•64 Dr. L. Silberstein on the Quantum 



average taken over all atoms, and the relevant part of the 

 disturbing function F is given bv 



4^~F= [B cos 2 £l+C sin 2 II - (B sin 2 H + Ccos 2 H) cos 2 i 



-A sin 2 ?] sin 2 



+ -&A + B+C)-(B cos 2 £l+C sin 2 n). . . (29) 



If, keeping in mind the finite breadth of the lines due to 

 42, we desire only to deal with the position of the centres of 

 these " lines " or bands, then it is enough to retain the 

 average of F taken over all emitting atoms, which we may 

 denote by F s . It is manifestly legitimate to take first this 

 average, and then the average, F s , over a period of the 

 undisturbed motion. Thus (29) reduces at once to 



F,=!j- '. ^ + ^" 2A (3sin a tsin 8 g-l)j . (29 s) 

 which is exactly of the same form as (13), with a 2 replaced 



Thus, taking the time average, the corresponding energy 

 will again be given by (28), with the only difference that 

 the coefficient 7, (28*1), will now be replaced by the more 

 general one, 



2fcRch \ . . 1/2 



y=— e 2-\ A -i(B+Q\ • 



The value of g i, e) will still be as in (21*2), and the 

 eccentricity € will, manifestly, be quantized as before. It 

 remains, however, to see whether ?', the inclination *, does 

 not now in this respect behave differently. 



Returning to equations (19) and to what immediately 

 followed upon them, we shall see that the only difference is 

 that the relation tan </>= tan 6 . cos i has now to be replaced by 



tan (<f> — fl) = tan 6 . cos i. 



This, however, does not affect the results. The geometrically 

 obvious relation 



p<j) =pcosi 



continues to hold, and therefore p cos i=n 1 /i/27r. And since 



* It will be remembered that i was taken with reference to the 

 J?C-plane, and this is the reason why A is privileged in the last two or 

 three formulae. 



