November 8, 1912] 



SCIENCE 



628 



mingling of the two streams of investigations 

 associated with the name of the French mathe- 

 matician Pieard and with the modern Italian 

 school. Twenty-four papers were read. The 

 chairmen of the later meetings were Professors 

 F. Severi, F. Morley, J. Drach. 



Section Ilia. Mathematical Physics. — 

 Chairman Professor H. Lamb commented 

 upon the division of applied mathematicians 

 into three classes, those whose interests lay 

 mainly in the pure mathematical aspect of the 

 problems of experience, those to whom analy- 

 sis was only a means towards the interpreta- 

 tion and coordination of phenomena, and those 

 specially represented in the Cambridge school 

 who found a sort of esthetic interest in the 

 reciprocal interplay of experience and theory. 

 Twenty-seven papers were read in this meeting 

 and those presided over by Prince Galatzin 

 and Professors T. Levi-Civita and P. Stackel. 



Section Illb. Economics, Statistics and 

 Actuarial Science. — ^Professor P. T. Edge- 

 worth, presiding at the first meeting, com- 

 mented on the fact that for the first time this 

 branch of applied mathematics had been given 

 equal rank with the older branches and re- 

 ferred to the pioneering work of Marshall as 

 a mathematical economist and to the im- 

 portance of the calculus of probabilities in the 

 development of actuarial science. Dr. M. F. 

 Sheppard and Dr. J. F. Steffensen presided at 

 the two last meetings. A total of 13 papers 

 made up the program of the three meetings. 



Section IVa. Philosophy and History — 

 Four meetings of this section were held, one 

 a joint meeting with Section lYh. Twenty- 

 two papers were offered. The meetings were 

 presided over by Hon. B. A. W. Eussell, Pro- 

 fessors A. Gutzmer, A. Padoa, F. Eudio. 



Section IVb, Didactics. — The first chair- 

 man, Mr. C. Godfrey, spoke regretfully of the 

 absence of Klein, who had done ■ so much in 

 promoting the work of the International Com- 

 mission on the Teaching of Mathematics. The 

 chairman happily characterized the section as 

 devoted to the study of functions of two vari- 

 ables, one being mathematics, the other the 

 student. Three of the five meetings of this 

 section were occupied with the presentation of 



reports from the various countries to the In- 

 ternational Commission. Over 150 reports 

 have been published and 50 more are in prepa- 

 ration. Professors C. Bourlet, J. W. A. 

 Young, E. Czuber, D. E. Smith, E. Fujisawa, 

 were chairmen of the meetings at which ten 

 papers were read. At a special meeting of 

 this section presided over by Sir J. J. Thom- 

 son, Professor Eunge read a paper on the 

 mathematical education of the physicist which 

 brought forth an animated discussion. 

 Eunge's report was made up from the answers 

 received to inquiries sent to universities in 

 many countries, whicl; summed up that need 

 was felt for mathematicians and physicists to 

 draw closer together, more attention should be 

 given to graphical and approximate methods 

 and to numerical computation by mathemat- 

 ical teachers and that instruction in mathe- 

 matics should be individual. Several speak- 

 ers in discussing the paper deplored the wid- 

 ening gap between the pure mathematician 

 and the physicist, but it was suggested that 

 the gap should be closed not by compelling 

 mathematical teachers to abandon logical pre- 

 cision, but by discarding things obsolete in 

 the traditional mathematical courses and di- 

 minishing the excessive amount of manipula- 

 tive work which is now demanded from phys- 

 ics students. 



Besides the sectional meetings there were 

 ten lectures given at the general meetings of 

 the congress. These lectures were: 



"n signifieato della critica dei prineipii nello 

 sviluppo delle matematiche, ' ' Professor F. En- 

 riques. 



' ' Periodicity in the solar system, ' ' Professor E. 

 W. Brown. 



' ' The history and evolution of arithmetic divi- 

 sion," P. J. Harding. 



' ' The principles of instrumental seismology, ' ' 

 Prince B. Galitzin. 



"Geloste und ungeloste Probleme ans der 

 Theorie der Primzahlverteilung und der Rie- 

 mannschen Zetaf unktion, ' ' Professor E. Landau. 



"Definition et domaine d 'existence des fonc- 

 tions monogfines uniformes," Professor E. Borel. 



' ' The place of mathematics in engineering 

 practise," Sir W. H. White. 



"Multiply charged atoms," Sir J. J. Thomson. 



