Consequences of the Electrical Theory of Matter. 165 



Einstein's formulae point at once to the perihelia of Mercury 

 and Mars as the only elements likely to be observably affected, 

 whereas on the present theory a more minute discussion is 

 required. 



Let V be the velocity of translation of the solar system 

 resolved in the plane of the planet's orbit. Resolve V into 

 components V cos w along the major axis and V sin «r along 

 the minor axis, the longitude of perihelion ts being measured 

 from the direction of V as zero-point. The component 

 V sin vr is the one which produces a correction to edvr; Vcos -sr 

 produces a precisely similar correction to de. This can be 

 seen from Lodge's formula (3), p. 86, viz. : 



fx r ., w 2 + v 2 fQ N wv cos \ 



h 2 I 2c 2 



in x wo cos \ A . n ) 

 + e cos (a — u) s~2 — vsmvY. 



sC J 



The small constant term {w 2 + v 2 )\2c 2 does not here concern us. 

 Omitting this, and remembering that a corresponds to 90° + ot, 

 and w cos \ to V in our notation, this gives 



Write sin # = sin (0— vr) cos sr + cos {0 — 1*) sin w. 

 Then 



= ^{l + (,.-gvcos OT )sin(^^)--g-Vsin OT cos(^-^)} 



• • • (1). 

 The equation of the undisturbed ellipse is* 



u=^ 2 \l + esin(0-*T)\, 



and if small variations de and d-v are given to e and -or, 



u= £\l + {e + de)sm{0-v)--ed*TCos(0--*r)\. (2) 



Comparing (1) and (2), we evidently must have 



de= — Ti -„.\ cos «r, 



2c z 



ecJvr= +«-o V sin -or. 



(3) 



The second of these is, of course, equivalent to Lodge's 



* The sine appears instead of the more usual cosine, because Lodge 

 makes 6 refer to the tangent instead of the radius. 



