CYG'NUS (Lat., from Gk. Iikvos, Ky•nos, the swan). A constellation in the Northern Hemisphere. between Lyra and Cassiopeia. eral stars in this constellation have received the particular attention of astronomers. See STARS. CYLINDER (OF. cilindre, Fr. rylindrc, from Lat. cylind•us, from Gk. ktlAtvdpoc, kylindros, roller, from KuMpderv, kylindcin, kylicin, to roll). A surface generated by a line (the generatrix) which moves parallel to a fixed line and touches a given curve (the directrix) is called a cylindrical surface. The space inclosed by it cylindrical surface is called a cylindrical space. The portion of a cylindrical space limited by two parallel planes cutting all the elements of the cylindrical surface is called a cylinder. If the directrix is a circle. the cylinder is called a circular cylinder: if the directrix is an ellipse, the evlinder is called an elliptic cylinder, and so on. If the elements (positions of the era trix ) a re dicular to the plane of the directrix, the inder is called a right cylinder, otherwise it is called oblique. If it rectangle be revolved about one of its sides, a cylinder of tion, or a right lar cylinder, is formed. The plane figures which form the ends of it cylinder are called its bases, and these are always congruent. The perpendicular distance between the bases is called the altitude. The lateral area of airy cylinder, expressed in surface units, is the product of the number of linear units in the perimeter of a section perpendicular to the ele ments (right section) and the number of linear units in an element.* The number of unit, of
volume of a cylinder is equal to the product ut the number of square units of the base and the number of linear units in, the altitude of the cylinder.
A ItioRT CIRCULAR erLINDEIL AN OBLIQUE CVLINDER.
lower and upper bases ; E. an ; R, aright a, the section.
A cylindrical surface may be considered as a conical surface (see CoNE) with the vertex at infinity. Hence, plane sections of the cylindrical space of a right circular cylinder lead to the so called conic ,ections, in particular. to the ellipse. If V 77 volume, C .7 curved surface, B E base, A E- total area of surfaces. a E altitude, radius of the base (or of the inscribed sphere) and Ii E the radius of the circumscribed sphere of a right circular cylinder, then V = C = 27rra, A = 2rra = 2irr + a), R = 2 4 5 4 line volume of asector of a cylinder of arc k° is 360 if the arc is given in radian measure. as a radians, the volume is If a plane parallel to the axis colts of a segment. the corresponding arc cut from the base being k°, the volume of k the cylindrical segment is V __.— (JSO 2 sin k°) , or if k° = a radians, (n— sin n).