the Osmotic Theory of Solutions. 607 



empty, 2, 3, and 4 (peripheral) gave rotations of 41 o, 0, 51°' 5, 

 and 47°0 respectively. 



The circumstance that the third and not the fourth sample 

 showed the greatest concentration was attributed to an 

 irregular stirring action produced by the opening of the 

 capsules ; clearly the results can only be regarded as 

 qualitative. But the changes in concentration recorded are, 

 as we will show, many times greater than theory indicates, 

 and the discrepancy is the more difficult to account for in 

 that any errors due to manipulation would lie in the contrary 

 direction. 



The calculation is as follows : — 



In a system which is rotating uniformly about a fixed axis, 

 with angular velocity co (radians a second), any particle of 

 mass m at a distance r from the axis requires an inwardly 

 directed force morr to maintain its position unaltered in the 

 system. Thus the system may be regarded as pervaded by a 

 field of force, everywhere outwardly directed, and derivable 

 from a potential function 



C = WV 2 (24) 



Therefore, in the drum under consideration, the difference 

 of potential between the axis and the periphery is 



AC=4( 2 ^ x ±0) 2 X 6 2 = 1140000 approximately. 



Now for the limiting equilibrium condition, when c 2 , ?/•, u, 

 and ttPi/tf^ are nearly uniform throughout the space, we have 

 from (23) 



Ac 2 = AC 'dw/'d c_ 2 9 



c 2 ,^/rtiP, tJr 2 ' % - \- r ) 



Here s L is practically unity, w is obtainable from Landolt 

 and Bornsteiirs tables ; ttP 1 fttc 2 , for so dilute a solution, 

 may be taken as following the gas law, and therefore we 

 can put (where 339 is the molecular weight of cane-sugar) 



UPj/fccg =22-3(1 + 15/273) x 1000/339. 



Multiplying this value by 1*01 x 10 6 to bring it to dynes 

 per square cm., and substituting the numerical values in (25) 

 we get 



Ac 2 /c 2 ='007. 



That is to say, the proportional difference in concentration 

 between the central and peripheral parts of the rotating solu- 

 tion should only be about 7 parts in 1000 in the final 



