Maskelyne's 1774 Schiehallion experiment revisited

摘要

Nevil Maskelyne's 1774 experiment on the Scottish mountain Schiehallion set out to derive the mean density of the Earth, from astronomical observations of the deflection of the vertical and calculation of the mountain's relative gravitational attraction. Using Maskelyne's results and lithological survey results, John Playfair estimated mean Earth specific gravity to be 4.56-4.87, while Charles Hutton argued in 1821 that the Earth was `very near five times the density of water; but not higher'. Hutton challenged future workers to identify any areas in which his analysis could be improved. The geometry of the 1774 experiment has therefore been recomputed within a digital elevation model extending 120?km from the mountain. Three contributions to the deflection of the vertical have been included: topography, and local and regional subsurface density variations. Local subsurface densities have been modelled using geological maps, cross-sections and laboratory measurements. Regional subsurface effects have been included from analysis of the Bouguer gravity anomaly. The outcome of the new modelling is to credit Maskelyne for his accurate astronomical observations, as together with the new density structure model, they yield a mean Earth density of 5480±250 kg m~(-3), in agreement with the modern value of 5515 kg m~(-3).