Cluster in a Gas under Influence of an Electric Field. 923 



consequently they are of great local density, Its magnitude, 

 measured by the lack of saturation between two given fields, 

 would therefore be roughly proportional to the square of the 

 number of ions produced, or proportional to the square of the 

 pressure of the gas. But the coefficient of general re- 

 combination varies roughly proportionally to the pressure 

 when it is less than one atmosphere. Thus the lack of 

 saturation due to initial recombination varies as the cube of 

 the pressure. In the experiments described in this paper it 

 would therefore be about 4-0V0 °^ WDa ^ it is at atmospheric 

 pressure and thus small. 



In a previous paper we have taken the number of negative 

 ions drawn through the gauze for different fields equal to the 

 corresponding positive leaks. This must lead to erroneous 

 results, since the positive leak increases considerably with 

 increase of electric field. This is due to the fact that 

 ionization by collision occurs even for comparatively weak 

 fields, for the mean free path of an ion must occasionally be 

 so large that the ion acquires sufficient energy under the 

 electric field, even when it is comparatively weak, to produce 

 further ions by collision. 



The Variation of the Velocity of an Ion Cluster with the 

 Electric Field applied when it is large. 



The writer * has given an equation connecting the velocity 

 of an ion cluster with its period of life during its passage 

 from gauze to plate and other quantities. If rj is small in 

 comparison with V^a, where rj denotes the fraction of the 

 number of clusters per c.c. becoming free ions per second 

 and V x the velocity of a cluster, the equation in question 

 becomes 



0- {£+*,}/■, (i) 



or Ce~ la Y 1 ci=k 2V i-k 1 Vot; (2) 



where is the current measured, and Jc 2 and k 1 the number 

 of clusters and free ions respectively drawn through the 

 gauze. When only a fraction of the clusters become free 

 ions on their passage over the distance I between gauze and 



vk-> 

 plate, the condition rj <Y l a is satisfied. For l~- is then 



small in comparison with k 2 , or ^<V J , while a is usually 

 greater than unity except for small values of X. If the 



* Proc. Camb. Phil. Soc. vol. xvii. pt. iii. p. 269 (1913). 



