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DE TWEEDE NAUWKEURIGHEIDSWATERPASSING VAN NEDERLAND 161
had to be applied at several nodal points in order to eliminate the effect of instability of the
benchmark concerned (table 8).
8.2 Orthometric correction
Since the equipotential surfaces were not equidistant, the orthometric correction for the lines
of the network were calculated using the Lallemand formula [15]. The relevant integral was
calculated with the aid of a graph; refer Fig. 32.
The corrections calculated were minimal and in only four cases exceeded the value 0.5 mm.
8.3 Combination of the levels measured and determination of the weighting coefficient
In the course of levelling many lines were measured a second and sometimes even a third
time. With the exception of three results (in lines numbered 3, 16, and 47), all these repeated
observations were included in the network calculation.
The weighting coefficient of the mean, estimated from a number ofmeasurements, was cal-
culated using the formula:
- l L
L=-=- (see table 9)
g, n
where g, = weight of the mean
= l/gi weighting coefficient in the mean
L =length of the line in kilometres
n =total number of times the line was levelled
Chapter 9 ADJUSTMENT
9.1 Composition of the network (Fig. 33)
The second geodetic levelling network was considerably more extensive than the first: the
length was 4592 km.
In order to limit the amount of calculation work for the adjustment, a selection was made
such that a main network of 26 closed loops, 67 lines, and 42 nodal points remained. In making
the selection as many underground benchmarks as possible were included. The length of the
main network (including 447.6 km of German lines) came to 2768 km.
9.2 Adjusting the main network (Fig. 34)
The adjustment was carried out simultaneously by two arithmeticians, working independently
of each other under the direction of Prof. J. M. TIENSTRA [26], [27], in accordance with
the Cholesky system. Twenty-six conditional equations were derived (table 9), from which the
coefficients of the 26 normal equations (table 11) were calculated. Solution of these normal
equations provided the values for the 26 correlates K, (table 12) with the respective matrix of