( 182 ) 



uud ^/ii^h-'^^'l'iy (t^"^. +>'"'^) ^) li-s been fuiiiid for the value 

 of ^1 + ^2 ~ 2 ''is? ''" expression which is always positive. On the 

 other hand, this expression, which is equal to 0, when ^i =ü'3,and 

 which is positive, as well when i, > b„ as when ^i < ^'^ , shows 

 that for a small difterence in size the value of ?', -{- b„ — 2Z'j3 is 

 very small. If we might neglect it, it would only depend on the 

 sign of 2c7,2 — a, — a., ^ whether mixture would cause contraction 

 or not. 



When 2a,2 — «, — «„ is positive, mixing is favoured by the mo- 

 lecular forces. For if we suppose the two gases before the mixing 



separated by a mathematic surface, — ^- and — =- are the forces which 



r, - r, = 



2 rt „ . 

 ü])pose mixture, and — '"- is the force, which draws the two sub- 



stances through the bounding surface. In this case we may put 

 I'j =v„, and the sign of 2a,„ — «, — a^ proves to be decisive. 



In general we are justified in expecting, that when mixing is 

 favoured by the molecular forces, and when in consequence of the 

 mixing a smaller molecular volume must be subtracted from the 

 external volume, both circumstances cause positive contraction (ne- 

 gative value of ^v). 



If (rt, + <^'3 ~" 2 0|„) and C'l + ''^■j — - ''12) Jii'e both positive, a 



temperature exists, below which Ao is positive and above which 



Ay is negative, just as is the case for the deviation from the law 



of Boyle for a simple substance. But in general we may expect 



that — Aw (volume contraction) will be small and that the thesis 



of Mr. Amagat will hold true with a high degree of approximation, 



at least in all cases, in which the properties of the components 



differ little. In the first place because a, + a,, — 2 a,„ and i, -\-h„ — 2 6,„ 



are both equal to 0, if the substances are the same, and we may 



therefore put, that when the difference is small, the value of these 



quantities will be small, compared to each of the terms, of which 



they consist, e.g. a^ -j- «„ — 2 a,„ is small as compared with a, orff„, 



and /'i4-i„ — 2&,2 is small as compared with i, or ^^.3. Secondly 



on account of the factor .((l — .i') ; for air this factor amounts to no 



4 

 more than -— . 



25 



Our equation cannot be tested at the values wliich Mr. Amagat 

 gives for air of the ordinary temperature and which begin at a 



') TliL-une Muléc. Arch. Xc'erl. Tuiu. XXI\'. 



