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See also:SPHEROID (Gr. c4aipa-etbis, like a See also:sphere) , a solid resembling, but not identical with, a See also:sphere in shape . In See also:geometry; the word is confined to the figures generated by an See also:ellipse revolving about a See also:diameter . If the See also:axis of revolution be the See also:major axis of the ellipse, the See also:spheroid is " prolate "; if the See also:minor axis, " oblate "; if any other, " universal." If the generating ellipse has for its See also:equation x2/See also:a2+y2/b2=1, and revolves about the major axis, i.e. the axis of x, the See also:volume of the solid generated is Irab2, and its See also:surface is 21r1 b2+(able) See also:sin-le{, where e denotes the eccentricity . If the See also:curve revolve about the minor axis, the volume is tra2b, and the surface is a{2a2+ (b2/e) See also:log (1 +e) /(I —e) 1 . The figure of the See also:earth is frequently referred to as an oblate spheroid; this, however, is hardly correct, for the See also:geoid has three unequal axes . The Cartesian equation to a spheroid assumes the forms x2/a2+(y2+z2)/b2=1, for the prolate, and (x2+z2)/a2+y2/b2=1, for the oblate, the origin being the centre and the co-See also:ordinate axes the axes of the See also:original ellipse, x2/a?+y2/b2=1, and the See also:line perpendicular to the See also:plane containing them . In physics, the See also:term " spheroidal See also:state " is given to the following phenomenon . If drops of a liquid be placed on a highly heated surface, for example, the See also:top of a See also:stove, the liquid forms a number of tremulous globules which continually circulate internally . There is no visible boiling, although the globule diminishes slowly in See also:size . The theory of the experiment is that the liquid is surrounded by an elastic envelope of its vapour which acts, as it were, as a See also:cushion preventing actual contact of the drop with the See also:plate . On the formation of a similar protective cushion of vapour depends the See also:immunity of such experiments as plunging a See also:hand into a See also:bath of molten See also:metal . |
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