Text book On Geodesy And Least Squares Prepared for the Use of Civil Engineerin

Cover Text book On Geodesy And Least Squares Prepared for the Use of Civil Engineerin
Text book On Geodesy And Least Squares Prepared for the Use of Civil Engineerin
C L Charles Lee Crandall
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For a point on the surface of the earth, if regarded as a sphere, the attraction is the same as if the mass were concentrated at the center. If a small mass is horizontally distant d from this point, the relative attractions of the earth and the small mass upon the point are M/R 2 and m/d 2 . Hence if = the deflection of the plumb line due to m, mR 2 The volume of the earth = -R 3, and its mean density is * Recent Progress in Geodesy, by E. D. Preston. Phil. Soc. Of Wash. Bui. Vol. XIII.
204 GE
...ODESY. ( 118, Fig. 88, about 5. 63 (as compared with 2. 3 for rock), while in round num- bers R = 6 370 000 m .
Denoting the volume of the mass m by v and its density by d, m=vd.
Substituting, 0" = 0. 001 373^ (119) The effect of elevated masses can thus be computed if the topography is known. If the mass is large in proportion to dis- tance, it should be divided up and vd/d 2 found for each part and added, or a more general expression found by calculus. * After correcting for the topography, deflections still remain, and these are accounted for by variations in density.


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