80 VISCOSITY OF GASES 201 



by most observers much of tener than pure gases to prove 

 the independence of the viscosity on the pressure and to in- 

 vestigate its dependence on the temperature. 



The theoretical considerations retain their validity also 

 for mixed gases, especially the deduction given in 75 of 

 the formula which expresses the theoretical value of the co- 

 efficient of viscosity. In this reasoning mean values were 

 always dealt with ; the mean momentum which is carried 

 by the moving particles in unit time over unit area in 

 a given direction was brought into account, and also the 

 mean value of the distance which is traversed by the 

 particles that cross the area. From the two we obtained 

 the amount of the friction which in a particular case is equal 

 to the coefficient of viscosity. This calculation, depending 

 on mean values, does not in any way assume equality of all 

 the molecules; for mean values of magnitudes that have 

 even very unequal values can be formed. The fundamental 

 formula of the theory is therefore valid also for gaseous 

 mixtures ; the question now only arises how to form the 

 necessary mean values. 



We can attempt this in different ways. We may either 

 direct our efforts to the carrying out of the mathematical 

 calculation as strictly as possible, and so far as is possible 

 without neglecting anything, or strive to find simpler for- 

 mulas, which are easy to evaluate for numerical calculations. 

 Maxwell l has followed the first way; here we employ an 

 easier method, which is due to Puluj. 2 



The formula for the coefficient of viscosity 



^\ B R A /Ty* 



1, = 0-30967 

 we use for a gaseous mixture in the form 

 17 = 0-30967 



where m is the molecular weight, and we thereby under- 

 stand m, O, and s- as representing mean values. If the 



1 Phil. Mag. 1868 [4] xxxv. p. 212 ; Scientific Papers, ii. p. 72. 



2 Wiener Sitzungsber. 1879, Ixx'.x. Abth. 2, pp. 97, 745 ; CarVs Bepert. d. 

 Experimentalphys. xv. p. 590. 



