AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 
209 
to some measured temperature, such as that of the oil bath or a point in the brass, can 
only be considered as approximately applicable to actual results. Even so, however, 
the degree of approximation is not very wide as long as the conditions are such that 
the journal “runs cool.” 
But, treated so, the equations fail to show in a satisfactory way what is one of the 
most important matters connected with lubrication—the circumstances which limit the 
load which a journal will carry. For, although it may be assumed that the limit is 
reached when ca, the shortest distance between the surfaces, becomes zero or less than 
a certain value, yet, according to the equations, assuming a and p to be constant, the 
value of c increases directly as U if the load be constant ; so that the limiting load 
should increase with U. But this is not the case, for it seems from experiments that 
at a certain value of U the limiting load is a maximum if it does not diminish for a 
further increase of IT- 
Although, therefore, the close agreement of the calculated distribution of the 
pressure over the bearing with that observed and the approximate agreement of the 
calculated values of the friction for different speeds and loads, such as result when p 
and a are considered constant, seem to afford sufficient verification of the theory, and 
hence a sufficient insight into the general action of lubrication, without entering into 
the difficult and somewhat conjectural subject of the effects of heat and elasticity, 
yet the possibility of obtaining definite evidence as to the circumstances which deter¬ 
mine the limits to lubrication, which, not having been experimentally discovered, are a 
great desideratum in practice, seemed to render it worth while making an attempt to 
find the laws connecting the velocity and load with a and p. 
As neither the temperature of the oil film or the interval between the surfaces can 
be measured, the only plan is to infer the law of the variations of these quantities 
from such complete series of experiments as Mr. Tower’s. In attempting this, a 
probable formula with arbitrary constants is first assumed or deduced from theoretical 
considerations, and then these constants are determined from the experiment and the 
general agreement tested. In order to determine the actual circumstances on which 
the constants depend, it is important to obtain the formula from theoretical considera¬ 
tions. This has therefore been done, although these considerations would not be 
sufficient to establish the formulae without a close agreement with the experiments. 
31. The Effect of the Load and Velocity to alter the Value of the Difference of Radii 
of the Brass and Journal, i.e., of a. 
The effect of the load is owing to the elasticity of the materials, hence it is probable 
that the effect will be proportional to the load L. To express this put— 
a=a 0 +mL ..(109) 
2 E 
MDCCCLXXX VI. 
