12 Prof. M. S. Smoluchowski on Conduction of 



osc 

 order of magnitude £-— , where p = density, s= specific beat, 



6- = mean molecular velocity. This result applies to the case 

 when every molecule assumes, by its impact on the solid wall, 

 the vis viva corresponding to the temperature of the latter ; 



but it ought to be multiplied by - — ~ , if only a partial 



equalization of temperatures is taking place, according to 

 the formula 



#05 #m? $ denoting the temperatures of the wall, of the 

 impinging and the emitted molecules. 



Messrs. Soddv and Berry use the same formula, with 

 slight difference of notation, putting 



n- n HG 



where n— number of molecules per cm. 3 at 0*01 mm. pressure, 

 N = number contained in one gram, H = molecular heat at 

 constant volume, G = mean molecular velocity. 



Their experiments enabled them to determine the ratio of 

 the observed transport of heat K to the calculated value Q 

 for 11 gases, and from these numbers, ranging between 1*09 

 and 0*25, they attempt to draw conclusions about the factor 

 which in the above has been accounted for by introduction 

 of the coefficient j3. These results, however, seemed 

 rather strange, since only values inferior to unity could be 

 expected. 



But when exact numbers are in question., the rou^h estimate 

 referred to above is evidently insufficient, and an exact 

 calculation ought to be substituted instead. 



Consider the gas contained between two parallel horizontal 

 plates, the upper one of temperature 2 , the lower one of 

 temperature 1 (supposed to be one degree lower). It is 

 convenient then, instead of making the above supposition 

 about /3, to follow Maxwell's supposition * that the surface 

 of a solid acts as a partial reflector, by reversing the normal 

 velocity component for the fraction (1—/) of the incident 

 molecules, while the rest are " absorbed " and emitted with 

 the velocity distribution corresponding to the temperature of 

 the wall. 



We suppose the gas to be so rarefied that the mean free 

 path of the molecules is much greater than the distance of 



* Maxwell, Phil. Trans, clii. p. 231 (1879). 



