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Full text of "Scientific Papers - Vi"

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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.