On the Equations of Conditions for LAPLACE Residuals (II)

-Application to a Problem concerning the Errors in the Geodetic Coordinates of the Japanese Datum Point-

Abstract

In the first paper, the author has derived a more general formula for the Laplace condition, from which two different equations of conditions for LAPLACE residuals were introduced, the one being suitable for a regional triangulation net and the other for a system of all the nets. This paper concerns the practical application of the latter equation to the Japanese system of the geodetic coordinates. By means of the astronomical results on the recently established LAPLACE stations, thirty-three in all, the errors in the geodetic coordinates of the Japanese datum point were provisionally evaluated by our formula. The numerical results obtained here may not be conclusive, as the observed data were insufficient in number, especially in the south-western part of Japan, and furthermore the horizontal earth-displacements could hardly be eliminated completely. The provisional values, however, are not markedly discordant with the other investigators' previously obtained by the usual method of “the deviations of verticals.” It is to be noted that these two independent treatments have common reference to the physical earth-surface in Japan and not to the “world-wide earth-ellipsoid.” A fact found worthy of some attentionin the course of this study is that the Japanese triangulation-net has been twisted considerably in the Hidaka district of Hokkaido where the deviations of verticals change remarkably from place to place.