/ 2 RT\ 2 RT 

 A ü 1 — --— = — -- n, w. 



315 



u," ^/a^^^>^• l/a, (l/a, — j/a,) 

 a, a. 



«i" i/a,y k" 



But because then l^a. = -^ !/«,, |.^a, — l/a, = -^ — r— l^«i. 



/ 2 RT\ 2 RT { \ /vïc, \ 



henee A „ (l - — ) = ^n, ,, (l - (/^-^jfV-O . (3-) 



As for ordinai\y substances in liquid state (below the boiling-point) 

 ^ji, ^ 1 RTk, and in the second member v^^^v maj' be put, we find 

 with ^/j- =z m : 



--êtM'-l^'i>'-<^-- 



m 



If e.g. m = 7ï» w® have with 71^ = 1 — x, n, := x for Ai; the 

 value Ve'^'(i — '^')^1 — ' ) (^1° — ■^'j")' so that the maximum contraction 

 (at .1' z=: Yi) becomes =724(1 — V'^X^x" — "ys") — hence very small 

 and of the order 1 — j/. 



With regard to the sign of Av it may be pointed out that ó, ^ 6,, 

 e.g. b^=^6b, corresponds with t'/^v,*. Then a^ is approximately 

 = ^Vï,, so that «i/ft, becomes z=id""'l\^^ or T^^^ Tjc,. But from this 

 it ensues that ^jyt, is generally somewhat greater than p^,, in conse- 

 quence of which 1 — 1/ becomes negative. And the reverse when 

 v/ should be <^ v,\ The quantity Ay will, therefore, nearly always 

 be negative, in other words volume contraction will take place. 



With regard to the differential variations of volume Ay, :=: y, — y," = 



ö(Ai;) ö(Av) 



= — and Av, :=Vj — v," = -r — , from the approximated expression 



(3a) follows, when «/^ is considered constant in the correction term 

 of the 1^' member : 



In approximation v/ l/a, = v," l/«i was taken, so that {/a^is = 



= -^ ï/öf« anci l/a = n, |/a, + 7i, l/«, = ^^«J n, — + n, ]= ~V^a^. 

 V, \ ^^ J v^ 



,. ,. ö/^^^^^o^, Ö / ^^ ■y" ^/ A 



In consequence ot this -^r — becomes = ^;^ — — — — - =: 



o/ii \ a J on \ a^ V,' J 



v/ b fn,\ . , . Ö fn,\ v.—n.v," n.v," 



= r^j — I — , m which r — I — )=: = —. Hence we have 



«. on, \vj On, \v. 



