Theory of Spectrum Emission. 63 



sign for a prolate nucleus*. The value of g(i, e) is still as 

 in (21-2), with (21*3). 



This set of formula? determines the spectra corresponding 

 to large electronic orbits round any axially symmetrical 

 nucleus. 



If, lor instance, the nucleus be a homogeneous rotational 

 ellipsoid of semi-axes a and b (the former being the axis of 

 symmetry), then A=?h 2 and J5=l(a 2 + b 2 j, so that 



If this ellipsoid be oblate, and if f be the eccentricity of 

 its generating ellipse, then 



2fcRch bf 



so that our previous a is to be replaced by bf/y/5> an< ^ * ne 

 positive sign is to be taken in (28). And if it be a prolate 

 ellipsoid then a is to be replaced by af/v 5, and the negative 

 sign is to be taken. In either case the effect on the spectrum 

 is seen to be, cceteris paribus, proportional tof 2 . 



6. Nucleus of any shape. In the most general case the 

 disturbing function is given by (26). The coefficients 

 A, B, C being all different from one another, the longitude 

 of the node 12, hitherto irrelevant and physically meaningless, 

 comes to its rights and, in addition to the perihelion, 

 becomes a fresh source of broadening of the spectrum lines. 

 For, as in the case of &>, there is no way of quantizing the 

 longitude of the node. 



If the orbit is written as in (15), if i be the inclination of 

 the orbit to the Bt -plane (so that tj 1 becomes our previous 77), 

 and if the longitude 12 of the ascending- node be counted 

 from the 7i-axis, we have 



cost;^ sin i sin 6, 



cos 7]. 2 = cos cos 12 — sin sin £2 cos i, 



cos 773= cos sin D + sin 6 cos 12 cos i. 



These values are to be substituted into (26). It will, for 

 the present, be enough to write down the result for the case 

 in which all node longitudes are equally distributed among 

 the atoms. Then a term containing sin 212 disappears in the 



* The previous two centres formed, of course, a nucleus of the latter 

 kind. 



