It will be seen that the above survey might have been effected by the method given in Prob. VIII., Chap. III.; but it is here assumed that the lines compassing the wood cannot be prolonged for the purpose of measuring tie lines, on account of obstructions, as is often the case.

Lakes, Meres, and large Ponds are surveyed and planned in the same manner as the wood just given.

2. The following figure represents a gulf or inlet of the sea, the survey of which is required to adapt it for the purposes of a harbour for ships.

The coast, here shewn, is the boundary of high water; the survey begins at O A, station-flags being fixed at B, C, D, E, F, and G, and angles taken at

A to F and G. The line BA, being first prolonged backwards to high water mark is then measured to B, and the angle ABC taken. Similarly all the succeeding lines are measured, and the angles taken; also at F and G the angles are taken to O A, and the line FG prolonged to high water mark, all the offsets be

C

ing taken as the work proceeds. The figure may now be laid down, precisely as in the last example, the magnitude of the angles shewing the directions of the lines, and the lines AF, A G, which could not be measured on account of the great width of the entrance of the harbour, proving the work by means of the angles, taken at A, and F, and G.

PROBLEM II.

THE SURVEYS OF ROADS AND RIVERS.

1. The following figure represents a river, the survey and plan of which is required, for the purpose of improving its navigation, making locks, &c.

A.

P

E

Station flags being set up, at or near the principal windings of the river, as at A, B, C, D, E, the line AB is measured, and the offsets taken to the nearest shore of the river, its widths, if very great, being determined by Prob. IV., Chap. III.; or by throwing a leaden ball across the river, with a slender cord attached thereto at one end, and holding the other end in the hand, and then drawing it back, and measuring the length of cord, required to reach the opposite shore. This last method is impracticable where the width of the river is very great. A flag is left at OP in A B, where the sight, in the general direction of the river, is unobstructed for a considerable distance. The measuring of AB being now finished, the angle at B is taken, which, being less than 180°, shews that BC turns to the left. On measuring to C the angle there is found to be greater than 180°, shewing that CD turns to the right; and thus the work proceeds to O E, where an angle is taken to the nowdistant flag at P. This last angle will prove the accuracy of the work when laid down.

If the width of the river be very great and unequal, a similar system of lines must be used on the opposite shore; otherwise, a correct map cannot be obtained, the two systems of lines being connected by finding occasional widths of the river, as already stated; thus the line B C may be prolonged across the river to connect another system of lines, if required.

2. If a road be represented by the winding figure, in the last example, it may be surveyed precisely in the same manner, excepting that it would be more convenient to have the system of lines A B C DE upon the road, instead of the side of it, that the offsets may be readily taken to the right and left of the several lines, recollecting to leave a flag, or some other prominent object, in or near the first line, as at O P, in the last figure, to which an angle may be taken, after the survey has proceeded a considerable distance, to prove the work.

The method of planning either a river or road will be sufficiently clear, from the first example in Prob. I.

The map of a river or road being thus obtained, if the area be required it may be readily found by the methods previously given, or, by taking widths at the end of every chain, estimated along the middle of the river or road, and taking a mean of the widths, which, multiplied by the length, will give the area sufficiently correct for most cases.

PROBLEM III.

THE SURVEY OF A PART OR THE WHOLE OF A CITY OR
LARGE TOWN.

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 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 © m. In this manner the survey may be continued to any required

extent.

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 art, that sketches of buildings, yards, gardens, &c., may be 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