By G. D. Garland, J. A. Jacobs and J. T. Wilson (Auth.)
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Additional resources for The Earth's Shape and Gravity
15) shows that ^2 which is Clairaut's result. = f w-/. 16) THE SHAPE OF THE SEA-LEVEL SURFACE 37 Clairaut's equation cannot be used as it stands for geodetic purposes, because of the neglect of terms of order /^, Darwin (1910) and many later workers (Gulatee, 1940) carried through a similar analysis without neglect of these terms. 17) where φ is the geographic latitude. 18) where m and / h a v e their previous meanings, and % is a constant which is determined by the internal density distribution.
It is, of course, normal to the geoid (Fig. 1). This is the direction indicated by the plumb line at any point, and is the local vertical. Because of the effect of local inñuences on the vertical, position on earth cannot be determined with precision by any method which involves the measurement of a direction with reference to it. F o r example, astronomical determination of latitude and longitude makes use of the elevation of a circumpolar star, and the time of transit of a star across the meridian.
Gravity measurements have been made in most of the mountainous regions of the world, and many examples (Fig. 3) could be given of this almost universal tendency. N o w there is nothing illogical in the inclusion of the Bouguer term for the attraction of material above sea level, and the large negative 52 THE EARTH'S SHAPE AND GRAVITY values can only mean that there is a deficiency in mass below sea level, with the deficiency increasing as the land surface rises. This is an exemplification of the important principle of the compensa tion of the earth's surface features by sub-surface mass distribu tions.
The Earth's Shape and Gravity by G. D. Garland, J. A. Jacobs and J. T. Wilson (Auth.)