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Pentagraph

figure, levers, fulcrum, fig, tracer, tubes, rulers and figures

PENTAGRAPH, an instrument where- by designs of any kind may be copied in what proportion you please, without be ing skilled in drawing. (Plate Penta graph, fig. 1), is a plan of a pentagraph, and (fig. 2 and 3), part of the same on a larger scale.

The pentagraph is made of brass, and consists of four levers A B D E, the two longest A B, are together at their ends, the other two, D E, are also jointed together at one of their ends, and to the levers A B at the others. In this manner the instrument always forms a parallelo gram, aAa =eEeandaBe=aDe; f, g, and h, are three tubes upon the le vers, two of which, f, g, slide along upon their respective levers, and can be fixed at any point by screws (one of these tubes is shewn separately in fig. 3), any one of these tubes is adapted to receive either a fulcrum or fixed centre, round which the whole instrument turns a blunt point or tracer, to pass ever the original design, which is to be copied ; or a crayon to draw the figure, or copy of the original design ; these three points must be al ways in one right line, and by the con struction of the levers,-if they are once set in a line, they will continue in it through any of its motions.

The proportion in which it wiil reduce any figure will be easily calculated from the same principles as the lever ; that the magnitude of the figures described by either of the points, will be in the same proportion to each other, as the distances of those points from the fulcrum, thus if the point/ be the fulcrum, and if the dis tance from f to g be half the distance from f to 11, the size of the figure describ ed by the point g will be half the size of the figure described at the same time by the point h. The fulcrum, as we have said before, can be changed, as also the pencil and the tracer, and any of the three can he applied to either of the tubes upon the levers, if the tracer is placed in the tube Is, the and the fulcrum at f, any figure described by the tracer 11, will be exactly copied one half the size by the pencil at g, and if on the contrary the pencil is placed at h, and the tracer at g, the figure drawn by the pencil will be twice the size of the original traced at g.

When the fulcrum is placed between the two points at g, the figures described by each point will be inverted with re spect to each other, though the same principle applies, that the magnitude of the figures will bear the same proportion to each other, as the distances of their tracing point from the fulcrum bear to each other. This last position of the in

strument is seldom used on account of the figure being inverted, except when the figures traced and copied are equal to each other, or nearly so, as the first posi tion will not allow of that.

It will be easily seen that by the sliding motion of the tubes, g andl, the propor tion between the three may be varied in any degree, and for this purpose the le vers are engraved, and divisions made to set the tubes by, so as to reduce it in any proportion, and at the same time put the three points in the same right line, other wise the figures will be strangely distort ed ; n n n is a silk thread, which the ope rator hooks round his fore finger, by pull ing this he raises up the crayon, g, so that it will not mark ; each joint of the instru ment is formed by a short axis, i, (fig. 2), made fast and moving with one lever, k, it has pivots at its ends, working in a small cock, 1, screwed to the upper side of the other lever : beneath each joint a small tube, is screwed, its upper end re ceives the lower pivot of the axis 1, and in the lower part a small spindle, n, is fitted, which has a castor at the bottom to support the weight of the instrument, by the turning of the spindle, n, the cas tor will run in any direction. One of these castors is also fixed at the outer end of the levers, A and B, as well as beneath each joint. Care should be taken that the table, upon which the instrument is used, is a perfect plane, otherwise errors will arise from the tracer or crayon being sometimes thrown out of the perpendicu lar, and it is for the same reason that the levers are jointed with an axis, as explain ed before.

Fig. 4, Plate Pentagraph, is the com mon parallel ruler, A B are two rulers connected by two bars C I), which are of equal lengths, and the distance between the pins by which the levers C D are fixed to the rulers are the same distance from each other in both rulers ; by this means it is easily seen, that the two rulers, A B, will always move parallel to each other.

Fig. 5. is another ruler differing from the other in being double ; the advantage of it over fig. 4, is, that the two rulers A B can be moved parallel to each other without sliding endways, as the other does, every part of the moving ruler de scribing the arc of a circle.