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When the instrument is correctly set, the tracing point, pencil, and fulcrum will be in one straight line, as shewn by the dotted line in the figure. The motions of the tracing point and pencil are then each compounded of two circular motions, one about the fulcrum, and the other about the joints at the ends of the bars, upon which they are respectively placed. The radii of these motions form sides about equal angles of two similar triangles, of which the dotted right line B C, passing through the tracing point, pencil, and fulcrum, forms one side: hence the distances passed over by the tracing point and pencil, in consequence of either of these motions, have the same ratio, and, therefore, the distances passed over in consequence of the combination of the two motions, have also the same ratio, which is that indicated by the setting of the instrument.

The engraving represents the pantagraph in the act of reducing a map to the scale of half the original. For this purpose the sliding indices are first clamped at the divisions on the arms, marked; the tracing point is then fixed in the socket at C, over the original map; the pencil is next placed in the tube of the sliding index, on the bar D F, over the paper to receive the copy; and the fulcrum to that at B, on the bar A B. The machine being now ready for use, if the tracing point C be passed delicately and steadily over every line of the map, a true copy, but of one half of the scale of the original, will be marked by the pencil on the paper beneath it. The fine thread, represented as passing from the pencil quite round the instrument to the tracing point C, enables the draughtsman at the tracing point to raise the pencil from the paper, while he passes the

tracer from one part of the original to another, and thus to prevent false lines to be made on the copy. The pencil holder is surmounted by a cup, into which sand or shot may be put, to press the pencil more heavily on the paper, when found necessary.

If the object were to enlarge the map to double its scale, then the tracer must be placed on the arm D F, and the pencil at C; and, if a copy were required of the same scale as the original, then, the sliding indices still remaining at the same divisions on DF and A B, the fulcrum must take the middle station, and the pencil and tracing point those on the exterior bars AB, AC of the instrument.

Though the pantagraph affords the most rapid means of reducing a map or drawing, we cannot recommend its use for enlarging a copy, or even for copying on the same scale, especially when the original drawing is a complicated one; we therefore proceed to mention some of the other means for the attainment of the two latter objects.

To produce a copy of the same size as the original.-Lay a sheet of tracing paper, having its under side rubbed over with powdered black lead, upon the paper intended to receive the copy; the original being then placed over both, the whole may be made to lay steadily by weights placed thereon: the tracing point may now be carefully passed over all the lines of the drawing, with a pressure proportionate to the thickness of the paper; and the paper beneath will receive corresponding marks, forming an exact copy, which is afterwards to be inked in.

NOTE. Copies of maps are also taken for ordinary purposes by laying tracing paper thereon, through which, from its almost transparent thinness, all the lines of the original can be seen, and readily traced with ink, on the tracing paper. Copies, thus obtained, are called tracings.

Another method. The drawing or map is placed on a large sheet of plate-glass, called a copying glass, and the paper to receive the copy placed over the drawing. The glass is then fixed in such a position as to have a strong light to fall upon it from behind, and to shine through it and both the original drawing and the paper to receive the copy. By this means the lines of the original drawing become visible through the paper to receive the copy, which can be made with precision and ease, without any risk of soiling or injuring the original.

To copy with exactness on a reduced or enlarged scale.-For this purpose we have recourse to the method of squares, by which the most minute details may be copied with accuracy. This perhaps may be best shown by an example. Let figure 1, in the annexed engraving represent a plan of an estate, which

it is required to copy upon a reduced scale of one half. The copy will therefore be half the length and half the breadth, and consequently will occupy but one fourth the space of the original. The subject is the map of an estate, but the process would be precisely the same, if it were an architectural, méchanical, or any other drawing.

Fig. 1.

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Fig. 2.

