208 
PROFESSOR 0. REYNOLDS ON THE THEORY OF LUBRICATION 
Section VIII. —The Effects of Heat and Elasticity. 
30.— p and a are only to be inferred from the experiments. 
The equations of the last section give directly the friction, the intensity of pressure, 
and the distance between the cylindrical surfaces, when the velocity, the radii of 
curvature of the journal and the brass, the length of the brass, and the manner of 
loading are known (i.e., when U, Tt, a, 6 X , L, and p are known); and, further, if M the 
moment of friction is known, the equations afford the means of determining a when p 
is known, or p when a is known. 
The quantities U, B, 0 X , and L are of a nature to be easily determined in any experi¬ 
ment or actual case, and M is easily measured in special experiments, but with a and 
p it is different. 
By no known means can the difference of radii (a) of the journal and its brass be 
determined to one ten-thousandth part of an inch, and this would be necessary in 
order to obtain a precise value of a. As a matter of fact even a rough measurement 
of a is impossible. To determine a, therefore, it is necessary to know the moment of 
friction or the distribution of pressure ; then if the value of p be known by experi¬ 
ments such as those described for olive oil (Section II.), a can be deduced from the 
equations for any particular value of p. But although the values of p may have been 
determined for all temperatures for the particular oil used, and that value chosen 
which corresponds with the temperature of the oil bath in the experiment, the ques¬ 
tion still arises whether the oil bath (or wherever the temperature is measured) is at 
the same temperature as the oil film. Considering the thinness of the film and the 
rapid conduction of heat by metal surfaces, it seemed at first sight reasonable to 
assume that there would be no great difference, but when on applying the equations 
to determine the value of a for one of the journals and brasses used in Mr. Tower’s 
experiments, it was found that the different experiments did not give the same values 
for a, and that the calculated values of a increased much faster with the velocity when 
the load was constant than with the load when the velocity was constant, it seemed 
probable that the temperature of the oil film must have varied in a manner unper¬ 
ceived, increasing with the velocity and diminishing the viscosity, which would 
account for an apparent increase of a. 
That a should increase with the load was to be expected, considering that the 
material of both journal and brass are elastic, and that the loads range up to as much 
as 600 lbs, per square inch, but there does not appear any reason why a should 
increase with the velocity unless there is an increase of temperature in the metal. If 
this occurs, the apparent increase of a would be part real and part due to the unappre¬ 
ciated diminution of p owing to the rise of temperature. 
Until some law of this variation of temperature and of the variation of a with the 
load is found, the results obtained from the equations, with values of p corresponding 
