Schiehallion Experiment - Measurements - Astronomical

Astronomical

Observatories were constructed to the north and south of the mountain, plus a bothy to accommodate equipment and the scientists. Most of the workforce was however housed in rough canvas tents. Maskelyne's astronomical measurements were the first to be conducted. It was necessary for him to determine the zenith distances with respect to the plumb line for a set of stars at the precise time that each passed due south. Weather conditions were frequently unfavourable due to mist and rain. However, from the south observatory, he was able to take 76 measurements on 34 stars in one direction, and then 93 observations on 39 stars in the other. From the north side, he then conducted a set of 68 observations on 32 stars and a set of 100 on 37 stars. By conducting sets of measurements with the plane of the zenith sector first facing east and then west, he successfully avoided any systematic errors arising from collimating the sector.

To determine the deflection due to the mountain, it was necessary to account for the curvature of the Earth: an observer will see the local zenith shift by the same angle as any change in latitude. After accounting for observational effects such as precession, aberration of light and nutation, Maskelyne showed that the difference between the locally-determined zenith for observers north and south of Schiehallion was 54.6 arc seconds. Once the surveying team had provided a difference of 42.94″ latitude between the two stations, he was able to subtract this, and after rounding to the accuracy of his observations, announce that the sum of the north and south deflections was 11.6″.

Maskelyne published his initial results in the Philosophical Transactions of the Royal Society in 1775, using preliminary data on the mountain's shape and hence the position of its center of gravity. This led him to expect a deflection of 20.9″ if the mean densities of Schiehallion and the Earth were equal. Since the deflection was about half this, he was able to make a preliminary announcement that the mean density of the Earth was approximately double that of Schiehallion. A more accurate value would have to await completion of the surveying process.

Maskelyne took the opportunity to note that Schiehallion exhibited a gravitational attraction, and thus all mountains did; and that Newton's inverse square law of gravitation had been confirmed. An appreciative Royal Society presented Maskelyne with the 1775 Copley Medal; the biographer Chalmers later noting that "If any doubts yet remained with respect to the truth of the Newtonian system, they were now totally removed".