176 PHENOMENA DEPENDENT ON MOLECULAR PATHS 75 



parallel to the surface, and so that the velocity is the same 

 at all points of a horizontal plane ; we further take the 

 velocity of flow at a distance x above the base to be 

 numerically equal to x, that is, 



v = x, 



or we assume that each particle passes in unit time over a 

 distance which is equal to its height above the base. In 

 this distribution of flow the friction per unit area between 

 any two layers is equal to the coefficient of viscosity. 



Besides this forward velocity v there is the heat-motion 

 of the gas. In comparison with this exceedingly rapid 

 motion, which in air, for instance, has at a mean speed 

 of 447 metres per second, the assumed forward velocity v, 

 which at the height x = 1 metre is only 1 metre per second, 

 is vanishingly small. The addition of this new motion will 

 therefore exert no sensible effect on that heat-motion or on 

 the length of free path, the collision-frequency, &c., so that 

 we can reckon the number of particles which leave one layer 

 and pass over into another as if they had their molecular 

 speed only. 



We calculate the friction between two layers which lie 

 the one on the other, with the horizontal plane at the 

 height x above the base for their plane of contact, by exactly 

 the same method as we used in 12 to calculate the pressure 

 in the interior of a gaseous mass. We put the number of 

 particles, which in unit time pass through unit area of the 

 limiting plane from the lower layer to the upper, equal to 

 %NG; for this we assume, as was first suggested by Joule, 

 that only a third of the .IV particles in unit volume come 

 into account as regards passage in a given direction, and, as 

 before, we take G to represent the mean value of the speed 

 as deduced from the mean kinetic energy ( 27). 



The particles forming this number have begun their path 

 towards the limiting layer at different depths, but on the 

 average they come from a distance from this layer which is 

 equal to the mean free path Z/, and therefore from a layer 

 which is at the height x L above the base. Their mean 

 forward velocity is therefore given by 

 v f = x L, 



