396 Prof. Townsend on the Conductivity produced 



It has been assumed that two new ions, one positive and 

 one negative, are produced by a collision on all occasions 

 when the velocity of the negative ion exceeds a certain fixed 

 value. It is probable that there are other circumstances 

 besides the velocity of the negative ion which determine what 

 takes place on collision, so that ions may be produced on 

 some occasions when the negative ion collides with a mole- 

 cule with a comparatively small velocity. A comparison 

 between the numbers obtained experimentally and those 



__NV 



given by the formula a = Ne x shows that this is the more 

 correct explanation. Thus with air it is only the larger 

 values of a that are accounted for by supposing that the 

 negative ion requires a velocity corresponding to a fall of 

 potential of 25 volts. It is evident, from the values of a 

 obtained experimentally for the smaller forces, that new ions 

 are produced when the velocity is much smaller than this. 

 Taking the value 15*2 already obtained for N, we may arrive 

 at a more correct formula if we include some encounters in 

 which the velocity is as small as that corresponding to a fall 

 of potential of about 10 volts. Let Ci be the average number 

 of new ions arising from C collisions, in which the velocity 

 is intermediate between the velocities corresponding to 10 

 and 20 volts. Let C 2 be the number arising from C col- 

 lisions when the velocities are intermediate between those 

 corresponding to 20 and 30 volts. It may be supposed that 

 for voltages above 30 the velocity acquired will be sufficient 

 to produce new ions at every collision. 



The number of collisions, which occur in one centimetre 

 when the velocity is intermediate between those corresponding 



ION" 20N" 



to 10 and 20 volts, is Nl e x — e x J. On the average 

 the number of ions arising from these collisions will be 



("1 / 10X 20Ts T v 



Hence a is the sum of three terms 



(V , 10X 20X\ C] / 20F 30X\ SOX 



u 



±Ui\ 220JN \ ( ' / 



The number N has been already found, and it only remains 



c c 



to deduce ~ and ■— from the experiments. It will be found 

 that the formula gives results in good agreement with those 



