234 Dr. D. N. Mallik and Prof. A. B. Das on the 



amounts, in view of the fact that the changes are effected by 

 (generalized) impulses. In any case a variation of energy in 

 a discontinuous manner is consistent with many well-known 

 phenomena. 



In the present paper we have attempted to interpret the 

 behaviour of electric discharge in a vacuum-tube in terms 

 of this theory. 



2. In a vacuum-tube, as we know, the discharge is non- 

 luminous or silent unless the difference of potential is 

 greater than a certain amount, so that there is a minimum 

 difference of potential for the passage of a spark. 



Now assuming the formula 



T? - V ch "- 1 



° ~~ z x in? ' 



where c = velocity of light, 

 X = wave-length, 

 A = Planck's constant, 

 N = Avogadro's number, 



B- = ttt for a gas, 



and E is the energy required for electronic oscillation 

 of wave-length ]£X, we observe that this quantity has a 

 certain constant value, depending only on the nature of the 

 gas. In other words, so long as a gas retains its specific 

 properties, so as to yield a characteristic spectrum, the total 

 energy required for luminosity has a constant value. That 

 is, the energy corresponding to the ionization of the gas 

 when attended with luminosity has a value which is 

 constant and independent of the pressure of the luminous 

 gas, so long at any rate as the gas continues to yield its 

 characteristic spectrum. 



3. If, then, E is the energy of a corpuscle which is in a 

 condition to ionize, 7E will be the energy that will b& 

 transferred to the ionized gas, where 7 is a proper fraction. 

 And for luminosity, 7E must be equal to E . It seems 

 reasonable to suppose, therefore, that the minimum energy 

 of the ionizing corpuscle must be E . And if we further 

 admit that E is proportional to spark-potential or at any 

 rate of the form «+ bV, where V is the spark potential, 

 the minimum spark potential V must be proportional to E . 



