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CYLINDER (Gr. KvAwSpos, from KvXivaet...

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Originally appearing in Volume V07, Page 690 of the 1911 Encyclopedia Britannica.
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See also:

CYLINDER (Gr. KvAwSpos, from KvXivaety, to See also:roll) . A cylindrical See also:surface, or briefly a cylinder, is the surface traced out by a See also:line, named the generatrix, which moves parallel to itself and always passes through the circumference of a See also:curve, named the directrix; the name cylinder is also given to the solid contained between such a surface and two parallel planes which intersect a generatrix. A " right cylinder " is the solid traced out by a rectangle which revolves about one of its sides, or the curved surface of this solid; the surface may also be defined as the See also:locus of a line which passes through the circumference of a circle, and is always perpendicular to the See also:plane of the circle. If the moving line be not perpendicular to the plane of the circle, but moves parallel to itself, and always passes through the circumference, it traces an " oblique cylinder." The " See also:axis " of a circular cylinder is the line joining the centres of two circular sections; it is the line through the centre of the directrix parallel to the generators. The characteristic See also:property of all cylindrical surfaces is that the tangent planes are parallel to the axis. They are " developable " surfaces, i.e. they can be applied to a plane surface without crinkling or tearing (see SURFACE). Any See also:section of a cylinder which contains the axis is termed a " See also:principal section "; in the See also:case of the solids this section is a rectangle; in the case of the surfaces, two parallel straight lines. A section of the right cylinder parallel to the See also:base is obviously a circle; any other section, excepting those limited by two 'See also:CYLLENE-See also:CYNEWULF .. generators, is an See also:ellipse. This last proposition may be stated"in the See also:form:—" The orthogonal See also:projection of a circle is an ellipse "; and it permits the ready See also:deduction of many properties of the ellipse from the circle. The section of an oblique cylinder by a plane perpendicular to the principal section, and inclined to the axis at the same See also:angle as the base, is named the " subcontrary section," and is always a circle; any other section is an ellipse.

The See also:

mensuration of the cylinder was worked out by See also:Archimedes, who showed that the See also:volume of any cylinder was equal to the product of the See also:area of the base into the height of the solid, and that the area of the curved surface was equal to that of a rectangle having its sides equal to the circumference of the base; and to the height of the solid. If the base be a circle of See also:radius r, and the height h, the volume is srr2h and the area of the curved surface 2arh. Archimedes also deduced relations between the See also:sphere (q.v.) and See also:cone (q.v.) and the circumscribing cylinder. The name " cylindroid has been given to two different surfaces. Thus it is a cylinder having equal and parallel elliptical bases; i.e. the surface traced out by an ellipse moving parallel to itself so that every point passes along a straight line, or by a line moving parallel to itself and always • passing through the circumference of a fixed ellipse. The name was also given by See also:Arthur See also:Cayley to the conoidal cubic surface which has for its See also:equation z(x2-I-y2) = 2mxy; every point on this surface lies on the line given by the intersection of the planes y=x tan 0, z=m See also:sin 20, for by eliminating 0 we obtain the equation to the surface.

End of Article: CYLINDER (Gr. KvAwSpos, from KvXivaety, to roll)

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