260 PROFESSOR TAIT ON THE 



[Strictly speaking, the exponent should have had an additional term of the 

 order eBa?/v ; but this is insensible compared with that retained until x is a 

 very large multiple of the mean free path. See the remarks in § 39 below.] 

 Each takes with it (besides its normal contribution, which need not be con- 

 sidered) the abnormal momentum 



PBcc, 



relatively to yz and parallel to y. 



Hence the whole momentum so transferred from x positive is 



FBn 



vV / sin0rf0 / s - exsec9 exdx, 



or 



Doubling this, to get the full differential effect across the plane of yz, it becomes 

 (§33) 



PBnC, PBra 0-838 



37T?is 2 Jh 3tt?is 2 Jh 



The multiplier of B, i.e. of dYjdx, is the coefficient of Viscosity. Its 

 numerical value, in terms of density and mean path, is 



4:0-412. 



Jh 



Clerk-Maxwell, in 1860, gave the value 



-0-376 , 



PL 

 Jh" 



which (because l = 707\/Q77, as in § 11) differs from this in the ratio 20 :21. In 

 this case the short cuts employed have obviously entailed little numerical error. 

 Since p\ is constant for any one gas, the Viscosity (as Maxwell pointed out) is 

 independent of the density. 



37. Both expressions are proportional to the square-root of the absolute 

 temperature. We may see at once that, on the hypothesis we have adopted, 

 such must be the case. For, if we suppose the speed of every sphere to be 

 suddenly increased m fold, the operations will go on precisely as before, only m 

 times faster. But the absolute temperature will be increased as m 2 : 1. Similar 

 anticipations may be made in the cases of Diffusion and of Thermal Conduc- 

 tivity. 



