232-234] Mechanical Illustrations 195 



Combining these equations with the general differential equation (464) 

 we obtain for the equation of this stream line near the origin 



eH=i/Si/K (468), 



a semi-cubic parabola. Equation (468) accordingly defines the "normal 

 state" for the imaginary gas now under consideration, and is in obvious 

 agreement with equation (463). 



If we replace K and H by their values in terms of the principal and 

 subsidiary temperatures, as given by the equations (465), 



we obtain as the relation between r and T in the normal state, 



/8 



Z 7 * (469). 



c 



233. The corresponding normal state when e = 0, is 



2K = 3H (470). 



It is interesting and important to notice that this last equation cannot be 

 deduced from equation (468) by putting e = 0. In other words a conserva- 

 tive gas is a true special case : it is not legitimate to regard it as the limit of 

 the general case. Hence also it is obviously futile to try to pass from the i 

 case of a conservative gas to the case of a non-conservative gas ; the slightest ' 

 amount of radiation of energy will entirely alter the circumstances of the 

 case. 



Recapitulation. 



234. The present position is therefore as follows. We have (Chapters 

 II. V.) developed the dynamical theory of a conservative gas, and have 

 found (Chapter VII.) that the results obtained do not agree with those of 

 observation. We have now seen why this is, and have seen also that nothing 

 less than an entirely new investigation, taking account of dissipation of 

 energy from the outset, can be expected to lead to true results. An investi- 

 gation of this kind has been attempted, but it has not been found to be 

 possible to obtain results of the definite kind which had previously been 

 obtained for a conservative gas. The impossibility of progress arose from a 

 cause inherent in the subject itself: the_results for a conservative gas are 

 independent of the constitution of the molecule, whereas those for a non- 

 conservative gas differ for different molecules. As we have no certain know- 

 ledge of the structure of molecufes we have, so far, been unwilling to make 

 any assumptions on this point. Now, however, that we have seen that further 

 progress is only possible by the help of some definite assumption, we must be 

 content to rest the remainder of our investigation upon hypothesis instead of 

 upon comparative certainty. 



132 



