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



If we put £ = 1*2, we get from this equation 



p = 50'7xl0- 7 , 



which is very nearly the value of p at 1*2° C; hence we 

 conclude £=1*2 and q, the amount of water deposited per 

 unit volume of the expanded gas, is 47*7 X 10~ 7 grms. 



It was found that, when the rays were on, the velocity of 

 the drops was *14cm./sec., while without the rays the velocity 

 was '41 cm./sec. 



Connexion between the Velocity and Size of the Drop. 



If v is the velocity with which a drop of water of radius a 

 falls through a gas whose coefficient of viscosity is n, then if 

 we neglect the density of the gas in comparison with that of 

 the drop 



l + 4# +«(£)' 



4 3 a \r P a \@ a ' 



^ircja 6 = birfia V 



(»39 



(see Lamb's ' Hydrodynamics/ ed. i. p. 230), where /3 is the 

 slipping coefficient. If there is no slip between the sphere 

 and the gas, /3 is infinite, and we have 



Y=- 9 —- (1) 



V 9 /* ' [ } 



while if fxlfia is large we have 



3 /ju 



Since a occurs in the denominator in the terms involving 

 1//3, the influence of slipping on the motion of very small 

 spheres such as those we are considering will be much more 

 important than its influence on the motion of spheres of the 

 size used for the bobs of pendulums, for which the influence of 

 slipping has been shown to be too small to be detected. We 

 cannot, therefore, without further consideration neglect in 

 our case the terms involving l//3a. Some light is thrown on 

 the question by the Kinetic Theory of Gases, for according to 

 that theory (see Maxwell, " Stresses in Rarefied Gases ; " 

 Collected Works, vol. ii. p. 709) fi//3 is of the order of the 

 mean free path of a molecule, i. e., for air at atmospheric 

 pressure of the order 10~ 5 centim.; hence, if a is large com- 

 pared with the mean free path, we should expect the relation 

 between the velocity and size to be that given by equation (1) . 



Taking the equation 



" 9 /»' 



