204 PROFESSOR 0. REYNOLDS ON THE THEORY OF LUBRICATION 
whence equations (47) 
c=-388a^.(96) 
£ 
a 
-•3635 
M 
mT 0 
(97) 
So long then as apz is not greater than 0’2, these approximate solutions are 
sufficiently applicable to any case. 
For greater values of the solution becomes more difficult, as long however as c is 
not greater than '5 the solution can be obtained for any particular value of c. 
29. Further Approximation to the Solution of the Equations for particular 
Values of c. 
The process here adopted is to assume a value for c. From equations (53) and (54) 
to find 
Ao=A 0 '+A 0 "y B 0 =B 0 'd-B 0 "y.(98) 
&c. &c. 
where A/ A 1 // B/ B 1 // are numerical. 
These coefficients are then introduced into equations (58) and (66) which on 
eliminating y give one equation for <£ 0 . 
The complex manner in which <f> 0 enters into the equation renders solution difficult 
except by trial, in which way values of </> 0 corresponding to different values of c have 
been found. 
The value of <£ 0 substituted in equations (58) or (66) gives y and ^q. 
The corresponding values of c a , (f> 0 and y being thus obtained, a complete table might 
be calculated. This, however, has not been done, as there does not exist sufficient 
experimental data to render such a table necessary. 
What has been done is to obtain <^q and for c='5, 6 1 having the value 1‘3704 as 
in equation (88) and in Tower’s experiments. 
The value c=' 5 was chosen by a process of trial in order to correspond with the 
experiments in which Mr. Tower measured the pressure at different parts of the 
journal as described in his second report, and as being the greatest value of c for 
which complete lubrication is certain. 
Putting c='5, equations (43) and (44) give 
