AND ITS APPLICATION TO MR. E. TOWER’S EXPERIMENTS. 
163 
will cause rupture in the oil film, which will then only bextend etween the brass ancl 
journal over a portion of the whole arc and a smaller portion as the load increases. 
Thus, since the amount of negative pressure which the oil will bear depends on 
circumstances which are uncertain, the limit of the safe load for complete lubrication 
is that which causes the least separating distance to be half the difference of radii of 
the brass and journal. 
The rupture of the oil film does not take place at the point of nearest approach, 
and hence the brass may still be entirely separate from the journal, and could the 
integrations be effected it would be possible to deal as definitely with this condition 
as with that of complete lubrication; but these difficulties have limited the actual 
application of the theory to complete lubrication. This however by no means requires 
an oil bath, but merely sufficient oil on the journal. 
What happens when the supply of oil is limited, i.e., insufficient for complete 
lubrication, cannot be definitely expressed without further integrations ; but sufficient 
may be seen to show that the brass will still be completely separated from the journal, 
although the separating film will not touch the brass, except over a limited area; but 
in this case it is easy to show by general reasoning that in the one extreme, where the 
supply of oil is limited, the friction increases directly as the load and is independent of 
the. velocity, while in the other, where the oil is abundant, the circumstances are those 
of the oil bath. 
The effect of the limited length of the journal is also apparent in the equations, as 
is also the effect of necking the shaft to form the journal, so that the ends of the brass 
are against flanges on the shaft. 
The theory is perfectly applicable to cases in which the direction of the load on 
the bearing varies, as with the crank pin and with the bearings of the crank shaft of 
the steam engine; but these cases have not been considered, as there are no definite 
experiments to compare. 
8. Although in the main the present investigation has been directed to the 
circumstances of Mr. Tower’s experiments, viz., a cylindrical journal revolving in a 
cylindrical brass, it has, on the one hand, been found necessary to proceed from the 
general equations of equilibrium of viscous fluids, and, on the other hand, to consider 
somewhat generally the physical property of viscosity and its dependence on 
temperature. 
The property of viscosity has been discussed at length in Section II.; which section 
also contains the account of an experimental investigation as to the viscosity of olive 
oil. 
The general theory deduced from the hydrodynamical equations for viscous fluids, 
with the methods of application, is given in Sections IV., V., VI., VII., and VIII. 
As there are some considerations which cannot be taken into account in the more 
general method, which method also tends to render obscure the more immediate 
purpose of the investigation, a preliminary discussion of the problem, illustrated by 
y 2 
