226 Theory of a Non-Conservative Gas [CH. x 



Since, then, the amount of dissociation in a gas increases with the 

 temperature, the effect of dissociation ought to be to cause the value of 7 to 

 decrease with the temperature. At any particular temperature we cannot 

 say whether the effect of molecular aggregation or of dissociation is likely to 

 be the greater. We cannot therefore say whether the actual value of 7 ought 

 to be greater or less than that given by formula (522); all we can feel any 

 confidence about is that the influence of both ought to be shewn in a 

 decrease of 7 as the temperature increases. This decrease is easily observed 

 in the case of large numbers of gases, and so far as I am aware, no gas is 

 known in which 7 increases with the temperature. 



The consideration of dissociation and aggregation, combined with the 

 imperfection of experimental results, may be capable alone of giving a suffi- 

 cient explanation of all discrepancies between theory and experiment. 



274. There is, however, another consideration, which ought to be 

 mentioned if only for the reason that it is impossible a priori to say how 

 much weight ought to be assigned to it. 



We have assumed that the subsidiary temperatures may be neglected 

 altogether, and unfortunately the general argument by which this assump- 

 tion was justified may break down in exactly those special cases which are 

 of the greatest importance. The essential points of the question are all 

 contained in the problem of the loaded spheres. We found, in equation (463), 

 that the normal state at low temperatures is defined by the relation 



/8i/K = 3cH (523). 



Here K is the energy of translation, and H is the energy of rotation 

 about an axis which is almost, but not quite, one of symmetry. The quantity 

 ft, which could be regarded as measuring the ease with which rotational 

 energy was set up by collisions, was small. Hence for sufficiently small 

 values of K, eH could be small, and the dissipation of energy was small. 

 In the case in nature to which this is analogous, ft is small on account of the 

 approximate symmetry about the axis, so that e H can be small, in agreement 

 with observation. But there is no evidence that e is not very small : indeed 

 the evidence points rather in the other direction, for we have already 

 supposed e to be very small as regards rotations about axes perpendicular 

 to the axis of symmetry. Thus it is possible that instead of equation (523) 

 being satisfied by the simultaneous smallness of ft and H it may be 

 satisfied by the simultaneous smallness of ft and e. This is quite con- 

 sistent with the observed smallness of dissipation : it affects the argument 

 of 232 in that instead of the equation for the normal state being equation 

 (523) it will be 



(524), 



