Consequences of the Electrical Theory oj Matter. 325 



rigorously into two components of constant magnitude *, 

 viz. : 



(1) A constant speed u perpendicular to the radius 



vector ; 



(2) A uniform translation u e parallel to the minor axis, 



in the direction 6 — 'U7-\- 90°. 



The approximation hitherto made by Lodge and the 

 writer consists in treating the planet's orbital velocity as 

 constant and perpendicular to the radius vector ; e. g., in 

 obtaining equation (5). This condition is rigorously ful- 

 filled by the first component u . The work will therefore 

 become exact if we take separate account of the second 

 component, u e. 



This second component simply combines with the general 

 motion through the sether, — V sin ot, in the same direction ; 

 and we have therefore to write u e — V sin ot for — V sin ot 

 in equation (3), p. 165, of my previous paper. Accordingly, 



de — -~ .Vcos ot, 



\. ■ . ■ (6) 



The signs have been amended in accordance with § 1. 



The strict value of u for an eccentric orbit is tj 

 2™ h 



or 



T(l-* 2 )*' 



The results (6) are inaccurate in one particular : since 

 6 is not strictly a constant, the terms containing V in (4) 

 will produce secular perturbations when e is no longer 

 neglected. The exact effects can be computed by the 

 methods of dynamical astronomy. The variations of the 

 elements due to radial and transverse forces S and T 

 respectively are given by the general formulse t 



«-J{s-n(«— )+t(«(»— )+5=r)}, 



In the present problem we have 



MS = -Vcos0~, MT = Vsin^^ n . 

 dV dt 



* I cannot find any explicit reference to this result in any of the text- 

 books I have consulted, though it is familiar as an examination question 

 and is really the basis of the practical calculation of stellar aberration. 



t See, for example, E. W. Brown, ' Lunar Theory,' pp. 61-62. 



