1886.] 



On the Theory of Lubrication. 



195 



to be approximately integrated by considering certain quantities 

 small, and the theoretical results thus definitely compared with the 

 experimental. 



The result of this comparison was to show that with a particular 

 journal and brass the mean thickness of the film would be sensibly 

 constant for all but extreme values of load divided by the viscosity, 

 and hence if the coefficient of viscosity were constant the resistance 

 would increase approximately as the speed. 



As this was not in accordance with Mr. Tower's experiments, in 

 which the resistance increased at a much slower rate, it appeared that 

 either the boundary actions became sensible, or that there must be a 

 rise in the temperature of the oil which had escaped the thermometer 

 used to measure the temperature of the journal. 



That there would be some excess of temperature in the oil film on 

 which all the work of overcoming friction is spent is certain, and 

 after carefully considering the means of escape of this heat, it appeared 

 probable that there would be a difference of several degrees between 

 the oil-bath and the film of oil. 



This increase of temperature would be attended with a diminution 

 of viscosity, so that as the resistance and temperature increased with 

 the velocity there would be a diminution of viscosity, which would 

 cause the increase of the resistance with the velocity to be less than 

 the simple ratio. 



In order to obtain a quantitative estimate of these secondary effects, 

 it was necessary to know the exact relation between the viscosity of 

 the oil and the temperature. For this purpose an experimental deter- 

 mination was made of the viscosity of olive oil at different tempera- 

 tures as compared with the known viscosity of water. From the 

 result of these experiments an empirical formula has been deduced 



<p and 0! and c have to be determined from the conditions of equilibrium, which 

 are 



J {<psin0-/cos0}dp=O ...... (44) 



fie {2»coB0+/Bin0}de = ! (45) 



>-o fde== % (46) 



where 29 x is the angle subtended by the brass, L the load, and M the moment of 

 friction. 



The solution of these equations may be accomplished when c is small and has been 

 approximately accomplished for particular values of c up to 0"5, the boundary con- 

 ditions as regards p being 



e=±e l p=p , 



wl;ence substituting the values of <f> Xl <p , c in (48) and (49), and integrating, the 

 values of the friction and values of the pressure are obtained. 



