cular metallic protractor, as the kind of protractor we have just been describing would not answer the purpose; its chief use being, as has been already described, to plot a traverse upon a moderately small scale. There are several constructions of the protractor adapted to the purpose now under consideration, but the most approved is represented in the subjoined figure. It consists of an entire circle, A A, connected with its centre by four radial bars, a a, &c. The centre of the metal is removed, and a circular disk of glass fixed in its place, on which are drawn two lines crossing each other at right angles, and dividing the small circle into four quadrants, the intersection of the lines denoting the centre of the protractor. When the instrument is used for laying down an angle, the protractor must be so placed on the paper that its centre exactly coincides with, or covers, the angular point, which may easily be done, as the paper can be seen through the glass centre-piece.

Round the centre, and concentric with the circle, is fitted a collar, b, carrying two arms, c c, one of which has a vernier at its extremity, adapted to the divided circle, and the other a milled head, d, which turns a pinion, working in a toothed rack round the exterior circle of the instrument: sometimes a third arm is applied at right angles to the other two, to which the pinion is attached, and a vernier can then (if required) be applied to each of the other two, and it also prevents the observer disturbing that part of the instrument with his hand when moving the pinion. The rack and pinion give motion to the arms, which can be thus turned quite round the circle for setting the vernier to any angle that may be required. Upon a joint near the extremity of the two arms (which form a diameter to the circle) turns a branch, e e, which for packing may be folded over the face of the instrument, but when in use must be placed in the position shewn in the figure: these branches carry, near each of their extremities, a fine steel pricker, the two points of which,

and the centre of the protractor, must (for the instrument to be correct) be in the same straight line. The points are prevented from scratching the paper as the arms are moved round, by steel springs, which lift the branches a small quantity, so that, after setting the centre of the protractor over the angular point, and the vernier in its required position, a slight downward pressure must be given to the branches, and each of the points will make a fine puncture in the paper: a line drawn through one of these punctures and the angular point will be the line required to form the angle.

Any inaccuracy in placing the centre of the protractor over the angular point may easily be discovered, for, if incorrectly done, a straight line drawn through the two punctures in the paper will not pass through the angular point, which it will do, if all be correct.

The face of the glass centre-piece on which the lines are drawn is placed as nearly even with the under surface of the instrument as possible, that no parallax may be occasioned by a space between the lines and the surface of the paper.

By help of the vernier the protractor is graduated to single minutes, which, taking into consideration the numerous sources of inaccuracy in this kind of proceeding, is the smallest angular quantity that we can pretend to lay down with certainty. Greater accuracy may perhaps be obtained by the help of a table of natural sines and a well-graduated beam-compass, as explained at page 114.

For plotting offsets, measured to the right and left of the station lines, ivory scales with fiducial edges are usually employed. The figure in the following page represents an ingenious contrivance for an offset scale, extensively employed on the Ordnance Survey of Ireland.

The graduated scale, A A, is perforated nearly its whole length by a dove-tail shaped groove, for the reception of a sliding piece, which is fastened to the cross-scale, B B, by the screw, C. It will readily be understood, from an inspection of the figure, that the cross scale, B, slides along the scale, A, the whole length of the groove, and at right angles to it. The graduations on both the scales represent either feet or links, &c., or whatever length may have been assumed as the unit in the operation of measuring. The mode of its application is simply this: place the scale, A A, on the paper, parallel to the line on which the offsets are to be plotted, and at such a distance that the zero division on the cross scale, B, (which is placed about its middle,) may coincide with it as the scale slides along, and also that the zero of the scale, A, may be exactly opposite that end of the line at which the measurement commenced; then, in sliding the scale, B, from the beginning of the line, stop it at every divisional line on A, corresponding to the distance on the station line at which an offset was taken,

and lay off the exact length of the offset from the edge of the scale, B, either to the right or left of the station line, to which it will be at right angles as taken in the field; the instrument thus gives both dimensions at the same time. It is perhaps needless to add that, the extremities of the offsets being connected, will represent the curved line, &c., to which they were measured; weights may be placed at the two ends of the scale, A A, to keep it steadily in its position. In our figure, the instrument is represented as in the act of plotting offsets upon a station line.

It very frequently happens that a surveyor requires copies to be made of his plans, and these occasionally on an enlarged or diminished scale. There are various methods of accomplishing this purpose, some of which we shall here enumerate.

