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Full text of "Scientific Papers - Vi"

1914] UNDER CAPILLARY FORCE • 259 In terms of y and oo from (7) , ~ dx /( i^a? _ ^Vl ' . / -V2 - tf ( fl. - + 1 - £1 H V ( V a- / j or if we write «2/a2=l-2, ................................. (9) 1 -Qg adz ~ ~z . V{1 + 2 (1 - z) H - £ (1 - z when we neglect higher powers of fl than O2. Reverting to as, we find for the integral of (10) ............ CU> no constant being added since y — 0 when as — a. If we stop* at H, we have _i ~ representing an ellipse whose minor axis OB is a (1 — O). When fl2 is retained, 0£ = (l-a + 02)a ......................... (13) The approximation in powers of ft could of course be continued if desired. So long as JQ < 1, j30 is positive and the (equal) curvatures at B are convex. When H = 1, j)0 == 0 and the surface at B is flat. In this case (8) gives or if we set x — a sin <f>, Here as = a corresponds to <jf> = ^TT, and as — 0 corresponds to <£ = 0. Hence (16) The integral in (16) may be expressed in "terms of gamma functions and we get (17) When fl > 1, the curvature at B is concave andp0 is negative, as is quite permissible. 17—2ig. 1 represents a section by a plane through the axis Oy, 0 being the point where the axis meets the equatorial plane. One of the principal