( isi ) 



( a, + «„ — 2 a, , J 



P\om this equiitiou (-i) follows: 1". tliat the absolute value of 

 the variation of volume at a given temperature is independent of 

 the pressure, under which the mixture takes place, of course only 

 as long as it does not surpass the limit, below which the calcu- 

 lations mentioned are sufficient approximations; 2°. that the maximum 

 value of this volume variation is found for * •== ^ ; so if the sub- 

 stances to be mixed have the same volume. For air, which is 

 composed of oxygen and nitrogen, the volumecontraction will amount 

 to no more than ^Vas of the value, found when equal volumes of 

 oxygen and nitrogen are mixed. The quantities must, of course, be 

 chosen in such a way, that in both cases the total volume of the 

 components is the same; 3". that it depends on the value of the 

 expression : 



I -]- Ut 



{b, +i,^_2/,„) (5) 



whether negative or positive contraction takes place. 



As in the characteristic equation the volume, occupied by the 

 molecular quantity under the pressure of one atmosphere and at 0°, 

 has been taken as unity of volume, the quantity A» is also expressed 

 in that unity. 



It is true that the unity of volume in the three equations (1), 

 (2) and (3) is not absolutely the same, on account of their different 

 degree of deviation from the law of Boyle, but the influence of 

 this fact may be neglected in these calculations, as the deviation 

 it causes, is a small quantity of higher order. 



If we proceed to the discussion of the expression (5), we see in 

 the first place that &, -\- h — 2^>,,, = comes to the same thing as 

 assuming the co-volume of a mixture equal to the sum of the co- 

 volumes of the components. 



The circumstance, that it is easier to arrange arbitrarily formed 

 bodies, which take up together a certain volume, in a given space, 

 when the bodies are different in size, than when they are all of 

 the same size, makes it probable, that the co-volume of a mixture 

 of molecules of different sizes will be smaller than 4 times the real 

 volume. In the deduction of the characteristic equation, in which, 

 however, the molecules are thought as spheres, this has been proved. 



