5i8 SCIENCE PROGRESS 



derive his equations from those of classical mechanics, but 

 makes them invariant in form, thus imitating Lagrange, who 

 obtained invariant equations of motion in dynamics, but going 

 further than Lagrange in extending the invariance to the space- 

 time frame, whereas Lagrange only postulated invariance for the 

 space co-ordinates. The writer then discusses the application 

 to a symmetrical field, and the results that are thus obtained, 

 concluding with the statement that the many speculations that 

 form part of the theory of relativity may finally be discredited, 

 but the positive theory of gravitation built up by Einstein will 

 not be affected thereby. 



What troubles Painlev^ is the fact that in Einstein's results 

 any function of the radius vector, within reason, can be sub- 

 stituted for the radius vector, ibid., and 677-^0 ; also J. Chazy, 

 ibid., 905-7. In truth it must be admitted that some relativists 

 do far too much juggling with this arbitrary function, and the 

 consequence is unnecessary bewilderment of the unsophisti- 

 cated. As Painlev^ points out, the arbitrariness in the choice 

 of radius vector is due to the scanty astronomical data to which 

 the theory can be at present applied. Some writers choose this 

 function so as to make the velocity of light at any point the 

 same in all directions, others so as to make the velocity of light 

 constant along any radius vector. Einstein himself is fond of 

 making the determinant ^ = — i , and so on. Perhaps a reason- 

 able choice would be to make the periodic time in a circular 

 orbit vanish when the radius is zero — but the writer of these 

 notes must not join in this process of speculation, at least not 

 here. 



Other French writers on the theory are E. Borel, ibid. 1 89- 

 91, who offers no opinion for or against ; E. Picard, ibid., 680-2, 

 who discusses the implications of space-time considered as one 

 organic conception ; P. Langevin, ibid., 831-4 ; and J. Le Roux, 

 ibid., 1074-7. Among general discussions of the theory must 

 also be mentioned the paper by L. T. More, " On the Postulates 

 and Conclusions of the Theory of Relativity," Phil. Mag. (vi) 

 42, 192 1, 841-52, whose decision is against the theory. Equally 

 unfavourable is the view of O. Meiszner, Phys. Zeit., xxii, 1921, 

 183-5 J E. Reichenbacher, ibid., 234-43, who declares that the 

 theory does not explain the nature of weight ; see also E. 

 Guillaume and C. Willigens, ibid., 109-14. Of great interest 

 are the discussions opened by A. S. Eddington at the Physical 

 Society, Proc. Phys. Soc, xxxii, 1921, 245-51, and at the Mathe- 

 matical Association, Math. Gaz., x, 1921, 228-33. 



Although the present article cannot enter into the optical 

 consequences of the theory, mention must be made of the 

 experiments by A. O. Rankine and L. Silberstein, who tried to 

 measure the effect on the velocity of light produced by a gravi- 



