ILLUSTRATIONS OF THE DYNAMICAL THEORY OF GASES. 391 



momentum =MB(z z') is communicated by each particle. The whole action due 

 to these collisions is therefore 



NMB ;A (z - z') e~ n dz dz' dn. 

 2nP x 



We must first integrate with respect to z' between z' = and z' = z nl; this 

 gives 



\NMB (n'P - z 2 ) e~ n dz dn 



for the action between the layer dz and all the layers below the plane xy. 

 Then integrate from z = to z nl, 



Integrate from n = to n = QO , and we find the whole friction between unit 



of area above and below the plane to be 



u du 



where \L is the ordinary coefficient of internal friction, 



1 Mv 



, , 

 (24), 



where p is the density, I the mean length of path of a particle, and v the 



, ., 2a /2k 



mean velocity v = f= = 2 / , 



J-JT V IT 



* /> V 2T 



Now Professor Stokes finds by experiments on air, 



If we suppose \/A = 930 feet per second for air at 60, and therefore the mean 

 velocity v = l505 feet per second, then the value of I, the mean distance 

 travelled over by a particle between consecutive collisions, =^4^000^ f an 

 inch, and each particle makes 8,077,200,000 collisions per second. 



A remarkable result here presented to us in equation (24), is that if this 

 explanation of gaseous friction be true, the coefficient of friction is independent 

 of the density. Such a consequence of a mathematical theory is very startling, 

 and the only experiment I have met with on the subject does not seem to 

 confirm it. We must next compare our theory with what is known of the 

 diffusion of gases, and the conduction of heat through a gas. 



