174 
PROFESSOR 0. REYNOLDS ON THE THEORY OF LUBRICATION 
The effect in this case will be nearly the same as in the compound movement 
(Case 3). 
Fig. 8. 
For if corresponding to the uniform movement U of AB, the velocity of the fluid 
varied uniformly from the surface AB to CD, then the quantity carried across any 
section PQ would be 
PQx? 
and consequently would be proportional to PQ ; but the quantities carried across all 
sections must be the same, as the surfaces do not change their relative distances; 
therefore there must be a general outflow from any vertical sections PQ, P'Q' given by 
f(PQ-P'Q'). 
This outflow will take place to the right and left of the section of greatest pressure. 
Let this be P^, then the flow past any other section PQ 
|(PQ-P 1 Q 1 ) 
to the right or left according as PQ is to the right or left of P 1 Q 1 . Hence at this 
section the motion will be one of uniform variation, and to the right and left the lines 
showing the motion and friction will be nearly as in fig. 7. This is shown in fig. 9. 
Fig. 9. 
This is the explanation of continuous lubrication. 
