﻿170 Prof. M. S. Smoluchowsk 



is approximately given by 



v {l-S) 



■o 2 



*>o S 3 W 



+ |,(18Aa-9A</,)+^_ 



The third power of S is generally negligible, and so will 

 he the fourth power too, provided Ad is large compared with 

 S 2 /8. It is not easy to define exactly the limits of this 

 restriction, as S 2 depends on the size of the volume considered. 

 If we calculate B 2 by means of (3) for a volume of a wave- 

 length cube, which may perhaps give a rough idea of it. we 

 should come to the conclusion that the neglect of & is 

 legitimate, except within the distance of j} )0 degree from 

 the critical temperature, but I should not venture any definite 

 statement thereon until the complete theory for this case is 

 worked out. The effect of the term with £ 4 would be to 

 give smaller values for the opalescence than for the simplified 

 formula, especially for the shorter wave-lengths, which may 

 influence also the colour of opalescence; but it is possible too 

 that the deviations from the proportionality to the inverse 

 fourth power of X (Rayleigh's blue) observed by Kamerlingh- 

 Onnes and Keesom within o, 5 of 6 C may be due rather to 

 the fact that at such temperatures the elements of space in 

 which the deviation from uniform density is considerable 

 are no longer small in comparison with X — as supposed in 

 the above theory. 



"Without going into these questions now, let us suppose 

 in the following that we observe the opalescence at such a 

 distance from the critical point that the neglect of the term 

 with £ 4 is legitimate. In this case formula [b) remains valid, 

 with substitution of 



|f =-6^(1^) + -^], . . (7) 



and the dependence on temperature and specific volume can 

 be represented by a system of hyperbolic, " iso-opalescent" 

 curves 



s[AS-3A3A(£ + 3IA(/> 2 ]=const. . . (8) 



Now let us imagine the substance to be contained in a 

 Natterer tube and its temperature slowly decreasing until 

 separation into two phases takes place. The temperature 



where this occurs for a given Ac£ is determined by the 

 equation of the border curve, which can be deduced in 



