In a case with the best instruments, the protractor and plain scale are always combined. The instrumentsin most general use are those of six inches; instruments are seldom made longer, but often smaller. Those of six inches are, however, to be preferred, in general, before any other size; they will effeet all that can be performed with the shortest ones, while, at the same time, they are better adapted to large work.

OF DRAWING COMPASSES.

Compasses are made either of silver or brass, but with steel points. The joints should always be framed of different substances; thus, one side, or part, should be of silver or brass, and the other of

A sector.

A parallel rule.

A protrac or.

A pair of proportional compasses, either with or without an adjusting screw.

A pair of wholes and halves.

Two drawing pens, and a pointril.

A pair of small hair compasses, with a head similar to those of the bow compasses.

A knife, a file, key, and screw-driver or the compasses in one piece.

A small set of fine water colours.

To these some of the following instruments are often added. A pair of beam compasses.

A pair of gunners callipers.

A pair of elliptical compasses.

A pair of spiral ditto.

A pair of perspective compasses.

A pair of compasses with a micrometer screw.

A rule for drawing lines, tending to a centre at a great

distance.

A protractor and parallel rule.

One or more parallel rules.

A pantographer, or Pentagraph.

A pair of sectoral compasses, forming, at the same time, a pair of beam and calliper compasses.

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If the arch or circle is to be described the steel points are best adapted to the price. I it is to be in ink or black seat aer de Cang pen, or crayon pics are to be used

To use a pair of computer. Place the cum am middle finger of the right mata de Toate pr lows in the shanks of the compass der rs t compasses, and the es mi sen i ime vry : 1s being done, push the crems BV de tr finger, elevating, at the same time be indeas with the nail cf the made inger all the compas ses are sufficiently opened to recere tie mode ant third finger; they may there extender & DESTI by pushing the furtermost jeg middle, or pressing it inward In describing circles, or artes set compasses on the centre. and the the compasses between the middle and four Im the other point pressing at the size alle 1 YOU DE paper. They should be red as vrat a 90 deand care should be taxes antto press formity them, but rather to let them as of the owl Tee the legs should never be

an obtuse angle with the paper or plane, on which they are used.

The ink and crayon points have a joint just under that part which fits into the compasses, by this they may be always so placed as to be set nearly perpendicular to the paper; the end of the shank of the best compasses is framed so as to form a strong spring, to bind firmly the moveable points, and prevent them from shaking. This is found to be a more effectual method than that by a screw.

Two additional pieces, are often applied to these compasses; these, by lengthening the leg, enable them to strike larger circles, or measure greater extents, than they would otherwise perform, and that without the inconveniences attending longer compasses. When compasses are furnished with this additional piece, the moveable leg has a joint that it may be placed perpendicular to the paper.

The bow compasses, are a small pair, usually with a point for ink; they are used to describe small arches or circles, which they do much more conveniently than large compasses, not only on account of their size, but also from the shape of the head, which rolls with great ease between the fingers.

f the drawing pen and protracting pin. The pen part of this instrument is used to draw strait lines; it consists of two blades with steel points fixed to a handle, the blades are so bent, that the ends of the steel points meet, and yet leave a sufficient cavity for the ink; the blades may be opened more or less by a screw, and, being properly set, will draw a line of any assigned thickness. One of the blades is framed with a joint, that the points may be separated, and thus cleaned more conveniently; a small quantity only of ink should be put at one time into the drawing pen, and this should be placed in the cavity, between the blades, by a common pen, or feeder; the drawing pen acts

better, if the pen, by which the ink is inserted, he made to pass through the blades. To use the drawing pen, first feed t with ink, then regulate it to the thickness of the required line by the screw. In drawing lines, incline the pen a small degree, taking care, however, that the edges of both the blades touch the paper, keeping the pen close to the rule and in the same direction during the whole operation: the blades should always be wiped very clean, before the pen is put away.

These directio's are equally applicable to the ink point of the compasses, only observing, that when an arch or circle is to be described, of more than an inch radius, the point should be so bent, that the blades of the pen may be nearly perpendicular to the paper, and both of them touch it at the same time.

The protracting pin, is only a short piece of steel wire, with a very fine point, fixed at one end of the upper part of the handle of the drawing pen. It is used to mark the intersection of lines, or to set off divisions from the plotting scale, and protractor.

OF THE SECTOR.

Amidst the variety of mathematical instruments that have been contrived to facilitate the art of drawing, there is none so extensive in its use, or of such general application as the sector. It is an universal scale, uniting, as it were angles and pa rallel lines, the rule and the compass, which are the only means that geometry makes use of for measuring, whether in speculation or practice. The real inventor of this valuable instrument is unknown; yet of so much merit has the invention appeared, that it was claimed by Galileo, and disputed by nations.

This instrument derives its name from the tenth definition of the third book of Euclid, where he defines the sector of a circle. It is formed of two equal rules called legs; these legs are moveable about the centre of a joint, and will; consequently, by their different openings, represent every possible variety of plane angles. The distance of the extremities of these rules are the subtenses or chords, or the arches they describe.

Sectors are made of different sizes, but their length is usually denominated from the length of the legs when the sector is shut. Thus a sector of six inches, when the legs are close together, forms a rule of 12 inches when opened; and a foot sector is two feet long, when opened to its greatest extent. In describing the lines usually placed on this inst ument, I refer to those commonly laid down on the best six-inch brass sectors. But as the principles are the same in all, and the differences little more than in the number of subdivisions, it is to be presumed that no difficulty will occur in the application of what is here said to sectors of a larger radius.

The scales, or lines graduated upon the faces of the instrument, and which are to be used as sectoral lines, proceed from the centre; and are, 1. Two scales of equal parts, one on each leg, marked LIN. or L. Each of these scales, from the great extensiveness of its use, is called the line of lines. 2. Two lines of chords, marked CHO. or c. 3. Two lines of secants marked SEC. or s. A line of polygons, marked POL. Upon the other face, the sectoral lines are, 1. Two lines of sines, marked sin or s. 2. Two lines of tangents, marked tan. 3. Between the lines of tangents and sines, there is another line of tangents to a lesser radius to supply the defect of the former, and extending from 450 to 75°.