298 Free Path Phenomena [OIL xv 



IT 2 , UV, etc., are given by equations (712) and (713). On substituting these 

 values in equation (717), we obtain 



= v 

 P Dt ~ dx 



T < I -^ T I ^ T ^ 



dx / \dyj \oz 



9a? 9 dz 



If there is no mass motion all the terms disappear after the first line, and 

 the equation reduces to 



the equation of conduction of heat in a gas at rest. Comparing this equation 

 with Fourier's equation 



we obtain 



or, introducing K from equation (716), 



* = f*C;* .............................. (719). 



In Chapter XIII, assuming the molecules to be elastic spheres, we 

 obtained the value 



S- = 1-6027 K C V 



which is only equal to about two-thirds of that just found. Regarding the 

 law of force for elastic spheres (n = oo ) and for the present point centres 

 (n = 5) as extremes between which the actual law of force must lie, we may 

 say that theory predicts for the ratio ^ : icG v , a value intermediate between 

 the limits 1-6027 and 2*5. 



Diffusion. 

 357. In equation (651) we obtained the general relation 



...... (720) - 



* Maxwell, as the result of an arithmetical mistake, gives the factor as f instead of |. The 

 error has been pointed out by Boltzmann and Poincare. 



