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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.
172ig. 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