806 



reciprocal value of a quantity proportional to the opalescence changes 

 linearly ^^i^'' tlie difterence of temperature T — 71, but b}^ extrapolation 

 does not vanish fur T = 1\ but for T— 7i.= Ó;012. When 

 therefore for this value of T — J/,, the denominator of (17) is equal 

 to zero, we can find from this, using van der Waals' equation, an 

 estimation for ^/a- The calculation yields : 



- = 0,0022 or f = 1,2.10-' cm. 



;. 



The quantity c is a measure for the size of the sphere of attraction. For 

 g= z= - I 1 ( ?' fi^y-) dxdydz 



CO 



(o distance to origin) whereas in the critical point 



+ < 



W' 



f{xyz) dx dy dzzzul. 



If ƒ were constant within a sphere with radius R, then £* would 

 be Vs ^^^> ^"d tlie above estimation would give 



R=:2,l . 10-' cm. 



S U M M A R Y. 



1. The known formulae of critical opalescence give an infinite 

 value at the critical point. Efforts to escape fVom this diificulty have 

 furnished formulae for the deviations of density with a dependence 

 n))on the volume, at variance with the assumed mutual independence 

 of the elements of volume. 



2. In order to obtain formulae applicable in the critical point, it 

 is found necessary to take into account the mutual intluence of the 

 elements of volume, it being shown that near the critical point this 

 influence is sensible for distances large in comparison with the radius 

 of the sphere of attraction. 



3. Two functions are introduced, one relating to the direct inter- 

 action of molecules, the other to the mutual infiuence of two elements 

 of \olume. An integral equation gives the relation between the two 

 functions. 



4. Corrected values are found for the mean deviations, and in 

 the formula of opalescence a correction is introduced. The latter 

 depends upon the sphere of attraction which can thus be calculated 

 fi'om observations. 



5. Further it is shown that the same results may be arrived at 

 by taking into account the mutual influence of the elements of 

 volume in the deductions of statistical mechanics, 



Groningen, Sept. 1914. 



