Difference between airy and Pratt concept on isostasy
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Part I of this review (Howarth, 2007) described how following Isaac Newton’s (1642–1727) postulate in 1686 that the Figure of the Earth was, like that of Jupiter, an oblate spheroid, and that both the force of gravity (indicated by the length of a pendulum beating seconds) and the length of a 1-degree arc of latitude ( θ ), should increase towards the poles as sin 2 ( θ ). In 1737 his hypothesis was found, by measurement of arc lengths, to be correct. In 1743, Alexis Claude Clairaut (1713–1765) showed how to compute the amount of flattening of the Earth’s spheroid from gravity measurements. By the early nineteenth century, acquisition of pendulum data from stations in many latitudes was enabling this characteristic to become increasingly well defined. However, occasional discrepant results were beginning to raise questions as to whether the nature of the substratum might, on occasion, influence the pendulum length measurements and statistical analysis of such data by Edward Sabine (1788–1883) and the English Astronomer Royal, George Biddell Airy (1801–1892) provided the first definite confirmation that this might be the case. The earliest practical investigations, which led to an indirect involvement with geology, were aimed at determining whether the attractive force exerted by the mass of a large mountain would be sufficient to deflect a plumb-line from the vertical. As the result of an oversight, Newton had underestimated this effect, concluding that “[a] mountain of an hemispherical figure, three miles high, and six broad, will not, by its attraction, draw the pendulum two minutes out of the true perpendicular.” (Newton 1726, Sec. 22; Cajori, 1934, p.570). Nevertheless, early investigators were keen to test his assertion. The first to do so were the French mathematician-astronomers, Pierre Bouguer (1698–1758) and Charles Marie de La Condamine (1701–1744) in December 1738, in the course of their measurement of the length of a three-degree equatorial arc across Peru and Ecuador. They chose to investigate the phenomenon at Chimboraço (Chimborazo, 6530 m), in Ecuador, the highest mountain then known in the New World, which rises some 3600 m above the tablelands near Quito (Bouguer 1749, pp. 379-390). Bouguer’s prior calculations indicated that the mountain’s influence on a plumb-line might equal 1/1000th part of that of the whole world, and he therefore anticipated a deviation from the vertical of about 43" of arc . They investigated this by sighting on the meridian altitudes of a set of chosen stars. Ascending to within 425 m of the summit on the south side of Chimborazo and using an astronomical quadrant whose zenith was fixed by means of a plumb-line, they determined the meridian altitudes of six stars to the north of their station ( N ), and of four to the south 1 ( S ). These observations were repeated on the following day. They then established a 1 lower station, 1.8 km to the west and 90 m lower than the first, and repeated the entire set of observations ( N , S ). It was assumed that the observed altitudes measured at the first 2 2 station would include the deflection ( τ ) of the plumb-line towards the mountain plus an error component ( ε ), whereas those from the more distant station would only contain the error component. The overall mean of the observed differences [( N - τ + ε ) - ( N + ε )] 1 2 between the six individual mean altitudes of the set of northerly stars at the two stations was 1' 19"; while for the four southerly stars, the mean of the differences [( S + τ + ε ) - 1 ( S + ε )] was 1' 34". Then, assuming that the observational errors were of similar 2 magnitude and cancelled out: τ = [( S - S ) - ( N - N )]/2, i.e. 7.5" of arc (Bouguer 1749, 1 2 1 2 p. 388). In considering the interpretation of his pendulum observations, Bouguer (1749, pp. 359–361) took into account both the effect caused by the elevation of the station at Quito above sea level, and the density of the matter forming the mountain chain in which it was situated relative to the density of the entire Earth.
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