstances determines similarity 

 or dissimilarity of intellectual developments. 

 Even if space allowed it would be a kind of in- 

 justice to delineate the content of this volume 

 here and so deprive the reader of it of the pleas- 

 ure of meeting its surprises first-hand. Suffice 

 it to say that the numerous beautiful photo- 

 graphic illustrations (made by Mr. L. L. Lock) 



