read, and a mean of the minutes; this column shows the site vernier; in the third, marked D, the degrees before the second, marked 0. V. the minutes read from the oppowritten the arc read from the vernier under the eye-glass; in In the first column of these tables, headed E. G. V., is To Frog's Point, EA, (back) M. 74 55 a the lines make with each other respectively; the letters designating the angles being on the same horizontal line on the left of the columns. From an examination of the different positions of the instrument, it appears that a back sight to any station, as from C to B, or from C to A, differs from the forward sight by 180°. So that any errors in placing the theodolite, levelling it, or taking down the angles, will be detected at once on the field. The first and second columns only need be filled up on the ground; the others being calculated from them. 186. The necessary angles being measured with the theodolite, the compass is next to be used. When the compass is used in conjunction with the theodolite, to fix the shorter lines and determine the smaller parts of the survey, the following is the manner of keeping the field notes. Plate 8 is divided into two equal parts by the two parallel lines that are near each other, and each division is considered a separate leaf. Each leaf is divided into three spaces, the middle one being considerably smaller than the other two, which are equal. The notes begin at the bottom of the first leaf, run up the page to the top; then commencing again at the bottom of the next leaf, they are continued to the top, thence to the bottom of the third leaf, and thus, for as many leaves as the work may require. The bearings are written in the middle space, and at the O points, where the lines run with the compass begin. At dif. ferent points of these lines, perpendiculars are erected, called offsets. The numbers inserted in the middle columns show the distances of the offsets from the beginning of the lines respectively, and the numbers in the side columns, the distances, measured on the offsets, to objects that lie on the right and left. The stations, at which the compass is placed, are numbered 1, 2, 3, 4, 5, 6, and 7. The characters in the left-hand columns are the conventional signs adopted by the Engineer Department to represent in topographical plans the objects for which they severally stand; they are used here for the double pur pose of showing the manner of determining points, and explaining the methods of delineation. As it is rather inconvenient in practice to erect a perpendicular to a line that shall pass through a given point without the line, it is in general better to determine particular points lying without the compass lines, by oblique, than by perpendicular offsets. When this is done, the bearings and distances are inserted in the side columns. The manner in which the points C and D are determined, is an application of this method. The work, with the compass, is begun at station A (Pl. 7), one extremity of the base line. From this point, the bearing of station D is taken, also the bearing of station 1, and both entered at the bottom and on the left of the page (Pl. 8), where the notes begin. The bearing of station D is due north, that of station 1. N 27' E. At station A, the distance AT to the river, measured on a perpendicular to Al, is 280 feet; this distance is also inserted in the notes. Passing along the line Al to a, 100 feet, a like distance ab is 220 feet: the 100 feet is entered in the middle column (Pl. 8), and the perpendicular distance in the space on the right. At 100 feet from a, on the left of the line Al, and in the perpendicular ba produced, are several pieces of artillery: at c, 280 feet from A, the park of artillery is but 60 feet from Al; these distances are also entered in the notes. At d, 380 feet from A, the distance dd', to the river, is 150 feet, to the cannon battery, 130 feet; and at 1, 460 feet from A, the distance to the river is 110 feet, and to the mortar battery 60 feet. At this point a new course begins. Its bearing is N. 113 E. Its commencement, is indicated in the notes, by 0, which is placed at the beginning of each course, and by a figure which shows the number of the station. The line 12 is passed over in a manner entirely similar to that already explained for Al, and the distances to objects on the right and left entered in the notes in the same way. And similarly for the lines 23, 34, 45, 56, 67, and 7B. The perpendiculars AT, ab, cc', dd', le, &c., are laid off with the surveying cross; they may, however, be laid off with the screw. a At station 3 the bearing is taken of station D; it is S.33 W.; the distance is 110 feet, both are entered in the notes. At station 5, the bearing of station C is S. 54° E., the distance 90 feet. If particular points are to be determined in position, and plotted on the map, it is best to use these oblique offsets; for, by taking the bearing and measuring the distance, the position of the object becomes known. The work with the compass finishes at station B. 187. We now take the plain table, put the paper upon it, , place it at F, the extremity of the offset at B, and distant from it 265 feet (see notes); level it, mark the point that is directly over the station, lay the fiducial edge of the ruler on that point, and sight to station B; then fasten the table with the clamp Draw on the paper, with a pencil or leg of the dividers, a line corresponding to FB; then sight to the points G and H, and draw the lines FG and FH Take the distance FB, equal to 265 feet, from a scale of equal parts, and apply it to the corresponding line on the paper ; this determines the point B on the paper. Remove the table to B, and place it in such a manner that the point B and the line BF paper shall be directly over B and the line BF on the ground; the instrument being levelled, let it be clamped. Then sight to the points G and H successively, and draw the lines BG, BH; these lines, by their intersection with the corresponding lines from F, determine the points G and H. Let now a new paper be placed on the table. Measure on BE, which is a known line, any distance BL, equal to 600 feet; and on the paper lay off this distance from a scale of equal parts. From B, sight to H, I, K, and the corners of the other building: then remove the table to L, and sight to H, and the other points. The line BH is determined on both papers, and if this line on one of them, be laid on the same line of the other, all the points and lines of the former will be given in position with respect to the points and lines of the latter. The width of the buildings can now be laid off, and the buildings drawn. Let a fence be supposed to run from F to M, from M to E, and from E to 0. A distance ER is now measured with the chain equal to 500 feet; the plain table is then placed at E and R, on the a 188. All the data necessary for the calculations are now known. We shall begin by finding the lines determined with the theodolite. CALCULATION. In the triangle AEB are known AB=97 roods, <B=26 42',CA=78° 23' (see notes); and, therefore, <E=74° 55'. As sin. <E 74°55' 9.984774 As sin. -E 74° 55' 9.984774 ° [ . ZE Is to AB 97 1.986772 Is to AB 97 1.986772 So is sin. LA 78 23 9.991012 So is sin. <B 26' 42 9.652555 . ° ' To EB 98.403 1.993010 To AE 45.139 1.654553 In the triangle ABC are known AB=97 rods, <B=EBCEBA=9026 -26° 42=63° 44', <C=789 03, ZA=EAC ° ° ' EAB=116 36 - 78 23 = 38° 13'. As sin. <C 78° 03: 9.990485 As sin. <C 78°03' 9.990485 Is to AB 97 1.986772 Is to AB 97 1.986772 So is sin. <B 63° 44' 9.952669 So is sin. <A 38° 13' 9.791436 To AC 88.911 1.948956 To BC 61.337. 1.787723 In the triangle BCD, there are known BC=61.337, <B= < 30 23', C= 123 29, and consequently the <D=25° 58'. As sin <D 25° 58 9.641324 As sin. <D 2558' 9.641324 Is to BC 61.337 1.787723 Is to BC 61.337 1 787723 So is sin. C 123 39 9.920352 So is sin. B 30° 23' 9.703964 To BD 116.614 2.066751 To CD 70.854 1.850363 In the triangle ACD, there are known AC=88.911, CD= 70.854, and the angle C=45 36. As AC +CD 159.765 2.203482 Is to AC-CD . 18.057 1.256646 So is tang. (D+A) 67° 12 10.376377 |