317 



= y," (1 + ^'^)» when — — --^ = i' 1 hence -^ = 1 -|- ?- J is put. and 



with 



a x*n (1 — xY a 



20 =z X (1 — x) ; u' == ; io„ = — , (6) 



^ ^ (1+r.i-) (!+»•) {l^rxy ' {]^rx)'(l + r) ^' 



the old expressions, but in which « has now a somewhat different 

 value than before, and will also be dependent on the temperature 

 (through m). 



When in approximation 



a a 



w z=z A Ü :=: — A U 



is written for (1) with omission of the first part, which is generalij 

 much smaller, we get approximately : 



w a 



A V u' 



If the critical pressures of different substances do not diverge too 

 much, also the values of "/i,j do not lie far apart in mixtures of 

 different pairs of substances, and we shall find values of at least 



the same order of magnitude for the quotient — ; a result to which 



also Mr. K.atz came experimentally in his latest paper (loc.cit.) ') — 

 at least as far as volume-contraction and heat of imbibition of 

 amorphous and crystalline swelling substances is concerned. That 

 the ratios there are quite analogous to those of liquid mixtures is 

 owing to this, that when one of the components is solid, it must 

 first be reduced to the liquid state, whence the pure heat of melting 

 of this components is simply added to w. But if A?; predominates, 

 also this heat might be omitted with respect to the second part. 



At any rate we shall never find exactly "/^.s for Wa^, because the 

 omitted part can never be entirely disregarded. For this reason also 

 the values of ^U„ will differ somewhat, even with almost equal 

 values of «/„s, which was also found by Katz. 



1) The curves of Fig. 1 and 2 are no hyperbolae, but oblique parabolae, 



as according to (6) ?'(;is = -— . If r were = o (v^^ = Vi°), the curve of 



i -\-rx 1 -[- *' 



the integral heat of mixing (i.e. 1 — x gr. mol. of I + x gr. niol. of 17) would 



be a pure parabola. If, however, Vci^ is not = Vi^, the top of the parabola will 



have been displaced somewhat to the side of the component with the smallest 



molecular volume, as is easy to verify. From ^^/dx = wefinda;=l:(l+l 1 +r), 



which gives x = 1/2 for r = 0, but x < 1/3 for r > 0. (v,^ > Vi"). 



