The Quantum Theory of Electric Discharge. 233 

 and in like manner (by changing the sign of S) , 



Mod. 2 Denominator=A: 2 (S + So) 2 {l+ t an 2 fitanh 2 A: 2 } ; 

 and hence 



Mod.*B=(§^|) 2 , (39) 



where S = cos'0(<r + a*)/ff (21) 



If 07 the perforated area, is relatively great, it makes little 

 difference what its actual value may be, but if <r is relatively 

 small, as in the case of strong resonance, it is otherwise. 



It would be preferable to suppose S fixed at S and to 

 calculate the effect of a variation of k with It given. The 

 resulting expressions are, however, rather complicated, and 

 it is evident without calculation that the reflexion will be 

 very sensitive to changes of wave-length when there is high 

 resonance as a consequence of small dissipation, and accurate 

 tuning. The spectrum of the reflected light [in the corre- 

 sponding optical circumstances] would then show a narrow 

 black band. 



XXII. The Quantum Theory of Electric Discharge. 

 By Dr. D. N. Mallik and Prof. A. B. Das, M.Sc* 



1. /^|N the quantum theory, the energy of a source of 

 V_/ radiation varies in a discontinuous manner by equal 

 quanta. If this is to be accepted, since electrons give out 

 radiation when their velocity is changed, the quantum theory 

 would seem to suggest that these changes are effected by a 

 series of jerks, that is in other words the changes involved 

 are due to impulses only. Moreover, since a material atom 

 is known to be made up of corpuscles and positive ions, 

 having configurations satisfying conditions of dynamical 

 stability, under their mutual attractions and repulsions, 

 it is necessary to admit that they are revolving doublets 

 or higher complexities, In view of their rapid movements 

 and collisions, such systems must be admitted to have 

 complex nutational motions as well. It stands to reason 

 therefore, that the energy of such a system cannot be a 

 continuously varying quantity. It must either remain 

 constant or, if it changes at all, it must change by finite 



* Communicated by the Authors. Paper read before the All India 

 Science Congress, 1919, Bombay. 



