August i8, 192 i] 



NATURE 



785 



this variation of inertia, if it were allowed to 

 accumulate for a century. If the speed were con- 

 stant it could not be detected ; but the speed is not 

 constant. The orbit is elliptical, for one thing ; 

 and the solar system is in motion, for another. 

 Sometimes, therefore, the solar drift will be added 

 to the orbital speed of Mercury, sometimes it will 

 be subtracted from it. 



Here then ,is a definite problem : to trace 

 the consequences of this variation of inertia on 

 the form or details of its orbit ; and this problem 

 I attacked in the Philosophical Magazine for 

 Augfust, 1917, and found that it must lead to a 

 cumulative apsidal revolution unless there were 

 some compensating; cause. The paper was 

 followed up by Prof. Eddington in September and 

 October 1917 and June 1918, by Mr. G. W. 

 Walker in April 191 8, and by myself again in 

 December 1917 and February 1918. 



We found that if the solar drift were sufficient, 

 both in magnitude and in direction, to give the 

 proper value for the perihelion progress of both 

 Mercury and Mars — as it easily might be — a 

 smaller effect could not be denied to some of the 

 other inner planets ; and there would be accom- 

 panying small eccentricity changes, not cor- 

 responding with observation. The best solar 

 drift is one with the speed 1-7 x 10— ^ c, and longi- 

 tude 173°, for its component in plane of ecliptic. 

 This will suit Mercury, both for apsidal revolution 

 and for eccentricity. The perturbations that 

 ought theoretically thus to be caused in the other 

 inner planets are tabulated below ; and, to com- 

 pare with these calculated values, the table gives 

 also the actual estimated or observ^ed outstand- 

 ing secular variations per century, both for the 

 perihelion progress, d^CT, and for the change of 

 eccentricity, de. (See Phil. Mag., February, 

 1918, pp. 148 and 154.) 



Outstanding Perturbations per Century. 



The discrepancies between theory and practical 

 estimate, though small, are considered to be 

 beyond anything that can reasonably be attributed 

 to errors of modern observation ; and if that is the 

 final verdict of astronomers, after reconsidera- 

 tion of the figures, it becomes a question what 

 is the compensating cause that prevents fluctua- 

 tions of inertia from taking effect. The only 

 cause that has suggested itself is a variation 

 in the Newtonian gravitation constant, due to 

 its being a function of velocity ; so that weight 

 is modified, somewhat in the same sort of way as 

 electrostatic forces are modified, by rapid motion. 

 {Phil. Mag.. February, 1918, p. 156.) 



Prof. Eddington has now agreed (see his admir- 

 NO. 2703, VOL. 107] 



able book, " Space, Time, and Gravitation,'* 

 p. J 25) that the result of the whole discussion is 

 to prove that gravitation has " joined the con- 

 spiracy," and has succeeded in concealing any 

 effect of uniform motion. 



But, on Eddington 's improved theory (i^M. 

 Mag., October, 1917), It achieves this result in an 

 odd way, and apparently does not sustain Ein- 

 stein's " Equivalence " thesis, that inertial mass 

 and gravitational mass are the same in all cir- 

 cumstances ; or, briefly, that weight is always pro- 

 portional to mass. Some caution is here required ; 

 for the proportionality of weight and inertia seems 

 to be interfered with at high speeds. Their pro- 

 duct, not their ratio, appears to be involved in a 

 planetary perturbation, regarded from the point 

 of view of the electrical theory of matter ; and 

 hence, if one increases, the other must decrease. 



Galileo's experiment on the Tower of Pisa, 

 roughly, and Newton's pendulum determinations, 

 more exactly, established the proportionality of 

 mass and weight; and recently Prof. Eotvos, fol- 

 lowed by Prof. Zeeman, has confirmed Newton's 

 conclusion to a high degree of accuracy, so far 

 as ordinary circumstances and slow motions are 

 concerned. (See the excellent new edition of Clerk 

 Maxwell's wonderful little book, " Matter and 

 Motion," brought out last year by Sir Joseph 

 Larmor (S.P.C.K.), pp. 34 and 143.) But the 

 astronomical evidence cited above seems to 

 require that the Newtonian gravitational constant 

 shall diminish at high speeds, being multiplied by 

 the factor i —u^/c^. Only thus can it compensate 

 the inevitable increase of inertia {i — u^ / c^)~~^ ; at 

 least if the increase of inertia sustains its full incre- 

 ment of weight. If the increase of inertia due to 

 motion is not subject to gravity, then \/{i—u^fc^) 

 will suffice as the factor of the gravitation con- 

 stant. {Phil. Mag., February, 1918, pp. 143, 145, 



155-) 



Assuming that so it will turn out, after further 



detailed scrutiny, it is clear that weight is affecteo 

 by high-speed locomotion. For the increased 

 mass of a fast-revolving planet would by itself 

 undoubtedly' cause a minute apsidal progression 

 sufficient to be observed ; and the fact that 

 for several of the inner planets the outstand- 

 ing perturbations are less than the calculated, 

 shows that compensation must somehow occur. 

 It is to be hoped that the peculiar nature of the 

 compensation, here suggested, may ultimately 

 throw light on the gravitational structure of the 

 aether. Meanwhile, unless some error is detected, 

 it appears in conflict with the universal propor- 

 tionality of mass and weight. 



We shall now proceed to a few remarks on 

 points connected with the more general theory 

 of relativity. 



Erratum. — In the first article of the present 

 series (Nature, Augfust 4), on p. 718, ist col., 1. 6 

 of 2nd para., delete the words "in v if it is 

 opposed to m"; and substitute "when the 

 observer reverses his motion." 



{To be continued.) 



