TRANSACTIONS OF SECTION A. 157 



showed no shift of the spectral lines, a fact which in itself ■would overthrow the 

 theory in question. Father Cortie pointed out that C<ampbeirs photographs, 

 taken in 1918 and measured by Curtis, gave no trace of any displacement of the 

 images of 43 stars distributed irregularly round the sun. 



Spectrum Emission of Atomic Systems containing a Double or More 

 Complex Nucleus. By L. Silberstein, Ph.D. 



The subject proper of the paper is preceded by a short historical account 

 of the work done since 1913 by Bohr, the pioneer of the quantum theory 

 of spectra; by Sommerfeld (relativistic refinement of Bohr's theory leading 

 to the fine structure of spectrum lines) ; and by Ep.stein (Stark effect). 



In all these investigations the nucleus of the atom is assumed to be a 

 homogeneous spherical charge, or, which is the same thing, a point charge. 



The corresponding spectra are all series of the Balmer type, = const. ( — ^ — ^j 



m and ti being integers. These series consist, apart from relativistic refine- 

 ments, of sharp (ideally monochromatic) lines. 



In order to obtain series of other more complicated types, and, moreover, 

 consisting of ' lines ' which, even without taking into account the relativistic 

 terms, will show a complicated fine structure, the author works out, on the 

 lines of the quantum theory, the spectra emitted by atoms containing 

 aspherical nuclei. As a first example the case of two fixed positive centres 

 as nucleus is treated without restrictions of the dimensions of the 

 electron's orbits. This being the famous soluble case of Euler and Jacobi, 

 the author treats it by the method of separation of variables. A variety of 

 orbits and of the corresponding types of spectrum series are described and 

 illustrated in their general features. The sub-case of comparatively large 

 orbits, which is physically the most interesting one, is treated, with all details, 

 by the method of perturbations. If 2a be the mutual distance of the two 

 centres, the negatived ■energy belonging to any stationary orbit, in three 



dimensions, is, u't {■• ( I -terms, 



W = - N 1 1+7 /•- - J F(W|,"».M3) } . ■ (I) 



where ks is the total charge of the nucleus, N the Bohr excression of the 

 Rydberg constant, 



7 = "^"' (2) 



M,, »:, «.3 three independent integers, and 



n = ni-l-n2-!-?!,, ; e the eccentricity of the 'osculating' orbit, which is quantitized 

 by the usual principles so that 



2 , (n- w,)" 



€ = i — s • 



n- 



and finally a a number contained between 1 and 3, namely 



tt = 1 + 2 sin'' S>, (4) 



& being the longitude of the perihelion counted from the equatorial plane. 

 For y = o, the series corresponding to (1), is a Balmer series of sharp lines. 

 The y^ term gives doublets, or triplets, etc., according to the value of 

 ni-|-W2-f-?i3 in the constant term; moreover, each of the components of these 

 doublets, etc., consists in general of several sub-components. Those corresponding 

 to Ji2 = o or 713 = are sharp, ideally monochromatic [these correspond to orbits 

 contained in the equatorial plane or to any circular orbits] ; all others have a 



