angular points as possible, by which the labour of removing the instrument backward and forward is considerably abridged. In choosing stations, avoid cattle or car-tracks, or other places where your station marks would be likely to be removed or obliterated,—a thing that frequently happens, to the great annoyance of the surveyor. The roads in this survey were sometimes determined from the lines employed to fill in the work, as well as the lines connecting the principal stations. Some of them were also surveyed by the method of traversinga term applied to all irregular surveying by the chain and theodolite. On starting from one of the gates leading into the Park, the instrument being set to zero, the telescope was directed to one of the most conspicuous stations, and after having turned it in the direction of the road to be surveyed, (the lower plate being clamped,) the angle was then read off, and the distance to the forward station chained. The instrument was then removed to the forward station, the upper plate being clamped, and a staff left at the starting point, the telescope was directed to the back station, and setting the upper plate free, the telescope was directed to the next forward station along the road, and the distance to the next forward station and reading on the theodolite registered in the field-book. Here it is necessary to observe, that the degrees shewn on the graduated limb of the theodolite are not the measure of the angle contained by these two lines, but rather the angle that this second line forms with that upon which the instrument was first set. P As the work progressed, other lines were selected, from which the forward bearings were measured. In pursuing this plan, greater accuracy is secured in plotting; as when all the angles are measured and plotted from one line, a trifling error committed in the direction of one line does not affect the next. When a great number of lines have reference to another given in position, the readiest and most correct way of plotting them is to use a circular protractor, made of pasteboard, with the centre cut out. Put the centre of the protractor at the angular point, and zero on the line whose position is given; then a ruler, having always its edge at the centre of the protractor, being applied to the several angles taken in the field, will point out the bearings of the respective portions of the road. Then by the parallel ruler, lines may be drawn parallel to these, on which the respective distances are to be laid off, from the scale of equal parts. This plan may be employed in plotting an estate which has been surveyed by measuring the sides and angles of its circumscribing polygon. But when great accuracy is required, a brass protractor with a vernier is better. When the road was considerably curved, offsets were measured to the curve from the several station lines, which were plotted in the usual way, and the extremities of the offsets joined by a regular curved line. When the road was straight, and of uniform width, offsets were taken only to one side; but where it varied in breadth, offsets were taken to both sides. A canal may be surveyed in the same way as a road; but when it is of unequal breadth, offsets must be taken to both sides, from station lines measured on each side of the canal. The triangles employed in the survey were all laid down from the lengths of their sides, not from the measure of their angles. Unfit as the sextant is to measure the angular distances between objects in planes inclined to the horizon, the use of the circumferenter is still more objectionable. The compass cannot take angles nearer than 15', independent of other errors arising from its centering and peculiar construction. Surveying by this magnetic instrument is founded on the supposition that the needle invariably preserves a parallel position, which is far from being the case, there being a variation by which it differs at different times of the day and year. The maximum of these variations takes place between noon and three o'clock in the afternoon, and the greatest diurnal variation generally takes place in the months of April, May, June, and July. In the year 1759, the diurnal variation of the needle was very carefully observed at London, and the greatest was found to be 13′ 21′′ in the month of June, and the least 6'.58 in the month of December. The results of recent discoveries disclose a very curious fact, namely, that all perpendicular objects, as houses, trees, &c. &c. have (at least in north latitude) a north pole at bottom, and a south pole at top, and that such objects exert a very sensible influence upon the needle; it may therefore be advisable, in delicate surveys, to keep at some distance from such objects, especially from houses where much iron is deposited The results of late discoveries have pointed out other irregularities in the needle, which, with those above alluded to, are sufficient to weaken our confidence in any surveying instrument founded on a principle so unsteady. As we are upon this subject, it may not be out of place to mention, that from numerous observations recently made, the variation commences two or three hours before noon, having previously returned to the position it had on the preceding day, and having been quiescent during the night. From this it appears that angles taken early in the morning are more to be depended on than those taken at a more advanced part of the day. It may be of importance to know, that the greatest error resulting from diurnal variation would be 31.067 links, and the least 16.212 links in a distance of one mile, which, upon a map laid down to a large scale, would cause great derangement. The preceding facts clearly shew how necessary large and accurately divided instruments are, when used for very distant objects, as in trigonometrical surveys; and also why the needle cannot be employed on such surveys. Some surveyors use the sextant in taking angles, which, except in the absence of a better instrument, should never be used; as the angles observed by it are always incorrect, except when the objects observed happen to be on the same horizontal plane, which is a case that seldom occurs in practice. By it, no doubt, the angular distance subtended at the place of the observer may be measured, but not the horizontal angular distance; therefore the former should be reduced to the latter. The process required to accomplish this is ach may be found respectively. The aggregate of all e triangles is the required area. It is necessary to know that when the polygon has 2 sides, to find the area it is only requisite to measure (n-2) sides, together with (n-1) angles; (n-1) sides, together with (n-2) angles; or n sides, together with (n-3) angles. It may, however, be advisable to measure as many of the sides and angles as are accessible, that the admeasurement might serve as a proof of the accuracy of the results by calculation. If all the internal angles of the polygon be measured, their sum ought to be equal to twice as many right angles as the figure has sides, wanting four right angles. When there is an angle that bends inwards, and when you measure the external angle, which is less than two right angles, deduct it from four right angles, and the remainder will be the internal angle. In measuring the sides, due allowance should be made in chaining hilly ground, otherwise the polygon would not close. In taking the angles round the polygon, it is not necessary to set the instrument to 360°, except in the first angle; but the preceding reading of the instrument must be always deducted from the subsequent one, and the difference will be the measure of the last angle. This practice has two advantages to recommend itthe time lost in setting the instrument to 360° at every angle is saved; and after having gone round the figure, the instrument itself affords a proof of the correctness of the angular part of the work-zero, on one of the verniers, always coinciding with 360°, if the angles are correctly taken. |