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In a case with the best instruments, the protractor 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 .# 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 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
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,
are used to tranfer 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 thirdfinger;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 uprightas 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 SCTéW. 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 perorm, 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 draning 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 penacts 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. This instrument derives its name from the tenth definition of the third book of Euclid, where he defines the sectorofa 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 instrument, 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 1. 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 45° to 75°. Each pair of these lines (except the line of polygons) is so adjusted as to make equal angles at the centre, and consequently at whatever distance the sector be opened, the angles will be always respectively equal. That is, the distance between 10 and 10 on the line of lines, will be equal to 60 and 60 on the line of chords, 90 and 90 on the line of sines, and 45 and 45 on the line of tangents. Besides the sectoral scales, there are others on each face, placed parallel to the outward edges, and used as those of the common plain scale. There are on the one face, 1. A line of