196 



•NATURE 



[October 7, 1920 



charge of Dr. H. H. Field, of Zurich. It was sug- 

 gested at the conference that these should be taken 

 into account in fixing the form which the Inter- 

 national Catalogue should take in the future. 



The immediate problem, then, is to secure the 



indexing of the scientific literature published during 

 thfe war. While this is being done, arrangements 

 can be made for the efficient continuation of the 

 work of cataloguing the scientific literature of the 

 world. 



The International Congress of Mathematicians. 



THLS congress was opened at .Strasbourg Univer- 

 sity on September 22 by the Rector, M. S. 

 Clarety. The oflicers of the congress were then 

 elected as follows: — Honorary President: M. Camille 

 Jordan. President: M. Emile Picard. Vice-Prcsi- 

 derUs : Prof. Ix'onard Dickson, Sir Josiph Larnior, 

 Prof. Norlund, M. de la Vallee-Poussin, .\i. H. Viilat, 

 and M. Volterra. Secretary: M. Koenigs. 



The delegates numbered 188 and represented 

 26 nations, amongst which may be mentioned Argen- 

 tina (4), Australia (i), Brazil (i), Canada (i), 

 Czecho-Slovakia (12), India (2), Japan (2), the Philip- 

 pine Islands (i), Poland (4), Russia (i), and Serbia (2). 

 The expenses of the congress, including the publishing 

 of tlie proceedings, have been completely provided for. 

 Of the sum required, 78,000 francs was contributed 

 by public bodies, by industrial and commercial con- 

 cerns, and by private persons. -An interesting fact is 

 that the French Government made its contribution of 

 10,000 francs through the Ministry of Foreign .\ffairs, 

 thereby recognising, it would appear, that such a con- 

 gress has a certain significance in international 

 politics. The subscriptions of delegates produced a 

 further sum of 12,000 francs. 



On Thursday, .September 23, a general lecture was 

 given by Sir Joseph Larmor on "Questions in Physical 

 Indetermination." Sir Joseph said that of the three 

 physical deductions upon which the validity of Einstein's 

 theory depended, the two which had been verified by 

 experiment, namely, the motion of the perihelion of 

 Mercury and the deflection of light-rays by the sun, 

 could be made to result equally well from a theory 

 involving an aether. But the third Einstein predic- 

 tion, the displacement of solar spectral lines, was in- 

 consistent with any aether theory. In his opinion, it 

 would be found, when conclusive observ-ations had 

 been made, that the third prediction was not verified. 

 The doctrine that the universe is completely "full" 

 originated with Descartes. The same doctrine was 

 held by Newton, Huygens, Faraday, Fresnel, and 

 Maxwell, but as a much more precise conception. 

 The vortex theory and the elastic solid aether theory 

 had had their day, but there was no reason at present 

 why we should not admit the existence of an aether — 

 a new aether the properties of which were so different 

 frorn, those of ordinary matter that they could be 

 expressed only in terms of non-Euclidean space. The 

 alternative was complete abstraction, the absence of 

 a basis on which to found our theories. The essence 

 of Newtonian space, as enunciated in the works of 

 Lie and Helmholtz, was the possibility of the exist- 

 ence of rigid bodies in motion. Newtonian space was 

 the space of mechanics, for which dx' + dy' + dz' was 

 invariant. 



For Faraday and Maxwell, on the other hand, radia- 

 tion was fundamental. The characteristic of Max- 

 wellian space was complete transmission. A pulse 

 travelled without change of form and without leaving 

 anything behind — a principle that was in accord with 

 experiments in light. This was the space of Min- 

 kowski, for which the corresponding invariant expres- 

 sion was dx^+dy'+dz^-c'dt\ 



.\s with Sir Joseph Larmor, so with most of the 

 other contributors to the subject of relativity, the 

 endeavour w-as directed towards the elimination of 

 those paradoxes which the human mind finds it 



NO. 2658, VOL. 106] 



difficult to accept rather than towards the further 

 development of the theory itself. Thus M. Guillaume, 

 setting forth from the remark that in the theory of 

 relativity we were dealing with the apparent posit'ions 

 of bodies and that the difficulties of the theory arose 

 from the fact that their " real " positions were sup- 

 posed unknown, offered an alternative analysis in 

 which the initial " real " positions of bodies were sup- 

 posed known. He obtained results in which some of 

 the paradoxes disappeared. M. Guillaume stated, 

 however, that he had been in correspondence with 

 Prof. Einstein, and had not been able to bring about 

 a reconciliation of the two points of view. 



The second general lecture, on " Relations between 

 , the Theory of Numbers and other Branches of Mathe- 

 matics," was delivered on Friday, September 24, by 

 Prof. Leonard Dickson, of Chicago. Prof. Dickson 

 showed how the problem of obtaining rational solu- 

 tions of certain classes of homogeneous equations was 

 connected with the known properties of certain sur- 

 faces and with the theory of hypercomplex numbers. 



In a lecture on the teaching of mathematical physics 

 M. Volterra said that what might be called "analytical 

 physics " now constituted an integral whole. Newton 

 had reduced the problem of the universe to a problem 

 in ballistics, and upon this basis Lagrange had founded 

 his analytical mechanics. In a similar w'av the con- 

 stitution of matter was for the modern physicist a 

 problem in electricity, and we awaited a new 

 Lagrange. .At the present time there were two dis- 

 tinct methods of teaching mathematical physics in 

 universities. The first might be called the mono- 

 graphical method. The student followed in succession 

 .separate courses in hydrodynamics, optics, and so on. 

 The weakness of this method was that there was no 

 grasp of the subject as a whole. In the other method 

 the student started with a course of mathematical 

 analysis, and, so equipped, he proceeded to the various 

 branches. The fault here was that in the first part 

 of the course he was working without seeing his 

 objective ; he did not understand the purpose of his 

 work or see its special difficulties. The course that 

 M. Volterra advocated consisted of three parts. The 

 first, on more or less historical lines, carried the 

 student as far as the general equations. The second 

 part w-as a discussion of those equations, including 

 a classification of them according to their charac- 

 teristics and a classification of the problems according' 

 to the methods of solution. The third part was the 

 solution and discussion of specific problems. This 

 scheme left for separate treatment those portions of 

 analytical physics which depended upon the calculus 

 of probability, as well as thermodynamics and some 

 minor branches. 



M. de la Vall^e-Poussin in his lecture, " Sur les 

 fonctions k variation bom^e et les questions qui s'y 

 rattachent," dealt with the fundamental theory of 

 integration in the light of Baire's classification of 

 functions. .All classes of functions (Baire) are in- 

 tegrable in the sense of Lebesgue. Stieltjes's integral 



(''/{x)da(x) 



can be defined by the process of Lebesgue, and 

 it exists for all Baire functions f. The functional 

 L'(0 (Fr^chet and Volterra), which has an assigned 



