Bouguer Redeemed: The Successful 1737-1740 Gravity Experiments on Pichincha and Chimborazo

During the 1735-1745 French Academy of Sciences expedition to Peru, Pierre Bouguer conducted two experiments confirming Newtonian gravitational attraction and estimating the mean density of the Earth. One set of experiments determined the variation in gravity with altitude using a pendulum at sea level, Quito (2,860 m) and the summit of Pichincha (4,784 m). Qualitatively correct, Bouguer reported a smaller decrease in gravity than that predicted from altitude increase alone, but he calculated that the mean density of the Earth was nearly five times that of the near-surface rocks, an overestimate by a factor of at least two. The better reported experiment was an attempt to detect the deflection of the vertical near the mountain Chimborazo. There was a large difference between Bouguer's predicted plumb-line deflection, 103", and that which he and La Condamine measured, just 7". I have investigated both experiments using a digital elevation model to compute the vertical and horizontal components of the gravity field caused by topography, and include the regional gravity signature of the Andean crustal root. The modelling indicates not only that Bouguer's pendulum measurements were extremely accurate, but also that his observations allow a good determination of the significant isostatic effect. In contrast, on Chimborazo, contrary to recent suggestions, isostatic effects are negligible, and Bouguer's deflection was, within error, in line with the modelled plumb-line deflection from topography. Both Bouguer's pendulum and plumb-line measurements were reliable and therefore he should now be redeemed from any inference of failure.