= ... Log tan = log tan 6° 44' 15'16" 9'0723873 3 Hence ẞ 180 + (30° 50′ 40′′ 85) -(6° 44′ 1516") In the two triangles there are two angles and one side given, whence the other sides and the ordinates of Po may be computed as usual. In the present case it would however be better to calculate from the large and well-conditioned triangle P1 Po P, of which the side P1 P3 is known. Sum. Sides in 45 53 22 72 9.8561247 I 8601694 36260952 4227 61 P, P. 97 48 27.00 9.9959553 3.7659258 5833°45 P, P, 36 18 10 27 9 7724468 I 7764915 3°5424173 3486 72 P, P. Bearing of P3 Po 54 44 27.27 log sin 54° 44′ 27 27" 99119828, log cos = Log P3 Po = #3.6260952 3'5380780 9.7613826 3.6260952 3'3874778 3452 06 E. ... Dep. = 3452 06, and diff. lat = 2440*49 It is to be observed, that when the sides and angles are given from the 'triangulation sheets,' the computation is not a formidable one. This method may therefore be useful in fixing intersected points from an existing triangulation. The formula given is the neatest, and is suitable for every case, it is derived from 'Adjustment of Observations,' by T. W. Wright, B.A. Observations from two unknown to two known points, and to each other. There is another problem which may be useful in taking up secondary points. Angles are observed from two unknown points to two known, and to each other. To fix the unknown points. Let A and B be the known points, X and Y the unknown points (fig. 122). Let the angles A X Y = 0, B XY = 4, be observed, as also A Y X = 02, BY X = 2. Assume some length for X Y, say I'000000 or 1000'0. 2 In the triangle X Y A, the angles 0, 0, are given, and the base X Y is assumed to be given as unity. Compute A X, AY in terms of X Y, also in the triangle X Y B compute BX and B Y also in terms of X Y. Now in the triangle A X B you have two sides A X, B X, known, in terms of the assumed values of X Y, also the included angle 0, +$1. Hence calculate A B in terms of X Y, also calculate the angles X A B and X B A. Do the same in A Y B. FIG. 122. 02 B To get the real value of the sides A X and A Y, &c., you have merely to say 'as the calculated value of A B is to its true value, from triangulation, so is the assumed value of X Y to its real value.' So for the other sides. That is to say, you have to add to the logarithmic value of their computed lengths, the constant. value of A B Log (calculated value of A B Use of two Trig. points from any existing Grand An. in lieu of a Base Line. Hitherto it has been asssumed that a base line has been measured, specially, for the survey. It may, however, happen that a Grand Triangulation exists, and that the survey in question is undertaken for the purpose of completing the map. Any two points A and B (fig. 123), of the great trigonometrical network, will serve as a base line, and it may be assumed that the distance between them is known far more accurately than any measurement can be made by the appliances obtainable by the surveyor. Then by measuring a base Ab, approximately, to serve as the known side for triangle No. 1 of the minor triangulation, and working round to the point B, we have only to get the length of A B from the minor triangulation in terms of the measured base Ab. Then, as the value of A B, so found, is to its true value from the main triangulation, so is the measured value of the base A b, to its true value and all the calculated sides of the minor triangulation must be adjusted in the same proportion, the adjust 17 D 18. 19 27 14 13 76 15 20 37 ვი 32 ཉྙཱ-----...- 12 B ment being made, as in the last case, by the addition or subtraction of a constant logarithm. Other points C and D of the great triangulation may be used as checks. Selection of The size of theodolite to be employed in a minor triangulation (setting aside money considerations), depends a good deal on the nature of the country to be surveyed. In any case an 8-inch theodolite of the transit pattern, would suffice for every purpose. With such an instrument 'azimuths' and 'latitudes' could be obtained with a considerable degree of accuracy. If a telegraph station were at hand, whereby time signals could be obtained from some standard timepiece, "longitudes' could also be obtained with some degree of precision. An 8-inch theodolite in open country, where transport is easy, is very suitable. In rough country a smaller and lighter instrument would be preferable. The larger and therefore the heavier the instrument, the more liable it is to injury in transport, and the greater is the cost and delay, in carrying it from place to place, and in setting it up. Generally, and especially in rugged country, the lightest instrument that will give the desired results, should be used. These can be obtained, (in a triangulation having one mile sides) by means of a 5-inch theodolite. In a triangulation of this description which the writer once inaugurated, and for some time directed, an old fashioned 5-inch cradle theodolite was used, by persons who had little previous experience of the work. The means available for erecting signals and the like were limited. Yet the work |