Theory of Spectrum Emission. 55 



Let us still write 



• n = Ji l + }i 2 + n. ii . 



Thus, ultimately, we shall have, for the total energy 

 corresponding to any of the contemplated "stationary" 

 orbits of the electron round the two-centres nucleus, 



eh ~~ n 2 r ' Qi-)h) 6 



where 



COS I — 



; > 6) \ . • • ( 21 ) 



2/cRcha , , . /oi.f\ 



7 = 2 — (a pure number), . . . \&VY) 



g(i, e) = l+36 2 -f sin 2 /. [1 +f e 2 (l + 2 sin 2 *>)], (31-2) 

 ;and, as in (20), 



= i-("^y. . . .(2i-3) 



ni + n 2 \ n J 



The corresponding spectrum series being given by 

 v = AW/ch, it is not difficult to see the meaning of fhese 

 formulae. 



If the two centres coincided (« = 0), 7 = 0, and we should 

 have an ordinary Balmerian series consisting of ideally sharp, 

 simple lines, the three independent integers then appearing 

 •only through n = rij+n a + n 3i and their individual contri- 

 butions being entirely irrelevant for the result. 



Owing to the complexity of the nucleus, as here con- 

 templated, there is a general shift of the spectrum, dependent 

 ■on the numerical value of <y\ and, instead of a single sharp 

 line f which would correspond to a given pair of initial and 

 final ?i-values), there is a plurality of lines, some sharp, but 

 most of finite breadth. Whether or not at least the general 

 Balmerian type of the distribution of these groups of lines 

 (as we may call all the lines corresponding to a fixed pair of 

 initial and final n- or sum-values) will be preserved, will 

 most essentially depend on the relative separation of the 

 centres, that is, on the numerical value of 7. If y l be but a 

 very small fraction, we shall still have a Balmer series, 

 although not of lines but of tightly packed groups, each 

 group being a doublet or a triplet, etc., as the case may 

 be, and each of their components consisting of several 

 sub-components, sharp or broad, — in short, a Balmer series 

 with fine structure of its members. But should 7 2 mount up 

 to more conspicuous values, even the type of the series would 

 be entirely modified, i. e., as in the case of the spectra of most 

 chemical elements, altogether different from the Balmerian 

 type. Both possibilities seem interesting and, perhaps, 

 promising. 



