84 Sir Oliver Lodge on 



If, however, instead of a reduction in force, the mass were 

 slightly greater than is proportional to weight, the result will 

 be similar, and similar aspidal progression should occur. It 

 is noteworthy that a discrepancy of electrical mass due to 

 planetary speeds will be o£ the order 10 ~ 8 , and that that is 

 of the same order as the above imagined discrepancy in n. 



But to determine the amount of the extra or unexplained 

 advance of perihelion properly, we must know the absolute 

 speed of the planet through the sether. This involves a 

 knowledge of the proper motion of the sun in our cosmic 

 group of stars, and also an estimate of the unknown drift 

 of that group itself as suggested by Kapteyn. 



Let the sun's true way be inclined to the plane of the 

 planet's ecliptic by an angle X (latitude). Let the sun's 

 gross velocity through the aether be w, meaning its motion 

 towards Vega (which alone would make X about 60°) com- 

 bined with the unknown drift of the whole cosmic group of 

 stars to which the sun belongs. Let the velocity of a planet 

 in its orbit be v, and let 6 be the angle which its direction 

 makes with the projection on its orbit of the sun's true way* 

 then, taking account of the normal component w sin X, as. 

 well as of the component in the plane of the orbit, wcos X, 

 the resultant speed of the planet through the sether is 



^/{yo 2 + v 2 + 2vio cos X cos 6) ; .... (1) 



so that its apparent mass at any point in its orbit is 



(. , w 2 + v 2 4- 2vw cos X cos 0\ . . - ., . . , 



1 ^ — | I times the gravitational mass. 



In nearly circular orbits this angle 6 may be taken as also 

 representing the angle between the radius vector and the 

 normal to the above line of reference; i. e. as the 6 of ordinary 

 polar coordinates. 



Now writing the differential polar equation for an inverse 

 square orbit as usual, with u the reciprocal of the radius 

 vector, and h twice the rate of description of areas, 



dhi _ F/m _ //, 



fju is the acceleration multiplied by the square of the distance, 

 and is constant for constant mass. But /uu contains the 

 effective inertia in its denominator, and is therefore affected 

 inversely by the mass factor just considered. So on the 

 electrical theory of matter the equation becomes 



dhi a /. w 2 + v 2 vw cos X J\ , 



det +u =W — 2? ?— oose )> ■ ( - 2 > 



