931 



and let us then CiilcultXto ƒ and n for given valne of /9. It soon 

 appears then that sini[)lication is only found ^/;A6?/i 6* = >i. The reader 

 may be left to ascertain this fact for himself. 



Accordingly we shall onlj- treat the case that 6 := ii is put in 

 (27") from the beginning. But tirst one more remark. 



The equation {21a) is a special case of the general assumption : 



f{v) 

 b = b,, — {b.j — 6„) — — 



in which ƒ (y) approaches to for i; = oo. We may, however, also 

 write for this : 



b-b, = {b, - 6J 1 



or still more general : 



b~ b. \" f(v) 



bg - bj a 



when f {v ^) ^^ Lim f iv) is denoted by a for v=zv^. If we now take 

 for f{v) the special function [(6 — b^) : {v — '^o)]^''.- ^'^is passes into : 



by — bj a yv- vj 



which corresponds with (27a), because a means the same thing as 

 ƒ. We can, therefore, consider van der Waals's form as a special 

 case of the qnite general form (28), when namely, {b — 6j : (y — y^) 

 is simply taken for f{v), and not this ratio to a certain power, 

 while also van der Waals substitutes v — b for v — v^. 



But whereas van der Waals's form with 7i=:2, 6^ = 1, f z=l 

 or more, has a physical meaning, being related to the deformation 

 of the molecule by pressure and temperature (which deformation in 

 our theory — see § J of the preceding paper — may be considered 

 negligible, and has, therefore, been left out of account\ our formula 

 is for the present without such a signiticance, and it must oidy be 

 considered as an empirical relation — just as many others, e.g. the 

 equation of the straight <iiameter, that for the vapour pressure, etc. 

 — to which possibly afterwards a physical meaning can be assigjied, 

 in relation with the diiferent factors which give rise to a quasi 

 variation of b. 



So we put: 



b—b, \> 1 /'b—b.y 



Og-bJ a \v-vj 



in which a = Lim I " ) at y = i\ , b = b^; while b. = v. is 



assumed. 



