August 25, 1904] 



NA TURE 



417 



On August 12 the Perseids were again in evidence, but 

 not very abundantly. At Bristol between loh. and 

 i2h. ynw. there were about 17 or 20 per hour, but the watch 

 was not quite continuous. The radiant was very sharply 

 defined at 47°+ 58° from about 20 paths. 



On .\ugust 13 the sky was less favourable : there was a 

 good deal of haze, and the stars were blurred and faint ; 

 only a few Perseids were seen in these adverse circumstances. 



Though the shower generally was not a plentiful one, it 

 is likely to prove interesting in some of its results, for a 

 number of its meteors appear to have been observed at more 

 than one station, and their real paths can be computed. 



1 hree features in reference to the shower of 1904 appear 

 to the writer to deserve special mention ; — 



(i) The sharply defined point of radiation on August 11 

 and 12. 



(2) The comparatively meagre character of the display. 



(3) The fact that nearly all the Perseids appeared on the 

 right (western side) of the radiant. This was very marked, 

 and tlie writer has been struck with the same peculiarity 

 in preceding years. There were many Perseids in Andro- 

 meda, Pegasus, Cassiopeia, Cepheus, and Cygnus, but 

 few in Camelopardus, Auriga, the Lynx, and Ursa Major. 



W. F. Denning. 



THE THIRD INTERNATIONAL CONGRESS 

 OF MA THEM A TICIANS. 



"T^HERE are few towns better suited for a scientific gather- 

 ing than Heidelberg, and few scientific gatherings 

 have passed off so successfully as the third International 

 Mathematical Congress which met there from August 8 

 to 13. The number of mathematicians attending the 

 congress was 330, giving with holders of ladies' tickets a 

 total membership of nearly 400. The German Government, 

 the tjrand Duke of Baden, the municipal and universitv 

 authorities of Heidelberg, the Deutsche Mathematiker 

 Vereinigung, and an influential executive committee all 

 joined in giving the congress a hearty welcome, and the 

 local arrangements were perfect. 



The formal proceedings opened on Tuesday, August 9, 

 under the presidency of Prof. H. Weber, of Strasburg. 

 The year 1904 being the centenary of the birth of Jacobi, 

 the occasion was selected for the delivery of an address by 

 Prof. Leo Konigsberger on Jacobi's life and works. .\ 

 large volume by Prof. Konigsberger dealing with the same 

 subject was published by Messrs. Teubner in connection 

 with the present commemorations. 



.-Vnother feature of the congress was the presentation, by 

 Prof. Klein, of the first copy of vol. i. of the " Encyklopadie 

 der niatematischen Wissenschaften," which volume has 

 just been completed. Considerable progress was also re- 

 ported in the preparation of the French edition of the 

 " Encyklopadie." 



Prof. Gutzmer, of Jena, presented a history of the Deutsche 

 Mathematiker Vereinigung, founded in 1890, as well as the 

 July part of the Jahresbericht of the society, containing 

 papers on the teaching of mathematics. 



Passing on to a review of the work done in the sectional 

 and general meetings, the most noticeable feature revealed 

 by the general spirit in which many of the papers were 

 written was the growing tendency in the mathematical 

 world to devote greater attention to the practical and ex- 

 perimental aspects of mathematics, especially in connection 

 with mathematical teaching. From such signs as this it 

 appears not unlikely that we are on the eve of a renaissance 

 period in the history of mathematics. A large collection of 

 models, mathematical instruments, apparatus, and books 

 was exhibited in the large hall of the museum. Prof. 

 Runge, of Hanover, exhibited and described Leibnitz's 

 calculating machine. .\ number of experiments on fluid 

 motion past various boundaries were shown by Prof. 

 Prandtl, of the same town. These differed from Prof. Hele- 

 .Shaw's experiments with thin films in that a vessel of some 

 depth (say an inch or two) was used, and water or liquid 

 of small viscosity employed ; in this case a series of vortices 

 were seen to be thrown off in succession from a cvlindrical 

 or other obstacle, and the various stages of forrnation of 

 each vortex were clearly demonstrated by photographs as 

 well as experimentally. 



