1050 



The \i\h\e of ///.:/>„ (and of r^• : ??„), i.e. of y, will depend on the 

 Aiiinc of llie o-ltical tempcrnture for different substances. Bnt for 

 oiu' and the .mine substance, considered at different teniperatui-cs, 

 0^. : />„ (and Vk •■ Vo) loses of" course its significance outside 7^.. This 

 is, however, not the case with />,, -. /\, which quantity is in relation 

 with b/; : ^0 through (30'') at the critical temperature. We have namely : 



I "A; / .rjt 



If in this we substitute the value 2/^. — i for (/y^. — /^„) :/>„, the value 

 (•27/,— J) : (27/,. + 1) for .I't = ih—öo) ■■ (vk—Vo) and the value {hk—^Y ■ 

 4y/. (^y/._|_j) for //^. — see above, and also 1, p. 818 — we find 

 after some reductions : 



^^V(2n-l)|X^^--^-^^^-+^\ . . . (83) 

 K )k ^ ' ^V 4y^-+l ^ 



in which y//c = 87,i.(7A:H-l):(2y^.— l)(4yi.+J), according to (31) ofTI. 

 This naturally suggests the idea of making the above considerations 

 more general by putting />,, : />„ = 27' ; so that not oidy at the critical 

 temperature the equation (33) holds, in which yj^ represents the 

 reduced coefficient of direction of the straight diameter in the neigh- 

 bourhood of Tk — but quite general at any arbitrary temperature 

 tiie relation 



K ^ ^ ^V 47+1 



in which, therefore, for an arbitrary substance y varies together 

 with y', when T changes. 



Then outside .7'/ the (juantity y is no longer in relation with any 

 t)i, : A„ or with the reduced coefficient of direction of the straight 

 diameter in that point — but yet represents for any arbitraiy tem- 

 perature : the value of '/., [bk •■ bj, or of the said coefficient of direction, 

 for another substance for which the critical temperature would corre- 

 spond lüith that temperature. Thus also outside T/, something is left 

 of the original meaning of y. 



So passing from 7'=0 to T = cc for 071e and the same substance 

 all the types will be met with, which are found for different sub- 

 stances at their critical temperatures. Everi/ substance approaches the 

 ideal type with constant b, wdien only the temperature is made to 

 approach to ; every substance approaches the limiting type of the 

 substances with high molecular weight [yi, = 1), if only the tempe- 

 rature be taken high enough. This has already been fully explained 

 in I (see § 7, p. 820—821), and there is no call to repeat the explana- 

 tion here. 



