SECTOR, in Geometry, is a part of a circle comprehended between two radii and an arc of the circle.

Sector is also a mathematical instrument, of use in finding the proportion between quantities of the same kind; as between lines and lines, surfaces and surfaces, &c. whence the French call it the compass of proportion. The great advantage of the sector above the common scales is, that it is made so as to fit all radii and all scales. By the lines of chords, sines, &c. upon the sector, we have lines of chords, sines, &c. to any radius between the length and breadth of the sector when open.

The sector is supposed to have been invented by Guido Baldo, or Ubaldo, about the year 1568. The first printed account of it was in 1584, by Gaspar Mordente, at Antwerp, who says that his brother, Fabricius Mordente, invented it in 1554. Treatises on its use have been written by Daniel Specle at Strasburg in 1589; also by Thomas Hood at London in 1598, and by Lewin Hulse at Frankfort-on-the-Maine in 1603, who says that it was invented long before by Justus Byrgius. But the honour of the invention was claimed by Galileo, who wrote on its use in 1607, and by Balthasar Capra of Milan. There are also treatises on it by our countrymen Gunter, Forster, and others.

Before the invention of logarithms, practical men were more easily contented with approximate solutions than they are at present. Now, however, any question that can be resolved by the sector can be about as readily answered by the smallest table of logarithms, and with perfect certainty, as far as the table extends. Hence it is that the sector is not much used, although it is commonly reckoned one of a complete set of mathematical instruments.

For treatises on its use, see Bion on Mathematical Instruments, translated by Stone; Robertson’s Treatise on Mathematical Instruments; and Adams’s Geometrical Essays.

Any one possessing a sector will easily understand its

’ This, however, is denied by Johnson, who affirms that the islanders of all degrees, whether of rank or understanding, universally admit it; except the ministers, who, according to him, reject it, in consequence of a system, against conviction. He affirms, too, that in 1773, there was in the Hebrides a second-sighted gentleman, who complained of the terrors to which he was exposed.[7:20:72] theory and use from the 14th problem of the fifth section of our treatise on GeoMEtry, where it is taught how to find a fourth proportional to three given lines.

Sector of a Sphere is the solid generated by the revolution of the sector of a circle about one of its radii; the other radius describing the surface of a cone, and the circular arc a circular portion of the surface of the sphere of the same radius. Hence the spherical sector consists of a right cone, and of a segment of the sphere having the same common base with the cone. The solid content will therefore be found by multiplying the base or spherical surface by the radius of the sphere, and taking one third of the product.

Sector of an Ellipse or Hyperbola, is the space contained by any two semidiameters, and the arc of the curve between them.

Astronomical Sector, or Equatorial Sector, an instrument for taking the difference of right ascensions and declinations of such stars as, on account of their great difference of declinations, will not pass through a fixed telescope. There is an instrument of this kind in the observatory at Greenwich, and it is described in Vince’s Practical Astronomy.

Zenith Sector, an instrument employed in extensive trigonometrical surveys. Its use is to determine with great accuracy the zenith distances of stars whose declinations differ but little from the latitude of an observer. A very fine instrument of this kind, constructed by Ramsden, is now using in the trigonometrical survey of Britain, and is fully described and figured in the Transactions of the Royal Society of London for 1803.