THE STRENGTH OF THE EARTH'S CRUST 



457 



used, but with radius of 32 km. instead of 50 km. The mass is 

 consequently but 26 per cent of that of the unit sphere. Let this 

 be expanded into three intersecting spheres with centers 32 km. 

 apart and arranged in a vertical line. The composite mass will 

 then extend from the surface to a depth of 128 km. and correspond 

 closely in effect to a prolate spheroid with vertical axis. 



The resulting values of the components of the gravitative force 

 for these four cases which are of importance for the development 

 of criteria may be tabulated as follows: 



TABLE XXV 



To complete the series the curves should be drawn for five inter- 

 secting spheres arranged in a vertical plane analogous to Case V, 

 first parallel and then at right angles to the plane of the section, 

 making cases E and F, but the general character of the resulting 

 curves may be inferred from the cases already given. Therefore, 

 in order to abbreviate the discussion, an additional figure for cases 

 E and F has been omitted. 



It is seen from inspection of Figs. 9 and 10 and Table XXV that 

 even for a constant mass and center of gravity the values of Fv 

 and Fh change rapidly with the changing form of the mass. Upon 

 the linear extension of a sphere into a form such as cases A and B 

 the maximum value of Fv falls to two-thirds of its original value. 

 For Case C it is still less. The ratio of the maximum value of 

 Fv divided by the maximum value of Fh is also seen to change, but 



