September 18, 1914] 



SCIENCE 



411 



author's extensive experience as a practical 

 computer, combined with his keen mathe- 

 matical insight, have enabled him to provide 

 against the usual difficulties and pitfalls which 

 beset the path of the beginner in this field. 



The second part treats the more advanced 

 parts of elementary trigonometry together 

 with applications to simple harmonic curves, 

 simple harmonic and wave motion, and har- 

 monic analysis. The two parts are intended 

 to cover the work in plane trigonometry usu- 

 ally given during the freshman course in the 

 colleges. Notwithstanding the unusually large 

 number of trigonometries which are now on 

 the market, this book seems to have important 

 characteristic properties. 



From the standpoint of pure mathematics 

 plane trigonometry may be of comparatively 

 little importance, but it occupies a strategic 

 point in the mathematical training of most 

 students who talce freshman mathematics in 

 our colleges and universities. The numerous 

 direct applications of this subject and the 

 training which it provides for a wise use of 

 approximate results combine to make it espe- 

 cially important that the student should have 

 clear views at this point in order that mathe- 

 matical thinking may become natural to him. 

 Professor Wilczynski's book seems to guard 

 to an unusual degree against vague or incor- 

 rect impressions. 



Professor Dickson's Elementary Theory of 

 Equations relates to a subject where both text- 

 books and students are much less numerous 

 than in the subject considered above. The 

 classic work by Bumside and Panton, in two 

 volumes, is too extensive for the available 

 time in many institutions. Moreover, it omits 

 the important subject of systems of linear 

 equations. Some of the more recent works 

 aim to lead up to modern theories too rapidly 

 to give enough room to the classic funda- 

 mental theories. 



In the present book the author has provided 

 for two courses by marking with a dagger 

 many of the more difficult sections which 

 could be omitted without breaking the con- 

 tinuity of the course. The aggregate of the 

 sections thus marked is more than fifty pages. 



and the rest constitutes a very brief course in 

 this subject. A large number of illustrative 

 problems are solved in the text, and about 

 five hundred graded exercises are distributed 

 through the various chapters. To the re- 

 viewer the book appears to excel all others ex- 

 tant for a first course in this subject. 



As might be expected, the author has paid 

 especial attention to rigor and conciseness 

 in presentation, and has made a wise selection 

 from the vast amount of material relating to 

 the subject in hand. His masterful skill in 

 reaching the essential points by the most direct 

 means is everywhere apparent. In addition 

 to a treatment of the rational integral func- 

 tion in one unknown, the book contains a good 

 introduction to the theory of determinants 

 and the solution of a system of simultaneous 

 linear equations. 



Por the sake of simplicity very few modem 

 concepts are introduced. The Galois theory is 

 entirely omitted and the subject of invariants 

 is only illustrated by a few examples. The 

 concept of rank of a determinant is intro- 

 duced but the closely related concepts of ma- 

 trix and rank of a matrix are not developed. 

 The introduction of these concepts would 

 have enabled the author to state more con- 

 cisely some results relating to a system of 

 linear equations. 



G. A. Miller 



Rubier and Buiher Planting. By E. H. Lock, 

 Sc.D. London, Cambridge University 

 Press; New York, G. P. Putnam's Sons. 

 1913. Pp. 13 and 245. 5 by 7 inches. 

 The purpose of the author of this book has 

 been to present an introductory outline of the 

 subject, as stated in the title, to meet the needs 

 of as wide a circle of readers as possible. 

 One can not but feel that the result would 

 have been more satisfying if the limitation of 

 the size of the volume had not prevented the 

 author from doing what he really wished to do. 

 A better end could perhaps have been gained 

 by confining the treatment to the most im- 

 portant rubber plant, economically regarded, 

 Hevea Braziliensis. Had this been done, the 

 least satisfactory chapters (II., X. and XL), 



