RECENT ADVANCES IN SCIENCE 543 



Motoji Kunujeda, Note on asymptotic formulae for oscillat- 

 ing Dirichlet's integrals, Quarterly Journal, xlviii. (2) (191 8), 

 pp. 1 13-136. 



Tsuruichi Hayashi, On the analytic function whose modulus 

 is a rational integral function of the imaginary part of its 

 argument, Science Reports of the Tohoko Imperial University, 

 viii. (1) (1919), pp. 17-31- .. 



Matsusaburo Fujiwara, Uber Irrationalitat unendlicher 

 Kettenbruche, Science Reports of the Tohoko Imperial Univer- 

 sity, viii. (1) (1919), pp. 1-10. 



A. Arwin, Uber die Losung der Kongruenz (\-f i) p — A. p — 1 

 = (mod p 2 ), Acta Mathematica, xlii. (2) (1919). 



E. Borel, Sur la Repartition Probable et les Fluctuations 

 des Distances Mutuelles d'un Nombre fini de Points, Droites 

 et Plans, Bulletin de la Societe Mathematique de France, xlvi. 

 (1919). 



G. A. Miller, Substitution groups on the terms of symmetric 

 polynomials, Quarterly Journal, xlviii. (2) (191 8), pp. 147-151. 



APPLIED MATHEMATICS. By S. Brodetsky, M.A., Ph.D., 



A.F.R.Ae.S., University, Leeds. 



In his opening address to the Mathematical and Physical Section 

 of the British Association meeting at Bournemouth this summer 

 (Nature, 2603, Sept. 18, 1919, pp. 52-9) Prof. Gray has some 

 useful remarks to offer on the teaching of dynamics. He con- 

 siders dynamics to be a physical subject, which should be 

 taught in physical departments of Universities, not in mathe- 

 matical or applied-mathematical departments. His aim is to 

 make the teaching of the subject more experimental. Every 

 experienced teacher of mechanics will agree with this plea, in 

 so far as it involves the introduction of properly devised experi- 

 ments into every elementary course on dynamics, or indeed 

 statics and hydrostatics too. It is surely possible to make 

 such a practical course more interesting and more varied than 

 the rather dreary set of experiments that the physical student 

 is usually made to work through in " properties of matter." 

 But the time is hardly ripe for the transference of the teaching 

 of dynamics to the physical departments of our Universities. 

 The teacher of dynamics is always called upon to give his 

 pupils much that is almost purely mathematical ; he is often 

 forced to supplement their slender stock of algebraical, geo- 

 metrical, and trigonometrical knowledge. The mathematical 

 department is the appropriate place for such teaching. 



Prof. Gray lays particular stress on a correct appreciation 

 of the dynamics of rotation, and desires the learning of dynamics 



