a, the whole work may be considered to have been performed with a sufficient degree of accuracy; but, if the error amount to more than a minute or two, we must proceed back again from f to e, and so on till we find out the station at which the error has occurred. If the ground along any of the lines a b, bc, &c., rise or fall, suppose, for instance, along bc, then we must direct the telescope from b, so as to make the cross wires bisect upon the staff, held upon the picket at c, a point at the same distance from the ground as the center of the telescope, and then upon one side of the vertical limb is pointed out the number of links to be deducted for each chain from the measured distance b c, to reduce it to the required horizontal distance. This reduction is then to be entered in the field book*

INSTRUMENTS FOR PLOTTING THE SURVEY.

In plotting the survey, as in taking it, due regard must be had to both accuracy and despatch, and we should aim to lay down the various points observed with an accuracy proportionate to the accuracy of the survey itself. To this end the principal points should be laid down by setting off with the beam compasses the computed sides of the triangles, the angles of which have been accurately observed with the large theodolite; and the direction of the meridian is to be laid down from an observation of the angle which it makes, with a side of one of these triangles, by means of the computed chords +, which chord is also to be set off with the beam compasses.

THE CIRCULAR PROTRACTOR.

The principal points having thus been laid down, the boundaries observed by the small theodolite may be put in by first laying down upon the paper a large circular protractor. This protractor may be pricked off by means of the circular metallic protractor represented in the accompanying figure, and the lines can then be transferred to any part of the paper by means of a large ruler and triangle, or by any parallel ruler The circular protractor is a complete circle, AA, connected with its center by four radii, a a a a. The center is left open, and surrounded by a concentric ring, or collar, b, which carries * The method of surveying with the chain and theodolite, explained above, is called surveying by a traverse.

If a table of chords be not at hand, take out the sine of half the angle from a table of natural sines, and, reckoning the first figure as integral, this will be the chord of the whole angle to radius 5, or, reckoning the first two figures integral, it will be the chord to radius 50.

two radial bars, c c. To the extremity of one bar is a pinion, d, working in a toothed rack quite round the outer circumference of the protractor. To the opposite extremity of the other bar, c, is fixed a vernier, which subdivides the primary divisions on the protractor to single minutes, and by estimation to 30 seconds. This vernier, as may readily be understood from the engraving, is carried round the protractor by turning the pinion d. Upon each radial bar, c c, is placed a branch e e, carying at its extremity a fine steel pricker, whose point is kept above the surface of the paper by a spring placed

under its support, which gives way when the branch is pressed downwards, and allows the point to make the necessary puncture in the paper. The branches e e are attached to the bars c c, with a joint which admits of their being folded backwards over the instrument when not in use, and for packing in its case. The center of the instrument is represented by the intersection of two lines drawn at right angles to each other on a piece of plate glass, which enables the person using it to place it so that the center, or intersection of the cross lines, may coincide with any given point on the plan. If the instrument is in correct order, a line connecting the fine pricking points with each other would pass through the center of the instrument, as denoted by the before-mentioned intersection of the cross-lines upon the glass, which, it may be observed, are drawn so nearly level with the under surface of the instrument as to do away with any serious amount of parallax, when setting the instrument over a point from which any angular lines are intended to be drawn. In using this instrument the ver

nier should first be set to zero (or the division marked 360) on the divided limb, and then placed on the paper, so that the two fine steel points may be on the given line (from whence other and angular lines are to be drawn), and the center of the instrument coincide with the given angular point on such line. This done, press the protractor gently down, which will fix it in position by means of very fine points on the under side. It is now ready to lay off the given angle, or any number of angles that may be required, which is done by turning the pinion d till the opposite vernier reads the required angle. Then press downwards the branches e e, which will cause the points to make punctures in the paper at opposite sides of the circle; which being afterwards connected, the line will pass through the given angular point, if the instrument was first correctly set. In this manner, at one setting of the instrument, a great number of angles, or a complete circular protractor, may be laid off from the same point.

