Theory of Spectrum Emission. 6L 



and if, for instance, we require the breadth of the line to 

 be |S\(=0'01 A.U., to which corresponds in, say, the red 

 region of the spectrum, 8v = 0*023 cm. -1 , we should have 



«2a== 0-0052, 

 that is to say, the value of a required to give such a line, 

 i5p A.U. broad, would be 



a = O 'fl0- n cm., 



i. e. for /c = l (as in the case of hydrogen) a = 5*2 . 10" u cm., 

 and so on. Notice that the breadth of the line would, cwteris 

 paribus, increase as K 4 a 2 . Thus, if Ave had, say, only 

 <x = 5. 10~ 12 cm. for such atoms as those of uranium (/c = 92) 

 the "line" in question would be drawn out into a very 

 broad band, in tact, a continuous spectrum extending over 

 7160 A.U.,and even a = 10~ 13 would still givea band stretching- 

 over little less than 3 A.U. And it will be kept in mind 

 that in those heavier atoms larger a are more likely than in 

 the light ones. 



5. Any axially symmetrical nucleus. As has been already 

 mentioned in the preceding Section, the set of formulae (21) 

 continues to hold for any axially symmetrical nucleus 

 whatever. The reason is that the disturbing function F is 

 for an atomic system with any such nucleus exactly of the 

 form (13). The only difference is that the previous semi- 

 distance a of the two centres acquires a more general 

 meaning, and the whole expression may have one or the 

 opposite sign according as the nucleus is " oblate " or 

 "prolate," in a generalized sense of these words. 



In fact, let the whole charge ice of the nucleus be distri- 

 buted in any manner whatever over a volume t. Let O be 

 the "centre of mass" (electric analogue of ordinary mass- 

 centre), and A, B, C the principal " moments of inertia" of 

 the whole charge, each divided by the charge, i. <?., if x ly y x , z x 

 be the coordinates of a charge element de along the principal 

 axes, with as origin, let 



A =^Q/i 2 -f-^i)de,etc (25) 



Let the electron be at P, and let K be the " moment of 

 inertia" of the nucleus about OP, divided by ice. Then, if 

 OP = r is large compared with the dimensions of the nucleus, 

 -the negative potential energy of the system will be, by a 

 well-known result of the ordinary potential theory, 



[r 2r* 



