﻿166 Prof. M. S. Smoluchowski on 



been discussed since by some authors. As this theory leads 

 to definite quantitative conclusions, calling for experimental 

 verification, I may be allowed to give a brief summary of it 

 and some further developments* relating to its control by 

 observation. 



The kinetic theory of opalescence is based on the self- 

 evident, as I think, supposition that the molecules in gases 

 and liquids (also in solids) cannot be distributed quite 

 uniformly in space, but are subjected to a process of ever 

 changing local agglomeration and dispersion, as a consequence 

 of their molecular movements. Let us denote the deviation 

 from normal uniform density by 8, so that the ratio of the 

 number n of molecules actually contained in a given volume 

 to the number v contained in case of uniform distribution is 

 given by ??/v=l-f 8. then it can be shown easily f that in 

 ideal gases the probability of a deviation between the limits 

 8 and 1 + 8 is 



M TO 



d8. 



and that the mean square of the deviation in density is 



S 2 =l/r, 



being thus exceedingly minute under normal conditions, 

 except for submieroscopic volumes. This is a special case 

 of the general formula, applicable to a substance following 

 any given characteristic equation 



[r) = be^\\p- 



W(v) = be lw °) (p-po)dv . . . . (1) 



(R being the gas constant for one gram substance), which 

 defines the probability of v molecules having a specific volume 

 v, when its normal value is v . The exponent, which is 

 identical with the work done by isothermal compression of 

 1 gr. substance from its normal specific volume, for uniform 

 density, to the considered value, can be developed in a series 

 after ascending powers of (v— v )= —v 8, 



J" 



<"-*-£<n- J ff©).* » 



* Extracted from Bulletin Intern. Acad. Cracovie, Juillet 1911. 



f M. Smoluchowski, Boltzmann-FestschHft, p. 62b' (1904 J ; the formula 

 requires some modification if v is riot a large number. Cf. Bateman, 

 Phil. Mag. xxi. p. 748 (1911), and also Svedberg and Inoiiye, Zeitsch. 

 Phys, Chem. lxxvii. p. 145 (1911). 



