-204 The Secular Perturbations of the Inner Planets, 



mean errors to make them all of equal weight, and solved 

 by the method o£ least squares. The method adopted being 

 the same as in my former paper, the best solution is 

 found to be /3=0'67, Z = O102, m=-0'097. Thus the 

 inclination to the ecliptic of the equatorial plane of 

 the disturbing matter is 8° 9' and the ascending node is 

 in longitude 46° 24'. The calculated perturbations pro- 

 duced by this matter are compared with observation in 

 the following table : — 



™ Cal- ~ , ^ . , , Mean Residual 



Element. >"" , Observed. Residual. • Viean ^ 



culated. error. Mean error 



rdi/dt 002 038 0-36 0-80 0'4 



Mercury i sin id Si /dt .. 0'94 0-61 -0'33 051 -0'6 



led-ar/dt 9'95 9-96 0-01 0-43 0-0 



rdi/dt 0-49 0-38 -O'll 0-33 03 



Venus ...J sin id Si /dt... 0'45 0*60 0*15 0-17 0*9 



ledv/dt 0-05 -004 -0*09 0'25 -0-4 



rdi/dt 0-01 -0-01 -0-02 0-20 -0'1 



Mars ...isinidSi/dt... 004 0'03 -0-01 0'22 -00 



[edfsr/dt 0'03 077 074 0*34 2-2 



It is seen that all the residuals except one are less than 

 their mean errors. This result is of course better than we 

 are entitled to expect; for of nine observed quantities, 

 three would be expected to deviate by more than their 

 mean errors. It shows, however, that the observed excesses 

 corresponding to Dr. Silberstein's theory are very easily 

 accounted for by an oblate distribution of gravitating 

 matter around the sun, and that the actual distribution will 

 not be very different from that found on this theory. 



The progression of the perihelion of Mars has still a 

 residual which is more than twice its mean error. It is 

 impossible to state on such a small margin of safety whether 

 any considerable part of this is real. It was shown by 

 Newcomb that the earth's attraction contributed 21 /,, 4 per 

 century to ed^/dt for Mars. Thus a mass 1/25 of the 

 earth's, and equally favourably placed, could account for 

 the residual. Newcomb pointed out that the known 

 asteroids could not attain anything like such a mass, but 

 if the invisible matter very much exceeded the visible 

 it might be possible to explain the motion of the perihelion 

 of Mars. Even if it were not so possible, however, the 

 residual is not large enough to invalidate the theory. 



The nodes of the ecliptic on the equatorial plane of the dis- 

 turbing matter would at the same time be expected to regress 

 Q"'28 in a century, the inclination to this plane remaining 

 unaltered. This would give rise to small changes in the 



