The possibility of separating Isotopes. 183 



suppose that m 1 >,m 2 ),'is approximately given by * 

 17 m 1 — m 2 X]X 2 



A.'t =: 



-\-m 2 y*15 — 8'25 X^' 



where X x , X 2 denote the proportions by volume of each gas 

 in the mixture ; thus X 1 -fX 2 =l. The diameters have here 

 been assumed equal, the molecules, moreover, being regarded 

 as elastic spheres. 



The equation giving the variation o£ \ 1 orX 2 corresponding 

 to a gradient of absolute temperature T in the direction of x 

 is 



dX, _ BX2 _ _ 7, B lo<z - T 

 B^ ~dx ~dx ' 



when the steady state has been attained. 



If Ai, X 2 do not vary much throughout the gas (and they 

 will not do so by reason of thermal diffusion alone, which is 

 only a weak separating agent), we have as the difference 

 between the values of X at the two ends of a tube maintained 

 at temperatures T, T' : 



\ 1 -V=-(X 2 -X 2 ') = MogT'/T. 



§ 2. It is, of interest to compare the separating power of 

 thermal diffusion with that of pressure diffusion. The latter 

 is considered in the paper first cited, where an estimate is 

 made of the difference of pressure and the resulting partial 

 separation obtainable by centrifuging the gas. The effect 

 in this case can be represented by the equation 



where 



9; 



V 



B>2 



7. Blog 



~ p d* 



V 





7c P = 



\{k 2 (?% — m 2 ) 

 \iirii + X 2 m 2 





Thus if the extreme pressures are p, p' the separation is 

 given bv 



X 1 -X/=-(X 2 -X 2 ')=/l > logp/y. 



* A numerical error may be pointed out on p. 185 of my paper, Phil. 

 Trans. A. 217, 1916. The first numerical constant in the denominator of 

 the expression for k T in the oxygen-nitrogen column should be 10T 

 instead of 22'2 ; the three particular values of k T calculated from the 

 expression should be 0-010, 0013, 0*0086, giving the values 2-0, 2'5, 2*8 

 for'D p /D T in the last columu. 



