APPLIED MATHEMATICS 521 



made a mistake in his approximation. A further problem is 

 to find the field of force of an electron : this is carried out by 

 J. B. Jeffery, Proc. Roy. Soc, 99A, 1921, 123-34, who gets a result 

 agreeing with Nordstrom and Weyl and gives some applications ; 

 it is also discussed by K. Ogura, Comptes Rendus, 173, 1921, 348- 

 50, 407-8. Of purely mathematical interest is the paper by 

 J. G. Campbell, " Einstein's Theory of Gravitation as a Hypo- 

 thesis in Differential Geometry," Proc. L.M.S. (2), 20, 1921, 

 1-14. E. Kasner, Amer. J. Math., xliii, 1921, 126-9, 130-3, 

 shows that an Einstein spread representing a permanent gravi- 

 tational field can never be regarded as immersed in a five-flat, 

 but that it can be represented in a flat space of six dimensions. 

 Kasner also discusses, ibid., 20-28, how the ^'s in ds^ can be 

 found if their ratios are given (by means of experiments with 

 light-signals). 



Other papers on relativity that should be of interest to the 

 applied mathematician are : 



Weyl, H., Uber die physikalischen Grundlagen der enveiterten Relativitats- 



theorie, Phys. Zeit., xxii, 1921, 473-80. 

 Lodge, O., Ether, Light, and Matter, Phil. Mag. (vi), 41, 1921, 940-3. 

 Eddington, a. S., The Relativity of Field and Matter, ibid., 42, 1921, 800-6. 

 Slate, F., A New Reading of Relativity, and other papers, ibid., 40, 1920, 



31-49 ; ibid., 41, 1921, 96-106, 652-64. 

 LiHOTZKY, E., Zur Frage der Verschiebung der scheinbaren Fixsternorte in 



Sonnennahe, Phys. Zeit., xxii, 1921, 69-71. 

 Bromwich, T. J. I'A., On Units and the Theory of Relativity, Phil. Mag. 



(vi), 42, 1921, 431-2. 

 Morton, W. B., Note on Einstein's Law for Addition of Velocities, ibid., 40, 



1920, 771-4. 



McAulay, a., Inertial Frames given by a Hyperbolic Space-time, ibid., 41, 



1921, 141-3. 



Buhl, A., Sur le role des sym^tries dans les theories relativistes, Comptes 



Rendus, 173, 1921, 829-31. 

 Buhl, A., Sur la formule de Stokes dans I'espace-temps, ibid., 171, 1920, 547-9. 

 JuvET, M., Les formules de Frenet pour un espace de M. Weyl, ibid., 172, 



1921, 1647-50. 

 Wilson, W., Space-time Manifolds and corresponding Gravitational Fields, 



Phil. Mag. (vi), 40, 1920, 703-12. 

 EscLANGON, E., Sur la relativite du temps, Comptes Rendus, 173, 1921, 1340-2. 

 Ogura, K., Sur le champ statique de gravitation dans I'espace vide, ibid., 



173, 1921, 521-3. 

 Ogura, K., Extension d'un theoreme de Liouville au champ de gravitation, 



ibid, 766-8. 

 Ogura, K., Sur la theorie de gravitation dans I'espace de 3 dimensions, ibid., 



909-11. 

 Eisenhart, L. p.. The Permanent Gravitational Field in the Einstein Theory, 



Proc. Nat. Acad. Sci., U.S.A., 6, 1920, 678-82. 

 Hill, F. W., and Jeffery, J. B., The Gravitational Field of a Particle in 



Einstein's Theory, Phil. Mag. (vi), 41, 1921, 823-6. 

 Wedderburn, J. H. M., On the Equations of Motion of a Single Particle, 



Proc. Roy. Soc. Edin., xli, 192 1, 26-33, who modifies the classical 



equations of motion so that the time is also included in the Beltramic 



expressions. 



