APPLIED MATHEMATICS 519 



tational field, Phil. Mag. (vi), 39, 1920, 586-91 . They found that 

 the ratio (vertical velocity minus horizontal velocity) velocity 

 is less than 8 x io~^'. But of more immediate interest to the 

 applied mathematician is the question of the perihelion of 

 Mercury. J. Le Roux, Comptes Rendus, 172, 1921, 1227-30, 

 1467-9, does not think that Einstein's explanation of the out- 

 standing discrepancy is really an argument in favour of rela- 

 tivity. G. Bertrand, ihid., 1921, 438-40, finds yet another 

 modification of Newton's law that will account for the dis- 

 crepancy. W. M. Smart, M.N., R.A.S., Ixxxii., 1921, 12-19, 

 considers the possibility of the existence of an unknown planet, 

 at the same mean distance from the sun as Mercury, and con- 

 cludes that its stellar magnitude would have to be between co 

 and 1*2. 



The problem of rotation is one of the great difficulties in 

 relativity mechanics. R. A. Sampson returns to this (see Sci. 

 Prog., 1921, 525) Phil. Mag. (vi), 40, 1920, 67-72, and expresses 

 the opinion that rectilinear motion is a degenerate case, and so 

 the conclusions derived from rectilinear motion cannot be applied 

 to circular motion. An interesting paper was written by G. 

 Lippmann, " Determination de I'axe de rotation, de la vitesse de 

 rotation d'un corps solide et realisation d'un corps solide sans 

 rotation," Comptes Rendus, 172, 1921, 5 5 7-61 ; see also E. 

 Picard, ibid., 629-30, L. Lecornu, ibid., 731. Other papers 

 are F. Kottler, " Rotierende Bezugssysteme in einer Minkow- 

 skischen Welt," Phys. Zeit., xxii, 192 1, 274-80, 480-4, and J. 

 Rey, " Sur I'experience de Perrot relative au mouvement de 

 rotation de la terre," Comptes Rendus, 171, 1920, 343-4- 



Concerning the foundations of relativity as contained in the 

 Lorenz transformation, a very interesting paper is that by L. A. 

 Pars, Phil. Mag. (vi.), 42, 1921, 249-58, who shows that it is 

 not necessary to assume the existence of an invariable velocity 

 (that of light), but that this follows from the very principles of 

 relativity. A. Righi, Comptes Rendus, 170, 1920, 1559-4, sug- 

 gests further decisive experiments (see also J. Villey, ibid., 171, 

 298-301), while a useful illustration of subjectivity in estimating 

 speeds is given by C. Richet, ibid., 173, 192 1, 805-6. 



The relativity theory of gravitation naturally suggests further 

 investigation of the properties of gravitational attraction, and 

 considerable interest has been aroused by the experiments of 

 A. Majorana. In Phil. Mag. (vi), 39, 1920, 488-504 he gives 

 an account of his experiments on the " quenching " of gravitation 

 by matter. He surrounded a leaden ball weighing 1,274 grams 

 with 104 kg. of mercury, and he found that the ball lost 

 7'7 y. lo"^" of its weight. From this he deduced the quenching 

 factor for matter of unit density to be 673 X lo"", which means 

 that gravitational force is reduced by this fraction of its value 



