216 



SCIENCE. 



[N. S. Vol. XXII. No. 555. 



along this line.' Even in mathematics too 

 little of the available material has been crit- 

 ically examined to make it possible to write a 

 complete and trustworthy history, but the sud- 

 den prominence of Japanese activity and 

 power gives unusual interest to any facts 

 relating to the thought and scientific develop- 

 ment of this country. 



The 2,000 mathematical works in the royal 

 library of Tokio, some of which date back to 

 1595, are a sufficient guarantee of high esteem 

 for mathematical knowledge. As the Japan- 

 ese mind is very practical and shows little 

 aptitude for the abstract and philosophical, it 

 is to be expected that their mathematical 

 achievements are in very close touch with 

 practical problems and are foreign to those 

 fields of mathematics which border on philos- 

 ophy. The determination of the area of the 

 circle in terms of its diameter is one of the 

 most important of these practical problems 

 and the Japanese took especial interest in 

 developments which were useful to obtain an 

 approximate solution of this problem. 



Such a solution is equivalent to an approxi- 

 mate determination of the ratio between the 

 diameter and the circumference of a circle. 

 This ratio, known as the Ludolphian number, 

 plays such a prominent role in the develop- 

 ment of mathematics that so eminent a mathe- 

 matician as Glaisher has remarked that its 

 history is almost identical with the history of 

 mathematics. The approximate value of this 

 number can be most readily obtained by in- 

 finite series, and this is the method which the 

 Japanese employed as early as the seventeenth 

 century. In doing this they used the bi- 

 nomial theorem for fractional exponents as 

 early if not earlier than Newton did. One 

 of the proudest triumphs of this master mind 

 was, therefore, achieved independently by the 

 race whose recent marvelous progress has been 

 attracting universal attention. 



One of the other prominent discoveries of 

 ISTewton, viz., the infinitesimal calculus, seems 

 also to have been discovered independently by 

 the Japanese; although the evidence on this 

 point is not conclusive. It is, however, cer- 

 tain that the Japanese were not far behind 



the Europeans in their mathematical attain- 

 ments during the latter part of the seven- 

 teenth century. Since then they have not 

 made the rapid progress which Europe has 

 witnessed as a result of the work of Euler, 

 Lagrange, Cauchy and Gauss. They did not 

 have any such leaders, and hence their ad- 

 vanced mathematics was practically neglected. 



Within recent years there has been a great 

 advance in mathematical instruction. A 

 large number of students are debarred from 

 the upper classes of the higher institutions on 

 account of their lack in mathematical train- 

 ing. There seems to be a very widespread 

 feeling that the educational system is mostly 

 in need of improvement along the line of 

 mathematical instruction and the efforts to- 

 wards progress along this line exhibit Japan- 

 ese vigor and courage. It will probably re- 

 quire a number of years before much will be 

 accomplished in higher mathematics. 



The most surprising fact about Japanese 

 mathematics is that, while the most elemen- 

 tary parts were regarded as common property, 

 the more advanced results were regarded as 

 secrets which should be communicated to a 

 very few. In fact, an oath of secrecy was 

 required of those who wished to hear lectures 

 on advanced mathematics. European history 

 furnishes a parallel to this in the Pythagorean 

 school, but it is so totally different from the 

 modern spirit that its existence 2,000 years 

 after Pythagoras was unexpected. Fortu- 

 nately all this has recently changed to such 

 an extent that a history of Japanese mathe- 

 matics could be published a few years ago. 

 A small part of this has been translated into 

 English.== 



G. A. Miller. 



Stanford University. 



PEOPOHED MAGNETIC AND ALLIED OB- 

 SERVATIONS DUPING THE TOTAL 

 SOLAR ECLIPSE, AUGUST 30, 1905. 



In response to my appeal for simultaneous 

 magnetic and allied observations during the 

 coming total solar eclipse, cooperative work 



' Tsuruichi Hayashi, ' A Brief History of the 

 Japanese INlathematics,' Nieuio Archief voor luis- 

 kunde, 1904, pp. 2&6-324; 1&05, pp. 325-361. 



