This very useful instrument consists of two equal rulers each six inches long, joined together by a brass folding joint. These rulers are generally made of boxwood or ivory; and on the face of the instrument, several lines or scales are engraven. Some of these lines or scales proceed from the centre of the joint, and are called sectorial lines, to distinguish them from others which are drawn parallel to the edge of the instrument, similar to those on the common Gunter's scale.

The sectorial lines are drawn twice on the same face of the instrument; that is to say, each line is drawn on both legs. Those on each face are, A scale of equal parts, marked L, A line of chords, marked C,

A line of secants, marked S,

A line of polygons, marked P, or Pol. These sectorial lines are marked on one face of the instrument; and on the other there are the following;

A line of sines, marked S,

A line of tangents, marked T, A line of tangents to a less radius, marked t. This last line is intended to supply the defect of the former, and extends from about 45 to 75 degrees.

The lines of chords, sines, tangents, and secants, but not the line of polygons, are numbered from the centre, and are so disposed as to form equal angles at the centre; and it follows from this, that at whatever distance the sector is opened, the angles which the lines form, will always be respectively equal. The distance, therefore, between 10 and 10, on the two lines marked L, will be equal to the distance of 60 and 60 on the two lines of chords, and also to 90 and 90 on the two lines of sines; etc. at any particular opening of the sector.

Any extent measured with a pair of compasses, from the centre of the joint to any division on the sectorial lines, is called a lateral distance; and any extent taken from a point in a line on the one leg, to the like point on the similar line on the other leg, is called a transverse or parallel distance.

With these remarks, we shall now proceed to explain the use of the sector, in so far as it is likely to be serviceable to mechanics.