76 VISCOSITY OF GASES 179 



times seen, so that the coefficient of viscosity takes the 

 simpler form 



7j = WG/47TS- 2 . 



In this form the expression for the viscosity-coefficient 

 contains no factor which at all depends on the pressure of 

 the gas, but only magnitudes which depend on the mass, 

 speed, and sphere of action of the molecules, and thus 

 generally on their state. The formula therefore gives the 

 proof of the well-known law of Maxwell that the viscosity 

 of a gas is independent of its density. 



At first sight this law must seem but little probable. 

 According to it the friction should retain the same intensity 

 when the gas increases in rarity. This seems to lead to a 

 conclusion which, although apparently admissible by the 

 last formula, contains a contradiction in itself, viz. that a 

 gas rarefied to density 0, and thus rarefied out of existence, 

 exerts the same friction as one that actually exists. We 

 see the fallacy of this conclusion l when we consider how 

 the formula was obtained ; it is a transformation of the 

 formula 



given in 75, according to which the viscosity 77 vanishes 

 with the density p, so long as neither the mean free path L 

 nor the mean speed G becomes infinitely great. But this 

 limiting case is obviously excluded in the deduction of the 

 formula given in 75, and therefore the theoretical formula 

 no longer holds for the coefficient of friction in the limiting 

 case for which p = 0. 



With the exception of this limiting case, Maxwell's 

 theoretically deduced formula seems still surprising enough 

 to justify our more closely describing the causes of its 

 being obtained which are hidden in the mathematical reason- 

 ing. For such an explanation in words the last formula, 

 whose meaning is easily perceived, offers itself suitably. 

 The friction 77 is the quantity of momentum which is 

 carried over from layer to layer under the before-mentioned 

 circumstances. The transfer occurs by means of the 



1 Compare further 81. 



N 2 



