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PROFESSOR 0. REYNOLDS ON THE THEORY OF LUBRICATION 
As regards the magnitude of this resultant it increases as HG diminishes to a 
certain limit, i.e. , as the surfaces approach, so that in this respect equilibrium is 
obviously secured, and it is only the direction of the resultant pressure and friction 
that need be considered. 
Since the fluid film is in equilibrium under the forces exerted by the two opposite 
surfaces these forces must be equal and opposite, so that it is only necessary to 
consider the forces exerted by AB on the fluid. 
From what has been already seen in Cases 6 and 7 it appears that the resultant 
line of pressure JM always lies on the right or on side of GH. The resultant 
friction clearly acts to the left, so that if JM be taken to represent the resultant 
pressure and MN the resultant friction, N is to the left of M and JN the resultant 
of pressure and friction is to the left of JM. 
Taking LJ to represent the load, then LN will represent the resultant moving 
force on CD that is on I. Since H will move in the opposite direction to I, and 
since the direction of the resultant pressure moves in the same direction as H, the effect 
of a moving force LN on I will be to move N towards L until they coincide. Thus as 
long as JM is within the arc covered by the brass a position of equilibrium is possible 
and the equilibrium will be stable. 
So far the condition of equilibrium shows that H will be on the left or off side of 
the line of load, and this holds whether the supply of oil is abundant or limited ; but 
while with a very limited supply of oil, i.e., a very short oil pad, H must always be in 
the immediate neighbourhood of 0, this is by no means the case as the length of the 
oil pad increases. 
Case 9. Cylindrical Surfaces in Oil Bath. —If the supply of oil is sufficient the 
oil film or pad between the surfaces will extend continuously from the extremities of 
the brass, unless such extension would cause negative pressure which might lead to 
discontinuity. In this case the conditions of equilibrium determine the position of H. 
The conditions of equilibrium are as before— 
1. That the horizontal component of the oil pressure on the brass shall balance the 
horizontal component of the friction; 
2. That the vertical components of the pressure and friction shall balance the load. 
Taking the surface of the brass, as is usual, to embrace nearly half the circumference 
of the journal and, to commence with, supposing the brass to be unloaded, the move¬ 
ment of H may be traced as the load increases. 
When there is no load the conditions of equilibrium are satisfied if the position of 
H is such that the vertical components of pressure and friction are each zero, and the 
horizontal components are equal and opposite. 
This will be when H is at 0 (fig. 13); for then, as has been shown, Case 5, the 
pressure on the left of H will be negative, and will be exactly equal to the pressure at 
corresponding points on the right, so that the vertical components left and right balance 
each other. On the other hand the horizontal component of the pressure to the left 
