452 JOSEPH BARRELL 



force, Fh, would be in the form of a caldera or crater ring. Accord- 

 ing as the attracting mass departed in its nature from a sphere 

 these shapes of the force surfaces would be modified, but the general 

 character of volcanic cone and caldera would remain. Negative 

 masses would have the forms reversed. If the disturbing masses 

 are at distances apart which average several times their depth, 

 then a relief map of the resultant forces would resemble a volcanic 

 field with the volcanoes isolated from each other. If the centers 

 are much closer, the relief map would come more to resemble those 

 lunar craters which show all degrees of superposition upon older 

 craters. The deeper the masses the broader the volcano-like 

 curves of forces upon the surface, but the lower will be the relief, 

 unless the disturbing spheres increase in mass with the square of 

 the depth. Stratiform-like masses, such as oblate , spheroids or 

 cylindrical disks, will show less pronounced effects than the equiva- 

 lent spheres and will simulate somewhat the effects of spheres at 

 a greater depth. The attempt to apply these principles as criteria 

 to the published data must be deferred until the influence of 

 abnormal masses in the zone of compensation has been considered 

 and also in somewhat more detail the influence of masses in other 

 forms than spheres. 



Influence of spheres within the zone of compensation. — The forces 

 produced by spheres within this zone are more readily treated 

 analytically, since it will be seen that the curvature of the earth 

 may be neglected. Otherwise this topic is to a considerable degree 

 an extension of the last. The unit mass which it is convenient 

 to adopt for this discussion is that of a sphere whose radius is 50 km. 

 and density o. 100, one-half the mass of the sphere previously con- 

 sidered. Its center is taken at a depth of 64 km., o.oi of the 

 earth's radius, and approximately at the middle of the zone of 

 compensation as given by Solution H. This gives the greatest 

 abnormality of mass in the middle of the zone of compensation 

 and will approximate to the mean effect of an outstanding density 

 distributed uniformly throughout that zone. At the epicenter the 

 attraction is wholly effective in producing gravity anomaly and is 

 measured by the formula 



