from the Quantum Theory of Spectral Emission. 627 



case, will serve, to illustrate at least some general principles 

 at which we have arrived by an experimental study or' the 

 spectral series. 



Summary. 



In this paper an attempt has been made to deduce the 

 laws of regularity in '.he spectral series of elements on 

 the basis of Bohr's quantum theory of spectral emission. 

 Starting from Sommerfeld's assumption that the ordinary 

 line-spectra of elements are due to the vibration of one 

 outer electron (the valency electron), it has been shown that 

 the Held of the nucleus and the remaining (n — 1) electrons 



may be represented by the Potential V= 1 2 ' : 



i.e., the field due to a single charge plus a doublet of 

 strength L. The axis of the doublet is variable, but the 

 emission is supposed to take place so quickly that in that 

 short time the axis does not appreciably change. 



The quanta conditions have been applied according to 

 Sommerfeld's rule, nh = \pidq { , and the energy of the 

 system has been reduced to the quanta numbers. The 

 energy comes out in the form 



VV = — 7 ro, n + z= y in tne paper, 



where n. 6 is the radial quantum, n is the azimuthal quantum, 

 and z is given by an equation of the sixth degree, involving- 

 only the azimuthal quantum, and is a function of n only. 



It has been next shown that if, in accordance with 

 Sommerfeld's principle, we assume n=l for the s-orbits, 

 )i = 2 for the p-orbits, n = 3 for the <i-orbits, n = 4, for the 

 6-orbits, then, with a xery simple assumption, we obtain 

 a single value for the energy of the s-orbits, a double value 

 for the energy in the p-orbit, a treble value for the ^-orbit. 

 Then, applying Bohr's law A</=W n — W«', we arrive at 

 Rydberg's laws of the regularity in spectral series, in the 

 ease of the alkali metals. 



Exact calculations are not tried on account of the 

 uncertainty of the value of L ; but it has been pointed out 

 that the values of s, (pi,pi), (d u d 2 , d 3 ) progressively decrease, 

 as is actually the case. 



If the value of L be supposed to vary with u 3 , the radial 

 quantum, then probably the above calculations would lead to 

 Ritz's law. 



