﻿6 Mr. William Sutherland on the 



half of the tube while the gas in the tube is at rest. Thus, in 

 Stefan's theory of diffusion already given, we have only 

 to put a 2 = and we can proceed at once to calculate the 

 velocity of evaporation in terms of the coefficient of diffusion. 

 In the expression (2) for R, ol^I + 71^71^ stands for «i+a 2 > so 

 that if a 2 = the term njn 2 in R drops out, and the equations 

 (3) and (4), which can be written p 1 a 1 = 'Ddp- l /dx y will in the 

 case of evaporation have to be written 



Let p 1 and p 2 be the partial pressures of vapour and gas, and 

 p the total pressure p± +p 2 at which the evaporation is going 

 on, then (ni + n 2 )/n 2 =p/p 2 ; and if p is the density of the 

 vapour under some standard pressure P, then pi can be taken 

 as equal to pj^i/P if the departure from Boyle's law is not 

 too great, and then the last equation becomes 



n „ _T)ppdp 1 _ Bpp d Pl _j. p dlogjp-p^ ^ 

 Pll ~ Fp 2 dx ~ ^{p-p 1 ) dx ~ P P dx 



but px^ is the mass of vapour that crosses each unit section 

 of the tube in unit time, and in the steady state is constant : 

 therefore d\og(p—p 1 )/dx is constant. Let h be the distance 

 of the liquid surface below the open end of the tube, where 

 pi is while at the liquid surface it is p g the saturation- 

 pressure of the liquid at the temperature of the experiment, 

 then 



d log (p-pd/d*= 1 °SP- 1 °8(P-P-) , 



and the law of evaporation for a liquid whose surface is kept 

 at distance h below the open end of a tube is 



PA s p~p> s 



If the level of the liquid is not kept constant in the tube, 

 but is allowed to fall as the liquid evaporates, then, as p^ is 

 the mass which evaporates in unit time, if a is the density of 

 the liquid and dh/dt the velocity with which the surface of 

 the liquid falls, p 1 a l = adh/dt y and then 



hdh=I>£Zdtlo g ^, 1 



i(V-V)=(*i-<,)Dglog-JL- j* * 

 This is Stefan's expression (Sitz. Akad. Wien, lxviii. 1873). 



