or the difference of longitude is 1° 21' 2" 2 the required longitude is 1° 11′ 36′′+1° 21′ 2′′·2 In this case the value of G found from the survey was 1° 2′ 46′′4; the error of 15"-8 in the above calculation being due to erroneous assumption in the length of the degree, which makes all the longitudes on the southern coast of England too small. The logarithmic calculation for azimuth is N=180°-84° 54′ 52′·5 — 1° 2′ 40′′·06=94° 2′ 27′′·44. The observed angle in this case was 94° 2′ 22′′ 75, the discrepancy of 4"69 being due to the error in longitude before mentioned. Adopting the same data for exemplifying the approximate formula. .. the required difference of latitude=274" 87—28′′·66 =246" 21. L'= 50° 37' 7'3+4′ 6·21 = 50° 41′ 13′′·51. And for difference of longitude, or the difference of longitude is 1° 20′ 56′′, and the required longitude is 1° 11′ 36′′ + 1° 20′ 56′′ =2° 32′ 32′′. The approximate calculation of difference of azimuth G Sine half difference = sin . sin (L+L') 2 G here hence N =0° 40′ 28′′; and ''(L+L′) = 50° 39′ 10′′·68 1. sin o° 40' 28" = 8.070 81 1. sin 50° 39′ 11′′=9888 36 1. sin o° 31′ 18′′=7959 17 180°-84° 54′ 52"5-1° 2′ 36′′=94° 2′ 31"5. The exemplification of the use of the approximations proves that they have been applied to a case slightly beyond their powers, as laid down by the limit given with the formulæ, for the arc exceeds one degree. Section 6. DEMARCATION OF SURVEY POINTS. The selection of survey stations, base lines, and survey lines, has necessarily to be suited to the description of survey contemplated; while the form of record must again be in accordance with the results obtained with the various instruments that may be adopted information on these points will be given attached to the various sorts of survey afterwards described, and models or examples of forms of record also given in every requisite case. The mode of demarcation of the various survey points must be in accordance with the time the marks will have to last, the nature of the ground on which they have to be placed, and their liability to removal or disturbance. The temporary marking of intermediate chained. distances, offset points, and such details is effected by pins, or skewers, which are best if accompanied with numbered tallies indicating the chainage for the end of any complete chain; or by 'whites,' which are cleftsticks holding little bits of white paper, on which any pencilled number can be written. If the soil is not soft enough for these to stick in it, a cross is scratched to indicate the exact mark, and the pin or stick is laid down with its point at the mark. The distant points required for ranging the direction of measurement, or for angular observation, are painted poles shod with iron; if the distances are not very long eight-feet poles, and for longer distances 12- and even 20- or 25-feet poles may be necessary, which then require rope stays. The shorter poles are painted in alternate lengths of black and white, the longer have the top painted and a red flag attached. They should be set truly vertical, and so fixed as to remain so. The loss of time from often having to send men long distances to reset poles on windy days may be very great. For very distant points in large triangulations, a signal pole with flag attached may be set up in a tree, and firmly bound to two or three branches; the station point corresponding to it is then carefully plumbed down to the ground and marked, if angular observation from that point is necessary. Spires and towers do not generally answer such purposes, as they involve satellite stations of observation; but these as well as other permanent well-defined objects, such as corners of buildings, are well suited as distant ranging points; and more important survey lines may sometimes be conveniently ranged in the direction between two such objects. When survey lines cross fences or walls, the crossing points may be notched with a chisel, or painted. Survey station-points are marked with pegs or stakes, if they are likely to be required after removal of the temporary poles; their position with reference to surrounding objects is measured and noted in the field-book, or failing these means, four pegs are so placed and driven in that the intersection of the diagonal measurements between them may fall at the station point. For precision the exact point may be pencilled by a cross-mark on the top of the stake and marked with a nail. If any such marks are required to remain permanently the pegs should be driven flush with the ground; or for greater permanence, a marked tile, brick, or small block of stone should be buried flush. All faulty or incorrect survey marks should invariably be removed or completely obliterated. Several sets of marks may have to be made over the same country, as, for instance, first, the survey marks; secondly, level marks; and if proposed works follow, thirdly, setting-out marks for position; and, fourthly, setting-out marks for level. To prevent confusion, sufficient distinction should be made in pegs or stakes belonging to the various series; some may be round, some square, and again the sectional dimensions may be made to vary in each set; or, again, they may have their tops diversely painted. Permanent floating stations are marked by buoys having some special mark or short pole. As they deviate with the tide and wind, however well they may be moored, the amount of possible deviation should be recorded in each case. Temporary or intermediate floating stations are left unmarked; their position is generally determined by three or four angles taken with the sextant to surrounding permanent marks; these should, if possible, be observed simultaneously. Very distant stations in survey, that happen to be rarely visible, are best observed at night, lamps being set for this purpose; or, in bright weather, the heliostat must be used in the daytime with the same object. A three-inch mirror, set on a tripod stand over the exact station-point, is sufficient to answer the purpose of giving the flashes. |