Theory of Spectrum Emission. 65 



Py is as before, we Lave also 27r(l— cos ■/) = >? 2 /t. In short, 

 all the equations (20), including 



cosz= — - — , 

 ^i + w 2 



retain their validity. 



Thus g(i, e) is, also in terms of the integers n 1? n 2i ^3, 



exactly as before. But with equal right as BC we could 



have taken CA or AB as reference planes for the inclination, 



and every time i would be quantized in exactly the same 



way. Thus, the asymmetry of the nucleus gives rise to new 



"stationary" orbits and, therefore, to new spectrum lines 



or bands. Ultimately, therefore, we shall have for the 



determination of the centres of the bands, writing W s instead 



of W in (28), the equation 



S^jiw-J^l, . . . (30) 

 ch n 2 ( - (n-?i 3 )°J 



where ^=^=(l + |e 2 )(l-| sin 2 i), . . . (30*1) 



with 6, i as in (20), and where 7 has any of the three values 



^Hi-K^^r, \B-i(C + A)t\ 



\C-\(A + B)\ 12 (30-2) 



The positive or the negative sign is to be taken in (30), 

 according as A is greater or smaller than ^(B+C), and 

 similarly for the remaining two values of 7. 



Thus the spectrum belonging to a nucleus without any 

 axis of symmetry would be much richer in lines or com- 

 ponents than that of an axially symmetrical nucleus, for 

 which we have had only, as in (28*1), 



\A-B\ 1/a 



instead of the three values in (30*2). But looking back 

 upon that case from the point of view of the present more 

 general case, i. e: putting in (302) C—B, we should have 

 for an axially symmetric nucleus not only the previously 

 described lines or " components " but also those corre- 

 sponding to 



J^Jl=k(B-A)[\ . . . (28-1') 



with (30) and (30*1). In fact, the former lines were 

 obtained by taking the equatorial plane as the plane i = 0, 

 and the reason was that this (or its normal, the axis of' 

 Phil. Mag. S. 6. Vol. 39. No. 229. Jan. 1920. F 



