from the Quantum Theory of Spectral Emission. 621 

 The kinetic energy of the moving electron is obviously 



T = A [mp + »<r 2 6 2 + r sin 2 6(f) 2 ] ■ 



the potential energy 



, r e 2 e\ico§6 



r ~ ? ,J 

 Two integrals can be at once written down : 



mr 2 sin 2 6(f) = Ci, 



r-2 . 2/32 i 2 • azuTsn -^ ■ 2L* COS T)tr 



To get another integral, we write 



d , o . ^ n :« <?Lsin 6 



It 



(mr 2 (J) — mr 2 sin 6 cos #</> 2 = 



oi • d , 2 a. c, 2 cos# T . 



d# sin 3 



Integrated, it gives 



(mr 2 6) 2 + /, „ + 2meL cos # = c 9 



v y sin' 



tf 



The expressions for three impulses mr, mr 2 6, and 

 mr 2 fsin 2 0(f) can now be written down : in terms of the 

 constants of integration we have 



mr 2 sin 2 6(f) = c b 



/ c? ~ 



w 2 6 =\/ Co— .—r^ — 2m eh cos 6, 

 V - sm-0 



mr = - \J — Wmr 2 -\-2me 2 r — c 2 . 

 The quanta conditions can be written down as 



) mr 2 tin 2 6(j)d(f) = n,h, (1) 



§mr 2 0d6 =n 2 h, (2) 



\ mrdr = n 3 h, (3) 



— W being twice the total energy of the system. The 

 integrals are to be extended over the whole range within 

 which the expression within the square root remains 

 positive. 



