196 



Prof. 0. Reynolds. 



[Feb. 11, 



for the viscosity of olive oil at all temperatures between 60° and 

 120° F * 



Besides the effect on fi the temperature might, owing to the diffe- 

 rent expansion of brass and iron, produce a sensible effect on the 

 small difference a in the radii of the brass and jonrnal, i.e., on the 

 mean thickness of the film, E was taken for the coefficient of this 

 effect, and since, owing to the elasticity of the material, the radius 

 would probably alter slightly with the load, m *was taken as a 

 coefficient for this effect, whence a is given by an equationf in terms 

 of a Q , its value with no load and a temperature zero. 



Substituting these values in the equations, the values of the pres- 

 sure and friction deduced from the equations are functions of the 

 temperature, which may be then assumed, so as to bring the calcu- 

 lated results into accord with the experimental. 



There was, however, another method of arriving, if not at the 

 actual temperatures, at a law connecting them with the frictions, 

 loads, and velocities. For the rise in temperature was caused by the 

 work spent in overcoming friction, while the heat thus generated had 

 to be carried or conducted away from the oil film. Consideration of 

 this work and the means of escape gave another equation between the 

 rise of temperature, the friction, and velocity. J 



The values of the constants in this equation can only be roughly 

 surmised from these experiments, without determining them by 

 substituting the experimental values of /, U, and T, as previously 

 determined, but it was then found that the experiments with the 

 lower loads gave remarkably consistent values for A, B, E, m, 

 and a , which was also treated as arbitrary. In [proceeding to the 

 higher loads for which the values of c were greater, the agreement 

 between the calculated and experimental results was not so close, and 

 the divergence increased as c increased. On careful examination, 

 however, it appeared that this discordance would be removed if the 

 experimental frictions were all reduced 20 per cent. This implied 

 that 20 per cent, of the actual friction arose from sources which did 

 not affect the pressure of the film of oil ; such a source would be the 

 friction of the ends of the brass against flanges on the shaft commonly 



* An inch being unit of length, a pound unit of force, and a second unit of time, 

 for olive oil 



yt t = O'O0OO4737e- 0O221T (8) 



t a=(a + mL) e ET (H7) 



X f— ^A + + EAT 2 (120) 



A + ET represents the rate at which the mechanical equivalent of heat is carried 

 away per unit rise of temperature ; B represents the rate at which^it is conducted 

 away. 



