746 



(o calculate the ainomit ut" the friction which is to be ascribed to 

 this cause. 



§ 2. Friction in consequence of impact forces. For an accurate 

 calculation of the friction through this cause the accurate knowledge 

 of the disti'ibution of the velocities would be required. I shall, however, 

 confine injself here to ari approximate method of calculation of about 

 the same nature as the method of calculation of the "friction by 

 means of transport" for gases by Maxwell in his papers in the 

 Phil. Mag. in i860. I shall, namely, assume thai the distribulion of 

 the velocities of the molecules the centres of which lie in a definite 

 layer j =: c, is found by compounding the velocity of the curient 

 of the liquid in that layer with a thermal motion for which the 

 unmodified partition of velocities of Maxwkll is thought to hold. 



The error that we nnike on this supposition will probably be 

 smaller for liquids than for gases. The free length of path is namely 

 very small here, and the supposition departs little from Maxwell's 

 supposition that the molecules haxe the velocity of current of the 

 layer in which they ha\e collided last. Even when Jkans' correction 

 is taken into account for the persistence of the velocities, we shall 

 have to assign a velocity to the molecules corresponding with the 

 velocity of current of a layer which is only a small fraction of ^x 

 removed from the layer in which their centre is situated. 1 shall 

 disregard this small fraction. 



When we now consider a definite horizontal layer, for which we 

 choose z =. 0, an instantaneous transfer of momentum through 

 this layer takes place at every collison for which the centres of the 

 colliding molecules lie on different sides of this layer. At every 

 impact an instantaneous transfer from above dowjiwards takes place 

 and one in opposite direction. These two quantities are equal and of 

 opposite signs. Hence we may also take into account double the 

 amount of the transfer from above downwards. We shall now first 

 consider the collisions for which the centre of molecide I lies between 

 the |)lanes z=zz^ and z^=: Zt^-\- ilz.^ ^^^ I> -i ^ — o cosy), the central 

 line^) forming an angle between y and y -\- dy with the 2-axis, and 

 lying in a [)lane forming an angle between /5 and (i -\- (l[^ with the 

 .I'^-plane. Further the components of velocity of molecule I will lie 

 between u^ and u^-\-(lu^. r^ and i\ -\- dv^ and ii\ and ti\ -\- dw.^, 

 those of molecule II lying between u.^ and u^ -\- du^ etc. The chance 

 that such components of velocity occur is represented for the two 

 molecules respectively by 



') Counted in the direction of molecule 1 towards II. 



