RECENT ADVANCES IN SCIENCE 



MATHEMATICS. By Philip E. B. Jourdain, M.A., Cambridge. 

 The Revue Semestrielle des Publications Mathematiques, which 

 was mentioned at length in the number of Science Progress 

 for July last (11, 89), can now be obtained in London from Mr. 

 D. J. Bryce, 149, Strand, W.C., and it will be seen, from what 

 has been said in the place referred to, that it is most important 

 that all British mathematicians should keep themselves abreast 

 of the very extensive literature of mathematics with the help of 

 this periodical. Two numbers appear in the course of every 

 year, and the yearly subscription is ys., post free. 



The Mittag-Leffler Institute of the future that was men- 

 tioned in the last number of Science Progress (11, 91) is 

 shortly described in Nature (1916, 97, 384). The object is 

 principally to encourage the study of pure mathematics in 

 Sweden, Denmark, Finland, and Norway ; but a prize for pure 

 mathematics is to be awarded, if possible, at least once every 

 six years, and it will be open to the whole world. 



History. — G. Mancini (Memorie delta Reale Acad, dei Lincei, 

 classe di Scienze Morali, Storiche e Filologiche (5), 191 5, 14) 

 publishes a manuscript De Corporibus Regularibus of Pietro 

 Franceschi called Delia Francesca and maintains the thesis, 

 which is not quite new, that the substance of this work was 

 purloined by Luca Pacioli (1445-1514) in his Divina Pro- 

 portione — a work dealing with the mensuration of plane and 

 solid figures. To Mancini 's memoir is prefixed a report on it 

 by Prof. Gino Loria (cf. also Nature, 1916, 97, 287). 



J. H. Graf (Boll, di bibl. e st. delle sci. mat. 191 6, 18, 49 ; 

 cf. Science Progress 191 6, 11, 91) continues the series of 

 letters from Casorati to Schlafli. 



The history of Lie's theory of contact-transformations is 

 dealt with in the fifth of the supplementary volumes to the 

 Jahresbericht der Deutschen Mathematiker-Vercinigung (Leipzig, 

 1 9 14) entitled Die Beruhrungstransformationen, Geschichte und 

 Invariantentheorie by H. Liebmann and F. Engel (Boll, di bibl. 

 e st. delle sci. mat. 191 6, 18, 78). 



Principles of Mathematics. — Prof. G. Mittag-Leffler was, as 

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