316 Prof. J. J. Thomson on Effect of Electrification 



i a drop of water of radius a 

 ance / from a charge e of elec 



Sp 1 e 2 f3 1 



with a drop of water of radius a placed with its centre at a 

 distance /from a charge e of electricity: — 



g 2 fg 1 a 2 1 1 



where the notation is the same as in the case of the uniform 

 field. In order to see what kind of effect the electrification 

 may produce, let us suppose that the distance between the 

 electrified point and the surface of the drop is very small 

 compared with the radius of the latter. In this case we may 

 put/— a = x, where ajx is large. Making this substitution, 

 we have approximately 



Sp_ _1 e 2 1 1 



p R0K a—p 1G7T a 2 x' r 



The effect due to surface-tension is 



S P== 2 T _1_ 

 p a—p a K0' 



Comparing these two expressions, w T e see that while the 

 effect due to surface-tension varies as 1/a, the contrary effect 

 due to electrification with a given value of x varies as 1/a 2 : 

 thus, for very small drops, the effect of the electrification to 

 promote condensation will overpower the effect of the surface- 

 tension to prevent it. The electrification thus overpowers the 

 cause which, under ordinary circumstances, puts an end to 

 the existence of the small drops. 



To compare the effects of electrification with those of 

 surface-tension, let us consider the case when the charge is as 

 small as it is possible for it to be, i. <?., when <?=12'9x 10~ n 

 approximately, which is the charge on a single atom ; let us 

 suppose that this charge is so close to the drop that x=li)~ 9 : 

 then, assuming that T for a small drop has the same value as 

 for a large one, T = 75. Thus the effect of electrification will 

 overpower that of surface-tension if 



(12*9)* X 10-" 



a< 



167rxl50xl(T 18 ' 



i. e., if a < 2 x 10" . Thus for drops of less than this size the 

 equilibrium vapour-pressure will be less than that over a flat 

 surface free from electrification, so that the precipitation of 

 the water-vapour into these small drops will be facilitated. 

 The preceding numbers apply to the case when the charge 

 of electricity is as small as possible. If we had a larger 



