FOUNDATIONS OF THE KINETIC THEORY OF GASES. 265 



43. The only variable factor (tijlfi) in these expressions for a. and for E, is 

 the same in both. Hence, as E does not vary with x, h'fhfc is constant, and so 

 also is a. Thus since, if t be absolute temperature, we have 



lir = constant ; 



we find at once, 



T 1 = A + Bx. 



Thus the distribution of temperature, and therefore that of density, is deter- 

 mined when the terminal conditions are given. The formula just given agrees 

 with the result first obtained by Clausius in an extremely elaborate investiga- 

 tion,* in which he showed that Maxwell's earliest theory of Heat-Conduction 

 by gases is defective. 



The general nature of the motion of the gas is now seen to be analogous to 

 that of liquid mud when a scavenger tries to sweep it into a heap. The broom 

 produces a translatory motion of the mud, which is counteracted by gravita- 

 tion-sliding due to the surface gradient : — just as the displacement (by trans- 

 lation) of the whole gas, from hot to cold, is counteracted by the greater 

 number of particles discharged (after collisions) from a colder and denser layer, 

 than from an adjoining warmer and less dense layer. 



44. The results of calculation of values of C,. given in the Appendix enable 

 us to put the expressions (!') and (3') into the more convenient forms 



a = 



h ' ^0-06 (!".) 



Jh b p 



E^-^AO-45 . . . . (3".) 



where it is to be remarked that the product p\ is independent of the tempera- 

 ture of the gas. 



The Conductivity, k, is defined by the equation 



*£--■■ 



and thus its value is 



V T 3 VV 



where r , h are simultaneous values of r and k. 



At 0° C. (i.e. t = 274) this is, for air, nearly 3.10 ~ 5 in thermal units on 

 the pound-foot-minute-Centigrade system : — i.e. about 1/28,000 of the con- 

 ductivity of iron, or 1/3600 of that of lead.t Of course, with our assumption 



* Pogg. Ann., cxv, 1862 ; Phi!. Mag., 1862, I. 

 f Trans. R. S. E., 1878, p. 717. 