When a copy is to be made of the same size as the original, it is a common practice to lay the plan upon the sheet of paper intended for the copy, and press them close together by means of weights; then, with a fine needle, prick through all the corners and leading points on the plan, making corresponding punctures in the paper beneath, which may then be connected by lines to complete the copy. But when the lines on the original are very crooked, this method cannot be successfully applied without the aid of a pair of compasses and tracing paper; when, having pricked off the principal points, the remainder may be found by the compasses, and the curved lines transferred by drawing them on tracing paper, the back of which being rubbed over with powdered black lead, and placed in its correct relative situation on the copy, a blunt point* may be drawn along the lines, which will leave corresponding lines on the copy beneath.

The point of a porcupine's quill, or the edge of the eye-end of a fine needle, make good tracing instruments.

Tracing paper is sometimes thus used for making a copy of the whole plan, but, as this process occupies so much time, it is frequently applied in the following manner: A sheet of tracing, or bank-post, paper, having one side covered with powdered blacklead, is laid between the original and the copy, the former being uppermost; a tracing point is then carefully passed over all the lines on the plan with a slight pressure, depending upon the thickness of the paper: the sheet beneath will receive corresponding marks, forming an exact copy, which may be inked-in at leisure.

Another method is by means of a large piece of plate glass, called a copying glass, upon which the plan is placed with a fair sheet of paper uppermost: the glass being then fixed in such a position as to have a strong light fall upon it behind, the whole plan becomes visible through the sheet of paper, upon which a fair copy can be made, without the danger of soiling or injuring the original by pricking through, &c.

When a plan is to be copied upon a reduced or enlarged scale, other means must be resorted to, which are also applicable to copying upon the same scale. One of them is by the use of proportional and triangular compasses, which it is only necessary to mention; another is by dividing the surface of the original into a great number of small squares, and drawing a similar number upon the copy, which must be formed larger or smaller than those on the original, in the exact proportion of the required difference of the scales: the squares in the latter may then be filled up with the same detail of the plan as is contained in the corresponding squares on the former. When, from the great value of the original, it becomes improper to draw lines upon or otherwise deface it, recourse has been had to a frame of wood or metal, having fine threads stretched across it each way, forming a series of squares: this being laid upon the plan, will, if accurately done, answer the same purpose.

The last method we shall speak of is by means of a well-known instrument called a pentagraph.

The subjoined engraving represents the pentagraph, which consists of four flat rulers, made either of wood or brass: the two outside ones are generally from 15 to 24 inches long, and the others about half that length; the longer ones, A B, and A C, are united together, at A, by a pivot, about which they turn, and the two smaller rulers are similarly attached to each other at D, and to the longer rulers at E and F. A sliding box is placed on each of the arms, A B and E D, which may be fixed by a clampscrew at any part of the ruler; these slides carry a tube, to contain either a blunt tracing point, a pencil, or pen, or the fulcrum G, which is a heavy weight of lead, having a point on the under side, to pierce the drawing-board and remain immoveable in its proper position, it being the centre upon which the whole instru

ment turns. Several ivory castors support the surface of the machine parallel to the paper, as well as facilitate its motions.

The arms, E D, and E B, are graduated and marked with the ratios,,, &c., so that when a copy of a plan is required to be made in any of these proportions, it is only requisite to fix, at the required ratio, the slides carrying the fulcrum, G, and the tube at D, with a pencil or pen, and the instrument will be ready for operation. Thus, suppose it were required to make a copy of a plan exactly one half the size of the original, our engraving represents the pentagraph so employed; the slide carrying the pencil at D, and that working on the fulcrum, G, are each fixed by their respective clamp-screws at the divisions marked; the original plan is placed under the tracing point, C, and exactly parallel to it is placed a sheet of paper under the pencil, D,-the pentagraph being first spread out so as to give room for the tracing point to be passed over every line on the plan, whilst the pencil at D is making corresponding marks on the copy, which it is evident will be equal to one half the size of the original. A fine string is attached to the pencil-holder, and passed round by E A, &c. to the tracing point, the pulling at which raises the pencil a small quantity above the paper, to prevent false or improper marks upon the copy. It should also be remarked, that the cup represented on the top of the pencilholder is intended to receive a weight, to keep the pencil down upon the paper, or when a stronger mark is required.

When the instrument is set for work, the tracing point, the pencil, and the fulcrum, must in all cases be in a straight line, which may be proved by stretching a fine string over them.