90 Sir Oliver Lodge on 



but still 6 and a are practically equal, so 



e sin 2 a dot + e cos 2 u da = 27rnk cos a, 



or 7 2irnk cos a 



a«= ) 



e 



"with k = vwcos\/2c 2 . Again the same result as (7). 



Prof. Einstein's result, as quoted by Prof. Eddington in 

 •Nature' of Dec. 28, 1916, is 



24tt 3 a? 



— o — mon ^r radians per revolution. 



(f 1 J (1 — e 2 ) 



To make my result agree with this in appearance, we must 

 gratuitously replace w cos i/> (which is quite foreign to 

 Prof. Einstein's ideas) by the following, 



bv. 



e 2 2a— r 



or, what is much the same for nearly circular orbits, we can 

 without reason write Qev instead of w cos <\>. But the differ- 

 ences, both in reasoning and in result, are fundamental. 



Problem for an orbit of greater eccentricity. 



The equations for an inverse square orbit whose excen- 

 tricity is not small are 



W 2 



V> //-• v 2 \ id 2 -\- 2vw cos<f>\ 



+ " = 77Vl 1 ? > 



cos <£ = cos X cos 6', }» . (9) 



sm{0'-0) = es'm(cc-0 , ) ) 

 v 2 = 2fAU—/j,/a, 



where 8' is the angle between the tangent and the projection 



of sun's way on the orbit, 

 6 is the angle between radius vector and the normal to 



that projection, 

 a is the angle between major axis and the same normal. 



But to get a cumulative result in a reasonable time the 

 period of revolution should be not too great. 



Other Planets. 



Substituting, from (8), 2*27xl0~ 4 c for wcoscf) in (7), we 

 can get the apsidal progression for any other planet of small 



