Cluster in a Gas under Influence of an Electric Field. 925 



the same effect exists for air. Thus the velocity of a cluster 



J X 



in C0 2 is not proportional to the electric field when — has 



the value 130 and higher values, and the same holds for air 

 when — has the value 173 and higher values, X being ex- 

 pressed in terms of volts per cm. and p in terms of mm. of 

 mercury. 



Approximate Evaluation of the Quantities contained 

 in Equation (2). 



Although we cannot in some cases use equation (2) to 



determine the quantities k 2 , k l9 and 77 in the way described, 



owing to a want of knowledge of the velocity of an ion cluster 



for large fields, yet by the help of the equations the order of 



magnitude of these quantities can be determined. If t x 



denote the period of life of an ion cluster, the number of 



clusters becoming free ions during their passage from gauze 



k I I 



to plate is — =• , where ^- is the time the clusters are under 

 h V 1 V 1 



way. For two different electrical fields X! and X 2 , to which 



correspond the ionic velocities V/ and Yi", we then have 



approximately 



fC 2 l rC 2 l SQ\ 



W - ^ 7 -" 1- " 2 ' {) 



where n x and n 2 denote the number of free ions drawn through 

 the gauze corresponding to the fields X x and X 2 calculated 

 on the supposition that no clusters become free ions during 



their passage from gauze to plate. Since t 1 = - * the equation 

 may be written ^ 



hvl(y-, - y7ij = n i- n 2, .... (4) 



and thus gives the order of magnitude of the quantity rjk 2 . 

 The order of magnitude ^ may then be determined by means 

 of equation (2). Since ~K. = k 2 + k\, where K denotes the 

 total number of ions drawn through the gauze and is approxi- 

 mately equal to the positive leak obtained, the order of 

 magnitude of k 2 and n can now readily be found. It can be 

 shown by this method that in the case of air, using the first 

 and third readings in Table I., the orders of magnitude of the 



* Loc. cit. p. 270. 



