81 VISCOSITY OF GASES 207 



Maxwell's law of the independence of the viscosity on the 

 density for very great rarefactions, such as are to be attained 

 by a mercury pump, they found the external friction consider- 

 ably lessened in gases rarefied so far, so that the coefficient 

 of slip f could no longer be put equal to 0, and the slip 

 could no longer be neglected. From their experiments, 

 which were carried out at pressures between O6 and 20 

 millimetres of mercury, it resulted that the value of the 

 coefficient of slip is inversely proportional to the density of 

 the gas. The external friction is consequently directly pro- 

 portional to the density. We cannot, after this experiment, 

 conclude from the law found for viscosity by Maxwell 

 that a gas of vanishingly small density would exert the same 

 friction on the motion of a body as a denser gas; the 

 influence of the friction will rather become less as the 

 rarefaction of the gas increases, not indeed by reason of the 

 internal friction diminishing, but because the external 

 friction decreases. 



82. Theory of External Friction 



Kundt and Warburg have already explained by the 

 kinetic theory the law empirically found for the coefficient 

 of slip, in so far as they have shown that on this theory f is 

 a magnitude which is proportional to the free path and, 

 therefore, inversely proportional to . the density. But, 

 apparently because a calculation founded on erroneous 

 assumptions did not lead to the correct value of the 

 numerical coefficient of the formula, they have not evaluated 

 their observations on external friction in a complete manner 

 for comparison with the absolute magnitude of the free 

 paths. 



The external friction which a gas in flow undergoes at a 

 fixed wall may be calculated just as in 11 we calculated 

 the pressure which it exerts on the wall. Just as in that 

 case, we have to find the number of particles which meet 

 the wall during unit time, say, one second, in consequence 

 of their molecular motion ; each of them loses a portion of its 

 forward velocity by its collision against the fixed wall ; the 



