SECTOR

(Lat.) In Geometry, the sector o/ a aVc/e is a portion of the area of the circle bounded by two radii and the intercepted arc. Sectors of different circles are said to be sitnilar when the sides or radii include equal angles. The area of a sector is equal to that of a triangle whose base is equal to the length of the contained arc, and altitude equal to the radius of the circle. Sector. A mathematical instrument, of considerable use in making diagrams, laying down plans, . Its principal advantage consists in the facility with which it gives a graphical determination of proportional quantities; and hence it is called by the French the compa qf proportion. The instrument consists of two rulers (generally of bra or ivory), representing the radii of a circular arc, and moveable round a joint, the middle of which forms the centre of the circle. From this centre there are drawn on the faces of the rulers various scales; the choice of which, and the order of their arrangement, may be determined by a consideration of the uses for which the instrument is chiefly intended. The scales usually put on sectors are of two kinds, — single and double; that is to say, such as are drawn only on one of the limbs, and such as are drawn on both limbs. The first kind, however (comprising, for example, a line of inches, of chords, sines, logarithms, .), are not peculiar to the sector, but are merely placed there for convenience, and may be used whether the instrument is shut or open. Of the lines repeated on both limbs the principal are the following: —!. A line of equal parts, by which, with a pair of compa es, we are enabled, on the principle that similar triangles have their homologous sides proportional, to find a third proportional to two given lines, a fourth proportional to three given lines, to diminish a line in any given proportion, . 2. A scale of chords, which enables us to protract an angle of any given number of degrees, to find the degrees which any given angle contains, to cut off an arc of any magnitude from the circumference of a given circle, . 3. Scales of sines, tangents, and secants, whereby the lengths of those trigonometrical lines corresponding to a given arc of a circle of any radius are determined. 4. A line of polygons, whereby the proportional length of the side of any regular polygon (of not more than twelve sidesj to the radius of the circumscribing circle is found. The sector may be used in trigonometry for obtaining a rough solution of all the cases of right-angled plane IOJ.9 SECU RIFE IIS. triangles; and it is also conveniently applied to the construction of various geometrical problems. For a description of its different uses, see Robertson's Treatise of such Mathematical Instruments as are usually put into a Portable Case. Sector. In Astronomy, an instrument constructed for the purpose of determining with great accuracy the zenith distances of stars pa ing within a fe w degrees of the zenith, where the effect of refraction is small. See Zenith Sector. SECULAK EQUATION, [s. 1112]