Astronomy and High-speed Inertia, 89 



And a very minute acceleration would become important 

 with lapse o£ time. But the modified /j, is no new thing, it 

 has been there all the time, and so presumably it is only the 

 fluctuations that we have to attend to. Moreover, the virtual 

 force, whether variable or not, being always central, does not 

 seem likely to affect h or T. 



In any case the action, being wholly in the plane of the 

 orbit, has no effect upon the nodes. 



Another way. 



To check the calculation of (7), take the expression for the 

 reciprocal of the semi latus rectum, (3) with (0 — a) = 90°, a 

 being the angle between the latus rectum and a projection 

 on to the orbit of the sun's way, 



1 a / w- + v 2 , /n , wv cos X Q . A 

 <W] = H 1_ ~^~ +ecos( - -^ 2?— 0Sm0 )> 



and see how cc must change to keep it constant although 

 increases by 2mr. 



Initially the variable part equals ecos^w — k sin 0, 

 finally it equals 0cos (|7r — da) — k(2nir + 6) sin 0, 

 so the difference, which is to be zero, gives 

 e sin da = 2n7rk cos a, 



or 7 nirvw cos A, cos a 



dcL— g , 



ere 



which is the same result as before. 



Another check. 



Initially let = a, so that the planet is at an apse and u is 

 constant for an instant ; then the terms in u 



e cos (0—ot) — k0 sin#, 



differentiated, become 



e(sm cos a — cos sin a) + k( sin + cos 0) = 0. 



After n revolutions has returned to its old value 4- 27rw, 

 but a has changed slightly to «', such that 



<?(sin cos a! — cos sin a') + k(sin + (0 + 2irn) cos 0) = 0. 



So subtracting 



€ sin 0(cosa' — cos a)— e cost?(sin a! — sin a) + #2-7rn cos# = 0; 



