264 
DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 
of a frequency v where, if h is Planck’s constant, hv is the difference of energy between 
two states—when the electron passes from one state 'to the other. In the case of 
elliptic motion, Sommerfeld finds it necessary for certain purposes to confine the 
eccentricities of the possible ellipses to definite discrete values, and thus obtains 
spectral lines which are not single, as in Bohr’s theory in its ordinary form, but which 
have a definite structure. In fact, his theory involves the supposition that the Balmer 
series is effectively a supposition of Diffuse, Sharp and Principal series, as in some of 
the suggestions mentioned in the last section. These series are superposed in the 
case of Hydrogen, on account of the simplicity of the atom, and general considerations 
indicate—though not with great precision—that they would be widely separated in 
the case of other elements. This is not the appropriate place for any discussion or 
exposition of the theory, for we are concerned solely with the actual structure to 
which it leads. 
The most important result is that the separation in H s is of the order suitable for 
a Diffuse or Sharp series, in comparison with that of H a . The latter is used— Buisson 
b o 
and Fabry’s value A H = 0'307, corresponding to SX — 0'132 A.U.—to determine a 
constant of the investigation, and the other separations are deduced in terms of this 
value. The results are as follows 
In H a the complete structure is that shown in fig. 2, where the separations are 
l 
I 
IlcC- 
Fig. 2. 
Up 
Fig. 3. 
shown on a wave-number scale. The “ main ” separation is called Ah, and the 
“satellite” separations are A : , A 2 , where 
Aj = -rx A H , A 2 = dy A h = 3 Aj. 
Since A n = 0‘307, we have 
A; = 0 030, 
A, = 0'090, 
