When the course, like AC, falls between the north and west points, the bearing is read, north 30° west, and is wriiten, N 30° W. When the course, like AF, N falls between the south and east points, the bearing is read, south B 70° cast, and is written, S 70° E. When the course, like AD, W E falls between the south and west А) D points, the bearing is read, south 70° west, and is written, S 70° S A course which runs due north, or due south, is designated by the letter N or S: and one which runs due east, or due west, by the letter E or W. 127. If, after having passed over a course, the bearing be taken to the back station, this bearing is called the back sight, or reverse bearing. 128. The perpendicular distance between the east and west lines, drawn through the extremities of a course, is called the northing or southing, according as the course is run towards the north or south. This distance is also called the difference of latitude, or simply the latitude, because it shows the distance which one of the points is north or south of the other. Thus, in running the course from A N to B, AC is the difference of latitude, C north. G W129. The perpendicular distance be А tween the meridians passing through the extremities of a course, is called the de S parture of that course, and is east or west, according as the course lies on the east or west side of the ineridian passing through the point of beginning. Thus, in running the course AB, CB is the departure, east. 130. It will be found convenient, in explaining the rules for surveying with the compass, to attribute to the latitudes and departures the algebraic signs, + and - ; which are read plus and minus. H with the sign t, and every southing as affected with the sign We shall also consider every easting as affected with the sign +, and every westing as affected with the sign 131. The meridian distance of a point is the perpendicular let fall on the meridian, from which the distance is estimated This meridian is called the assumed meridian. Thus, if the distance be estimated from NS, BC will be the meridian distance of the point B. 132. The meridian distance of a line, is the distance of the middlc point of that line from an assumed meridian : and is cast or west, according as this point lies on the cast or west side of the assumed meridian. Thus, FG drawn through the middle point of AB, is the meridian distance of the line AB. The sign + will always be given to the meridian distance of a point or line, when it lies on the east of the assumed meridian, and the sign –, when it lies on the west. 133. 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, however, an uniformity in the language of the rules, we shall suppose the land to be always kept on the right hand of the surveyor. N PL Let ABCD be a piece of ground to be surveyed, A the point where the work is to be begun, and NS a B meridian. K 1) On a sheet of paper, rule three E columns, as in next page, and head them stations, bearings, distances, il w N Place the compass at A and take the bearing to B, which is PAB: suppose this angle has been found to be 31. The bearing from A to B is then N 314° W. Enter this B bearing in the field notes opposite W station 1. Then measure the distance from A to B, which we will suppose to be 10 ch, and insert that distance opposite station 1, in the 11 column of distances. We next take the bearing from B to C, N 623' E, and then measure the distance BC=9 ch 25 l, 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 451° W, and then measure the distance DA=10 ch 40 1. We have thus made all the measurements on the field which are necessary to determine the content of the ground. 134. REMARK I. 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 311° E. The reverse bearing from C, is S 633° W: that is, it is the And generally, a reverse bearing, or back sight, is always equal to the forward bearing, and differs from it in both of the letters by which it is designated. 135. REMARK II. 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 ferruginous substances. To guard against these sources of error, the reverse bearing should be taken at every station : if this and the forward bearing are of the same value, the work is probably right; but if they differ considerably, they should both be taken again. 136. REMARK III. 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 Cl, 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. 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 also, the sum of the eastings is equal to the sum of the westings. We therefore conclude, that when any survey is correctly made, 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 the distance passed over in the direction due east, equal to that passed over in the direction due west. Having now explained the necessary operations on the field, we shall proceed to show the manner of computing the content of the ground. We shall first explain TIIE TRAVERSE TABLE. 137. This table shows the difference of latitude, and the departure, corresponding to any bearing, and for courses less than 100. Let AB denote any course, NS the N meridian, and NAB the bearing of AB. c-.?? B Then will AC be the difference of lati G tude, and BC the departure. W E A А It is evident that the course, the difference of latitude, and the departure, are respectively, the hypothenuse, the base, s and the perpendicular of a right-angled triangle, of which the bearing is the angle at the base. If there be two bearings, which are complements of each other, or of which the sum is 90°, the difference of latitude corresponding to the one, will be the departure of the other, and reciprocally. For, if BC were a meridian, CBA which is the complement of CAB, would be the bearing of BA; CB would be the difference of latitude, and CA would be the departure. In the traverse table, the figures at the top and bottom of each page, show the bearings to degrees and parts of a degree; and the columns on the left and right, the distances to which the latitudes and departures correspond. If the bearing is less than 45', the angle will be found at the top of the page ; if greater, at the bottom. Then, if the distance is less than 50, it will be found in the column “ distance,” on the left hand page; if greater than 50, in the corresponding column of the right hand page. The table is calculated only to quarter degrees, for the bearings cannot be relied on to smaller parts of a degree. The latitudes or departures of courses of different length, but which have the same bearing, will be proportional to the lengths of the courses. Thus, in the last figure, the latitudes AG, AC, or the departures GF, CB, are to each other as the courses AF, AB. Therefore, when the distance is greater than 100, it may be divided by any number which will give an exact quo |