7 Testing of a small experimental model

The functioning of a small experimental model of a floating mirror horizon was tested at the Geodetical Observatory PecnýŒ in Ondrejov. The mirror had a diameter of 10.8 cm, a thickness of 1.17 cm, and the steel balls in conical bearings had a 11.9 mm diameter, with a clearance to the centring arms of 0.02 mm. The centring arms were made of duralumin and the basin for mercury was of stainless steel. As mercury could not form amalgam with the latter material, a minimum height of a layer of mercury completely covering the bottom of the whole basin was 1.75 mm. This height, below the bottom surface of the mirror, was maintained for all trials. (Total height of the mercury column was 3.0 mm). Trials have shown that the tested model has the expected properties. If the mirror was rotated, oscillating at a frequency of approximately 1.4 Hz, it achieved its equilibrium position in approximately 12 s. The frequency of oscillations (observed as oscillations of a reflected image in a telescope) was about the same as that of a freely oscillating surface of the mercury when the mirror was removed (and when the basin with mercury was rotated instead of the mirror). However, in this case, the free surface of the mercury did not come to rest until after about 40 s. This illustrates the effectiveness of the damping by the new system. When the steel balls were fixed in their bearings, the reflected image still had the previous frequency of oscillations, but the system came to rest after about 17-18 s; which is almost a 50% increase on the time interval with free balls.

Consistency of the balanced (levelled) positions of the mirror was assessed by an autocollimation method: by means of a Wild T3 universal theodolite, zenith distances of the telescope's diaphragm reflected from the mirror were observed. Multiple observations of the mirror's re-established vertical position at the zenith distance of $30^\circ$ - and in various directions - indicated an accuracy $\geq 0.1{''}$. (Accuracy of a single measure was typically 0.3''). However, with a higher angular resolution of readings, the actual accuracy of the mirror, being consistently levelled, could be still higher, approaching that of the levelled (free) surface of mercury. As there are no horizontal force components acting on the mirror in its static equilibrium, no friction force to oppose the mirror's balancing moment $M_{\rm c}$ should arise between the centring arms and the steel balls (when these are in contact). Moreover, the contact is minimized to points (theoretically).

Also, if the instrument were rotated by a motor to follow stars during observation, the mirror's levelled position would not be affected when the velocity of rotation became constant. The velocity of rotation is then so low ($\omega\leq 7.29\ 10^{-5}$ rad s^-1), that even if the motor were stopped, upon impact of the centring arms on the balls, the balls would (using previous relations) elevate by $\Delta h=2.4\ 10^{-8}$ mm with a mirror of 2R=10 cm and H=1.5 cm, with balls having a diameter of 10 mm; and by $\Delta h=3.3\ 10^{-8}$ mm with a mirror of 2R=20 cm and H=3.5 cm and a diameter of balls of 30 mm. This means - considering that there is also an additive effect of friction in the conical bearings -- that the system would

behave as if the centring balls were fixed in their position, as though it were a static system in equilibrium. Because of the mentioned clearance of 0.02 mm, within this limit the mirror has some freedom for translational motion. But this would also not affect the levelled position of the mirror, as we mentioned before.

To verify the limiting accuracy of the mirror's levelling would require a method of higher resolution (autocollimation on a meridian circle instrument, e.g.), or prolonged observations to stars with the device installed in an astronomical instrument.

A comparison was also made between the quality of images reflected from the mirror and those from the free surface of mercury. The cross-wires reflected in the autocollimation method from the mirror were distinctly sharper than those reflected from mercury, although very clean (polarographic) mercury of high chemical purity was used in the experiments. For the properties discussed, the new device could find some applications in astronomical instruments. It could also be installed in a new model of a circumzenithal.

Acknowledgements

The author wishes to express his appreciation to colleagues G. KarskýŒ and V. Skoupý, from the Geodetical Observatory PecnýŒ in Ondrejov, for their assistance in testing the experimental model of a floating mirror horizon, as well as to A. Müller, F. Sedlácek and J. Vlásek from the mechanical workshop of the Research Institute of Geodesy, Topography and Cartography in (Prague) Zdiby, who made the device according to author's proposal.