seatiering for the critical state, had been corrected by exactly taking 
into account the influence of the arrangement of the molecules in 
space, after a new probability-method. In fact, the intensity of the 
scattered light could be given for the critical point itself. 
The former difficulty however has not quite disappeared in that 
way. For when we compute from the given formula the total 
scattered energy, in order to find in this way the extinction of the 
incident light, then a logarithmie expression arises which still 
becomes infinite in the critical point. 
The performance of a better approximation also appeared of 
practical importance, because it has already been shown Le. that 
the magnitude of the sphere of attraction might experimentally be 
found from measurements of the opalescence. Therefore a theoreti- 
cally accurate formula for the extinction is of great importance. 
It could be seen befcrehand that the inaccuracy of the given 
derivation bad to be ascribed to the optical treatment, which was 
far too rough. Presently I have sueceeded in finding a better value 
of the extinction, by deriving it directly from the theory of electrons. 
To this end it appeared necessary to calculate explicitly the formerly 
introduced funetion g, which indicates the course of the mean 
density of the molecular clusters. L wiil start with this calculation. 
The result thereof is by itself interesting, as I think the problem 
of the “Neigung zur Schwarmbildung”’, which SMOLUCHOWSKI *) posed 
in 1904, is solved definitively by it. 
2. ‘Two different functions were introduced Le. : the first, f(x,y, 2), 
represents the influence which a known deviation of density in the 
point wv, y,2 has on the mean density in the origin, if the mean 
density obtains at the same time at all other points of the neigh- 
bourhood. The second gy (7, y, 2) represents the mean density in 
(v,y,2), when it is only known that there exists a certain deviation 
of density in the origin. Of these functions it has been shown l.c. 
that they are connected by an integral-equation, which can be put 
in the following form 
ae 
9 (5102) fff» (vj EY Yr 2) f (e,y,2) dadydz = f (#,,y,,2,) (1) 
From this integral-equation we also derived a simple relation 
between the volume-integrals of gy and f, for which we respectively 
write Gand #: 
1) M. Smorvenowskr. Boltzmann-Festschrift 1904. 