NO. 18 I 7, VOL. 70] 



Prof. Greenhill's discourse on the theory of the top, con- 

 sidered historically, also contained an attempt to give 

 graphical representations of the motion of the top, and was 

 illustrated by experiments with bicycle wheels and other 

 equally simple apparatus. 



Coming to matters of more purely educational interest. 

 Prof. Klein, in his address to the applied mathematics 

 section, gave an amusing account of the methods in vogue 

 in certain German middle schools for obviating the use of 

 the calculus, a state of affairs reminding one of the old 

 Cambridge "three days." Prof. Loria, of Genoa, stated 

 that the attempt to abolish Euclid in Italy had failed owing 

 to the badness of the text-books brought out to meet the 

 new conditions, that a Government prize had been in con- 

 sequence offered for a good manual on geometry, and that 

 the books of Veronese, Enriques, .^maldi, Paolis and 

 others were the result. 



Prof. Gutzmer urged that elasticity and thermodynamics 

 should form part of the training of every professor of applied 

 mathematics. Resolutions were passed by the congress 

 urging the Government to provide models and projection- 

 lanterns for use in teaching mathematics in the German 

 schools and technical colleges. .'\ further resolution related 

 to the teaching of geometrical drawing in schools. 



In connection with the historical section, a resolution was 

 passed relating to the publication of Euler's works by the 

 Carnegie Institution. Prof. Schlesinger announced the 

 appearance of the first volume of the works of L. Fuchs, 

 and a bibliography of Wronski's works was presented by 

 Prof. S. Dickstein. 



Of papers in applied mathematics, the most remarkable 

 was Prof. Sommerf eld's investigation on the motion of 

 electrons ; the remaining papers dealt inter alia with the 

 problem of three bodies (Profs. Delaunay and Levi-Civita), 

 equations of wave motion (Profs. Volterra and Hadamard), 

 attractions (Prof. Genese), and geodesy (Prof. Borsch and 

 others). 



In pure mathematics the most striking papers were those 

 by Prof. Hilbert on integral equations and on the found- 

 ations of arithmetic, and Prof. Konig's proof that the 

 continuum cannot be equivalent to any well ordered group. 

 Prof. Painlev4, of Paris, gave an admirable discourse on 

 the integration of differential equations ; Prof. Segre, of 

 Turin, on the geometry of to-day ; and Prof. Wirtinger, of 

 Vienna, on Riemann's lectures on hypergeometric series. 

 We also note papers by Prof. Schlesinger on Riemann's 

 problem, by Prof. Borel on approximations of continuous 

 functions, and many others too numerous to mention. Prof. 

 E. Study showed that the paradoxical result 2 = 4 could be 

 obtained from considerations of intersections of quadric 

 surfaces. 



The congress was international in every sense, the 

 membership including representatives of Germany, France, 

 Great Britain, Italy, Switzerland, Austria, Sweden, Den- 

 mark, Spain, Russia, Japan, the United States, Greece, and 

 other countries. Only seven of the members present were 

 from Great Britain. 



For the meeting place of the next congress in 1908, Rome 

 has been selected, and the congress will take place at a 

 somewhat earlier time of the year (probably about Easter). 

 In this connection a prize is offered for the best thesis on the 

 theory of algebraic gauche curves. It has been decided to 

 hold the next following congress in England. 



Not the least important feature of the congress was the 

 large amount of local interest shown in the organisation 

 of social entertainments. On Wednesday, August 10, 

 a dinner was given to all the members in the new 

 Town Hall of Heidelberg. On the Thursday we were 

 received and entertained at Schwetzingen by the Hereditary 

 Grand Duke of Baden. The next evening we sailed down 

 the Neckar in illuminated barges, and on reaching Heidel- 

 berg the castle was illuminated by red fire, the proceedings 

 ending with fireworks, including a set-piece of the Pytha- 

 gorean Theorem (Euc. i., 47). The last evening we were 

 entertained at a concert at the castle, followed by another 

 illumination and a Kommers, for which a special song- 

 book had been published that included a number of amusing 

 inathematical songs written for the occasion. To make this 

 insight into German student life more real, two delegates 

 were elected by the students of German universities to 

 officiate in the uniform of their corps, and with their swords. 