THE T SQUARE AND SEMICIRCULAR PROTRACTOR.

We cannot speak too highly of a method by which a traverse can be most expeditiously as well as accurately plotted,

by means of the T square and semicircular protractor, the manner of using which is thus described by Mr. Howlett, chief draughtsman, Royal Ordnance Office, in vol. i of Papers

on Subjects connected with the Duties of the Royal En gineers:

"As, when away from home, it seldom happens that the surveyor can obtain a good drawing board, or even a table with a good straight edge, I fix a flat ruler, A, to the table B B B, by means of a pair of clamps, CD, and against this ruler I work the pattern square E, one side of which has the stock flush with the blade; or, if a straight-edged board be at hand, then the square may be turned over, and used against that edge instead of the ruler A. Here, then, is the most perfect kind of parallel ruler that art can produce, capable of carrying the protractor over the whole of a sheet of plotting paper of any size, and may be used upon a table of any form. It is convenient to suppose the north on the left hand, and the upper edge of the blade to represent the meridian of the station.

"This protractor is held in the hand while the vernier is set, which is an immense comfort to the sight; and it will be seen that, as both sides of the arm are parallel with the zero and center, the angle may be drawn on the paper against either side, as the light or other circumstances may render desirable."

From this description and a mere glance at the engraving, it is clear that angles taken with the theodolite can be transferred to the plot as accurately as the protractor can be set, namely, to a single minute, and that, too, in a rapid and pleasant

manner.

Another most admirable and expeditious method of plotting, especially useful when it is a principal point to obtain the area of an estate or parish, &c., is to procure or form a table of northings, southings, eastings, and westings*, for all angles made with a meridian line, and for all distances from 1 to 100. These distances may be either links, feet, chains, or estimated in any denomination whatever, and the corresponding northings, southings, eastings, and westings will be in the same denomination. This table is in fact nothing more than the products of the sines and cosines of the angles, made with the meridian line, multiplied by the several distances, and the following is the method of using it. Take out from this table the northings, southings, eastings, and westings made on each of the lines of the survey, the line from which the angles have been measured being for this purpose assumed as the meridian, no matter in what direction it may lie, and place them in a table, which we may call a traverse table, in four separate columns, being the third, fourth, fifth, and sixth columns of the tablet, headed

* This table is the same as the table given in books on navigation, and then called a table of latitude and departure.

+ The first and second columns of the traverse table contain the courses and distances.

N., S., E., and W. respectively. Add up these several columns, and, if the work is so far correct, the sum of the northings will equal the sum of the southings, and the sum of the eastings will equal the sum of the westings. Then in two additional columns enter the whole quantities of northing and easting, made at the termination of each of the several bounding lines of the survey; which quantities will be determined by putting zero for the greatest southing, and adding or subtracting the northing or southing made on each particular line to or from the whole quantity of northing made at the beginning of this line, or at the termination of the preceding line; and again, by putting zero for the greatest westing, and adding or subtracting the easting or westing made on each line to or from the whole quantity of easting at the beginning of the line.

This preparatory table having been formed, the plot may be laid down with great ease and accuracy by means of a plotting scale, formed of two ivory graduated rules, one of which, n n, represents the assumed meridian along which the northings

are to be measured, and the other, e e, represents the east and west line, and serves to set off the eastings. The rule, n n, is perforated throughout nearly its whole length with a dovetail groove, receiving an accurately fitted sliding piece, to which the rule, ee, is fixed

by the screw s, so as to slide along, and always have its edges at right angles to the edges of the rule n n. The rule, nn, is to be placed on the paper with its zero division opposite that point of the line assumed as a meridian, at which the plotting is to be commenced, and with its edges parallel to this line, and at such distance from it, that the zero division on the rule, e e, may be upon the assumed meridian. The rule, n n, is then to be fixed by placing weights upon its extremities, or by clamps The scale, e e, being now slid along till either of its edges coin cides with the divisions upon the scale, n n, answering to the whole quantities of northing at the termination of each line of the survey, the divisions upon the scale, e e, answering to the