November 6, 1914] 



SCIENCE 



675 



the class to wliom it was addressed. The tra- 

 ditions of the volume have been V7ell supported 

 by Mr. Llevcellyn Preece, Sir William's son. 

 While many of the original illustrations have 

 been preserved and reproduced in the new edi- 

 tion, more than a hundred new illustrations 

 have been incorporated. 



It is so rarely that we find a man's scientific 

 and literary production adequately brought up 

 to date by the labor of his son, that the book 

 before us would have a claim for recognition 

 on this account alone. 



In view of so much new material which has 

 been introduced, it seems invidious to com- 

 plain of omissions. It is to be regretted, how- 

 ever, that the last chapter of the original edi- 

 tion, devoted to " Commercial Telegraphy " 

 and dealing with the very interesting and spe- 

 cial administrative features of the British 

 telegraphs, should have had to disappear, in 

 making up the new volume. There was a char- 

 acteristic quality in that presentation which 

 ■we think will be missed in the new edition, and 

 which is valuable to students of telegraphy. 



The new chapters on Kepeaters, Quadruplex, 

 Multiplex, the Telephone and Wireless Teleg- 

 Baphy are excellent, and the treatment which 

 they offer of those subjects accords remarkably 

 ■well with the style of the original volume. 



A. E. Kennellt 



A History of Japanese Mathematics. By 



David Eugene Smith and Toshio Mikami. 



The Open Court Publishing Company, 



Chicago, 1914. Pp. vii + 288. 



This interesting story of Japanese mathe- 

 matics is presented in most attractive garb. 

 The paper, the type and the illustrations make 

 •f it a work which it is a delight to handle, 

 but an American must feel some regret that 

 Ihis beautiful book with the imprint of an 

 American publishing house is nevertheless 

 from the press of a German printer, W. Dru- 

 gulin, Leipzig. 



The Japanese mathematics is largely indig- 

 enous and, as the authors well state, it is " like 

 her art, exquisite rather than grand." Of the 

 six periods into which the history of their 

 miathematics may be divided the first extends 



to 552 A.D., and is almost entirely a native 

 development. The second period, from 552 to 

 1600, was characterized by the predominance 

 of Chinese mathematics. The third period 

 was a kind of renaissance which reached its 

 highest development in Seki Kowa (1642- 

 1708), the most famous Japanese mathemati- 

 cian. The fourth and fifth periods, from 16Y5 

 to 1775 and from 1775 to 1868, are marked by 

 the development of the wasan, or native mathe- 

 matics. Even before these periods the Jesuits 

 had secured a foothold in China, and a Japan- 

 ese student of mathematics was working under 

 Van Schooten in Leyden as early as 1661, so 

 that some influence of European mathematics 

 may be confidently assumed. The sixth period 

 is the period of the present day which, in 

 mathematics, at least, knows nothing of polit- 

 ical and racial boundaries. 



The uncertainty of the first and second 

 periods is best illustrated by the fact that but 

 17 pages are devoted to their consideration. 

 A passage in the discussion of the Chinese 

 "Arithmetical Eules in Nine Sections" is 

 also significant : " If these problems were in 

 the original text, and that text has the anti- 

 quity usually assigned to it, concerning neither 

 of which we are at all certain, then they con- 

 tain the oldest kno-wn quadratic equation." 



Tangible arithmetic seems to have secured 

 its greatest development among the Japanese. 

 The fundamental operations with the sorolan, 

 a modification of the Chinese swan-pan, are 

 explained in a detailed manner, and illus- 

 trated with excellent photographs. Certainly 

 it is striking that in Chinese swan-pan has 

 the meaning " reckoning table," which corre- 

 sponds precisely to the Greek word from which 

 " abacus " is derived, this also haying the 

 meaning " table," particularly for bankers. 

 The sangi, or computing rods, are explained 

 both as used for representing numbers and 

 also as applied to the solution of algebraic 

 equations. 



Extensive numerical computation appealed 

 greatly to the Japanese as well as to the Chi- 

 nese mathematician. The game side of mathe- 

 matics is represented by magic squares, and 

 even magic circles. An approach to the meth- 



