212 PROFESSOR O. REYNOLDS ON THE THEORY OF LUBRICATION 
Whence substituting in the equation which results from (51) c being small 
/=£ U . .(118) 
J a 
Putting T, t . for any particular temperature fx x a x corresponding values 
f= — Ue~ {c+e}(t- T i) . (119) 
J a x + ml 
From (113) 
/=A{T,+ET 3 ,} + ?T».(120) 
These equations (119) and (120) are independent, and therefore furnish a check 
upon each other when the constants are known. 
Thus substituting the experimental values of U and yin (120) a series of values of 
T m are obtained, which when substituted in (119) should give the same value oiy 
. In these equations the meaning of the constants is as follows :— 
C is the rate at which viscosity increases with temperature. 
E is the rate at which a increases with temperature, owing to the different ex¬ 
pansion of brass and iron. 
AU expresses generally the mechanical equivalent of the heat which is carried 
out of the oil film by the motion of the oil and journal for each degree rise of 
temperature in the film. 
B expresses the mechanical equivalent of the heat conducted away through the 
brass and journal. 
The respective importance of these two coefficients is easily apparent. When the 
velocities are low but little heat will be carried out, and hence the temperature of the 
journal depends solely on the value of B. But when the velocities are high, B 
becomes insignificant compared with AU, and it is A alone which keeps the journal cool. 
The value of A may to some extent be inferred from the quantities which enter into 
it as in equation (114). Thus in the case of Mr. Tower’s experiment, since 
R = 2 0=1-37 a— ‘00075 J = '772 
D = 0-033 S = 0'31 (for olive oil) 
A = '0063q.(121) 
It is very difficult to form an estimate of q, but it would seem probable that it has a 
value not far from 2 ; and, as will be subsequently shown, in the case of Mr. Tower’s 
experiments, q is about 3 5 or 
A = 0-0223 
(122) 
