On the Equation of Conditions for Laplace Residuals (III):-Practical Application to the Adjustment of Tenjinno Triangulation Net, Including 1 Base-line and 2 Laplace-stations-
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As the sequel of the second paper showing a practical application of one of the working formulae for the Laplace residuals, the present paper is devoted to a numerical illustlation that the other working formula (3.5) in the first paper is effectively available for the adjustment of a regional triangulation-net. The sample adopted here is the revised " Tenjinno " triangulation-net, since it contains one remeasured base-line and two recently obseved Laplace stations, where the Laplace residuals are remarkably abnormal. By making use of the formula as not a condition but an error-equation, a set of the error-equations composed of the side-equations, the angle-equations and the Laplace-residual-equations, was adjusted so as to get the most probable values of variations of the geographical coordinates by means of the method of the least squares. The net-adjustment, however, was carried out in two different treatments (a) and (b), corresponding to two kinds of the angle-value, the one observed and the other station-adjusted, both of which have been applied with the same corrections of the normal section and of the plumb-line. The adjusted results were sosatisfactory that the mean error of an obsevation of unit weight in each case was considerably smaller than the one obtained from the usual figure net-adjustment, and furthermore the Laplace residuals were regarded as null in the range of the obsevational errors. For comparison, the third net-adjustment (c) was carried out, excluding only the Laplace-residualequations from the set of error-equations in the case (b). In this case, the adjusted Laplace residuals were reduced to -″1.88, -″1.63, - ″1.76 at "Taisho-yama" and -1″. 94, -1″ .73, -1″.86 at " Mikuniyama ", although the obseved ones were +6″.95, +5″.91, +4″.33; +2″.74, +5″.43, +8″.51 respectively. Whereas the adjusted values of the angles and the side-lengths proved, as expected, to be almost the same as those of the case (b). In the anthor's view, the case (a) may be the most favourable, and if the Laplace residuals are not given, the side-equations and the angle-equations correspondieg to the case (a) should be adjusted, though an error of orientation of the net will remaim as it is.
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