Consequences oj ihe Electrical Theory of Matter. o23 



in forming (1) is equivalent to neglecting the difference of 

 longitudinal and transverse masses and using the latter 

 throughout. At first sight it might seem that for a nearly 

 circular orbit the force is nearly transverse, so that the use 

 of the transverse mass is justifiable. But we are here con- 

 cerned with the true path of the planet through the aether, 

 which is a spiral, and the force is not really transverse. By 

 basing the analysis on momentum we obtain a simpler 

 treatment, which avoids the introduction of two kinds of 

 mass. 



2. Turning now to the question of absolute instead of 

 relative momentum, it is found that yet another correction 

 will be needed. If V is the velocity of the sun through the 

 aether, u the orbital velocity of the planet, the absolute 

 momentum is m(V +u); and the rate of change of momentum 

 is 



du dm _ dm 



dV _ 

 since ~r- = U. 

 dt 



In Lodge's original analysis only the first term was taken 

 into account. We have introduced the correction repre- 

 sented by the second term. There remains the third term to 

 consider. If the inertia of the planet increases during any 

 part of its orbital motion, an additional impulse will be needed 

 merely to enable it to keep up with the sun's motion through 

 space ; otherwise the translational velocity decreases as the 

 inertia increases, in accordance with the conservation of 

 momentum. 



Let V be the sun's velocity through the aether, and let the 

 longitude d of the planet be measured from the direction of V 

 as zero-point; accordingly, the radial and transverse com- 

 ponents of V are V cos 6 and —V sin 6. Then the momenta 

 of the planet relative to axes fixed in the aether are 



hi — m( V cos 6 + r) , 



h 2 = m( — Vsin 6>-j-r0), 



in the instantaneous radial and transverse directions re- 

 spectively. 



Forming the equations corresponding to (2), we have 



j- 0mr) — mr6 2 + V cos 6 ~ = — F, 

 dt K dt 



-r (mrO) + mr 6 — V sin -=- = 



(*) 



