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Full text of "Scientific Papers - Vi"

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1914] UNDER CAPILLARY FORCE 261 Another case of special interest is the last figure reaching the axis of symmetry at all, which occurs at the point as = 0. We do not know beforehand to what value of H this corresponds, and curves must be drawn tentatively. It appears that O — 2*4 approximately, and the values of y obtained from this curve are given in columns 3 and 6 of the table. Fig. (2)*. rig. (i). Fig. (2). ± X ±y ±y' ± X ±y ±y' O'O 2-16 o-oo 2-6 2-06 0-75 0-2 2-16 o-oi 2-8 2-03 0-83 0'4 2-16 0-03 3-0 1-99 0-90 0-6 2-16 0-06 ; 3-2 1-95 0-95 0-8 2-16 o-io 3-4 1-89 0-99 1-0 2'15 0'14 3-6 1-81 1-01 1-2 2-15 0-20 3-8 1-72 1-02 1-4 2-15 0-27 4-0 1-61 1-00 1-6 2-15 0-34 4-2 1-49 0-98 1-8 2-14 0-42 4-4 1-32 0'89 2-0 2-12 0-50 4'6 I'll 0'78 2-2 2-11 0-58 , 4-8 0-80 0-67 2-4 2-09 0-65 4-9 0-59 0-41 5-0 o-oo o-oo There is a little difficulty in drawing the curve through the point of zero curvature. I found it best to begin at both ends (oc = 0, y = 0) and (cc = 5, y = 0) with an assumed value of XI and examine whether the two parts could be made to fit. * [1916. These figures were omitted in the original memoir.]ts of x equal to %2; thus arriving in succession at the points for which x = 4*8, 4'6, 4'4, &c. For these portions we employ the mean curvatures, corresponding to x — 4'9, 4'7, &c. calculated from (19). It is convenient to use squared paper and fair results may be obtained with the ordinary ruler and compasses. There is no need actually to draw the normals. But for such work the procedure recommended by Boys* offers great advantages. The ruler and compasses are replaced by a straight scale divided upon, a strip of semi-transparent celluloid. At one point on the scale a fine pencil point protrudes through a small hole and describes the diminutive circular arc. Another point of the scale at the required distance occupies the centre of the circle and is held temporarily at rest with the aid of a small brass tripod standing on sharp needle points. After each step the celluloid is held firmly to the paper and the tripod is moved to the point of the scale required to give the next value of the curvature. The ordinates of the curve so drawn are given in the second and fifth columns of the annexed table. It will be seen that from x — 0 to x = 2 the curve is very flat. Fig. (1).