Mercury into its tsotopic Forms by Centrifugiag. 821 

 Thus finally we have 



, n, (M^-M^; 

 lo <y — = — - 



If we are dealing with a centrifugal field of force, the 

 equation obviously is 



dn Y dn 2 3 mi — m 2 9 

 ra 3 n 2 2 W 



which gives log -1 — *- 2 . © V 2 + C. 



Iii this case we cannot eliminate C so easily as we do not 

 know — for any given value of r. 



7l 2 



As, however, we are not very certain as to the exact 

 conditions, I propose to deal with the question as though the 

 centrifuge tube was in an uniform gravitational field of 

 magnitude equal to the centrifugal field at the central section 

 of the tube. This is of course only an approximation, but it 

 will be probably good enough to enable us to obtain some 

 idea of the magnitude of the result to be expected. 



The particulars of the centrifuge used in our experiments 

 on the effect of centrifuging liquid lead (see Phil. Mag. 

 March 1920) are approximately as follows : — 



Length of centrifuge tube — 6 cm. 



Distance of inner end of tube from 



centre of rotation = 4 cm. . 



Number of revolutions per sec. —150 



Hence acceleration at centre of tube = ©V 



and at outer end of tube, 



Mi-Mj 



= (150x2tt) 3 x7, 



i n i iV1 i- 



lo gr= -la 



gx, 



n 2 ~ U0 



_ 4 x (150 x 2tt) 2 x 7 x 3 

 ~ .83-15 x 300 xlO 6 ' 

 Since = air temperature — 300° Abs. (approx.), 



R = 83-I5xl0 e , g = co 2 r, 

 M 1 -M 2 = 4 =(150 x 2tt) 2 x 1, 



and x is to be measured from centre of tube, and is there- 

 fore =3 cm. 



This gives finally that - 1 =1*003. 



IX 2 



We have now to consider what effect this small change in 

 the concentration of the two isotopes would have on the 

 mean density. 



