﻿Opalescence of Gases in the Critical State. 



167 



while the constant b is got by performing the integration 

 over all possible values of 6\ Thus we get the approximate 

 mean square of the deviation in density 



^-ttV < 8 > 



fV 2 ' 



(~d»)o 



We see that the tendency to local agglomerations is ex- 

 cessively great in the immediate neighbourhood of the critical 

 point, where the terms with (dpfdv)o and ('d 2 p/'dv 2 ) are 

 vanishing, so that this formula has to be corrected by taking 

 into account the fourth power of 8. 



These agglomerations and rarefactions must give rise to 

 corresponding local deviations of the index of refraction from 

 its mean value, and thus the coarse-grainedness of the sub- 

 stance must reveal itself by TyndalPs phenomenon, with a 

 very pronounced maximal value at the critical point. In 

 this way the critical. opalescence explains itself very simply 

 as the result of a phenomenon the existence of which cannot 

 be denied by anybody accepting the principles of the kinetic 

 theory, even if exception be taken to the above quantitative 

 formulse, derived from theoretical considerations which cannot 

 be set forth here in detail. 



Rothmund*, who has given valuable experimental contri- 

 butions to this subject, prefers Donnan's capillary theory of 

 these phenomena, but he does not put forward any argument 

 against the above explanation, except perhaps a general dis- 

 like of kinetic theory which nowadays will hardly be con- 

 sidered as very conclusive. There is the common supposition 

 of coarse-grainedness underlying both theories, and it is 

 proved, indeed, by TyndalFs phenomenon. Donnan, how- 

 ever, and in general those authors who cling also for this 

 case to the thermodynamic conception of definite separate 

 phases, must consider the opalescent substance as an emulsion 

 of one phase in another, both being physically different, 

 homogeneous substances, and are forced to admit ad hoc 

 invented highly artificial and questionable suppositions about 

 capillary tension at the surface of separation. 



According to the kinetic theory, on the contrary, the 

 thermodynamic macroscopic conceptions of phases, surfaces 

 of separation, and surface-tension are altogether inapplicable 

 to this case ; there are no discontinuities of phase, only con- 

 tinuous transitions, ever changing diffuse agglomerations, 

 governed by the laws of statistical equilibrium. According 

 to it the phenomenon of critical opalescence is intrinsically 

 * Zeitsrh. Phys. Chcm. xxvi. p. 433 (1898) ; lxiii. p. 54 (1908). 



