PROBLEM III. THE SURVEY OF A PART OR THE WHOLE OF A CITY OR CASE I. Commence the survey at the meeting of three or more of the principal streets, through which the longest prospects can be obtained, for the purpose of laying out the main lines. Having then selected a proper station, fix the theodolite thereon, making a line in one of the principal streets a base line, and directing it to some prominent or well-defined point as to a projecting corner of a house, or to a lamp, or railing-post, or to the right or left side of a conspicuous door or window, which point must be described in the note book, that it may be remembered. Angles must first be taken between the base line and the other lines, diverging from the first station, defining carefully the directions of these lines, as in the case of the base line. This done, measure these lines with the chain, taking offsets to all corners of streets, bendings, or windings, and to all remarkable objects, as churches, halls, colleges, eminent buildings, &c.; also, defining the extent of buildings belonging to each separate owner, or joint-owners, especially if such buildings are required to be taken down for engineering purposes, or for improvements: at the same time recollecting to leave stations opposite the ends of the streets to the right and left, and to take the angles of the directions. This operation must be repeated on the other main lines, till the survey is completed. Thus, having fixed the theodolite at A, take the angles of lines meeting there, referring them to the base line AB, that the magnitude of the angle may shew their direction: then measure A B, taking offsets to the buildings of different proprietors, as to the buildings marked a, b, c, &c., on which the dimensions of their several parts, yards, &c., must be put in the note book, that they may be accurately mapped, preparatory to their valuation, if required to be taken down for engineering purposes, or for parish rating; stations being left at m and n, for the lines in the streets on the right, and the angles of their directions taken; strong iron pins, driven into the crevices of the pavement, being the usual station marks in large towns. The measurement thus proceeds to O B, where the angles of the streets diverging from it are now taken. The line BC is next measured in like manner, and the angles taken at ◇ C; after which the measurement proceeds to On, in the base A B; thus constituting the triangle n B C, a station being left at D in Cn. From D the survey proceeds to O E, and from thence to OA, where the work commenced, a station having been left in the line DE at o for the line to In this manner the survey may be continued to any required extent. m. This survey, so far as it has been here shewn may be plotted independent of the angles taken with the theodolite, by first laying down the triangle n B C, and then determining the position of E by intersection from stations A and D, when the line mo will prove the work. But it rarely happens, in the practice of town surveying, that a fundamental triangle can be obtained, sufficiently large to lay down the work in this manner; it is merely here shewn that such a case is possible; for had the street, in which the line Cn is measured, been so bent as not to admit a right line along it, the use of the theodolite would have been indispensable in this survey. Assuming, therefore, that Cn is not a right line, but bent at D; then, in the five-sided figure A B C D E, the accuracy of the measurement of the angles may be proved, by taking the sum of all the interior angles as in Ex. 1, Prob. I.; and the work further proved, by the closing of the lines at O A, as well as at the several other stations. The form of the field (or rather town) notes in this case, is the same as those already given in the field book, Plate p. 82, excepting that the entries must be made at a sufficient distance apart, that sketches of buildings, yards, gardens, &c., may be clearly made, with the measures of their several parts put on them in links, and the angles must be noted in the same manner as in the example of the wood, Prob. I. CASE II. If a very large town be required to be surveyed, the best method is to measure a base line of considerable length, on elevated and open ground, on the outside of the town and at two stations at its extremities take horizontal angles to the towers of churches and other lofty buildings in the town, and the intersections of the lines of sight, from these angles will determine the positions of the towers, &c.; which may then be made stations for the survey of the several streets, which may now be conducted in the manner shown in Case I. Moreover a third station must be taken in the line thus measured, at which angles must be taken to all the towers, &c., which angles, being laid down, their lines of sight will pass through the intersections of the lines of sight taken from the other two stations, if the work be correct, otherwise an error has been made in taking some of the angles, which must be corrected, before the survey of the streets, &c., be commenced. The several distances of the towers and other lofty buildings may be calculated by Trigonometry (see Trigonometry, Weale's Series), and the several lines, or triangulation, connecting the said towers, &c., may thence be laid down, without plotting the exterior base line and the lines of sight, taken from it. This last method of proceeding is shown in the following Problem, and is adopted by the Ordnance authorities. CASE III. If the town be long and narrow, with straight openings across, either through straight streets, or partly through streets and gardens, a triangulation may be formed on the open ground outside the town and the main lines may be connected by other lines passing through these openings, in which stations may be obtained for the survey of the other streets. Such a survey would resemble the parish-surveys, already described. This method was partly adopted by the author in the survey of Dover for Rowland Rees, Esq., Architect and Surveyor for that borough, the theodolite being only used in those parts where this method was impracticable. PROBLEM IV. TO DETERMINE THE POSITIONS OF SEVERAL DISTANT POINTS, OBJECTS, OR STATIONS, BY TAKING ANGLES AT TWO STATIONS AT THE ENDS OF A GIVEN LINE. Let A, B, C, D, E, F be six stations, the positions of which Measure a line MN on level ground, and stations may be seen from M and N, and at E N C each of the stations M and N, take angles with the theodolite to all the stations; its zero, in taking the angles at each station, being directed to the opposite end of the given line, that the magnitude of the angle may determine the direction of each line of sight to the distant stations. The line MN being then laid down, and the angles taken at its ex tremities, the intersections of the lines of sight MA, MB, &c., and of NA, NB, &c., will determine the positions of the several distant points A, B, &c., from whence their distances may be found, and made base lines for the further extension of the survey, if required. The accuracy of the work may be proved by taking a O o, at any point in MN, and taking from thence angles to all the distant stations; which angles, being laid down, their lines of sight will pass through the intersections A, B, &c., if the work has been correctly done. When all the distant stations or objects cannot be seen from two given stations, then three stations may be taken, or as many as are necessary; connecting the stations thus used, by measuring their distances, and proving their positions by other lines, or by angles: the zero of the theodolite in taking the angles to the distant stations being always directed to the last given station. Moreover, the angles to all remarkable objects that can be seen from two given stations may be taken at the same time; thus may their positions also be determined by the intersection of two or more lines of sight. In this manner very extensive surveys may be effected, occasionally checking the accuracy of the work by measuring the distances of some of the distant stations, where it can be the most conveniently done. The distances from A to B, from B to C, &c., may bo calculated by Trigonometry, as in the preceding Problem. TO SURVEY A DISTRICT WHERE OBSTRUCTIONS OCCUR, FOR A RAILWAY, CANAL, ETC. In the figure, RW is a portion of a projected railway, and AB, BC the main lines to survey that portion of the district occupied by or af fected by the railway. The first main line AB runs along a road, till it is obstructed by a large wood on the right, a brook being close to its left, and, since the direction of the railway changes near the point of obstruction to the left, a new main line B C is taken. Here the use of the theodolite is indispensable to take the angle of the two main lines AB, BC at B, as it is impossible, on account of the obstructions in question, to obtain tie lines to connect the main lines, excepting with great trouble. The parts of the survey adjoining the wood and the brook may be filled up in the usual way, while angles must be taken from two or more stations, to determine the posi |