draw straight lines; it consists of two blade's 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 the feeder; the drawing pen acts better, if the feeder, or 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 while operating: the blades should be wiped clean after use.*

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 k, 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.

The feeder, fig. O, plate 1, is a thin flat piece of metal; it sometimes forms one end of a cap to fit on a pencil, or it is framed at the top of the tracing point, as in the figure. It serves to place the ink between the blades of the drawing pens, or to pass be

* For unequal and regular parallel lines, the double drawing pen, W, is extremely useful. EDIT.

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tween them when the ink does not flow freely. The tracing point, or pointrel, is a pointed piece of steel fitted to a brass handle; it is used to draw obscure. lines, or to trace the out-lines of a drawing or print, when an exact copy is required, an article that will be fully explained in the course of this work; it forms the bottom part of the feeder O.

Of triangular compasses. A pair of these are represented at fig. N, plate 1. They consist of a pair of compasses, to whose head a joint and socket is fitted for the reception of a third leg, which may be moved in almost every direction.

These compasses, though exceedingly useful, are but little known; they are very serviceable in copying all kinds of drawings, as from two fixed points they will always ascertain the exact position of a third point.

Fig. 12, plate 3, represents another kind, which has some advantages over the preceding. 1. That there are many situations so oblique, that the third point cannot be ascertained by the former, though it may by these. 2. It extends much further than the other, in proportion to its size. 3. The points are in all positions perpendicular to the paper.

Of wholes and halves, fig. R, plate 1. A name given to these compasses, because that when the longer legs are opened to any given line, the shorter ones will be opened to the half of that line; being always a bisection.

Fig. V, represents a new pair of very curious and portable compasses, which may be considered as a case of instruments in itself. The ink and pencil points slide into the legs by spring sockets at a; the ink, or pencil point, is readily placed, by only sliding either out of the socket, reversing it, and sliding in the plain point in its stead.

Proportional compasses. These compasses are of two kinds, one plain, represented fig. A, plate 1; the other with an adjusting screw, of which there are two views, one edgeways, fig. 8, plate 3, the other in the

front, fig. 7, plate 3: the principle on which they both act is exactly the same; those with an adjusting screw are more easily set to any given division or line, and are also more firmly fixed, when adjusted.

There is a groove in each shank of these compasses, and the centre is moveable, being constructed to slide with regularity in these grooves, and when properly placed, is fixed by a nut and screw; on one side of these grooves are placed two scales, one for lines, the other for circles. By the scale of lines, a right line may be divided into any number of equal parts expressed on the scale. By the scale for circles, a regular polygon may be inscribed in a circle, provided the sides do not exceed the numbers on the scale. Sometimes are added a scale for superficies and a scale for solids.

To divide a given line into a proposed number (11) equal parts. 1. Shut the compasses. 2. Unscrew the milled nut, and move the slider until the line across it coincides with the 11th division on the scale. 3. Tighten the screw, that the slider may be immoveable. 4. Open the compasses, so that the longer points may take in exactly the given line, and the shorter will give youth of that line.

To inscribe in a circle aregular polygon of 12 sides. 1. Shut the compasses. 2. Unscrew the inilled nut, and set the division on the slider to coincide with the 12th division on the scale of circles. 3. Fasten the

milled nut. 4. Open the compasses, so that the longer legs may take the radius, and the distance between the shorter legs will be the side of the required polygon.

To use the proportional compasses with an adjusting screw. The application being exactly the same as the simple one, we have nothing more to describe than the use and advantage of the adjusting screw. 1. Shut the legs close, slacken the screws of the nuts g and f; move the nuts and slider k to the division wanted, as near as can be readily done by the hand,

and screw fast the nut f: then, by turning the ad juster h, the mark on the slider k may be brought exactly to the division: screw fast the nut g. 2. Open the compasses; gently lift the end e of the screw of the nut fout of the hole in the bottom of the nut g; move the beam round its pillar a, and slip the point e into the hole in the pin n, which is fixed to the under leg; slacken the screw of the nut f; take the given line between the longer points of the compasses, and screw fast the nut f: then may the shorter points of the compasses be used, without any danger of the legs changing their position; this being one of the inconveniences that attended the proportional compasses, before this ingenious contrivance.

Fig. 10, plate3, represents a pair of beam compasses; they are used for taking off and transferring divisions from a diagonal or nonius scale, describing large arches, and bisecting lines or arches. It is the instrument upon which Mr. Bird principally depended, in dividing those instruments, whose accuracy has so much contributed to the progress of astronomy. These compasses consist of a long beam made of brass or wood, furnished with two brass boxes, the one fixed at the end, the other sliding along the beam, to any part of which it may be firmly fixed by the screw P. An adjusting screw and micrometer are adapted to the box A at the end of the beam; by these, the point connected therewith may be moved with extreme regularity and exactness, even less than the thousandth part of an inch.

Fig. 13, plate 3, is a small pair of beam compasses, with a micrometer and adjusting screw, for accurately ascertaining and laying down small distances, to the 1000th part of an inch or less.

Fig. 11, plate 3, represents a scale of equal parts, constructed by Mr. Sisson; that figured here contains two scales, one of three chains, the other of four chains in an inch, being those most frequently used; each of these is divided into 10 links, which

are again subdivided by a nonius into single links; the index carries the protracting pin for setting off the lengths of the several station lines on the plan. By means of an instrument of this kind, the length of a station line may be laid down on paper with as much exactness as it can be measured on land.

OF PARALLEL RULES.

Parallel lines occur so continually in every species of mathematical drawing, that it is no wonder so many instruments have been contrived to delineate them with more expedition than could be effected by the general geometrical methods: of the various contrivances for this purpose, the following are those most approved.

1. The common parallel rule, fig. A, plate 2. This consists of two straight rules, which are connected together, and always maintained in a parallel position by the two equal and parallel bars, which move very freely on their centres, or rivets, by which they are fastened to the straight rules.

2. The double parallel rule, fig. B, plate 2. This instrument is constructed exactly upon the same principles as the foregoing, but with this advantage, that in using it, the moveable rule may always be so placed, that its ends may be exactly over, or even with, the ends of the fixed rule, whereas in the former kind, they are always shifting away from the ends of the fixed rule.

This instrument consists of two equal flat rules, and a middle piece; they are connected together by four brass bars, the ends of two bars are rivetted on the middle line of one of the straight rules; the ends of the other two bars are rivetted on the middle line of the other straight rule; the other ends of the brass bars are taken two and two, and rivetted on the middle piece, as is evident from the figure; it would be