vertically through the middle of the large aperture, as shown in Fig. 3. The compass-box DCE is circular, and generally about six inches in diameter. At the centre is a small pin, on which the magnetic needle is poised. This needle, if allowed to turn freely around the point of support, will settle to a state of rest: the direction which it then indicates, is that of the magnetic meridian. In the interior of the compass-box, there is a graduated circle divided to degrees, and sometimes to half degrees: the degrees are numbered from the extremities of the diameter NS, both ways to 90°. The length of the magnetic needle is a little less than the diameter of the graduated circle, so that the needle can move freely around its centre, within the circle, and its positions be noted on the graduated arc. The compass-box is turned about its centre, without moving the plate AB, by means of the milled screw L: and is fastened to the plate AB, by the screw P. In using the compass, it is important to ascertain the exact angle which may be included between the magnetic meridian and the course. The course is always indicated by the line drawn through the eye and the sights AF and BG. To measure this angle, accurately, a small arc HI is described on the bar AB, having its centre at the centre of the compass-box. This arc is divided to degrees, and sometimes to the parts of a degree. A vernier is also used, which is permanently attached to the compass-box. When the 0 point of this vernier coincides with the 0 point of the graduated arc HI, the line of the compass-box marked NS, lies in the plane of the sights. Suppose the 0 of the vernier to coincide with the 0 of the lines of division of the graduated circle, let the whole degrees be read. Then, turn the compass-box by means of the screw L, until the needle points exactly to the line which marked the whole degrees: the space passed over by the 0 of the vernier, shows the parts of a degree that are to be added, to give the true reading. WORK ON THE FIELD. 75. When a piece of ground is to be surveyed, we begin at some prominent corner of the field, and go entirely around the land, measuring the lengths of the bounding lines with the chain, and taking their bearings with the compass. It is not material whether the ground be kept on the right hand or on the left, and all the rules deduced for one of the cases, are equally applicable to the other. To preserve uniformity, however, in the language of the rules, we shall suppose the land to be always kept on the right hand of the surveyor. Let ABCD be a piece of ground to be surveyed, A the point where the work is to be begun, and NS a meridian. On a sheet of paper, rule three columns, as follows, and head them. stations, bearings, distances. N Place the compass at A, and take the bearing to B, which is PAB: suppose this angle has been found to be 314°. The bearing from A to B is then N. 314° W. Enter this bearing in the field notes opposite station 1. Then measure the distance from A to B, which we will suppose to be 10 ch. 40 l., and insert that distance opposite station 1, in the column of distances. We next take the bearing from B to C, N. 62° E., and then measure the distance BC: 9 ch. 20 1., both of which we insert = in the notes opposite station 2. At station C we take the bearing to D, S. 36° E., and then measure the distance CD = 7 ch. 60 l., and place them in the notes opposite station 3. At D we take the bearing to A, S. 45° W., and measure the distance DA = 10 ch. We shall then have made all the measurements on the field which are necessary to determine the contents of the ground. PRINCIPLES. 76. The reverse-bearing or back-sight, from B to A, is the angle ABH; and since the meridians NS and HG are parallel, this angle is equal to the bearing NAB. The reverse-bearing is, therefore, S. 31° E. The reverse-bearing from C, is S 62° W.; that is, it is the angle ICB = GBC. And generally, A reverse-bearing, or back-sight, is always equal to the forward-bearing, and differs from it only in both of the letters by which it is designated. 77. In taking the bearings with the compass, there are two sources of error. 1st. The inaccuracy of the observations: 2d. Local attractions, or the derangement which the needle experiences when brought into the vicinity of iron-ore beds, or any B N P W K D E To guard against these sources of error, the reverse-bearing should be taken at every station: if this and the forwardbearing are of the same value, the work is probably right; but if they differ considerably, they should both be taken again. 78. In passing over the course AB, the northing is found to be HB, and the departure, which is west, is represented by AH. Of the course BC, the northing is expressed by BG, and the departure, which is east, by GC. Of the course CD, the southing is expressed by CI, and the departure, which is east, by CF. Of the course DA, the southing is expressed by KA, and the departure, which is west, by DK. It is seen from the figure, that the sum of the northings is equal to HB + BG = HG; and that the sum of the southings is equal to CI+ KA = PA= HG: hence, the sum of the northings is equal to the sum of the southings. AS 'R If we consider the departures, it is apparent that the sum of the eastings is equal to GC + CF = GF; and that the sum of the westings is equal to AH + DK = GF: hence, the sum of the eastings is equal to the sum of the westings. We therefore see, that when the survey is correct, the sum of the northings will be equal to the sum of the southings, and the sum of the eastings to the sum of the westings. It would, indeed, appear plain, even without a rigorous demonstration, that after having gone entirely round a piece of land, the distance passed over in, the direction due north must be equal to that passed over in the direction due south; and that the distance passed over in the direction due east must be equal to that passed over in the direction due west. 79. The boundaries of a field are generally occupied by fences, and frequently also by a border of shrubbery, so that chaining along the true boundary is impossible. In such cases, it becomes necessary to measure an offset at each end of the course (and at right angles to m- M it), and of sufficient length to clear the obstructions; the measurement is then made between these temporary stations. It is evident that the bearing and length of mn, the offset-course, are the same as those of MN. When such offset-courses are necessary for several successive courses, errors are likely to be committed, unless the surveyor is careful to make new offsets for each course. འདེ The offset-courses, for the lines LM, MN, and NO, are respectively lm, m'n, and n'o. Such offsets, in field surveys, may generally be measured by the flag-staff, and the right angle may be determined with sufficient accuracy by the eye. It is, of course, immaterial, so far as accuracy is concerned, upon which side of the line the offset is taken, whether it be |