1886.] 



On the Theory of Lubrication. 



193 



and seizing, according to the perfection or imperfection of the 

 lubrication." 



On reading Mr. Tower's first report, it occurred to the author 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, whereas in his results it does not increase 

 according to this law. 



Considering how very general the law of resistance as the square of 

 the speed is with fluids, there is nothing remarkable in it being 

 assumed to hold in such a case. But the study of the behaviour of 

 fluid in very narrow channels, and particularly the recent determina- 

 tion by the author of the critical velocity at which the 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 

 velocities as that of the surface of the journal, the resistance would 

 vary, cceteris paribus, as the velocity. And 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 influence on the resistance ; and further still, the resistance 

 would depend on the viscosity (commonly called the body) 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 something 

 at a temperature of 90° F. (he does not state precisely what), it did 

 not at first appear that there could be any considerable temperature 

 effect in his results. 



The application of hydrodynamical equations for viscous fluids to 

 circumstances similar to those of a journal and a brass in an oil-bath, 

 in so far as they are known, at once led to an equation* between the 

 variation of pressure over the surface and the velocity, which appeared 

 to explain the existence of the film of oil at high pressure. 



This equation was mentioned in a paper read before Section A 

 at the British Association, at Montreal, 1884. It also appears from a 

 paragraph in the Presidential Address (p. 14, Brit. Assoc. Rep., 1884) 



* dp _ 6/iU(A — A x ) 

 dx P 



in which p is the intensity of pressure, fi coefficient of viscosity, x the direction of 

 motion, k the interval between the journal and the brass, h l being the value of /* 

 for which the pressure is a maximum, TJ the surface velocity in the direction of x. 



!No. of equation 

 in the paper. 



. . (31) 



