The London, Edinburgh and Dublin philosophical magazine and journal of science . a2 (21) a2 — cti x2(a2 — a{) by means of which the curves may be traced tentatively. If we retain the normal PQ, as we may conveniently doin using Boys method, we have the simpler expression ^ + -2-. . (22) 1 1 <™2/0 2 2 4T a2 — ai When the radius CP of the section is very small in v. comparison with the radius of the ring OC, the conditions areapproximately satisfied by a circular form. We write CP = ry Revolving Liquid under Capillary Force. 167 OC=a, PCX = 0. Then, r being supposed constant, theprincipal rad
The London, Edinburgh and Dublin philosophical magazine and journal of science . a2 (21) a2 — cti x2(a2 — a{) by means of which the curves may be traced tentatively. If we retain the normal PQ, as we may conveniently doin using Boys method, we have the simpler expression ^ + -2-. . (22) 1 1 <™2/0 2 2 4T a2 — ai When the radius CP of the section is very small in v. comparison with the radius of the ring OC, the conditions areapproximately satisfied by a circular form. We write CP = ry Revolving Liquid under Capillary Force. 167 OC=a, PCX = 0. Then, r being supposed constant, theprincipal radii of curvature are r and a sec6 + r, so that theequation of equilibrium is Po 1 cos# to2 , >..„ /oox £? = -+ — ^ - ^(a + rcos^)2, . (23) 1 r a + r cos 6 21 v 7 v 7 in which p0 should be constant as 6 varies. In this cos0 If r A 3r\ r 0/1 r2 ozl \ S+F^T* = «t -ra+V1 + ^-2)COS^^COs2^^2COS^N (l+>s^=l-£+JcoS^£2cos2^. Thus approximatelya»o « r , r2 \ „/, 3r2 < +«{-£-£»}+•»»•»• (24) The term in cos 6 will vanish if we take co so that ^-K1-?) <» The coefficient of cos 26 then becomes - ^ + cubes of - (26) If we are content to neglect r/a in comparison with unity,the condition of equilibrium is satisfied by the circular form;otherwise there is an inequality of pressure of this order inthe term proportional to cos 2
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
