Equations of Motion of a Viscous Liquid. 47 



crease in motion is very ^'reat all of the terms except the tirst 

 may be dropped. This j^ives 



1 /(lu\_(lll 



dt\ njilv 



The retarding force on the face dy dz is 



du , , 

 lj.--dydz, 

 dx 



and on the opposite face 



IJL — dy dz+/j. — dy dz d.v, 

 dx dx^ 



showing a loss for the element of 



d'H , , , 



;j. dii dz dx 



dx' ■' 



when the tluid is viscous. 



The retardation in the direction of the x axis must equal 

 the retardation of inflow, for otherwise there would be a dis- 

 continuity. 



It is necessary to extend this principle to the case where 

 the inflow is across two faces instead of one. 



I> FIG. 7. E 



AB . AD—HI. JJ^= total areal increase of inflow. 

 AB.AD u' 



HI. IJ u 

 AB. AD-HI. IJ n'-u 



But 



AB.AD dt 



u^—u_ 1 /. u 



dtit^ dt\ 11 + du 



u\it 



= rate of inflow. 



