820 Mr. J. H. J. Poole on the possibility of separating 



them present per c.c. This really amounts to the fact that 

 the number of A molecules which diffuse out of the layer 

 downwards owing to the gravitational effect must be equal 

 to the number which diffuse into the layer from below owing 

 to the increase of concentration downwards, so that the total 

 number of A molecules in the layer remains constant, i.e., 

 the mercury is in a state of statistical equilibrium. 



Let W= average molecular energy. 



Then the osmotic pressure = n \Y» where /i = number of- 

 molecules per cc. 



Hence we have at once : 



tW m dn 1 =- — —?- (mi — m.-,)q . dx 

 (hi i du x __ 3 (m l — )n 2 )g . dx 



2 W 



But 



dni _ da 2 

 dx dx ' 



i d)i\ i dn 2 _ o {m 1 ~'m 2 )g 



Is 1 %J 



W %dX, 



»! J n 2 - W 



, )ii n (m i — m* )qx fi 



l °zi = 2 w +c - 



Now, since we have chosen our origin so that ?7. 1 = w 2 when 

 x = 0. must be zero. 

 Hence 



, iii _ 3 (m\— m 2 )gx 



W 



But W=|^, 



where R is the gas constant, 6 the absolute temperature, and 

 N the number of molecules per gram-molecule. 



rci N(m 1 -m 2 )gx 

 g n 2 ~ R0 



It is probable that the mercury molecule is monatomic, as 

 all metals appear to be so. 



Hence Nra r = one gram-atom of isotope A 



and N (raj — m 2 ) = M x — M 2 grm., 



where M x and M 2 are the atomic weights of the two isotopes. 



