4 Schuster, Rate at which Ions are Generated. 



Integrating the above equation we find that if n^ be 

 the ionic density at time y^ and % at time i)^ 



-^-- = «(«i-e„) (2) 



n^ n„ 

 Similarly at time (^2 



i-i=a(«,-«„) (3) 



«2 no 



Imagine now the tube to be placed in H in the 

 accompanying figure and the ionic density over a cross- 

 section at M to be n^ ; if n represents the density at a 

 time that the ions pass within the condenser and are caught 

 by it, equation (2) can be made to apply. Similarly in 

 equation (3) n^ may represent the ionic density at N 

 when the radium is placed in K provided N and M are 

 taken at equal distances from H and K respectively. 

 Subtracting the two equations we find 



With the radium in H let the inner rod of the condenser 

 fall from potential V^ to V in time ^j, and with the 

 radium K let the same fall of potential take place in time 

 t^. Then if Q be the volume of air entering the apparatus 

 in unit time the number of ions entering is Qn-^^ty and 

 Qn^t^. respectively, so that if e is the ionic charge and C 

 the capacity of the condenser. 



and 



Qen„t„=C{V,- F„) 

 from which we find 



02 — 61 is the time taken for the air to travel through a 

 distance equal to that between H and K ; hence if d be 

 that distance and U the velocity of the air 



The ratio a e may thus be calculated if the velocity of 



