July 8, 1921] 



SCIENCE 



33 



TABLE II 



Filial Discordances in the Secular Motions of the Elements of the Fowr Inner Planets 



and the outer, or less dense, portion extends 

 beyond the orbit of the earth nearly to that of 

 Mars. The effect of each ellipsoid upon the 

 perihelia, the nodes, and the inclinations of 

 the planets can be found by simple formulas 

 of celestial mechanics, and the positions and 

 densities of those ellipsoids, which will best 

 account for all the motions, can be deter- 

 mined. liTo distribution can be found that 

 will rigorously satisfy all the motions, but 

 the positions and densities of three ellipsoids 

 can be found which will approximately satisfy 

 all the equations and practically account for 

 all the discordances in the motions of the 



The table given aboye shows with what a 

 high degree of accuracy the motions of the 

 planets can be accounted for under the action 

 of this widely scattered matter. For purposes 

 of comparison the Einstein motion is also 

 given. 



The relative probabilities of two theories, or 

 two solutions of a problem, are usually de- 

 termined from the final differences, or re- 

 siduals, as these differences are called. That 

 solution is deemed the more probable which 

 makes the sum of the squares of the residuals 

 the smaller. If this test be applied to the 

 residuals as given in the above table, the re- 

 sults are: 



Einstein theory 436 



Solar envelope, Seeliger 259 



Solar envelope, Poor 14 



And these clearly indicate how very much 

 more probable is the explanation of the mo- 

 tions of the planets as due to the presence of 

 matter in space, than as due to the hypotheses 

 of Einstein. 



Einstein and his followers have cited the 

 motions of the planets as proof of the truth 

 of his hypotheses. The evidence does not sus- 

 tain this — his hypotheses and formulas are 

 neither sufficient nor necessary to explain the 

 discordances in these motions. They are not 

 sufficient, for they account for only one among 

 the numerous discordances — that of the peri- 

 helion of Mercury; they are not necessary 

 for all the discordances, including that of 

 Mercury, can readily be accounted for by the 

 action, under the ^Newtonian law, of matter 

 known to be in the immediate vicinity of the 

 sun and the planets. 



It is, however, possible that the Einstein 

 hypotheses be true, and that the discordant 

 motions of the planets result from a combina- 

 tion of the Einstein motions and the effect of 

 the widely distributed matter in space. Just 

 as a definite distribution of matter can be 

 found which will explain the discordances 

 given by Newcomb, so also another and differ- 

 ent distribution can be found that will more 

 or less fully account for the discordances re- 

 maining after applying the Einstein effects. 

 But it is clear that the relativity theory alone 

 is not sufficient to explain the motions of the 

 planets. 



