95 



If (f^ is the deviation in density in a point .r := 0, y =: 0, z = 0, 

 then we get for the deviation of density d in a point ,i\ y, z : 



^ = 9 C^' .'/> ^)(\dv (8) 



where ch^ is tiie element of volume. 

 Further 



^^ f^o = f' (•'•' !h -) f^o" dv = (I (./; y z) o . . . . (9) 



where q is the number of particles per unit of volume. 

 We now have 



„Ly r= 71, pu -\- • . -riy pk, — n P. 

 Now ?2, = r -[- rfj J w,, if then we introduce (8) and consider 



p,y as function of d'yz, bearing in mind that rfj = ^, we find 



dv 



,~Ly.={v-n)\P ^r i g,yF,ydv\ 



Tlie influence of the second part may become considerable with 

 a strong correlation. 



Also in determining „A% the correlation can be taken into con- 

 sideration. Then in the first place we get the old terms, but moreover 

 (9) yields still new terms in n;% n-,, and ?i; ?z>', ?z> ??«. These terms are: 



2 I' {v — n) I p-jy gx^ dv 



— (r — ?)) I p-jy giy dv 



— 2 n P {v — n) I piy g)y d v 



-^r 2v \ Pry. p.jy. g)u dvj d V,j,. 



If then A',; is determined, only the last term remains and a part 

 of the term before last, so that we get 



A" = 2 r (P -f I pyy pyy ^/y d v.j, d V, 



+ \ Pa giy d r). 



These considerations may also be applied, as least approximately, 

 to the changes, which accidental derivations in density undergo in 

 result of diffusion. Our formulae show then that close to a critical 

 point the deviations in density as a result of their correlation, are 

 not only stronger on the average, but also more strongly changeable. 



Utrecht, March 1917. Fnstitute for Theoretical Physics. 



