178 
PROFESSOR 0. REYNOLDS ON THE THEORY OF LUBRICATION 
And since the quantity which passes P 3 Q 2 will not be sufficient to occupy the larger 
sections on the left, the fluid will not touch the upper surface to the left of P 2 . The 
limit will therefore be at P 2 , the fluid passing away with AB in a film of thickness b. 
This is the ordinary case of partial lubrication : AB, the surface of the journal, is 
covered with a film of oil; CD, the surface of the brass or bearing, is separated from 
AB by a pad of oil near H, the point of nearest approach. 
This pad is under pressure, which is a maximum at P l5 and slopes away to nothing 
at D and P 2 , the extremities of the pad, as is shown by the curve above, fig. 12. 
17. The Relation betiveen Resistance, Load, and Speed for Limited Lubrication. 
In Case 7 a definite quantity of oil must be in the film round the journal, or in 
the pad between the surfaces. As the surfaces approach the pad will increase and 
the film diminish, and vice versd. The resistance increases with the length of the pad 
and with the diminution of the distance between the surfaces. The mean intensity 
of pressure increases with the length of the pad, and inversely with the thickness of 
the film, but not in either case in the simple ratio. The total pressure which is equal 
to the load increases with the intensity of pressure and the length of the pad. 
The definite expressions of these relations depend on certain integrations, which 
have not yet been effected. From the general relations pointed out, it follows that an 
increase of load will diminish HG and P 1 Q 1 , and consequently the thickness of the 
film round the journal, and will increase the length of the pad. It will therefore 
increase the friction. 
Thus with a limited supply of oil the friction will increase with the load in some 
ratio not precisely determined. 
Further, both the friction and the pressure increase in the direct ratio of the speed, 
provided the distance between the surfaces and the length of the pad remains con¬ 
stant ; then, if the load remains constant, the thickness of the film must increase, and 
the length of the pad diminish with the speed; and both these effects will diminish 
friction in exactly the same ratio as the reduction of load diminishes friction. 
Thus if with a speed U a load W and friction F a certain thickness of oil is 
maintained, the same will be maintained with a speed MU, a load MW, and the 
friction will be MF. 
How far this increase of friction is to be attributed to the increased velocity, and 
how far to the increased load, is not yet shown in the theory for this case; but, as 
has been pointed out, if the load be altered from MW to W, the velocity remaining 
the same, the friction will be altered from MF in the direction of F. Therefore, with 
the load constant, it does appear from the theory that the friction will not increase 
as the first power of the velocity. 
There is nothing therefore in this theory contrary to the experience that, with very 
limited lubrication, the friction is proportional to the load and independent of the 
