Scientific Papers - Vi

918] ON THE THEOEY OF LUBRICATION
In terms of k and c by (34)
n - —, __
531
3 A8
ad by (7)
P - 1 f 2 -
-f 2&3 - 3
.(38)
- 3
The maximum* of f(k) is 0-20626, and it occurs when •llowing shows also the neighbouring values :
= r87. The
I
1-86 1-87 1-88
/(*) 0-20625
0-20626 0-20618
0-964 1-024 1-086
It will be seen that while k — T86 is inadmissible as not satisfying (37), = 1'87 is admissible and makes
P = 0-20626 -, ........................... (40)*
"i
D great increase on (18). It may be repeated that k is the ratio of the two sicknesses of the layer (h^/hj), and that by (34)
c2/c3 = 2-588 .................................. (41)*
his defines the form of the upper surface which gives the maximum total ressure when the minimum thickness and the total length are given, and . is the solution of the problem as" proposed. But it must not be overlooked lat it violates the supposition upon which the original equation (5) was >unded. The solution of an accurate equation would probably involve some mnding off of the sharp corners, not greatly affecting the numerical results.
The distance x of the centre of pressure from the narrow end is given by
ic = 0-4262c, .............................. (42)*
iffering very little from the value found in (20). From (10) with use of (38)
e get
F 4c(fr-l)* _ Ac
/*Cr~~&1(l + 2#-3Jfea) (2fc + l)V ............... ( }
F P :/c = l-87,
. ' .F/P = 4-091/ii/c, ........................... (45)*
little less than was found in (21). The maximum total pressure and the
[* The maximum occurs when 4/c2-8/c + l = 0, precisely when (37) begins to hold (of.
\/3 otnote on p. 530); this explains the numerical coincidence. Taking k = l + -^- we have
= -4273c, P/P=4-098&i/c. W. F. S.]
34—2fixed, every admissible variation of h diminishes P. But the ratio c.2/Ci is still at disposal within certain limits, while c-i + C2 (= c) is prescribed.