200 
PROFESSOR O. REYNOLDS ON THE THEORY OF LUBRICATION 
From (46) 
M f 2B 
— — = K 3 | 2B 0 ^ 1 — 2B X sin 6 l sin <£ 0 +-^ sin 2 6 X cos 2</> 0 
2B. 
sin 2 n6 l cos 2n<f> 0 
( 68 ) 
The equations (66), (67), (68), together with. (58), which expresses the boundary- 
conditions as regards pressure, are the integral equations of equilibrium for the fluid 
between the brass and journal, and hence for the brass. 
The quantities involved in these equations are 
It, U, M, L, [jl, 6 i and a, c, <f> 0) <f> v 
If, therefore, the former are given, the latter are determined by the solution of these 
equations. 
Section YII. —Solution of the Equations for Cylindrical Surfaces. 
28. c and % small compared with Unity. 
In this case equations (55) become 
A o=-X 
A,= 1 
A 2 = 0, &c. 
B 0 =l 
B 1= 0 l 
B 3 — 0, &c. _ 
. (69) 
Equation (58) gives 
0=^!+ si n si n </>o 
(70) 
Equation (66) gives 
Equation (67) gives 
and equation (68) gives 
(73) 
Also equation (57) 
p— yq^Kp^cos 6 1 cos cos (6 — <f))} .(74) 
