AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 
187 
Again, since in the case of lubrication we always have to clo with a film of fluid 
between nearly parallel surfaces, of which the radii of curvature are large compared 
with the thickness of the film, we may without error disregard any curvature there 
may be in the surfaces, and put 
x for distances measured on one of the surfaces in the direction of relative 
motion, 
z for distances measured on the same surface in the direction perpendicular to 
relative motion, 
y for distances measured everywhere at right angles to the surface. 
Then, if the surfaces remain in their original direction, since they are nearly parallel, 
v will be small compared with u and w, and the variations of u and w in the 
directions x and z are small compared with their variations in the 
direction y. 
The equations (12) for the interior of the film then become 
Equations (10) become 
dp _ d~u 
dx ^ d,y 2 
dp 
dy 
= 0 
dp d?v :' 
~dz =,a d : f 
„ du , dv , dvj 
0 =- —4-— 
dx dy dz 
du A 
P*y 2-V Py~J 
dw 
Vy~~—V~-y—\ L 'y^ 
P*X = Pn = 0 
! 
J 
(13) 
(14) 
20. The fluid is subject to boundary conditions as regards pressure and velocity. 
These are— 
(1) At the lubricated surfaces the fluid has the velocity of those surfaces ; 
(2) At the extremities of the surfaces or film the pressure depends on external 
conditions. 
Thus taking the solid surfaces as y— 0, y—h, and as being limited in the direction 
x and 2 by the curve 
flpy )=o 
2 B 2 
