200 



Prof. 0. Reynolds. 



[Feb. 11, 



except over a limited area, and it is shown by general reasoning that 

 in the one extreme, when the oil is very 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 bearings, and the escape of the 

 oil at the ends, is also apparent in the equations. 



Although in the main the present investigation has been directed 

 to the circumstances of Mr. Tower's experiments, namely, a cylin- 

 drical journal revolving in a cylindrical brass, the main object has 

 been to establish a general and complete theory based on the hydro- 

 dynamical equations for viscous fluids. Hence it has been thought 

 necessary to proceed from the general equations, and to deduce the 

 equations of lubrication in a general form, from which the particular 

 form for application has been obtained. It has been found necessary 

 also to consider somewhat generally the characters of fluid friction 

 and viscosity. 



The property of viscosity has been discussed in Section II of the 

 paper, which section also contains the account of the experimental 

 investigation as to the viscosity of olive oil. The general theory 

 deduced from the hydrodynamical equations for viscous fluids with 

 methods of application, including two cases besides the cylindrical 

 journal in which the equations become completely integrable, viz., 

 two plane surfaces of elliptical shape approaching, and one plane 

 sliding over another not quite parallel plane surface, is given in 

 Sections IV, V, VI, and VII. 



The physical considerations of the effect of the heat generated are 

 discussed in Section VIII. 



As there are some circumstances which cannot betaken into account 

 in the definite reasoning, particularly as regards incomplete lubrica- 

 tion, besides which, as the definite reasoning tends to obscure the 

 more immediate purpose of the investigation, a preliminary discussion 

 of the problem presented by lubrication, illustrated by aid of graphic 

 methods, has been introduced as Section III. 



Finally, the definite application to Mr. Tower's experiments is given 

 in Section IX, which concludes as follows : — 



The experiments to which the theory has been definitely applied 

 may be taken to include all Mr. Tower's experiments with the 4-inch 

 journal and oil- bath, in which the number of revolutions per minute 

 was between 100 and 450, and the nominal loads in pounds per square 

 inch between 100 and 415. The other experiments with the oil-bath 

 were w T ith loads from 415 till the journal seized at 520, 573, or 625, 

 and a set of experiments with brass No. 2 at 20 revolutions per 

 minute. All these experiments were under extreme conditions, for 

 which by the theory o was so great as to render lubrication incom- 



