925 



which eiiabloy iis to find out sometliing ahout the coiirse of' tlie 

 fiinetioii l)z=zf [v\ For the sake of accuracy the original v;,, is every- 

 where written in the above formulae, and not the />„ put equal to 

 it. The quantity t\ is namely the liquid volume at 7'=0 extra- 

 polated from the equation of the straight diameter. From 7- t^ AH" ^^2) — 

 - 1 = 7(1 — m) follows namely, when (^/^ = and m = 0, that the 

 reduced limit of density [d.^)^, i.e. y/,. : i'o, becomes equal to .s't=2 (l-j-y). 

 It is this v^ which occurs in the above relations. 



In virtue of the fact that when the limiting volume of h corre- 

 sponding to this limiting volume i\, i.e. h„, is assumed different 

 from i\, very intricate, if not impossible results are obtained for 

 h:=:/{v) — whereas the assumption />,, = ?',, leads to couiparativelj 

 simple results, 1 have been led to identify h^, with i\. So we assume 

 that at the limiting v^alue of v for 7 =0 (calculated from the formula 

 of the straight diameter) also ö = v, and so also p = oo. Hence 

 what we call v;,, and /% in what follows is the same as van der 

 Waals understands by ?;/;„, and />/,„, •) — with this difference, how- 



fdb\ 

 ever, that - is m>t^=\, but always much smaller than i, and 



will even appear to be = (at 7 =: V^)- I'hat the latter is really 

 the case, follows also from this, that in the limiting case 7 = 72 

 (ideal substances) — where therefore h,j = h„, and the course of the 

 function h=fiv) is represented by a .straight line parallel to the 

 v-axis — necessarily />'„ must be := 0. 



Let us now proceed to determine the shape of the function 

 h=z/{v). According to what was observed in § 1 of the foregoing 

 [)aper, we consider the variation of f) with the volume entirely as 

 an apparent ckamje, and that chiefly on the ground of the joint 

 action of two influences, the diminution of the factor 4 in è^ = 4/?i 

 {in = nucleus volume of the molecules) to about 2m at 6„ ^ at 

 least at the ordinary temperatui'es ; and the simultaneously acting 

 influence of temporary molecule aggregations (quasi association). 

 These two influences will make the quantity /> in r — h diminish 

 from 4??? to about 2ni. 



But at very low temperatures, at which />,, will approach more 

 and more to fj^ (see § 7 loc. cit.) till /),, = /)„ at 7'=ü, this varia- 

 bility disappears — and the question rises how this is possible. 

 Does èo = 2//i then rise to hq = 4:rn, or does 6^ = 4?/i descend to 



1) These Proc. XV p. 1132 at the top, 1138 and p. 1142 at the top, where, 

 everywhere vlim = bin,, is assumed. On jj 1138 also vii,u = ro (from the straight 

 diameter) is put. Our y^ and 6,, are llioreCore exactly the same quantities as 

 VAN DER Waals' vim and biim. 



60* 



