The largest Mercury mirror telescope is the Large Zenith Telescope in Vancouver, Canada. When spinning the Mercury is spread out in a layer that is about 2 milimeter thick at every point on the dish.
I want to examine the following simple case: a Mercury mirror located on the equator, spinning counterclockwise.
To form a perfect paraboloid surface the Mercury must experience the same gravitational acceleration at every point on the dish. Then the incline of the dish gives rise to just the right centripetal force towards the center of the dish.
Given the equatorial location the relevant rotation-of-Earth-effect is the Eötvös effect. Let's distinguish between a 'southern half' and a 'northern half' of the Mercury mirror. The Mercury in the southern half experiences too little gravitational acceleration; it will tend to slide outward, up the incline. Conversely, the Mercury in the northern half experiences too much gravitational acceleration, and it will tend to slide down the incline.
To mitigate the distorting effect you could try a tilt of the mirror's spin axis. However, you can counteract the rotation-of-Earth-effect only partially.
The magnitude of the effect is proportional to the velocity relative to the Earth, hence the magnitude of the effect is different at different distances to the center of the mirror. A level of tilt that is just right for the outer rim of the Mercury mirror will be too large for the rest. The best you can do is a compromise that minimizes the effect averaged over the entire dish.
It seems to me that the above qualitative reasoning is unassailable. While distortion due to the rotation-of-Earth-effect can be counteracted, it cannot be eliminated.
However, Paul Hickson, director of the Large Zenith Telescope, has come to an altogether different conclusion. In a 2001 article titled Eliminating the Coriolis Effect in Liquid Mirrors he states that the rotation-of-Earth-effect can be eliminated entirely.
I have difficulty following the steps of Hickson's derivation, so much so that I cannot pinpoint the error that I feel must be there.
There is a another article by Hickson on the same subject, published in 2006. Hydrodynamics of rotating liquid mirrors (Unlike the 2001 article not a free download; I don't have that article). In the abstract it is stated that the shape of the mirror is highly sensitive to the tilt of the axis.
The question is the title of this post:
Mercury mirror telescopes: is it possible to eliminate the rotation of Earth effect?