Consideration of the sources of error of the astronomical levelling appears to lead to an error or weight function of the form (6), possibly in some cases the more general expression (7). The coefficients must in every single instance be empirically determined from the material itself; here we primarily make use of the triangle closure errors in combination with the demand that the mean error μ0 of the unit of weight be the same, independent of the size of the triangle.—Application of this procedure to the material from Finland (255 stations of deviation of the vertical, combined into 337 triangles) can be regarded as a confirmation of expression (6) with e=±0″.30, κ=±0″.010/km, μ0=±6.7 cm (s0=31.6 km). The coefficients are between themselves so similar, that their combined effect can hardly be distinguished from a purely cubic function, which therefore was used as a base for the computation of the geoid.—On the other hand, bothDe Graaff-Hunter's material from Czecho-Slovakia [3] and that ofLitschauer from Austria [8] lead to purely quadratic functions of error, a result which can be interpreted so, that in these cases the coefficient of the biquadratic interpolation term is so small, that it cannot be statistically demonstrated.