62 Prof. D. N. Mallik and Mr. A. B. Das on Electric 



Ao-ain, the energy carried to the cathode by the positive 

 ions may be written equal to 



_L e - kx (aNq' + ynq), 



where k is a coefficient determining the dissipation of 

 energy during the passage of these ions. 



Also, the energy carried to the anode by the negative ions 

 may similarly be written equal to 



— -^— e ~ k ' x ' (otNq' + ynq) 



(J. J. Thomson's ' Conduction of Electricity through Gases/ 

 2nded. p. 490), 



where d = distance between the electrodes ; 



V = difference of potential between the electrodes 

 assumed to vary uniformly. 



.-. E= e ^[(aNq' + ynq)x(e- kx + e- kfx ')da!. 



a ^ 



But from (5) and (6), if a, 7 be regarded as constant, 



0^y+w)(«-7)«^ +7§ ; 



/. uNq' + ynq=(uN 1 q 1 f + ^n 1 q l )e^ a -^ x .... (8) 



if N = Nx, n=ni at the cathode. 

 Hence, 



V p i 



E = -j- («Nig/ + yn iqi ) ^ x(t"-y*(e- kx + er 



- k ' x ) dx 



Ye ,rde^-y- k)d e^~y k,d -l , 



= T («N 1?1 +yn iqi ) \j^pr k - {a _ y _ k)2 * 



similar terms in k' 



= Xe{aN l q 1 ' + yn 1 q 1 )?, say. 



If a = 7 = 0, the above equation reduces to E = 0. This we 

 may suppose to be the case during the rotatory stage in air 

 [Phil. Mag. Oct. 1912]. Therefore, since in this case N = w, 

 and the pressure varies inversely as mean free path, we get 

 the equation 



i Y -i'V = neXv(q' + q~X 



