( 2:is ) 



, J a\bi , a'a ^2 , , a'x hx 

 a 1 — 0\ — a 2 — og — öx — "x — 



1 . «'i ^1 - a's «'2 ^3 «1 «'* ^x 



_ _| -_ 1 1_, — _ 1 ,_^ _— 



in whieli r'i, «2 and « represent the volumes, occupied by the com- 

 ponents anil by the mixture under the same pressure. As long as 

 we restrict ourselves to large volumes, we may take vi, «2 and v as 

 being equal to each other, and then we find for the second term 

 of A,' (whicli must be divided by v) the value: 



(1 — .r) a{ (o'l — 2 h{) + X a', {a'o — 2 to) — a' ^ («':,■ — 2 h,) . 



The sign of this quantity for the different values of a- will decide 

 whether Zi^, when the value of v is decreasing, will decrease or 

 increase and the value which this quantity possesses, will be decisive 

 as to the degree of this variation. This quantity disappears for 

 US = and x= 1, and must therefore have as {I — 0) as a factor. If 

 the remaining factor were independent of a-, there would again be 

 symmetry in the values of A», also when the volume decreases. If, 

 however, this factor depends on ^, there remains symmetry in the 

 limiting value of An, but this symmetry must disappear sooner or 

 later, when the pressure increases. The remaining factor has the 

 following intricate form, which I shall give in the five parts, into 

 which it may be divided: 



(3 _ 3 a' + a^) a\ {a\ — 2h{) («) 



4 (1 + a' + .x"-) o's (ff'2 — 2 bo) (./?) 



- 2 (1 - .r)2 j «',2 («'1 - 2 /--i) + a'l («',2 - 2 /,j2) } . . (7) 



— 2 ,r2 \r'\Aa2--h) + a'.2{a\2 — 2by.^\ . . {d) 

 - a: (1 - .r) j 4 a'i2 (a'12 - 2 b^o) + a\ («'2 - 2 62) + a'2 (a', -2b,) \ {f) 



If we put a'l + «'2 —2 a']o = Art' and ij + 63 — 2 b,^ = A6, the 

 sum of these five terms may bo brought under the following form : 



