144 Foundations of the Kinetic Theory of Gases. 



ri/h, these expressions become 



E=:~h 



6 ^ V4 O 1 -5C 3 + C 5 )=2a-*>X0-45. 



Since E is constant, by the conditions, we see that a also 

 must be constant. Hence, as Ivr (where t is absolute tempe- 

 rature) is constant, we have t* -7- constant, or 



T f =A + B^, 



which, when the terminal conditions are assigned, gives the 

 steady distribution of temperature. The motion of the gas is 

 analogous to that of liquid mud when a scavenger tries to 

 sweep it into a heap. The broom produces a general transla- 

 tion which is counteracted by the gravitation due to the 

 slope, just as the translation of the gas is balanced by the 

 greater number of particles escaping from the colder and 

 denser layers than from the warmer and less dense. 



In thermal foot-minute-centigrade measure, the conductivity 

 of air, at one atmosphere and ordinary temperatures, appears 

 from the above expressions to be about 



•J 



jf 4 3.10-, 



or about 1/28,000 of that of iron. No account, of course, is 

 taken of rotation or vibration of individual particles. 



(4) In the case of diffusion, in a long tube of unit section, 

 suppose that we have, at section x of the tube, n x PjS and 

 n 2 P 2 s per cubic unit, with translational speeds a x and a 2 , 

 respectively. If G-j be the whole mass of the first gas on the 

 negative side of the section, it is shown that the rate of flow 

 of that gas is 



Obviously 



The motion of the layer of Y x $ at x is (if approximately steady) 

 given by the equation 



ifPi«A__ 8 M „» Mh + h,) P,P 2 , , 



