( mi 'j 



tlio pairs in question ■will have a Icns-shaporl space of the volume 



2 K = — (16 o'^ — 12 a- :v -\r :>"') (4) 



in common (I.e. p. IGG) '). The sum of all these lens-sha[)eil spaces 

 ■which occur with all possible pairs of moiccules, is represented by 

 Z. Therefore 



Z=fKJn = "^l^j:-- </.,. (IG .3 _ 12 0-- . + .3) =11^ 



(5) 



and 



D.^ = V-2Gl> + Z (G) 



The value of D, in ■which the approximation has been ■worked 

 out one term further, is called B^. To find it, we must first sub- 

 tract from /^3 the sums of all volumes which belong to the distance- 

 spheres of three molecules at the same time, aud which is according 

 to Mr. VAN Laar 



in which /3 is the quantity which he has calculated and which he 

 has also represented by /:? on the last page of his discussion. 

 Secondly however we have also to add a correction term to Z, which 

 we shall represent by ^, so that 



\7 GH- ^GH^ 



n,= V-2Gb+^-y^~^ -2/9 ~-^^ • • . (7) 



We get the correction term l. by the fcdlowing consideration. The 

 proportion (2) is only right as a first approximatiou. If we try to 

 obtain to a greater accuiacy, the last tei'm of the proportion should 

 not be represented simply by F, as the whole volume of the vessel 

 is not at the disposal of all the n molecules. In the same way a 

 correction term is to be inserted in the last member but one of the 



') ('ompaie lilso: VAN ])KR WaaI.s, Ainst. Aciid. «1 0(rt. lSü(i jind 20 Out,, 1898. 



