and the Spectrum of Helium. 101 



rh 

 momentum of an electron is ^— (t integral), and that the law 



of electronic repulsion has any possible form. 



We must thus modify the law of angular momentum. It 

 must be so changed that the angular momentum still contains 



the factor ^— , or the whole relation with Planck's theory is 



J/7T 



lost. But at the same time, it must cease to be an integral 



multiple of ~— . We write, therefore, /"(t)— for the angular 



momentum, where /(r) is a function not only of an integer t, 

 but also of the nuclear charge and the number of elections 

 in the atom. 



With this specification, we can resume consideration of 

 the inverse square law. It is easily shown that the energy 

 radiated in forming the atom is 



where N<? is the nuclear charge, and n the number of electrons. 

 We must deal first with the factor n. Unless f(r) qc */n, the 

 Rydberg constant cannot be preserved, provided that only 

 one quantum of energy is evolved in passing from this state 

 to any other. If we modify the theory, however, so that 



every electron emits a quantum, — is the determining 

 feature in the frequency emitted. 



An angular momentum depending on the square root of 

 the number of electrons can hardly be imagined as possible: 

 so that the theory should probably be thus modified. This 

 modification was indicated in the earlier paper* as necessary 

 to Moseley's interpretation of his X-ray results. It is here 

 required for ordinary spectra as well. 



But the Rydberg constant is still not preserved unless 

 /'(r) is proportional to N — JS n . This is an even more diffi- 

 cult connexion to imagine, for it would destroy the whole 

 meaning of the relation of the atom to Planck's theory. 

 Moreover, when n = l. f(j) has all integral values and not 

 half integral ones if Bohr's theory of the Pickering series 

 is correct. I£/(t) were necessarily proportional to N — £8,,, 

 it could only have values which were multiples of 2 in this 

 case (S n =0), and this would cut out the Pickering series. 

 The only conclusion therefore is that we cannot preserve 

 Ry dberg's constant by any theory wliich ascribes the 

 Pickering series to helium. Once it is so ascribed, the 



* T. 562. 



