500 



the temperatiire-slope and B tlie tangential force which the gas 

 owing to its flow back along the axis of the tube exerts on the wall. 

 M and B according to Knudskn 'j are thus given bj : 



M = k, Xm ill — = — ■/• ' 



' 128 dl ' 128.0,30967 dl 



and 



3 ap dp .T W 



N the number of molecules per cc. iii the mass of a molecule, ^ 

 the viscosity and X the mean free path. 



If P. is not small as compared to R, we n<ay not assume, as is 

 done in the derivation of the formulae, that a molecule in a collision 

 with a second molecule possesses the velocity corresponding to the 

 temperature at a point at a distance /. ; in that case the collisions 

 with the wall have also to be taken into account. The paths described 

 by the molecules since the last collision are then found as follows: 



In a disk of unit length cut out from the tube there are rtR^N 



molecules and therefore jtRN^ mutual collisions occur per second 



and 'IjtR^JVÜ collisions with the wall; the joint number of 

 collisions is thus 



2-rRlN<i-{-jrR'N— per second, 



and each molecule collides ( -— H ) S2 times, while describing a 



path ii. The path described without collision is therefore on the 

 average 



1 I ') 



\ 



\ \ ^ I 



1- — 1 H 



X^ 2.R ^ 2R 



This leads to the following condition of equilibrium 



/ ;'.T ;. dii 3.TA- R'dp\ , dp 



V 128 ' X dl 256.0,30967 ). dl J dl 



^ 1-1 



2R 



as 1] = 0,30967 Nm ";. or 



') M. Knudsen, Ann. d. Phys. 33, p. 1435, 1910. 31, p. 633, 1910 and 31, 

 p. 205, 1910 and Sophus Webek, Leiden, Conim. 137f. 



-) The tempprature change of llie coefficient of aocomraodation for collisions 

 with the wall is disregarded on account of its smallness. 



