October 4, 1901.] 



SCIENCE. 



533 



of muscle and nerve. The mechanical phe- 

 nomena of the circulation are also adequately 

 treated in a series of exercises on an ingeniously- 

 constructed artificial scheme. 



It would have been better, we think, to omit 

 much of the elementary physics which bulks so 

 largely in some of the chapters. The simple 

 experiments on magnetic induction, lines of 

 force and electromagnetic induction, given in 

 Chapter II. , would be in their proper place in 

 a manual of practical physics. We doubt the 

 wisdom of encouraging the medical student to 

 neglect his physics, as he so often does at the 

 period of his preliminary scientific studies, in the 

 sure and certain hope that ' all he really re- 

 quires,' the titbits of that severe and repellant 

 science — will be served up to him later on in 

 semi-digested form in the course of physiology. 



The proofs have been read with commendable 

 care, and few actual errors have escaped de- 

 tection. On page 188, however, it is wrongly 

 stated that ' in muscle the electrotonic currents 

 are much stronger than in nerve.' The asser- 

 tion, on page 189, that 'the electrotonic cur- 

 rents are absent in nerves which lack a myelin 

 sheath ' seems a little too absolute, although 

 everybody admits that they are weaker than in 

 medullated nerves. On page 250 one is rather 

 staggered by the argument that ' were the slow 

 passage of the blood in the capillaries due 

 simply to friction, the blood would move still 

 more slowly in the veins because the retarding 

 influence of the friction in the viens would be 

 added to that of the capillaries.' This would 

 hold true if the blood possessed only kinetic 

 energy. But since the blood in the capillaries 

 is under a higher pressure than in the veins, 

 there is a surplus of potential energy which is 

 capable of being converted into kinetic. 



It is a good idea to encourage the learner to 

 discuss his results by setting him here and there 

 a definite question for consideration. A critical 

 comparison of the isotonic and isometric causes 

 of contraction (pp. 221, 229) affords a valuable 

 mental gymnastic to the student who has just 

 been exercising his manual dexterity in obtain- 

 ing them. And if Swift could extract an 

 elegant meditation (according to the style and 

 manner of the Hon. Eobert Boyle) from so dry 

 a piece of timber as a broomstick, the ingenuous 



reader will waste no sympathy on the twentieth- 

 century medical student, even when he is re- 

 quested to tackle a somewhat unpromising 

 theme, to write, for example (according to his 

 own style and manner) ' a critical account of 

 the muscle-lever in his laboratory note-book.' 



G. N. I. S. 



Theory of Functions of a Complex Variable. By 

 A. R. Forsyth, Sc.D., F.R.S., Fellow of 

 Trinity College, Cambridge, Sadlerian Pro- 

 fessor of Pure Mathematics. Second Edition. 

 Cambridge, at the University Press. 1900. 

 8vo. Pp. xxiv-f-782. 



The publication of a second edition of Pro- 

 fessor Forsyth's very valuable and comprehen- 

 sive work on the theory of functions is a matter 

 of no little interest and importance to the 

 mathematical world. The first edition, which 

 appeared in the spring of 1893, was the first 

 extended systematic presentation in English of 

 a field of modern mathematics now generally 

 recognized as the most useful as well as the 

 most fascinating. Furthermore it was the 

 most comprehensive treatise on the subject in 

 any language, treating a greater number of de- 

 partments, exhibiting a greater variety of 

 methods, and giving more references to impor- 

 tant oi'iginal contributions than any previous 

 work. Its position in all these respects has 

 been modified since only by a single work, the 

 elaborate historical and bibliographical report 

 of Professors Brill and Noether published in 

 the third volume of the ' Jahresbericht der 

 deutschen Mathematiker-Vereinigung. ' 



The new edition has been enlarged by about 

 one hundred pages. By means of these ad- 

 ditional jDages and also by omitting about 

 twenty pages devoted in the earlier edition to 

 binomial differential equations, the author has 

 been enabled to introduce an elementary dis- 

 cussion of the birational transformations and to 

 give some account of Abel's theorem and its 

 applications. 



In the work of revision many improvements 

 in the details of presentation have been intro- 

 duced. The author has altered the wording of 

 a considerable number of theorems and demon- 

 strations which before contained slips of one 

 sort or another. The work has thereby gained 



