Page 2 Advertisements Column 5

Wellington Independent, Volume XXIV, Issue 2806, 6 March 1869, Page 2

Log. AC + x, x being the small logarithmic correction due to a gradual accumulation of error, then Log. AC + x = Log. AB + (Log. sin B + x/2) + (Log. cosec. C + x/2) . Take out the Logarithmic difference due to one second for these angles in every triangle of the series as indicated by a dot in the diagram and call the sum of these Log. differences s ; then d/s will be an arc of correction in seconds to be applied to each of the above mentioned angles. When the accumulated error causes the side AB to exceed its proper value, this correction is substractive from those angles to which the sine is applied and additive to those taking the cosecant, but the contrary is to take place when side AB is found to be short of its proper value. The sides may either be recomputed with these new angles or corrected in proportion to the angular corrections applied, and the discrepancy in the side AB will then totally disappear. These corrections are only to be applied when the errors are extremely minute and within the probability of errors in observation. (See Instructions for topographical surveying by Lt.-Col. Waugh, Bengal Engineers). Polygons succeeding in order to be computed on the same principles. 34. Successive polygons CDEHIK, &c, should be operated upon in the same manner, observing in every case that two sides have always become unalterably fixed, the one affording a base for continuation whilst the other serves as a check. In this manner any number of triangles may be extended and the work verified during progress until the measured base of verification is reached. When the triangles form into Quadrilaterals as GLMF they present no check unless the bearings of both diagonals have been observed. Elimination of error in this latter case is analogous to the method just described, computing the triangles in the following order FLG, GML, GFM. Test of Triangulation by base of Verification. 35. One of the severest tests that a Trigonometrical survey can be submitted to is a comparison of the computed length of the second measured base, brought up in the manner described with its actual measure. The maximum error allowable is one foot per mile, but in practice it has been found to be considerably within this limit. Should, however, the errors be large but not exceeding the above limit, their elimination on the principles before mentioned should be accomplished; this process entails the reworking of the computations. Meridional and Perpendicular Co-ordinates. 36. The next process is to compute the meridional co-ordinates of every station from some one station generally chosen in a central part of the survey, If, however, one of the stations is also that of a previously executed trigonometrical survey, it would be proper to adopt it for this purpose, since it will furnish a point of departure and direction of the meridian in terms of the former survey and an ascertained height above sea level. The bearing of any one side in the triangulation having been determined upon those of all the rest are obtained by ihe application of the corrected mean angles of the computations. Suppose B to be the point of departure, first compute the meridian distance of A with the given bearing and length of side AB, then that of C from the two stations A and B, and in like manner those of D, E, F, &c , consecutively. It is to be remarked that the two resulting distances for any station should uniformly agree to a decimal of a link, since there exists no inconsistency between the angles and sides of the triangles. The differences between the meridian and perpendicular distances between any two stations afford data for computing the bearing and length of side, and by comparison with the observed bearing presents another check upon the accuracy of the work. Plotting. 37. The scale to be adopted for the map is 80 chains to an inch. Previous to plotting the paper should be divided into squares representing meridian and perpendicular lines six miles apart. These lines besides facilitating the protraction of the work serve as measures of latitude and departure for the connexion of sheet to sheet and eventually become convenient basis for setting off the true meridional and longitudinal lines. Also, with the aid of a table of Natural Tangents bearings may easily and accurately be protracted from them, and they preserve a uniform scale for reference notwithstanding the expansion or contraction of the paper caused by changes of temperature. It is recommended to plot the stations from their computed Meridional co-ordinates and then to verify each by the protraction of its bearing and distance from other stations. The bearings and lengths of the sides must be neatly written upon all the lines specifying whether derived from observation, computation, or measurement conformable with the rules furnished in Appendix. The Meridianal Co-ordinates are to be written against every station. Differences compared between plane and spherical measurements as affecting the Survey. 38. As the spherical excess has been omitted to be taken into account in the computations of the triangles, for the reasons advanced in Paragraph 29, the results may be affirmed to be based upon the false supposition of the earth being a plane instead of a sphere. Now, as the difference between an arc on the earth's surface and its chord amounts only to 24 feet in 69½ miles, and as the limit of error