310 Mr. S. H. Burbury on some Problems 



where </>(&> 2 ) is an undetermined function of co. The distur- 

 bance is of the first order. 



15. Conduction of heat in a single gas. — Let' there be a 

 horizontal tube, AB, filled with a single gas. Let the 

 temperature be higher at A than at B, and be maintained 

 constant at each of those points, and let the pressure be uni- 



N 

 form throughout the tube, so that j- =P, a constant, pro- 

 portional to the pressure. With the same notation as in the 

 last example, let us consider the molecules of the class 

 \ fiv co 2 dcodS which enter the elementary cylinder from the 

 left in unit of time. Their number is, putting k for Jim, 



\-N(-Ve-*»Wd<0dS. 



£)' 



The number of the same class which pass out of the ele- 

 mentary cylinder by its right-hand face per unit of time is 





N and k being variable. 



Therefore, but for encounters, the number of the class 

 within our elementary cylinder would be increased in unit of 

 time by 



or the number of the class per unit of volume would be in- 

 creased in unit of time by 



that is by 



*^$y ?<•*(**- i)si- 



5 

 This is positive or negative according as kco' 2 > or < -. 



For high values of eo there is an increase, for low values a 

 diminution. This increase or diminution is in steady motion 

 compensated by encounters, because molecules with high 

 velocities are on average moving more to the right than to the 



