THE STRENGTH OF THE EARTH'S CRUST 461 



be M. The ratios of the value of Fh at M to the value at ^M 

 are given below as measured from the curves. 



Ratios of Fh at M to Fh at 3M 



Sphere 2.4 



Case A 2.1 



Case B 4.3 



Case C 3.4 



Case D 2.0 



It is seen that, from the difficulty in the precise location of M and 

 hence the difficulty in locating a point as at 2M or ^M, and further- 

 more the probability that other masses may influence to a degree 

 not readily determinable the value at ;^M, this test cannot ordinarily 

 be determinative. However, for spheroids with polar axes vertical, 

 markedly prolate masses give a ratio distinctly smaller than for a 

 sphere, the curve of deflections falling off more abruptly; markedly 

 oblate masses, on the other hand, give a ratio distinctly larger than 

 that for a sphere, the curve of deflection beyond the point of 

 maximum being flatter. 



If the outstanding mass approximates to an oblate spheroid with 

 polar axis vertical, then the assumption of a spherical nature will 

 locate the center of mass too deep and imply a greater mass than 

 really exists. If, on the contrary, the form of the outstanding 

 mass approaches the form of a vertical prolate spheroid, the inter- 

 pretation of the deflections as caused by a sphere would locate the 

 center of figure too high and give it too small a mass. 



Suppose the curves for Fh shown in cases C and D have their 

 maxima well determined in position and in magnitude, but that 

 the values of the curves at distances two or three times beyond are 

 not accurately known. Let these maxima be interpreted as pro- 

 duced by spheres. The depth and masses of the spheres which give 

 these maximum deflections will be too great by the amounts shown 

 in the following tabulation (Table XXVI, p. 462). 



Where the data are sufficiently complete the form and depth 

 of mass may both be determined, though a high precision is not 

 to be expected. But in most cases with the present geodetic data 

 the form of the mass will not be determinable and all that can be 



