16 SCIENCE PROGRESS 



In matters of more general interest in our subject it is use- 

 ful to note the progress made in the application of mathe- 

 matics to applied mathematical problems. Thus F. Hitch- 

 cock {Phil. Mag. vi, 35, 191 8, 461-71) continues his work 

 on the Laplacian operator in connection with homogeneous 

 functions. In a paper of mathematical interest, T. Kubota 

 (Tohdku Math. Journ. 14, 191 8, 20-7) discusses the conditions 

 that the centre of gravity of a convex curve shall coincide with 

 that of any of the convex parallel curves. The investigation is 

 extended to surfaces. A. Buhl (Comptes Rendus, 166, 191 8, 

 454-6) finds the moments of inertia of some layers of matter 

 on a surface by means of a certain integral. P. Appell (Comptes 

 Rendus, 166, 1918, 513-16) discusses the means of representing the 

 Newtonian mechanics for a system of particles or a rigid body. 

 H. Vergue (Bulletin des Sc. Math. (2) 41, 191 8) completes his 

 articles on the general equations of mechanics. K. Ogura 

 (Tohdku Math. Journ. 13, 191 8, 172-204) gives a geometrical 

 study of the mechanics of a particle from the standpoint of line 

 geometry. R. Bricard (Comptes Rendus, 166, 191 8, 734-5), in a 

 paper " Sur le mouvement a deuxparametres autour d'un point 

 fixe," discusses the rigid dynamics of a body about a point or 

 of one sphere on another fixed sphere. Of great interest is the 

 paper by E. H. Neville, on moving axes with variable angles 

 (Quart. Journ. of Math, xlviii. 191 8, 136-41). An account of 

 Neville's powerful method of treating problems involving moving 

 axes in such subjects as dynamics and differential geometry 

 was given at the Mathematical Congress in Cambridge in 191 2. 

 This new paper contains a brief statement of the ideas of the 

 method and the formulation of the fundamental equations. 



The following additional papers have been published re- 

 cently : 



Statics. E. V. Huntingdon, Bibliographical Note on the Use of the Word 



"Mass" in Current Textbooks, Amer. Math. Monthly, 25, 1918, 1-15. 

 S. Brodetsky, The Elementary Theory of Statical Stability, Math. Gax. ix. 1918, 



233-6. 

 E. M. Horsburgh, An Approximate Formula for the Length of an Arc of a 



Suspended Rope, Proc. Edin. Math. Soc. xxxvi. 191 7-18, 94-5. 

 B. DE Fontviolant, several notes on the effect of a wind on a bridge, 



Comptes Rendus, 166, 191 8, passim. 

 A. W. Conway, On an Expansion of the Point Potential, Proc. Roy. Soc. 94, 



A, 1918, 436-52. 

 R. F. Muirhead, Rolling Loads : A New Graphical Method, Proc. Edin. Math. 



Soc. xxxvi. 1917-18, 96-102. 



