Notices respecting New Boohs. 497 



however, equally legitimate to apply the same term to the capacity 

 of the body for acquiring energy under given velocity. As kinetic 

 energy depends on the square of the velocity there is a trouble- 

 some factor |, which must either be got rid of by an equally 

 vexatious system of units or else it must be left in the equations. 

 The confusion occasioned by it is exhibited on p. 66, where we read 

 that the customary unit of kinetic energy " is one-lialf of that 

 possessed by one gramme when moving with a velocity of one 

 centimetre per second. It is called the erg." 



Readers of the book, whether they agree with the views of the 

 author or not, cannot fail to have their attention drawn to the 

 fundamental concepts of mechanics and physics and the evidence 

 on which they are founded ; this must necessarily lead to clearer 

 views and a greater appreciation of the modern theories sketched 

 briefly in the second part of this volume. J. L. H. 



An Introduction to the Theory of Analytic Functions. By J. Hark- 



ness, M.A., and F. Morley, Sc.D. (London, Macmillan, 1898, 



pp. xvi + 336.) 

 The previous treatise on the Theory of Functions by the same 

 writers was published in 1893. This work, as the authors state 

 and as is obvious on examination, is not an abridged and element- 

 ary version of the other, but is almost a totally independent work. 

 Our last remark is due to the fact that there are fewer references 

 on account of a fuller list having been given before. Let the 

 Authors speak for themselves : " It has been composed with 

 different ends in mind, deals in many places with distinct orders of 

 ideas, and presents from an independent point of view such portions 

 of the subjert as are common to both volumes. 



" Owing to the nonexistence of any English text-book giving a 

 consecutivj and elementary account of the fundamental concepts 

 and processes employed in the theory of functions, the authors 

 have sent forth their volume to meet this pressing want." The rest 

 of the preface gives an interesting sketch of what they attempt, 

 and after a perusal of great part of their work, we are convinced 

 that they will meet with the reward they hope for. 



There are twenty-two chapters in all, an Index, and Contents. 

 The earlier portion on the Ordinal Number System, Geometric 

 Representation of Complex Numbers, the Bilinear Transformation 

 and the Geometric Theory of the Logarithm and the Exponential, we 

 read with much interest and found them to be very clearly done. 

 Chapters viii.-xii. discuss the different points of difficulty connected 

 with Power Series. Then we have (xiii.) the Analytic Theory of the 

 Exponential and Logarithm. Chapters xv.-xviii. consider Weier- 

 strass's Factor-theorem, Integration, Laurent's Theorem and the 

 Theta-functions, and functions arising from a network. Elliptic 

 and Algebraic functions (on Eiemann surfaces) follow, and the book 

 closes with Cauchy's Theory and the Potential. Possessors of the 

 earlier volume will see that some of the headings above are identi- 

 cal with those in that work, but they will find that the treatment 

 is fresh, as stated in the extract from the preface above. 



