"It may be necessary to observe, that 20 feet should be transferred to the rod from a standard measure. And with respect to expansion and contraction, it is pretty well known that well-seasoned deal is subject to very little alteration, while it is kept dry. "If a measurement of this kind be performed with tolerable care, we may safely conclude there will not exist an error of more than one-tenth of an inch in each rod of 20 feet, or 26 inches in a mile. Supposing, however, the accumulated errors amount to five feet in a base of two miles, and that a series of triangles, whose sides are about three miles, to be determined from such a base-then combining the probable errors from observations made with a theodolite-the uncertainty in a direct distance of 20 miles from the base, cannot amount to 30 yards. Erroneous as this may be considered, we believe most of the county maps have been laid down from operations less accurate." In ordinary surveys, it is not necessary to enter into calculations, on account of the sphericity of the globe; nor indeed into many other niceties, such as would be imperative, were the object to measure an arc of the meridian, or perform any other grand trigonometrical operation. On common occasions it suffices to consider the earth as a plane or flat surface, and all the sides of the triangles as right lines, instead of curves. The ground having been selected for measuring a base, and this operation performed with all the accuracy the means will admit of, the next step is to choose the most eligible points for carrying on the triangulation-a survey being conducted by means of a series of triangles, of which the base line forms one side of the first. With this view, conspicuous situations are fixed on, as the tops of hills, church towers, &c. These primary stations ought generally to be of a distance from each other, bearing some proportion to the length of the base and extent of the proposed survey. For instance, if the base be two miles, and extent of the survey 15 or 20 miles, the sides of the triangles may be from two to four miles; much, however, must always depend on the relative positions of commanding points for stations, and on the two first triangles of the survey. For example: - Suppose AB to represent a base line, and that C and Dare eligible stations, forming two triangles, ACB and ADB. Knowing the length AB, and the angles at A and B, the length of CD is found by an easy calculation in trigonometry; and that line becomes nearly as good a base, in point of measurement, as AB, while it pos A C D B sesses the advantage of being longer, and thus enabling us to increase the sides of our triangles.* Wherever the instrument is set up, observations should be taken to all remarkable objects; these, being repeatedly intersected, furnish a check on the work as its proceeds, and their several positions are furthermore determined for future use. When possible, all the three angles of the principal triangles should be observed; then, as the sum of the three angles ought to be 180°, we are enabled to judge of the accuracy of the observations, and in some degree of the perfection of the instrument used. The sides of all the principal triangles should be calculated, and laid down by means of beam compasses * This method of obtaining a longer base, as it may be termed, becomes useful when a base is measured on low ground between hills, as must frequently be done; such situations being often level, and suitable for the purpose. as protraction by the sides is always more correct than by the angles. In triangles on a large scale, an error of a single minute, in protracting an angle, would sensibly affect the length of the sides. As it is impossible to avoid some degree of error in taking angles, we should endeavour so to order our operations that the error may have the least possible influence on those sides, the exact measure of which is the object to be obtained. When the base cannot be equal to the side or sides sought, it should be as long as possible; and the angles at the base should be nearly equal. Sometimes it occurs that the three angles of a triangle cannot be observed; in that case, the angle obtained by intersection should be as near as possible a right one. Acute intersections are at all times to be avoided. The fewer the principal stations, the less will be the labour of the survey; it will also be more accurate, and less liable to mistakes while in the field, or errors when plotting the work at home. Military men generally fill in the principal triangles by means of the pocket sextant and surveying compass, when the survey is not required to be minutely exact in all its details. These general observations might be multiplied to an unlimited extent; and yet, after all, when a survey is to be undertaken, the surveyor must depend chiefly on his own judgment, to lay out the work to the greatest advantage, according to the nature of the country, and other circumstances that will affect his operations. |