the Pliysical Properties of Gases 



(Ifi 

 dy 



181 



ax dy dz 



also 



dx 



dx 



d.h 



dfi 



d/i 



dx 



dy' 



dz 



df. 







dx 







= 0; 



= 0; 

 = 0. 



Hence we see that the stability-cubic is satisfied by \ = ; or 

 for certain disturbances in the gas, it tends to retain them, 

 and for those disturbances we must take into consideration 

 quantities of the second degree. 



30. If we could solve generally the equations in § 22, we 

 should then be able to determine the relative effects of the 

 radii of action and of the dissociation-temperatures on the re- 

 sulting state of the compound. But all we can do is to give 

 numerical values to the constants involved, determine the cor- 

 responding states in several tj'pical cases, and infer general 

 laws. This work is great, and the result scarcely worth the 

 labour ; but in one purely imaginary case the equations become 

 simpler, viz. when the two component gases are mechanically 

 similar. In this case I find, supposing 61 = 62= f ^0? ^^^ 



533=— =Si, that ^=?/, x' ■=-y' gives the single suitable solu- 

 V 2 



tion, and that the relations between x^ z at different tempera- 

 tures are given by the abscissae and ordinates of the curve in 

 fig. 2, the corresponding values of x' being \/5 x distance 

 from A B. The curve outside A B represents a set of un- 

 suitable solutions in which x' is negative. From this the 

 curves in fig. 3 have been laid down. The abscissae represent 

 the temperatures in terms of E = ^q, the ordinates of A B 

 the proportion of compound molecules to moving particles, 

 and the ordinates of C I) the proportion of moving particles to 

 the whole number of atoms, A being unity. It is notice- 

 able that, as the temperature increases, the proportions of com- 

 pound vary very slightly at very low temperatures, then vary 

 very rapidly, and again very slowly at temperatures above 6^. 

 If §0=5000, then at a temperature of 527° C. the proportion 

 of compound is about \, It may also be noticed that x first 



