49* VISCOSITY OF GASES 453 



hitherto exclusively considered, in which the molecules slide or 

 roll over each other without, on the average, coming nearer to or 

 going further from each other. But the different mathematical 

 theories do not agree together in respect to the numerical ratio of 

 these two coefficients of friction. 



The value which the kinetic theory of gases requires for the 

 second coefficient of friction can be calculated from the same 

 formulae as before, if only the single alteration is made, that 

 instead of the velocity-component v, which is parallel to the 

 surface of friction dy dz, we consider a velocity u perpendicular to 

 it. We have, consequently, in the formula given in 47* for the 

 momentum carried across the element dy dz, no further change to 

 make than to employ the exponent q with the value 



q = km(u z + u r2 2um r cos s) 



and to exchange the factor m sin s cos for m cos s. Thus the 

 momentum normal to the surface of friction which is carried over 

 dy dz in unit time is 



, r oo pco c\n r2ir _ TV,., 



Q = dttdimJ(JcmlnV\ du dr \ ds \ dA Be 1<a e V sins cos 2 s; 



Jo Jo Jo Jo 

 on carrying out the integrations with the assumption that 



u 1 = u -h i (^ cos s + ~- sin s cos <t> + C \ U sin s sin <b]r + 

 ~ 1 \dx dy dz T J 



which corresponds to a former assumption, and that 

 e - q _ e -km* ^ + 2&wiom / cos s) 



with sufficient approximation, we find the values 

 Q! = \p + y'u + \n' dujdx 



Q. 2 = \p + y'u \r)' du/dx, 

 where 



p = ffwMl 2 



is the pressure, and y f and r) f are constants whose meaning is 



= 2y 



' =3,. 



The latter is the second coefficient of viscosity for which we are 



seeking ; y f disappears from the difference Q. 2 Q\ between the 



momenta carried the one way and the other, which has the value 



Q 2 Q l = p tf du/dx =p - 3/7 du/dx 



