538 Prof. J. J. Thomson on the Charge of Electricity 



centimetre of the gas, u the mean velocity of the positive and 

 negative ions under unit potential gradient, A the area of the 

 plates, E the potential-gradient, this quantity of electricity is 

 also equal to wew EA, hence we have 



CY=neu EA ; 



so that if we know n and u we can from this equation deduce 

 the value of e. 



The method of making the experiments was as follows : — 

 The aluminium plate and the water-surface were connected 

 with the poles of two Leclanche cells, and the rate of fall, r l} 

 of the drops produced by an expansion when the rays were 

 not on measured ; the rays were now turned on, and the rate 

 of fall, r 2 , of the cloud now produced by the expansion deter- 

 mined ; the rays were now turned off, and a third expansion 

 taken, and the rate of fall of the cloud, r 3 , found ; if r 3 was 

 appreciably less than r 1? it was taken as indicating that the 

 ions produced by the rays were too numerous to be caught by 

 one expansion, and the intensity of the rays was therefore cut 

 down by inserting aluminium foil between the bulb and the 

 vessel ; this process was repeated until r 3 was equal to r i9 and 

 then it was assumed that all the ions were caught by the 

 cloud produced by the expansion. From the rate of fall the 

 size of the drops was calculated from the formula 



2 qa? 



where v is the velocity, a the radius of the drop, and //. the 

 coefficient of viscosity of the gas through which the drop 

 falls. If q is the mass of water deposited from a cubic centi- 

 metre of the gas, we have 



q=n^7ra 2 . 



The method used to determine q is that given by Wilson in 

 his paper on the formation of clouds in dust-free air (Phil. 

 Trans. 1897, A, p. 299). We have the equation 



Lq = CM(t^t 2 ), 



where L is the latent heat of evaporation of water, C the 

 specific heat of the gas at constant volume, M the mass of 

 unit volume of the gas, t 2 the lowest temperature reached by 

 the expansion, t the temperature when the drops are fully 

 grown. 

 Since 



g=pi-p, 



where pi is the density of the water-vapour before conden- 



