88 Prof. L. Boltzmann on some Questions 



velocity b, in the direction of the ?/-axis, then the number of 

 molecules whose absolute velocity lies between v and v + dv, 

 and makes with the positive ?/-axis an angle lying between e 

 and e + de, is equal to 



-VI 



3 

 e -htf-kb*+2hbvcoB* v 2 s i n e ^ e d Vt 



If we consider all the molecules having a given absolute 

 velocity v, we find for their mean velocity parallel to the 

 y-axis the value 



v J o " e 2hbv cose cose sin ede , e ubv +1 \ \ 



f>-eose sin ^ e = V \FK=l-m} 



2hbv 2 

 which, for small values of b, reduces to — ^- , which latter 



value is of course more easily obtained by assuming b very 

 small at once. The mean velocity parallel to the y-axis is 

 therefore not perhaps equal to b for all molecules, but greater 

 for the more rapid molecules. If b is not constant, but equal 

 to B%, as is the case in gaseous friction, then also the mean 

 momentum of the molecules which have the velocity v is not 



equal to PBa', but to -»- PB^y 2 . If we leave all of Prof. Tait's 

 o 



calculations completely unaltered, but simply substitute for 



the expression PB#, which he introduces in his second paper 



2 A 

 (p. 260, line 6 from the top), the expression -^ PB.vu 2 here 



o 



found, we again arrive at 0. E. Meyer's formula for the 

 coefficient of friction (cf. Part ii. of my ' Theory of Gaseous 

 Friction,' p. 46). We have then applied the right correction 

 at once for the order of magnitude B to the motion of each 

 molecule, and for the rest may take as the basis of our calcu- 

 lation the special condition of a gas at rest. 



(2) A condition of a single gas which is totally different 

 from the special condition must no doubt approach the special 

 condition with the same rapidity as the mean kinetic energy 

 of a molecule becomes equalized in two mixed gases ; but it 

 does not follow that any unimportant deviation from the 

 special condition following a certain regularity — as, for 

 example, is produced by gaseous friction — will be equalized 

 with the same rapidity. On this latter point, I believe a 

 conclusion is to be obtained only from the equations which I 

 have given in my older papers, and which allow the cal- 

 culation of a quantity which is a minimum for the special 



