AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 
185 
For when the supply of oil is short HG will be very small and H will be close to O. 
So that the wearing area will probably extend to both sides of O, and thus the brass 
be partially, if not altogether, prepared for running in the opposite direction. 
When the supply of oil is complete, however, as has been shown, H is 50° or 60° 
from 0, unless the load is in excess, so that the wear in the neighbourhood of H on 
the one side of O would not extend to a point 100° or 120° over to the other side. 
Even in the case of a perfectly smooth brass the running of the journal under a 
sufficient load in one direction should, supposing some wear, according to the theory 
render the brass less well able to carry the load when running in the opposite 
direction. For, as has already appeared, the pressure between the journal and brass 
depends on the radius of curvature of the brass on the on side being greater than 
that of the journal. If then the effect of wear is to diminish the radius of the brass 
on the off side, so that when the motion is reversed the radius of the new on side is 
equal to or less than that of the journal, wdiile the radius of the new off side is 
greater, the oil pressure would not rise. And this is the effect of wear; for as will 
be definitely shown, the effect of the oil pressure is to increase the radius of curvature 
of the brass, and as the centre of wear is well on the off side, the effect of sufficient 
wear will be to bring the radius on this side, while the pressure is on, more nearly to 
that of the journal, so that on the pressure being removed the brass on this side may 
resume a radius even less than that of the journal. 
Section IV.— The Equations of Hydrodynamics as Applied to Lubrication. 
19. According to the usual method of expressing the stress in a viscous fluid (which 
is the same as in an elastic solid)* : 
du . dv . dw 
v**— -p~m d ,.+,7 +, + 2 /^ 
du 0 
i 
dx dy dz 
du . dv . did 
Pn—P~ M&,+ dy + dz ,)+ 2 L& ^ 
dx 
dv 
0 (du dv dw\ dw 
P,= -p-i fffc+* / +& / ) + 2 ^ 
dy 
Iw 
dz 
( 9 ) 
(dv du\ 
P^—Py-=Affffrj y j 
(dw dv 
Pr-=P-;=l\^ y +^. 
(du dud 
( 10 ) 
* Store's “On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and 
Motion of Elastic Solids.”—Trans. Cambridge Phil. Soc., vol. viii., p. 287. Also reprint, vol. i, p. 84. 
Also Lamb’s ‘Motion of Fluids,’ p. 219. 
MDCCCLXXXVT. 2 B 
