PART I. After this, the field is to be delineated on paper, by a line of chords, and a line of equal parts: and the area is to be found by the problems in the fecond part. Small fields are very eafily furveyed by the help of a plane table, which is a rectangular board, supported by a fulcrum, fo as to turn every way, by means of a ball and focket. It has a moveable frame furrounding it, for keeping the paper laid on it tight to it one fide of the frame is divided into equal parts, all around it, and the other fide is divided into 360 degrees, by lines directed to a point in the middle of the board. The board has alfo a compafs, and a large index, with either telescopic or open fights. Pl. II. Fig. 29. delineate a field, by the help of a plane table, from one station fo taken, that all the angles may be feen from it, and their distances measured. Let the field be ABCDE. Let the table be erected at any convenient place, and fix the paper on it, in which let fome point F be taken near the middle, to represent the station. Then applying the index to this point, direct it to one of the angles, as A, and from F draw a faint line along the edge of the index. Then measure the distance of that angle from the ftation, and set it off on the faint line from F, by the line of equal parts, and at its end make a mark to represent the angle A of the field. The fame is to be done with the rest of the angles, and with every remarkable point neceffary to be put on the plan. And if the marks reprefenting the angles be joined, the figure on the table will be fimilar to the field, by the 5th Prop. B. 6. of Euclid. COR. It is evident, that the fame thing may be done by the theodolite; for having taken all the angles at the point F, and measured the lines from the ftation to the angles of the field, draw triangles fimilar to thefe on the paper, and the figure thus made will reprefent the field. But the angles must be examined, for they should be together 360°, by the 32d. B. 1. of Eucl. Note, The furveyer fhould have a field-book ruled in columns, in which he is to place diftinctly all the angles and fides, and the offsets, cross-hedges, houfes, ponds, ftiles, brooks, &c. PROB. PRO B. XIX. O lay down a field, by means of two ftations, PART I. from each of which all the angles can be feen. T Place the inftrument at the station F, and having chosen a point on the paper upon the table, to reprefent it, apply the index to it, and direct it fucceffively to all the angles, and draw lines along its edge: Then direct the index to the other station G, and draw a line, on which fet off the diftance of the ftations, from a line of equal parts. Next remove the inftrument to the station G, and applying the index to the line joining F and G, turn the inftrument until the first station is feen through the fights; there fix the inftrument, and applying the index to G, direct it to all the angles, and draw lines as before: and the interfection of the lines drawn to the fame angle will reprefent that angle and lines joining these interfections will form a figure like the field. COR. It is evident, that the fame may be easily done by the theodolite, by taking the angles which the line between the ftations makes with the nearest angles of the field, and the angles at the ftations fubtended by the fides of the field; and this is the common way, especially in laying down large fields, farms, or eftates. Note, Great care fhould be taken in chufing the ftations; their distance should not be too small, nor the angles fubtended by it, at the corners of the field, very acute, or very obtuse. To lay down a field by going round it. Let ABCEDHG be the field. In going round it, measure its fides, and take its angles with the theodolite. Then let a figure, fimilar to it, be drawn upon paper. If there be a mountain or hollow in any fide, its horizontal diftance is to be taken, and the place of the mountain is to be fhaded. If any place within the field, as F, is to be laid down, take the angles BAF and ABF, or rather measure AF and BF, and lay down the triangle AFB. Note 1. Be careful to diftinguifh exterior angles, as E and G, that they may be made fuch on the plan. And to know if the angles be right, fubtract each of the exterior angles from 360 degrees, and add the remainders to the other angles and 360 Fig. 30. Pl. II. Fig. 3. PART I. 360 degrees; the fum divided by 90 degrees, gives twice the number of fides 2. a Cor. 32. 1. E. PROB. XXI. Pl. II. Fig. 32. To lay down a plane field with the chain. Measure round it, and likewife measure lines across, from corner to corner, fo as to divide it into triangles. Or after measuring round it, measure the distance of fome station C, from its feveral angles, then lay down one of the triangles, as ABC, and upon BC describe the next triangle BCD, and fo on; then, becaufe each triangle on the paper is fimilar to that in the field, the whole is like the whole. IF SCHOLIUM. F the field be fmall, and all its angles can be seen from one ftation, it is to be measured by Prob. 18. If it be large, and great exactnefs is not required, it may be measured by Prob. 19. of this. But in fields that are irregular, or mountainous, we are to proceed as in Prob. 21. of this, and the 20th Problem may be fometimes of use, for we can truft more to the measuring of fides, than to the obferving of angles. It is neceffary to take the bearing of fome line in the field, by the compafs, in order to give it its true fituation on the paper, and to connect it properly with the adjacent fields. After the figure is drawn upon paper, with the scale and compaffes, it is to be transferred to clean paper, by laying the draught upon the clean paper, and marking the angles, and remarkable points, with the point of a small needle, by means of which points it can be drawn anew; and then let the whole be illuminated, by colours proper to each part, and make a compafs in fome convenient part of it, and a fcale in the margin. PART |
