476 Sir Oliver J. Lodge [Feb. 28, 



The next disturbance — the emission of an a ray and another )8 ray — may 

 be expected to occur, by preference, when the quasi-tidal power of the electron 

 is greatest, i.e. when it is at the nearest apse, or when several of the inner- 

 most particles are in conjunction there. Granting this for the moment, the 

 velocity of any one of them at that place will be 





With this speed, or something near it, the particle is projected into its final 

 orbit, the central force being now restored to its old value, though the atomic 

 weight has gone down a step. The semi axis major of the final orbit is 

 independent of the direction of projection, and is given by 



1 = ^-1^ 

 a' ~ W [X ' 



whence 



, _ a{l- e) N'^g ^ N'^ -^ 



^ ~ 2- k{X-\-e) (N + 1) (N - 2) N^ - 4 * 



2 

 The frequency is inversely as the 3/2 power of a', the excentricity is e' = , and 



the new radius differs from the old one by the ratio 



W -4.' 



an expression which looks as if it ought to account for Balmer's series of 

 spectrum lines. 



APPENDIX II. 



Effect of Syncheonous Ultea-violet oe X-Kadiation. 



Referring to pages 465, 470 and 474, about storing a feeble disturbance 

 by resonance, the equations of planetary motion are 



X = — fix /r^ and y — — fj.y / r^. 



Upon this we have to superpose a train of waves of very small amplitude 



y — Kcos - - {x — nt), 

 V \ 



where n is to be the " mean motion " of the planet, w = -y/i i^^ J. 



The essential part of this can be presented && y = — n" y to be added to 

 the main term. Hence the equations become 



x=-f'4; y=-f.yll^+±), and r= ^^^ is the integral of - ^. 

 r^ \r^ a^/ at a^ 



