46* VISCOSITY OF GASES 445 



and the number of those which traverse the length r without 

 collision, and therefore pass through dy dz, is determined by the 



function 



e -r/ 



Thus the number of particles which in unit time pass through 

 dy dz with speed w starting from a volume-element situated at the 

 point (x, y, z) is 



d / ydzN(km/7r)%e~ km '*Be~ Brl<0 w 2 dwdr cos s sin s ds dfy. 



As before, we assume that each of these particles possesses 

 the speed v f with which the gas flows through the point given by 

 r, s, (p. Thus we obtain the value 



f 00 f f\n C2TT 



Q=dy dz Nm(km/ir)*} do u> 2 Bg-* ^ 2 J dr e~* rlai ] Q ds sin s cos SJ Q dtyv 



for the momentum which in unit time is carried over the element 

 dy dz in the one or the other direction, according as we put for 

 v r the values v'\ or i/ 2 given before; and the coefficient of friction 

 is determined, as before, by doable the value of the factor of 

 (dv/dx)dy dz in the development in series, or 



w w 2 Be-* w<ua j dr rer* rl<0 j "ds sin s cos 2 sf 

 which reduces on integration to 



or, as it may be written, 



The value of this integral has been calculated byBoltzmann 

 and also by T ait. The former found 



n = 0-088942636 m/sV(A;m), 



and with this T a i t ' s l value agrees, as well as one calculated by 

 Conrau, 2 of which I have been privately informed. Using the 

 mean values of the speed and free path, viz. 



we find finally 



T/ = 0-350203 p&L = 0-322648 P GL. 



1 Compare Boltzmann, Wiener Sitzungsber. 1887, xcvi. Abth. 2, p. 895. 



2 See 48*. 



