424 Mr. E. Rutherford on the Velocity and Bate 



the rate of production of the ions by the rays is equal to their 

 rate of recombination. If q be the number of conducting 

 particles per c.c. produced per second by the rays, and N the 

 final number, then when a steady state is reached 



g = aN 2 , 



where a is a constant for any particular gas but varies for 

 different gases. When the rays are stopped the rate of 

 diminution of the number of conducting particles is given by 



dn 



dt ~' 1 i 



= —an* 



or if N is the maximum number and n the number after an 

 interval t, 



1 1 



n N 



The time T for the number of conducting particles to fall 

 to half their total number is given by 



N 



Now the rates of leak at the electrodes in the tube are pro- 

 portional to n, since an electromotive force is applied to the 

 gas sufficient to completely saturate the gas. From the ex- 

 perimental data of the rates of leak at different intervals we 

 may compare the experimental results with those obtained 

 from the formula 



n N 



This can be best shown by plotting curves whose ordinates 

 represent conductivities and abscissae time intervals. 



Fig. 1 shows such curves where the continuous curve re- 

 presents the relation between the conductivity and time as 

 determined by experiment, and the dotted curve the theoretical 

 relation which is deduced. In order to compare the curves, 

 one point on the experimental curve is chosen also as a point 

 on the theoretical curve. In fig. 1, the common point is P, 

 where the conductivity has fallen to half its value. 



It will be observed that the two curves are in close agree- 

 ment, and the differences between them are well within the 

 limits of experimental error. This shows that the formula 



dn 2 



-=- = — air 

 dt 



