180 Mr. W. M. Hicks on some Effects of Dissociation 



case II. the gas returns to its normal state by oscillations 

 tlirough it, whose amplitude continually diminishes without 

 limit. 



28. As the temperature of the gas increases, the propor- 

 tions vary in general continuously ; so that, if two states are 

 possible, the state at any time will depend on its previous 

 history. If one set of solutions remains real and gives a 

 stable state at all temperatures, we may call that a normal 

 state of the gas. For instance, in the case of hydrogen and 

 oxygen, that set which answers to the state of steam is the 

 normal state : as the temperature increases, the proportions of 

 water-vapour, hydrogen, and oxygen vary continuously and 

 always give a stable state. On the other hand, that set which 

 answers to the state 2H + is not normal: as the temperature 

 rises, the proportions vary continuously up to a certain tem- 

 perature, when they produce an unstable state ; and the gas 

 changes abruptly into a more stable one, which may be a nor- 

 mal state or one whose point of instability is at a higher tem- 

 perature. 



Any non-normal state may change into a normal state ; but 

 a normal state cannot, by mere alteration of temperature with- 

 out external influence, be changed into a non-normal one. 

 For instance, steam may be heated up to a point where there 

 is scarcely any proportion of Hg 0, but if it be cooled back it 

 will change continuously to its former state. If 2H + be 

 heated up to the same temperature, at a certain temperature 

 we get a sudden change to the normal state of steam ; then 

 the proportions vary as in the former case, and as the tempe- 

 rature falls it does not pass back to its former state of 2 H + 0. 

 In order, therefore, to obtain a gas in a non-normal state we 

 must bring some external influence to bear on it. 



29. As the temperature increases, two sets of solutions may 

 become equal. To which set will the gas belong as the tem- 

 perature increases or decreases through this point ? In general, 

 if any disturbance occurs, such as increase of temperature, a 

 certain time is required for the gas to adjust itself to its new 

 conditions. Would that state be taken up which most quickly 

 adjusts itself? In this case we may learn something from the 

 stability-equation in § 27. 



If two solutions become equal, then the intersection of two 

 of the surfaces 



/i=(^, y, ^) = 0, f2{x,7/,z) = 0, M^,^,z) = 



must touch the third. Let ^i, ?/i, Ci be such a point ; Z, w, n 

 the direction-cosines of intersection of/i and/g. Then 



