54 MM. A. Kundt and E. Warburg on Friction 



vered by Maxwell, in regard to the friction, conduction of heat, 

 and diffusion of gases, have been confirmed by the experiments 

 of Maxwell, 0. E. Meyer, Loschmidt, Stefan. Only with respect 

 to the absolute value of the coefficient of heat-conduction of air 

 as calculated by Maxwell does a deviation appear, according to 

 Boltzmann ; but the law that this coefficient is independent of 

 the pressure has been experimentally proved by Stefan between 

 ■J and 1 atmosphere. The confidence excited by these results 

 has induced us to pursue the theory to further consequences. 



As is well known, so far as it has yet been worked out, this 

 theory necessarily presupposes that the so-called mean length of 

 path of the molecules is a quantity that may be neglected against 

 the linear dimensions of the space filled with the gas. But as 

 the mean length of path is inversely proportional to the density, 

 that is equivalent to saying that the density of the gas in a given 

 space must not be too little. We do not know that the theory 

 has yet been developed for cases in which the above supposition 

 falls ; the experiments have always been so arranged that it holds 

 good. The aim of our investigation (of which we take leave to 

 lay the following brief abstract of the results before the Academy) 

 is to trace the properties of gases beyond the limits of density 

 mentioned. 



Friction. 



Let us first consider the following simple case. A layer of air 

 of the thickness d is between two solid plane partitions, of which 

 the one is at rest, while the other moves with the velocity u\. 

 When the gas is more and more rarefied, the mean length of 

 path / more and more increases ; an easy calculation shows that 

 the gas of the layer has still sensibly the same properties in 

 regard to friction as the same gas in thicker layers, so long as 



-j< y-j. Up to that point the retarding force exerted upon the 



moved partition will be, to a thousandth part of its value, con- 

 stant, and, as calculation shows, rapidly diminish when the cor- 

 responding degree of rarefaction is exceeded. 



We are here struck by an apparent contradiction to this result 



of the theory; for we found that even when -j = ^-r, a perceptible 



diminution of the retarding forces commences, becoming greater 

 as the pressure diminishes. The contradiction, however, is only 

 apparent ; the phenomena observed may be deduced from a pro- 

 position which we have derived from the theory, viz. that there 

 is sliding of a gas on a solid partition, and that the coefficient of 

 sliding is inversely proportional to the pressure. 



Indeed the velocity v of the layer of gas adjacent to the moved 



