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The twin Laplace point Ubachsberg - Tongeren, applying the black method

 PoG 14, G.J. Husti, The twin Laplace point Ubachsberg - Tongeren, applying the black method

G.J. Husti

Publications on Geodesy 14 (Vol. 4 Nr. 1). Delft, 1971. 30 pagina's.
ISBN-13: 978 90 6132 214 6. ISBN-10: 90 6132 214 6.


In the summer of 1968 astronomical observations were carried out at the primary stations Ubachsberg (The Netherlands) and Tongeren (Belgium) in order to make a twin Laplace point of these two stations. This work was undertaken in behalf of the New Adjustment of the European Triangulation. The latitude, longitude, and azimuth were determined simultaneously applying Blacks method and using a Wild T4 universal theodolite. The results obtained are shown in section 8.

The main purpose of the measurements was to determine the geodetic azimuth Ag = A + (l - l)sin j0 , which was obtained with high accuracy, because of the strong negative correlation between the astronomical azimuth and astronomical longitude.

The misclosure between the two stations of this twin Laplace point amounts to 0''.57.
Furthermore, the accuracy requirements for Laplace points in The Netherlands were investigated.
Based on the deviation of the geodetic part of the Laplace equation, it was found that a standard deviation of 0".25 in the geodetic azimuth suffices.
The observer's personal equation was determined using an artificial moving star.


List of symbols and constants  4
Summary  5

  1. Introduction  5
  2. The Black method  6
  3. Selection of stars  9
  4. Instruments  10
  5. Testing of the equipment  12
  6. Instrument set-up at Ubachsberg and Tongeren  12
  7. Measuring programme  14
  8. Results  16
  9. Reduction to centre  17
  10. Computation of the misclosure  18
  11. Standard deviation of the observations  18
  12. Standard deviation of the geodetic part of the Laplace equation  21
  13. Personal equation of the observer  22

References  23
Appendixes  25

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