•192 REPORT— 1891-. 



current carried by the negative ions is equal to that carried by the positive. 

 Thus, if q be the current, we have 



(7 = 1-4x10--N;h,X 



Thus the specific resistance of the gas is 



10^ _ 



1-4xNhii 



Suppose that the hydrogen ions gave rise to a pressure of x atmo- 

 spheres, then 



Nmj=:a; x 10~^ approximately, 



so that the specific resistance is 



1071-4 x,i; 



Now, from experiments with electrolytes we find that we can easily 

 detect by this method the conductivity of substances whose specific 

 resistance is 10^" ; hence we could detect the conductivity of the gas even 

 though .r were as small as 1/7000; that is, we could easily detect the 

 presence of free ions though they only amount to one part in 7000 of the 

 total gas. It is important to notice that, inasmuch as the conductivity 

 varies inversely as the pressure of the undissociated gas, we should be able 

 to detect the existence of the same percentage of free ions at all pressures. 



Let us now consider the case when the electric intensity is variable. 

 Suppose that it is proportional to cos jJt, say X=Xo cos pt ', then we have 



or 



^ _ Xo cos (p<— €) 



when 



tan e=j=^ 



When the alterations in the electric intensity are so slow that ;; is small 

 compared with G2P, the solution is practically of the same form as when 

 the electric intensity is steady. But when the oscillations are so rapid 

 that^j is large compared with G210, then approximately 



u,=z — 'i Sin wi 

 P 



and the maximum velocity is independent of the pressure. In this case 

 the direction of the electric intensity gets reversed many times in the 

 interval between two collisions of the ion ; thus the ions, when they have 

 acquired a high velocity under the electric intensity, do not, as in the case 

 when the electric intensity is steady, lose their energy by impact against 

 other molecules, and so raise the temperature of the surrounding gas ; when 

 p is very large, the force is reversed before the ions collide, and the velocity 

 of the ion gets reduced by the action of the electric force. There is in 

 this case very little heat-production ; the efiect of the free ions is rather to 

 alter the self-induction of the circuit than its resistance. Thus, if a light 