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Draw the lines FI, FG at right angles to each other; from the point F towards I and G, set off any number of equal parts, as Fa, ab, bc, &c. on the line FI, and Fi, ik, kl, &c., on the line FG: from the points in the line FI, draw lines parallel to the other line F G, as a a, b b, c c, &c., and from the points on F G, draw lines parallel to FI, as ii, kk, ll, &c., which being sufficiently extended towards I and G, the whole of the original drawing will be covered with a reticule of small but equal squares. Next draw upon the paper intended for the copy, a similar set of squares, but having each side only onehalf the length of the former, as is represented in figure 2. It will now be evident that if the lines AB, BC, CD, &c., figure 1, be drawn in the corresponding squares in figure 2, a correct copy of the original will be produced, and of half the original scale. Commencing then at A, observe where in the original the angle A falls, which is towards the bottom of the square, marked de. In the corresponding square, therefore, of the copy, and in the same proportion towards the left-hand side of it, place the same point in the copy: from thence tracing where the curved line AF crosses the bottom line of that square, which crossing is about two fifths of the width of the square from the left hand corner towards the right, and cross it similarly in the copy. Again, as it crosses the right hand bottom corner in the second square below de, describe it so in the

copy find the position of the points similarly where it crosses. the lines fƒ and g g, above the line 17, by comparing the distances of such crossings from the nearest corner of a square in the original, and similarly marking the required crossings on the corresponding lines on the copy. Lastly, determine the place of the point B, in the third square below g h on the top line ; and a line drawn from A in the copy, through these several points to B, will be a correct reduced copy of the original line. Proceed in like manner with every other line on the plan, and its various details, and you will have the plot or drawing, laid down to a small scale, yet bearing all the proportions in itself exactly as the original.

process

It may appear almost superfluous to remark, that the of enlarging drawings, by means of squares, is a similar operation to the above, excepting that the points are to be determined on the smaller squares of the original, and transferred to the larger squares of the copy. The process of enlarging, under any circumstances, does not, however, admit of the same accuracy as reducing.

THE PRISMATIC COMPASS.

With this instrument horizontal angles can be observed with great rapidity, and, when used with a tripod stand, with a considerable degree of accuracy; it is, therefore, a useful instrument for filling in the details of an extensive survey, after the principal points have been laid down by means of observations made with the theodolite, hereafter to be described. It was used for this purpose by the gentlemen engaged in making the Ordinance surveys.

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C is a compass card, divided usually to every 20', or third

part of a degree, and having attached to its under side a magnetic needle; n is a spring, which, being touched by the finger, acts upon the card and checks its vibrations, so as to bring it sooner to rest, when making an observation. S is the sight vane, having a fine thread stretched along its opening, which is to cut the point to be observed by the instrument. The sight vane is mounted upon a hinge joint, so that it can be turned down flat in the box, when not in use. F is the prism, attached to a plate sliding in a socket, and thus admitting of being raised or lowered at pleasure, and also supplied with a hinge joint, so that it can also be turned down into the box, when not in use. In the plate to which the prism is attached, and which projects beyond the prism, is a narrow slit, forming the sight through which the vision is directed, when making an observation. On looking through this slit, and raising or lowering the prism in its socket, distinct vision of the divisions on the compass card, immediately under the sight-vane, is soon obtained; and these divisions, seen through the prism, all appear, as each is successively brought into coincidence with the thread of the sight-vane by turning the instrument round, as continuations of the thread, which is seen distinctly through the part of the slit that projects beyond the prism.

The method of using the instrument is as follows:-the sight-vane S, and the prism P, being turned up on their hinge joints, as represented in the figure, hold the instrument as nearly in a horizontal position as you can judge, or, if a tripod stand be used, set it as nearly as you can in a horizontal position by moving the legs of the stand, that thence the card may play freely. Raise the prism in its socket till the divisions on the card are seen distinctly through it, and, turning the instrument round, until the object to be observed is seen through the portion of the slit projecting beyond the prism, in exact coincidence with the thread of the sight-vane, bring the card to rest by touching the spring n; and then reading at the division upon the card, which appears in coincidence with the prolongation of the thread, gives the magnetic azimuth or bearing of the object observed, or the angle which a straight line, drawn from the eye to the object, makes with the magnetic meridian.* The magnetic azimuth of a second object being

* The magnetic meridian now makes an angle of 24° with the true meridian at London, the north point of the compass being 24" west of the true north point. This angle is called the variation of the compass, and is different at different places, and also at the same place at different times. Since this variation will affect equally, or nearly so, all azimuths observed within a limited extent, and during a limited time, the angles subtended by any two of the

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