PROB. XXVIII. To take an extensive survey. Choose for stations the most eminent places, from which the rincipal parts of the survey may be seen. Particularly choose uch eminences as lie near the boundaries. Take the angles which these stations make with one another with great accuacy, and measure carefully in a straight line the distances rom station to station, marking the places where the lines ass ditches, roads, rivulets, &c., and take offsets to near bjects, leaving in the ground a mark at every place where you marked the distance in the field-book, distinguishing these narks by letters or figures, that they may not be mistaken for ne another. In this way you will obtain the situation of the rincipal parts. Then take other stations within these, and neasure the distances as before. And thus divide and sublivide the survey, till you come to single fields, which may be neasured by some of the preceding methods. The longer the distance is between the stations, if accuately measured, the more correct will the work be; but this cannot be ascertained by a single measurement, without using various methods of determining it. At the same time, an error in these primary distances affects the whole survey; and therefore every care ought to be taken to prevent it. After the principal parts of the survey are laid down accurately, so as to have the whole divided into small compartments, these may be filled up by the plane-table, one by one. In laying down the plan, proceed in the same way, first laying down the principal distances and the boundaries, and then the interior parts as they are surveyed; and in filling up the particular departments, care must be taken to lay down the boundaries of parishes, estates, farms, &c. and to point out the particular situations of towns, villages, churches, gentlemen's seats, towers, farm-steads, also rivers, lakes, ponds, woods, plantations, rocks, precipices, and all the eminences, mines, pits, quarries, and in general every thing which can contribute to give a proper understanding of the nature of the survey. All these must be neatly sketched and properly coloured, and the names of the places are to be printed in them. 1. I took two stations near a road, of which B lay from A, N. 61° E. 1850 links; and from A took the bearings of the eminences C, S. 70° E., D, S. 62° E., and E, S. 36° E., and at B took their bearings C, S. 14° E., D, S. 61° W., and E, S. 26° W. Required their distances from the stations, and their bearings and distances from one another. Ans. BC 1684 14, AE 1201.788, CD 596-64, and D 758.41 links. S Having drawn the plan of the observations in Example 1, it is required to lay down on it, and to calculate the properties contained in the field-book of the following examples. (2.) Diagonal. H 313 Gr The distances not mentioned in these two examples are to e taken from the preceding ones. PROB. XXIX. To find the contents of a survey. The areas of single fields, bounded by straight lines, may be und from the lines measured in the field, by the first twelve roblems of MENSURATION OF SUPERFICIES. TO CALCULATE OFFSETS. The most accurate method is o compute them separately, as triangles and trapeziods, by Prob. IV. and VII. of MENSURATION OF SUPERFICIES. METHOD 2. If the distances between the perpendiculars be early equal. To half the sum of the perpendiculars at the extremities of the base, add all the rest, and multiply the sum by the base, and divide the product by the number of divisions in the base made by these perpendiculars. COMMON METHOD. Divide the sum of the perpendiculars by the number of them for a mean perpendicular, by which multiply the base. |