15S PROFESSOR O. REYNOLDS ON THE THEORY OF LUBRICATION 
Section IY.—The Equations of Hydrodynamics as Applied to Lubrication. 
ARTICLE. 
The complete equations for interior of viscous fluid simplified .. 19 
The boundary conditions .. 20 
The first integration of the resulting equations—equations of lubrication. 21 
The conditions under which further integration has been undertaken. 22 
Section Y.—Application to Cases in which the Equations are Completely Integrable. 
Parallel plane surfaces approaching each other, the surfaces having elliptical boundaries 23 
Plane surfaces of unlimited length..... 24 
Section VI.—The Integration of the Equations for Cylindrical Surfaces. 
General adaptation of the equations .... 25 
The method of approximate integration .;. 26 
Integration of the equations ..... 27 
Section VII.—Solution of the Equations for Cylindrical Surfaces. 
c and small compared with unity.... 28 
Further approximation to the solution of the equations for particular values of c, 
Plate 8, figs. 1, 2, and 3 ...... 29 
-5 the limit to this method of integrating .... 29 a 
Section VIII.—Tee Effects of Heat and Elasticity. 
/i and a are only to be inferred from experiments ...... 30 
The effect of the load and the velocity to alter a . 31 
The effect of speed on the temperature .. 32 
The formuhe for temperature and friction, and interpretation of constants. 33 
The maximum load at any speed .. 33 a 
Section IX.—Application of the Equations to Mr, Tower’s Experiments. 
References to Mr. Tower’s reports, Tables I., IX., and XII. ... 34 
The effect of necking the journal..... 35 
First approximation to the difference in the radii of the journal and brass No. 1 .... 36 
The rise in temperature of the film, owing to friction. 37 
The actual temperature of the film .. 38 
The variation of a with the load ... .... 39 
Application of the equations to the circumstances of Mr. Tower’s experiments, 
Table IV...... 40 
The velocity of maximum carrying power. 41 
Application of the equations to determine the oil pressure with brass No. 2. 42 
Conclusion... ... 43 
