78 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS. 



continues to grow indefinitely in the lapse of time in an invariable 

 direction. Hence there must be a source of current in the electrometer, 

 as intimated. 



69. Theory. Let V n be the potential of the needle, V c the voltaic 

 potential difference of the two metals of the condenser, the shell being 

 put to earth, V the potential of the insulated conductor BB, measured 

 by the electrometer. Let n be the apparent ionization in the electro- 

 meter, N the (radium) ionization in the condenser (length /, radii R^R^} . 

 Let C be the total capacity of the systems CBBE. Then 



where A is a constant, u and v the normal velocities of the positive and 

 negative ions, e the charge of the electron. The needle is supposed to be 

 positively charged. This may be written 



V=V a -K(V-V c ) 

 where for N = o, K = o, or 



i. e., the current in the electrometer, observed in the absence of radium, 

 from needle to quadrants. This is directly measurable with accuracy. It 

 is nearly proportional to V n since V is much within i per cent of V n . 

 The integral of this equation is, t being the time, 



V=(VJK)(i-KV c /V a )(i-e~ Kt ) 



the sign of V is negative if V a <KV c> which is the case below. If there 

 is an initial potential V Q imparted by the standard cell, which is then 

 removed, 



V=V e- Kt +(VJK)(i-KV c /V a )(i-e- Kt ) 



If, now, the needle is left positively charged, but the condenser metals 

 exchanged (commutated), so that the aluminum core is earthed and the 

 shell now put in contact with the electrometer (see figure) , the equation 

 becomes 



Here K refers to the negative current or normal velocity of negative ions 

 v. Similarly let K r refer to the normal velocity of positive ions u. Also 

 let = N/K and K f = N/K'. Then if k = V c lv' a , and k f = V c /f'V a 



~ Kt ' ~ Kt 



= V a (i -kN)e~ Kt V' = V a (i+kN}e 



