SECTOR (drawing instrument), an instrument invented by Gunter, which has the appearance of a small carpenter's rule, marked with scales in every part ; the greater number of these scales not being laid down parallel to the edges of the rule, but converging towards the pivot oar which the moving arm of the rule turns while the instrument is opened. Only these converging scales properly belong to the sector ; the others are merely laid down for convenience on such blank spaces as are left by the converging or sectorial scales.
The sector is a large number of pairs of compasses packed up into one, and most explanations of the instrument attempt to describe them all in one. It will, however, be more convenient to separate one pair of compasses from the rest, and to describe its use. Each piece of the ruler is marked with the same scales. Take one of these scales, o A, and that which corresponds to it, on; then A o n is a pair of coin passes which can be opened or shut at pleasure. Suppose two scales, Fay of chords, to be laid down on 0A and o s, which are chords of 90°, o P and o q being radii, or chords of 60°. If a P be four inches, we
have then before us two scales of chords with the radius of four inches actually laid down, and any chords might be taken off them as from a common sole: for instance, if the marks of 35° be at c and D, then either o C or o n is the chord of 35° to a radius of four inches. But suppose it required to find the chord of 35°, not to a radius of four inches, but to one of inches. We know that 4 : 3.61 : : ch. 35° (rad. 4) : ch. 35° (rad. 3.61); and the fourth term of this proportion is to be found. Now this may be done with sufficient accuracy, and without any drawing, as follows : Take a common pair of compasses, and open them to 3.61 on a sub divided scale of inches. Then open the sector until the points of the compasses are made to fall on P and Q, which, if the sector open rather easily, may be done very quickly. We have then PQ = inches, and c D is the chord of 35' to that radium ; for by similar triangles