458 JOSEPH BARRELL 



more slowly, decreasing for the spreading-out of the mass in a 

 horizontal direction, increasing for a linear vertical extension. For 

 the spheroids whose axes are in the relation of i to 2 and to which 

 the spheres are equivalent in volume, the changes would be still 

 more marked. This is because the dupKcations of mass due to the 

 intersecting spheres are near the center and in Case C a top view 

 would show considerable deficiencies of mass in the equatorial zone 

 between the spheres and the spheroid. These intersecting spheres 

 are consequently more effective in producing gravity anomaly 

 and somewhat more effective in producing deflection of the vertical 

 in the zone of maximum deflection. For cylindrical disks of the 

 same mass and proportions as the spheroids the changes away 

 from the values for a sphere would be still greater, since a greater 

 proportion of the mass would be removed from the center to the 

 edges of the body. 



Distinctive effects of individual spheres and spheroids. — In the 

 subjection of deflection measurements to the hypothesis of isostasy 

 Hayford found it necessary to consider the effects of topography 

 to a distance of 4,125 km. and in the determination of gravity 

 anomalies the topography of the whole earth and its compensation 

 were considered. To what extent then do distant masses affect 

 the local residuals and vitiate any attempt to analyze the effects 

 of local masses ? In answer, it is seen that the effects of distant 

 masses are negligible. It is the great topographic contrast of 

 ocean basins and continental platforms, to a lesser extent the large 

 variations of relief within these areas, which require their effects 

 to be considered to such a great distance. But it is found that 

 this larger relief of the crust is nine-tenths compensated and the 

 outstanding masses so far as known do not show any marked 

 segregation as to sign within the continental areas as opposed to 

 the oceanic areas. Furthermore, the unit areas departing markedly 

 from isostatic equilibrium are much smaller than these major 

 segments of the crust. Therefore where it is the effect of the out- 

 standing masses which is under consideration they are seen to 

 be individually small in comparison with the greater relief features 

 of the globe, and further, they mutually cancel their efl'ects. The 

 local outstanding masses are furthermore of the same order of 



