204 Dr. M. Smoluchowski de Smolan on 



For x sensibly greater than the mean free path this curve 

 is identical with a straight line, as was to be expected before- 

 hand, but it is so situated as if the wall had not the tempera- 

 ture O but # + OA, or as if the wall, keeping the temperature 

 O , were put back by the distance OB = y. 



Without further calculation so much is evident, considering 

 the linear form of the equation, that the ordinates, when the 

 value of the constant is changed, are proportional to it ; that 

 the value of 7, however, remains unchanged. 



In the same way it is easy to see that the abscissae corre- 

 sponding to given ordinates must be proportional to the 

 value of X, the only parameter of the curve. But the value 

 of the coefficient of proportionality can be found only by 

 solving the above equation, which involves very long and 

 tedious calculations. I have found as an approximate 

 result*, 



^[ ' 70+ 3(r^)> w 



/3 is a factor which is used in order to determine the ex- 

 change of temperature produced by the impact of a molecule 

 on the wall, viz., in this way, that the average temperature 

 of the rebounding molecules £ will be in the following relation 

 to their average temperature m before the impact : 



*~ l+j3 ' {J) 



which is the same equation as (7). 



11. The way in which Maxwell calculated the coefficient 

 of slipping in his paper " On Stresses in Rarefied Gasesf," 

 supposing the molecules to be centres of a repulsive force 

 proportional to the reciprocal fifth power of distance, is much 

 superior, in some respects, to the above, as the effects of the 

 encounters and the changing distribution of velocities among 

 the molecules are taken into account quite rigorously, but it 

 is to be considered only as an approximation too, since 

 Maxwell supposes the state of the gas at the surface to be 

 the same as in the interior, which evidently is not quite 

 correct. 



The action of the surface of the solid body is supposed by 

 him to consist 



(!)• In reflecting the fraction 1— /of the incident molecules 

 with unchanged velocities. 



* In a paper which will appear shortly in the Sitzungsber. d. Wien. 

 Akad. 

 t Phil. Trans. R. S. vol. i. 1879. 



