160 
PROFESSOR O. REYNOLDS ON THE THEORY OF LUBRICATION 
found considerable regularity in the results ; these, however, were very different from 
those with the bath. Then with intermediate lubrication he obtained intermediate 
results, of which he says :—“ Indeed, the results, generally speaking, were so 
uncertain and irregular that they may be summed up in a few words. The friction 
depends on the quantity and uniform distribution of the oil, and may be anything 
between the oil bath results and seizing, according to the perfection or imperfection 
of the lubrication.” 
3. On reading Mr. Tower’s report it occurred to the author as possible that in the 
case of the oil bath the film of oil might be sufficiently thick for the unknown 
boundary actions to disappear, in which case the results would be deducible from the 
equations of hydrodynamics. Mr. Tower appears to have considered this, for he 
remarks that according to the theory of fluid friction the resistance would be as the 
square of the velocity, wPereas in his results it does not increase according to this 
law. Considering how very general the law of resistance as the square of the 
velocity is with fluids, there is nothing remarkable in the assumption of its holding in 
such a case. But the study of the behaviour of fluid in very small channels, and 
particularly the recent determination by the author of the critical velocity at which 
this law changes from that of the square of the velocity to that of the simple ratio, 
shows that with such highly viscous fluids as oils, such small spaces as those existing 
between the journal and its bearing, and such limited velocity as that of the surface 
of the journal, the resistance would vary, cceteris paribus, as the velocity. Further, 
the thickness of the oil film would not be uniform and might be affected by the 
velocity, and as the resistance would vary, cceteris paribus, inversely as the thickness 
of the film, the velocity might exert in this way a secondary effect on the resistance ; 
and, further still, the resistance would depend on the viscosity of the oil, and this 
depends on the temperature. But as Mr. Tower had been careful to make all his 
experiments in the same series with the journal at a temperature of 90° Fahr., it did 
not at first appear that there could be any considerable temperature effect in his 
results. 
4. The application of the hydrodynamical equations to circumstances similar in so 
far as they were known to those of Mr. Tower’s experiments, at once led to an 
equation between the variation of pressure over the surface and the velocity, which 
equation appeared to explain the existence of the film of oil at high pressure. This 
equation was mentioned in a paper read before Section A. of the British Association 
at Montreal, 1884. It also appears from a paragraph in the President’s Address 
(Brit. Assoc. Hep., 1S84, p. 14) that Professor Stokes and Lord Rayleigh had 
simultaneously arrived at a similar result. At that time the author had no idea of 
attempting its integration. On subsequent consideration, liow T ever, it appeared that 
the equation might be transformed so as to be approximately integrated, and the 
theoretical results thus definitely compared with the experimental. 
5. The result of this comparison was to show that with a particular journal and 
