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purposes, some to facilitate operation, and others to promote accuracy.

As almost every artist, whose operations are connected with mathematical designing, furnishes himself with a case of drawing instruments suited to his peculiar purposes, they are fitted up in various modes, some containing more, others, fewer instruments. The smallest collection put into a case, consists of a plane scale, a pair of compasses with a moveable leg, and two spare points, which may be applied occasionally to the compasses; one of these points is to hold ink; the other, a porte crayon, for holding a piece of black-lead pencil. What is called a full pocket case, contains the following instruments.

A pair of large compasses with a moveable point, an ink point, a pencil point, and one for dotting; either of those points may be inserted in the compasses, instead of the moveable leg.

A pair of plain compasses somewhat smaller than those with the moveable leg.

A pair of bow compasses.

A drawing pen with a protracting pin in the upper part.

A sector.

A plain scale.

A protractor.
A parallel rule.

A pencil and screw-driver.*

Large collections are called, magazine cases of instru ments; these generally contain

A pair of six inch compasses with a moveable leg, an ink point, a dotting point, the crayon point, so contrived as to hold a whole pencil, two additional pieces to lengthen occasionally one leg of the compasses, and thereby enable them to measure greater extents, and describe circles of a larger radius.

A pair of hair compasses.

A pair of bow compasses.
A pair of triangular compasses.

In a case with the best instruments, the protrac tor and plain scale are always combined. The instruments in 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 effect 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 protractor.

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 dis

tance.

A protractor and parallèl 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.

steel. The difference in the texture and pores of the two metals causes the parts to adhere less together, diminishes the wear, and promotes uniformity in their motion. The truth of the work is ascertained by the smoothness and equality of the motion at the joint, for all shake and irregularity is a certain sign of imperfection. The points should be of steel, so tempered, as neither to be easily bent or blunted; not too fine and tapering, and yet meeting closely when the compasses are shut.

As an instrument of art, compasses are so well known, that it would be superfluous to enumerate the various uses; suffice it then to say, that they are used to transfer small distances, measure given spaces, and describe arches and circles.

If the arch or circle is to be described obscurely, the steel points are best adapted to the purpose; if it is to be in ink or black lead, either the drawing pen, or crayon points are to be used.

To use a pair of compasses. Place the thumb and middle finger of the right hand in the opposite hollows in the shanks of the compasses, then press the compasses, and the legs will open a little way; this being done, push the innermost leg, with the third finger, elevating, at the same time, the furthermost, with the nail of the middle finger, till the compasses are sufficiently opened to receive the middle and third finger; they may then be extended at pleasure, by pushing the furthermost leg outwards with the middle, or pressing it inwards with the four finger. In describing circles, or arches, set one foot of the compasses on the centre, and then roll the head of the compasses between the middle and four finger, the other point pressing at the same time upon the paper. They should be held as upright as possible, and care should be taken not to press forcibly upon them,but rather to let them act by their own weight; the legs should never be so far extended, as to form

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 bon 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.

Of 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, be made to pass through the blades. To use the drawing pen, first feed it 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 directions 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 parallel 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.

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