Sum of Direct Co-ordinates x = 11273 Log. 105204 T-21363 ... + 0.164 +1.075 x= +11.273 Sum of Perpendr. = + 0.261 pe This constant logarithm added to the logarithms of the rambulator distances will furnish the logarithms of the same distances in terms of the unit of the Trigonometrical Survey. The following is the method of computing a Ray Trace Survey without the aid of the trigonometrical distance, wherewith it is connected. The method just explained for the computation of a route survey, requires a previous knowledge of the distance of S to S'; but it sometimes happens in practice that this information is not forthcoming and cannot be ascertained without a tedious computation, in which case, the following method of deduction should be adopted, which determines the true positions of the Route Survey points, without reference to the direct distance between the two trigonometrical Stations, wherewith they are connected. In the diagram (page 374) S and S1 are two trigonometrical Stations, and 1 02 03 are points of a Route Survey, which originates in S and terminates at S1. The elements supposed to be given are the latitude and longitude of S and also the azimuth of 1 from S. With the perambulator distance S to 1 and the elements above given, deduce the latitude and longitude of 1, as also the back azimuth of S; with the back azimuth of S and the observed angle at O1, compute the forward azimuth of 02 from 1; with this azimuth again, and the given perambulalator distance 1 to 02, deduce the latitude and longitude of 2; by a similar process, the latitudes and longitudes of the other points of the Route Survey, as likewise of trigonometrical Station S1 may be derived. When the computation arrives at S', the deduced latitude and longitude of this Station will probably differ from their respective trigonometrical values; the discrepancies thus displayed present, under an accumulated form, the whole error of the survey. To eliminate this error: add all the perambulator distances together, and take the logarithm of the sum; to the arithmetical complement of this logarithm, add the log. of the error in latitude, the sum will be a constant log.; to this constant log., add separately and in the order in which they stand, the logs. of the several perambulator distances of the survey, and find the natural numbers corresponding to these sums: now the correction for the first Route Survey point is the first natural number; the correction for the second point is the sum of the first and second natural numbers; simi larly the correction for the third Route Survey point is the sum of the first three natural numbers; and in the same manner, the correction for the other points, and also that for trigonometrical Station S1 may be deduced. It is evident, that the deduced correction for S1ought to be identical with the whole error exhibited by the survey, and when this takes place, the computation of the corrections may be assumed as having been correctly performed; in this computation the logs. used should be carried to five decimals, and the natural numbers deduced should be limited to a tenth of a second. The error in longitude may be corrected in the same way as that in latitude; this mode of dispersing the error of a Route Survey is likewise applicable when the positions of S and S1 have been fixed by astronomical observation. The method of carrying out the Ray Trace System by minor triangulation will be treated of in a subsequent Chapter. CHAPTER XVI. ON TRIGONOMETRICAL SURVEYING, AND THE MODE OF OPERATIONS TO BE PURSUED IN HILLY COUNTRIES. IN the system of survey which has been described in the last few chapters, shewing the style of a Revenue Survey, which embraces all villages situated in a champaign or wellcultivated country, the relative positions of the several Stations are ascertained by direct linear-measurement, but in a less favored, or mountainous and densely-wooded country, where, on account of the inequalities of surface, the measurements are liable to more than ordinary errors, and to connect the measurement of one village with another, with any degree of expedition, is almost rendered impossible, it is necessary, in order to prevent accumulation of errors, that the detailed measurements be based on an accurate system of triangulation. To pursue a Topographical Survey of countries of the above description, which latterly have been met with to a considerable extent in the course of the Revenue Operations in India, a Trigonometrical Basis becomes essential, we therefore propose to enter into such details for the prosecution of a Trigonometrical Survey, founded on the principles and system as now actually in use, as will enable the Surveyor to prepare himself for every emergency, for all surveys executed without due regard to this precaution, however carefully the details may be performed, partake of the character of detached operations, which are incapable of union inter se, or of harmonious combination with other surveys. Base Line. All Trigonometrical Operations emanate either from some actually measured line, called a Base Line, or from a side of some other Trigonometrical Survey, the length of which is known by calculation. As a general rule, for all surveys of a secondary order, the measurement of a base should never be attempted, if by any possibility the side of a triangle of the Great Trigonometrical Survey, can be obtained, and it will be found preferable to go a little out of the way to secure this, and to perform a little extra triangulation, in consequence, than to spend time on so difficult and tedious a task, as the measurement of a base, with rude and imperfect instruments, the results of which will never equal the value of a computed side, deduced with the scrupulous care and nicety of an important Trigonometrical Survey. The measurement of a Base Line, from which the sides of the triangles of an extensive series are to be calculated, such as for the measurement of an arc of the meridian, although apparently easy, is the most difficult and important part of a Trigonometrical Survey, as upon its accuracy, that of every triangle depends, and one in which every refinement, which mechanical ingenuity can devise, has been adopted, with a view to obtain Mathematical accuracy. The length of the base is made to depend in general on the proposed length of the sides of the triangles, which are to be deduced from it, but circumstances seldom allow it to exceed from seven to eight miles in extent, as its position is to be selected on an even plain, as nearly as possible horizontal, and otherwise conveniently adapted for purposes of measurement, where both ends of the base would be visible from each other, as well as from such stations with which they should form Symmetrical Triangles. Our limits will not admit of entering into a description of the different implements, which have at divers times been made use of for the measurement of a Base Line. Formerly |