Atmospheric Effects on the Cross-Sea Levelling Observed at the Straits of Tsugaru

Abstract

In the cross-sea levelling carried out at the straits of Tsugaru, the zenith distances were observed simultaneously at two opposite stations, and the relative height was calculated by the usual tangent formula. The formula holds only if the refraction coefficients be identical in one direction and the opposite (Kij= Kji). Such assumption, however, may hardly be true in general, especially in such long sight-lines as in the case of the straits of Tsugaru (about 20 Km). Taking the fact into account, we put Kji=Kij+ΔK, and the refraction coefficients Kij and Kji were respectively evaluated in two independent ways: one way was made use of the refraction formula, into which the meteorological data were introduced, while the other was applied Eggert's formulae, in which the refraction coefficients were represented by the power series of the relative height, instead of his original form. As a result, the corrections to be applied to the apparent relative height were found to be+13 cm and+19 cm respectively.