58 Dr. L. Silberstein on the Quantum 



But, by the orbit equation (15), p 2 /fce' 2 m' is the parameter 

 (hitus rectum) of the orbit, i. e. Ct(l — e 2 ), if a be the mean 

 distance or the semimajor axis of the orbit*. Thus, the 

 required form of (21), 



h n> r w (l-^r • • • (21] 



where g is as in (21*2). This shows us that for all not very 

 eccentric orbits the supplementary term, due to anisotropy 



of nucleus, is of the order of f - ) , which is a fraction at any 



rate. At the same time we see that the coefficient 7 has the 

 simple geometrical meaning 



7=V (22 a) 



[This is a constant, as it should be ; for, by (20), a itself 

 is proportional to n 2 . The last formula, coupled with (22), 



gives 2/ca= -n 2 , which contains the warning not to expect 



sufficient accuracy from our formulae for those atoms for 

 which the fraction 2/ca may acquire a comparatively huge 



value. I From (210 we see also that even for small - the 



deviation of the series from the Balmer type can become 

 dominant if the orbits are strongly eccentric, that is to say, 

 when n 3 is a large number in comparison with n x + n 2 . 



Returning once more to formulae (21), (21*2), (21 - 3), let 

 us consider them in connexion with the various shapes and 

 orientations of the orbits. 



From the last set of these formulae we see that all meridian 

 -orbits (i. e. those contained in any meridian plane, cos? = 0) 

 are given by 



n Y = ; 



the corresponding value of g is 



* Thus, the smallest non-vanishing value of p being h/ln, the smallest 

 ■" stationary " orbit has the parameter or, if circular, the radius 



1 e 2 . 1"03 -,„ o 



«^M-¥ W " cm '' 



inversely proportional to k. It will be important to keep this well in 

 mind, especially for the heavier atoms. 



