FOUNDATIONS OF THE KINETIC THEORY OF GASES. 259 



Y/"FM — — '"" / !« 2 « 3 4- Q 12^ 1 "*" ^L w o3 _i_ £_?», 2, 3 1 



= — -p{n i % 3 + 2n 1 n 2 !? + n. 2 \ 3 }; 



for Pi = P 2 = Pi+P2_l (^+'>A\JP > 



1\ h 2 h x + h 2 n\ h l h 2 ) n ' 



where 



n = n 1 + n 2 . 



In the special case s 1 = s 2 = s, this becomes, as in § 30, 



vS(Itr) = — irpns 3 . 



To obtain an idea as to how the " ultimate volume," spoken of in that 

 section, is affected by the difference of size of the particles, suppose n x = n 2 . 

 The values of the above quantities are 



— t-^'{s 1 3 + 2s 3 +s 2 3 } and — irnps 3 ; 



so that (as we might have expected) disparity of size, with the same mean of 

 diameters, increases the quantity in question. 

 Thus, if 



s 1 : s : s 2 : : 1 : 2 : 3 , 



the ratio of the expressions above is 11 : 8. The utmost value it can have (when 

 sjs 2 is infinite, or is evanescent) is 5 : 2. 



XII. Viscosity. 



36. Suppose the motion of the gas, as a whole, to be of the nature of a 

 simple shear ; such that, relatively to the particles in the plane of yz, those in 

 the plane x have a common speed 



V = Bx 



parallel to y. V, even when x is (say) a few inches, is supposed small compared 

 with the speed of mean square. We have to determine the amount of 

 momentum parallel to y which passes, per second, across unit area of the plane 

 of yz. 



In the stratum between x and x + Sx there are, per second per unit surface, 

 nvevhx collisions discharging particles with speed v to v + dv (distributed 

 uniformly in all directions) combined, of course, with the speed of translation 

 of the stratum. The number of these particles which cross the plane of yz at 

 angles to 6 + dO with the axis of x is 



g-«* 8 ece s i n QdQ/2. 

 VOL. XXXIII. PART II. 2 P 



