260 EXPLORATION GEOPHYSICS 



local inhomogeneities may be great enough to cause considerable difficulty 

 in geodetic measurements. 



A Geodetic Use of Gravity Values. — The flattening or degree of 

 departure from the spherical form of the earth can be computed from abso- 

 lute gravity values. This is of importance geodetically in order to find the 

 best assumed shape for the earth to produce maps with a minimum of 

 distortion. The compression, or flattening, of the earth can be calculated 

 from Clairaut's theorem as follows : 



^^-^ = 5/2 -^ - ^^—^ (19) 



In the equation h = the length of the earth's polar axis and a = the length 

 of the equatorial axis (assuming that the equatorial section is circular, or 

 that the earth is a 2-axial ellipsoid), g = gravity and subscripts p and e 

 designate pole and equator respectively; i.e., Cg = equatorial centrifugal 

 force. 



The second term in the right hand side of the equation is the gravita- 

 tional flattening previously mentioned. 



Clairaut's theorem states that the difference in polar and equatorial axes 

 divided by the polar axis is equal to 5/2 the centrifugal force at the equator, 

 divided by the force of gravity at the equator, less the gravitational flatten- 

 ing. Since these quantities related by the equation can be measured or 

 calculated, the shape of the earth can be determined. 



From a careful study of gravity values in all parts of the world, the 

 following: value for axial difference ratio has been established : 



Cf^)- 



± 0.7 meter 



298.3 



Isostasy 



If the shape of a mountain or valley or any other topographical feature 

 and the densities of the materials composing the feature and surrounding 

 it are known, it is possible to compute the effect of the topographical 

 feature on the gravitational field. It is found, however, that for large 

 features, the effects so computed are generally much greater than the 

 measured effect. The discrepancy in most cases is far in excess of the 

 probable variations due to inaccuracy of data or calculations. This fact 

 forms the experimental basis of the hypothesis of isostasy or isostatic 

 compensation, t 



According to this hypothesis the apparent excess of matter represented by a hill or 

 the apparent deficiency of matter represented by a valley or an ocean basin is compen- 

 sated by underlying materials. Thus, beneath each hill there is somewhere sufficient 

 material of lower density to compensate for the hill so that in reality there is little, if 

 any, real excess of matter. Quite generally, the hypothesis of isostatic compensation 



t William Bowie, Isostasy (E. P. Button Co., 1927); "Isostatic Investigations, etc." U.S. 

 Coast and Geodetic Spec. Pub. Dept. of Commerce, 99, Serial 246, 1924. 



