Electric and Magnetic Fields on Spectral Lines. 507 



energy of a system of vibrating electrified particles cannot 

 be transferred into radiation, and vice versa, in the continuous 

 way assumed in the ordinary electrodynamics, but only in 

 finite quanta of the amount liv, where h is a universal con- 

 stant and v the frequency of the radiation *. Applying this 

 •assumption to the emission of a line-spectrum, and assuming 

 that a certain spectral line of frequency v corresponds to a 

 radiation emitted during the transition of an elementary 

 system from a state in which its energy is A 1 to one in which 

 it is A o, we have 



^=A 1 — A 2 (1) 



According to Balmer, Rydberg, and Ritz the frequency of 

 the lines in the line-spectrum of an element can be expressed 

 by the formula 



v=f r (n 1 )-f s 0n,), (2) 



where n 1 and n 2 are whole numbers and / 1? / 2 , 

 functions of n, which can be expressed by 



K 



a series of 



/*(*)= is M n )> 



(3) 



where K is a universal constant and (j> a function which for 

 large values of n approaches the value unity. The complete 

 spectrum is obtained by combining the numbers n l and n. 2 

 as well as the functions /i,/ 2 . . . , in every possible way. 

 On the above view this can be interpreted by assuming : 



(1) That every line in the spectrum corresponds to a 

 radiation emitted by a certain elementary system during its 

 passage between two states in which the energy, omitting an 

 arbitrary constant, is given by —hf s {n^) and — /*/»•(%) 

 respectively ; 



(2) That the system can pass between any two such states 

 during emission of a homooeneous radiation. 



The states in question will be denoted as " stationary 

 states." 



* In Planck's original theory certain other assumptions about the 

 properties of the vibrating- systems were used. However, Debye (Ann. 

 d. Phys. xxxiii. p. 1427 (1910)) has shown that it is possible to deduce 

 Planck's formula of radiation without using* any assumption about the 

 vibrators, if it be supposed that energy cau be transferred between them 

 and the radiation, only in finite quanta liv. It may further be remarked 

 that Poincare (Journ. d. Physique, ii. p. 5 (1912)) has deduced the 

 necessity of assuming that the transference of energy takes place in 

 •quanta liv in order to explain the experimental laws of black radiation. 



