228 JOSEPH BARRELL 



the distribution of anomalies appears to depend more upon the 

 internal than upon the external departures from regional uni- 

 formity and complete isostasy. The internal heterogeneities of 

 mass are therefore presumably greater than the shiftings of mass 

 due to external activities. 



CRITERIA FOR SEPARATING VERTICALLY IRREGULAR COMPENSATION 

 FROM REGIONALLY INCOMPLETE COMPENSATION 



Suppose the topography smoothed out to a mean level over 

 areas as large as the limits for regional isostasy. The deflection 

 residuals and gravity anomalies would then be due to one or more 

 of three internal causes; first, vertically irregular or laterally 

 displaced compensation; second, regionally incomplete compensa- 

 tion above the bottom of the zone of compensation because of the 

 effective rigidity of the crust above that level; third, regionally 

 incomplete compensation above a certain level because the zone 

 of compensation may be deeper in places, transferring stresses 

 into a deeper rigid earth. The existence of a general approach 

 toward compensation and away from absolute rigidity suggests 

 that the last is not so important as the first two causes. Under 

 this section then will be considered these two causes, their effects 

 upon the deflections of the vertical and the intensity of gravity, 

 with the purpose of drawing criteria by which the action of the 

 two causes may be recognized and separated. To do this it will be 

 necessary to discuss here to some extent the theory of the attraction 

 of underground masses upon stations at the surface of the earth. 

 It has been shown that balanced irregularities in the vertical 

 distribution of densities through the zone of compensation could 

 give pronounced anomalies without disturbing the isostatic equilib- 

 rium at the bottom of the zone, since the total weight of the column 

 could still be normal. To show the effect of such balanced irregu- 

 larities upon a point outside of the column : 



Take a vertical line and a horizontal line which intersect. The 

 masses whose effects are to be investigated will be distributed on 

 the vertical line. The effects are to be determined for points on 

 the horizontal line. To express the trigonometric relations between 

 any point on the vertical and any point on the horizontal line, let 

 a point on the vertical line at depth D be defined as at a vertical 



