1165 



The further question arises, whether the theory is Ccapable of explaining 

 tlie viscosity of gas-mixtares, in particuhir tlie interesting fact, that, 

 e.g. for the two above combinations, the viscosity goes through a 

 maximum. In order to derive a foi-mula for the viscosity of mixtures 

 it is necessary first to consider tiie case of a pure substance. Tlie 

 coetKicieut 0.44 in the formula for ii, used above, is the result of the 

 multiplicaticn of the factor 0.35 which is obtained, when the pers/sfeiia^ 



is left out of account, and a persistence-factor , where i>=i0.40() 



1 ^ 



2 



represents the persistence. 



The coefficient - in the denominator which is absent in the persist- 



ence-factor of the diffusion-formula may be justified as follows '). 

 When a molecule is tiaced on its way from the moment that it 

 collides, it is found, that on the average it does not describe a distance 

 / in the dii-ection of motion, before its velocity in this direction is 

 exhausted and therefore all directions become equally probable, Ixit 

 a distance : 



/ + /^ + /^^ + . . 



1—^ 



In the case of viscosity howevei- we are dealing with the transport 

 of momentum : it would on the one hand be incorrect to assume, 

 that the momentum of a molecule at each collision immediately 

 assumes the value belonging to the point where the collision occurs; 

 if that were the case, the persistence would have no influence on 

 the viscosity and would have to be left out of account. On the other 

 hand it cannot be assumed, that the molecule keeps its momentum 

 till the moment, when it has lost its velocity in the direction of 

 motion, and then suddenly, as regards momentum, goes into 

 equilibrium with the neighbouring molecules. It is much more reason- 

 able to assume, that at each collision the excess of momentum is 

 equally distributed over the two molecules : on this supposition the 

 persistence-factor will obviously be given by the series 



1 1 1 



1 + -- 19' ^. ^ {y + . . = 



2 '4 ~1 — ^.'^ 



by which Jeans's result is obtained. 



If we now apply this principle to mixtures, it seems natural to 

 suppose, that for collisions between unlike molecules the persistence 



V J. H. Jeans. Theory of gases p. 249—250. 1904. 



