75 VISCOSITY OF GASES 177 



and the momentum which is carried over on the average by 

 every single molecule from the lower to the upper layer 

 amounts to 



mv' = m(x L} ; 



on the whole, then, the momentum 

 NmG(x - L) 



is carried in unit time over unit area of the plane at the 

 height x by the particles which cross the plane from the 

 layers below it to those above. 



There simultaneously goes in the opposite direction from 

 the upper to the lower layers the amount of momentum 



Therefore the layers above the limiting plane lose in unit 

 time the momentum 



NmG(x + L) - NmG(x - L) 



while the lower layers gam t^e'same amount. According to 

 the explanation of viscosity, which we have given in the sense 

 of the kinetic theory, the internal friction exerted on unit 

 surface is therefore 



tl = NmGL, 



and this magnitude is the coefficient of viscosity of the gas. 



The formula we have obtained has an unmistakable 

 likeness to that found for the pressure, viz. 



p = iNmG* ; 



it differs from it only by having the free path L, i.e. a 

 magnitude of the dimensions of length, in place of the 

 factor G which denotes the molecular velocity. Thus the 

 idea of friction being a kind of pressure, which was brought 

 forward in 74, is justified, and the value of a coefficient of 

 viscosity may be referred in the same way x as a pressure to 

 the usual units, the gram, centimetre, and second. 



To avoid, however, all uncertainty afterwards, we must 

 point out that it would be incorrect to leave out of account 

 the difference between the two magnitudes, a velocity and a 



1 [The dimensions are, however, not the same; those of p are ML~ 1 T~ 2 

 and those of i\ are ML~ l T~ l . TB.] 



N 



