Cluster in a Gas under Influence of an Electric Field. 927 



at atmospheric pressure is given by t Y = — and is thus equal 



to 4*19 x 10 ~ 7 sec. If y denote the fraction of free ions 



becoming clusters per second in a number of ions in 



equilibrium yk 1 =n]k2, and thus 7 = 8*98 XlO 7 at standard 



k 

 pressure, the ratio -^ * being independent of the pressure. 



1 , . . 1 



The period of life t 2 of a free ion is given by t 2 = - and thus 



equal to I'll XlO" 8 sec. ? 



From the kinetic theory of gases it follows that an air 

 molecule undergoes 1*6 X 10 10 collisions per second with other 

 molecules at standard pressure and temperature of 30°. A 

 negative ion cluster therefore undergoes on the average 

 6*7 X 10 3 collisions before becoming an elementary ion, and 

 an elementary ion undergoes 1*8 X 10 2 collisions before it 

 successfully forms a cluster. 



In the application of equation (1) in a previous paper 

 mentioned, the total numbers of ions drawn through the 

 gauze for different fields were taken equal to the corresponding- 

 positive leaks obtained, which gives a considerable increase 

 of the numbers in question with increase of electric field. 

 But we have just seen that this is not permissible ; the 

 quantity in question is practically independent of the electric 

 field when it is large. A recalculation from the data given 

 in the paper + gives us the equations 



5-040 x 10'» = k 2V + 1-341 x 10 6 , 



5-092 x TO 6 = * 2 *7 + 1-740 x 10 6 , 



from which it appears that the deviations of the velocity of 

 a cluster from being proportional to the electric field are not 

 yet so large as to interfere with the calculations. Thus the 

 velocity of a cluster is proportional to the electric field for 



77 and lower values of — . From these equations we obtain 



V 

 k x — '\l, and hence k 2 = 18*33 since k t + ,k 2 = 18*5. One of 



the equations then gives us 77 = 1-506 X 10 4 corresponding to 

 a pressure of 15 mm. of mercury, and at atmospheric pressure 

 therefore ^ = '763 xlO 6 . The distance between gauze and 

 plate in these experiments, it should be mentioned, was 

 '5 cm. The value of V x a for one of the fields is 



1320 x 1-87 x 7ii0 x 10-73 _ n6 



and thus large in comparison with 1*506 x 10 4 the value of 

 #, which is the criterion for the applicability of equation (2). 



* Loc. cit. t Loc. tit. p. 272. 



