The Philosophical magazine; a journal of theoretical, experimental and applied physics . s the same, and the principal ordinates ofwhich are a maximum and a minimum respectively. Table III. e. «i/Y. X/«i. X/Y. 0. /3,/Y. X//3,. X/Y. o u 1000 1-571 1-571 180 1000 0-000 0-000 10 1008 1 -567 1579 190 0-992 0008 0-008 30 1-074 1-527 1-640 210 0-931 0-073 0-068 45 1184 1-458 1-726 225 0844 0-179 0151 60 1-372 1-333 1-829 240 0-729 0-366 0-2(i7 80 1-725 1-036 1-787 260 0-580 0-852 0 494 90 1-810 0-834 1-509 270 0-552 1-200 0-663 100 ? 1-725 0-630 1-086 280 0-580 1-486 0-862 120 1-372 0-316 0-433 300
The Philosophical magazine; a journal of theoretical, experimental and applied physics . s the same, and the principal ordinates ofwhich are a maximum and a minimum respectively. Table III. e. «i/Y. X/«i. X/Y. 0. /3,/Y. X//3,. X/Y. o u 1000 1-571 1-571 180 1000 0-000 0-000 10 1008 1 -567 1579 190 0-992 0008 0-008 30 1-074 1-527 1-640 210 0-931 0-073 0-068 45 1184 1-458 1-726 225 0844 0-179 0151 60 1-372 1-333 1-829 240 0-729 0-366 0-2(i7 80 1-725 1-036 1-787 260 0-580 0-852 0 494 90 1-810 0-834 1-509 270 0-552 1-200 0-663 100 ? 1-725 0-630 1-086 280 0-580 1-486 0-862 120 1-372 0-316 0-433 300 0-729 1-671 1-218 135 1-184 0-166 0-196 315 0-844 1-647 1-391 150 1074 0-071 0-076 330 0-931 1-607 1-495 170 1-008 0-008 0-008 350 0-992 1-576 1-563 180 1000 0000 0-000 360 1-000 1-571 1-571 The march of the functions is shown by means of thecurves in figs. III., IV., and V. Thus, if/_> be the length of theprincipal ordinate (whether it be a maximum or a minimum),fig. III. shows the relation between p/Y and 6, fig. IV. thatbetween X/p and 6, and fig. V. that between X/Y and iSO 210 240 »70 300 330 0 30 Fig. I. {x=9, r/=.p,y By plottuig the values of X/Y we find that the maximumoccurs when ^=70°. The corresponding value of i is 54:°-15, 44 Mr. A. W. Riickcr on the Critical Mean Curvature and this gives «/Y=l-545, X/« = l-2044, X/Y=1-8G0. Tf, then, we suppose the rings to approach to or recede fromeach other, and the volume and diameter of the fihn to be atthe same time idtered so that it ahvays satisfies the conditionsof critical mean curvature, it will undergo the followingchanges of form. Starting with the rings in contact, and supposing that asthey separate the film has a slight bulge, it will first be anodoid, and the length and principal diameter will increasetogether. When the length is a little more than one and ahalf (1509) diameters of the rings the film is spherical, andthe principal diameter is then a maximum (a/Y=l*810). Asthe diameter begins to decreas
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