[ 434 ] 



XLIX. Notices respecting New Books. 



Elliptic Functions, an Elementary Text-hook for Students of Mathe- 

 matics. By A. L. Baker, C.E., Ph.D. (New York : Wiley & 

 Sons, 1890. Pp. iv + 118.) 



^PHE Editor's object is to put within reach of the English 

 -*- (? English-speaking) student " a tolerably complete outline of 

 the subject [of Elliptic Functions], clothed in simple mathematical 

 language and methods," and so to "smooth the road" to this 

 important branch of Mathematics. Abundant material is to be 

 found in the works of Abel, Euler, Jacobi, and Legendre, not to 

 mention the writings of mathematicians of more recent date. The 

 earlier matter is not easily accessible to the ordinary student, and 

 Mr. Baker deserves our thanks for his labour in the volume before 

 us. He has not aimed at originality, which is not to be looked 

 for in the description of work he has undertaken, but he has tried 

 to simplify the methods in use, so as to make them intelligible to 

 the average student. He adopts the Gudermannian notation as 

 being simpler than the Jacobian, and employs zero subscripts " to 

 indicate decreasing series in the Landen transformation, and of 

 numerical subscripts to indicate increasing series." He gives a 

 list of works consulted, and states that he has refrained from any 

 reference to the Gudermann or Weierstrass functions "as not 

 within the scope of this work." There are seventeen chapters in 

 all, with an introductory chapter which is a condensation of an 

 article on the subject by the late Prof. Moseley. There are several 

 typographical errors, of an elementary character, and now and 

 again the compiler uses terms which are explained subsequently. 

 The last chapter contains applications to the Lemniscate, the ellipse, 

 and hyperbola, and besides there are exercises scattered through- 

 out, the rest of the book. 



An Introduction to the Logic of Algebra, with Illustrative Exercises. 

 By E. W. Davis, Ph.D. (New York : Wiley & Sons, 1890. 

 Pp. xv + 119.) 



We have read this Introduction, which is a good piece of solid 

 work, with much interest. The author states that "the book is 

 precisely described by the title, and is mainly the outgrowth of a 

 conviction that the logic of Algebra is a very much neglected 

 study." Some idea of the writer's mode of treatment will be got 

 from the following statement of the various sources drawn upon 

 in its compilation. The more important w T orks consulted are : — 

 Argand, Sur le maniere de representer quantites imaginaires ; 

 Clifford, Common Sense of the Exact Sciences ; De Morgan, Trigo- 

 nometry and Double Algebra, and Introduction to his Calculus ; 

 Dirichlet, Zahlen-theorie ; and Tannery, Theorie des fonctions 



