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[ 203 J 



XVI. The Secular Perturbations of the Inner Planets. 

 Note by Harold Jeffreys, M.A., D.Sc* 



CCORDING to Dr. Silberstein's theory! the values 



of e-j- for the four inner planets are as follow, the 



unit being 1" per century : — 



Mercury. Venus. Earth. Mars. 



-1-48 -0-01 -0-01 -0-02 



The observed values of the excesses above the perturbations 

 calculated on the simple Newtonian law are 



+.8-48 + -43, -O05±-25> +0-10 + -13, 4-0'75±'34. 



Thus if we adopt the new theory instead of the old, the 

 excesses become 



+ 9-96±'43, -O04±-25 ; +0-11 + -13, + 0-77 + -34. 



The eccentricities and the planes of the orbits are not 

 affected by the alteration, and the other residuals are 

 therefore the same as those found by Newcomb. 



The question to be decided is whether they can, as a 

 whole, be accounted for by the attraction of other matter. 

 As I have pointed out in an earlier paper (M. N. Roy. Astr. 

 Soc. Dec. 1916, p. 112), any such matter must be very near 

 the sun ; so that the disturbing function can be expressed 

 in the form 



R = far~ 5 {r 2 — Z(lx 4- my + nz) 2 }, 



a, I, and m being unknown constants. 



Taking /3= 1'296 x 10 8 a, I showed that the perturbations 

 produced by such a distribution of matter are given by the 

 formulas in the third column of the following table : — 



Calculated Observed 



Element. perturbation. perturbation. Mean error. 



rdi/dt (-49"9/-52-7»)/3 038 0-80 



Mercury -j sin ida/dt ... (52-7J-49-9-?»-8-79)/3 . 0-61 0-51 



iedvr/dt (0-66J-0-61m + 14-72)j3. 9'96 0"43 



rdi/dt (-2-071 -10-14m)i3 0-38 0"33 



Venus ..A sin id Q /dt... (10'147-2-57m- 0-62)0. 0"60 0-17 



led-ar/dt 0'073 -0'04 025 



rdi/dt (-0-3Ql-0-42m)(3 -001 0-20 



Mars ...isinidSi/dt... (0-42J_0-36m-0-012)/3 0-03 0-22 



I e&ar/dt 0-05,3 077 0"34 



Nine equations of condition are thus obtained to determine 

 /3, I, and m. They are then divided by their respective 



* Communicated by the Author. 



t " General Relativity without the Equivalence Hypothesis," Phil. 

 Mag. for July 1918, pp. 94-128. 



