222 
PROFESSOR O. REYNOLDS ON THE THEORY OF LUBRICATION 
and since, by equation (134), when L'=100 
_ nfi x 
-01345 
= ‘0007413ft.(142) 
= ‘00074n (approximately). 
This is the value of a x with a load of 100 lbs. per square inch. 
39. The Variation of a with the Load. 
All Mr. Tower’s experiments, when the loads are moderate and the velocities high, 
show a diminution of resistance with an increased load. 
Since c increases with the load and the friction increases as c increases, a and p 
being constant, the diminution of friction with increased loads shows either that the 
load increases the temperature of the film and so diminishes the viscosity, or increases 
the radius of curvature of the brass as compared with that of the journal, i.e., 
increases a. 
These effects have been investigated by substituting the experimental values of f 
and I/, obtained with the same velocity in equations (119) and (120). 
In this way, from equation (119) the value of m is determined, where, from 
equations (117) and (135), 
a x = (a 0 -f?7iL , )ne' 0222(T "“ To) .(143) 
And the equation (120) gives the effects of the load on the value of the constant A. 
After trial, however, it appears that the effects of the load upon the constant A are 
small so long as the loads are moderate, and that the diminution of the resistance 
with the increased load is explained by the value obtained for m from equation (119). 
From this equation, taking L\ f' 1 , I/ 2 f' 2 , simultaneous values of IT and f, and 
assuming T x independent of the load 
ft 0 + viL\ _ ff 
a 0 + mL'j f n 
which gives the value of m. 
The slight irregularities in the experiments affect the values of m thus found to a 
considerable extent, and a mean has been taken, which is 
m= , 002a 0 .(145) 
Putting T, r =70‘5, T 0 = 60, ‘00074, when I/=100, from equation (143) 
« 0 -f -mV! — ‘000586 In. 
Therefore 
u 0 — ‘0004885ft 
(146) 
