186 The possibility of separating Isotopes. 



conditions. Suppose, for instance, that the cylinder is of 

 length /, and that the origin of x is at the middle point 

 along the axis. A fairly uniform increase of T along the 

 cylinder can be represented by the formula, convenient for 

 the present purpose, 



& T logT=B + Bsin^, 



whence we obtain the result 



Xi = Xio — B^l— e » u )$m-j-, 



which is stationary at the two ends of the cylinder, as it 

 should be ; X 10 is the value of X x at the middle of the cylinder.. 

 When the process of diffusion has been nine-tenths com- 

 pleted, we have 



,-£»»< = ! 

 10 



or 



I 2 W,10 



IT' 



D„ 



Taking D 12 = l'20fi/p, and assuming that fi cc T ' 7 , as is 

 probably nearly true, we have 



(D 12 ) T = l-20^(fY 



Pi) \J-0/ 



PoX 



where p , p are the values of p, and p at temperature T , say. 

 At 0° C. and atmospheric pressure yu, = 3*10~ 4 , ^ = 0'9 . 10~ 3 ,. 

 so that at 80° absolute the value of D 12 is approximately 

 0*050. Hence 



log e 10 

 '~<M)507r 2 ' -^ bl ' 



if the cylinder is 10 cm. long, £ = 460 seconds, or about 

 8 minutes. This very short time applies to a cylinder ; for 

 two bulbs connected by a tube (which should be vertical, 

 to avoid convection from the lower, cold, to the upper, hot, 

 lulb) it would be considerably greater. But unless some 

 serious mistake has been made in the above calculation, it 

 would seem that the time required is to be reckoned in hours, 

 at most. Hence thermal diffusion, many times repeated, 

 should prove a practicable method of separating isotopes of 

 the kind considered. 



Cambridge, 



May 1919. 



