194 



Prof. 0. Reynolds. 



[Feb. 11, 



that Prof. Stokes and Lord Rayleigh had simultaneously arrived at a 

 similar result. At that time the author had no idea of attempting 

 the integration of this equation. On subsequent consideration, how- 

 ever, it appeared that the equation might be so transformed* as 



Fia. 1. 



* If the journal and brass are both of circular section, as in fig. 1, and E, is the 

 radius of the journal, R + a radius of brass, J the centre of the journal, I the centre 

 of the brass, JI = ca, HG- the shortest distance across the film, 10 the line of loads 

 through the middle of the brass, A the extremity of the brass on the off side, B on 

 the on side, P x the point of greatest pressure, 



Putting OLE = O --^ 



01^ = 0! 



OIP = 



h = a{l + c sin (0 — O ) } 

 &! = a jl + c sin (0i — <j> ) j 



the equation (31) becomes 



dp_6K/ic{sin (0-0 o ) -sin (fa-fa)} 



Id <r{l + csin (0-0 o ) } 3 ^ 



If JL is small. This equation, which is at once integrabie when c is small, has been 

 ±t 



integrated by approximation when c is as large as 0"5. 

 The friction is given by an equation 



f=-\A{c,iu(e-fa)}- f , /1j [Jl " lJ ; M , .... (49) 

 ad L } ail + csind — <p Y 



This is also approximately integrated up to c = , 5. 



