AND ITS APPLICATION TO MR, B. TOWER’S EXPERIMENTS. 
177 
16. The Effect of a Limiting Supply of Lubricating Material. 
In the cases already considered C and D have been the actual limits of the upper 
surface. If the supply of lubricant is limited C and D may be the extreme points to 
which the separating film reaches on the upper surface, which may be unlimited, as in 
fig. 12. 
Case 7. Supply of Lubricant Limited. —If the surface AB be supposed to have 
been covered with a film of oil, the oil adhering to the surface and moving with it, 
then the surface CD to have been brought up to a less distance than that occupied 
by the film of oil, the oil will accumulate as it is brought up by the motion of AB, 
forming a pad between the surfaces particularly on the side D. 
The thickness of the film as it leaves the side C being reduced until the whole 
surface AB is covered with a film of such thinness that as much leaves at C as is 
brought up to D, then the condition will be steady. 
Putting b for the thickness of the film of oil outside the pad, the quantity of oil 
brought up to D by the motion of this film will be per second 
bJJ, 
and the quantity which passes the section P 1 Q 1 , across which the velocity varies 
uniformly, will be 
PiQiU 
2 ’ 
Therefore since there is no further accumulation 
also, since GPo^GPi (fig. 10, Case 5) 
MDCCCLXXX VI. 
2 A 
PiQi=2&, 
P 3 Q 2 = 2 b 
