THE STRENGTH OF THE EARTH'S CRUST 



231 



then diminishes, but less rapidly than the gravity anomaly. It is 

 important to notice that in both cases the total influence due to 

 masses of opposite sign diminishes much more rapidly, and where 

 their distance apart is 0.25 their influence is small at distance R 

 and negligible at 2R. This gives a means of determining whether, 

 in the crust, anomalies and deflections are due to regional departures 

 from isostasy or to balanced irregularities in density without 

 absence of isostasy at the base of the zone. 



To give a further illustration of balanced departures in density 

 spread over a greater vertical distance, and representing in that 

 way perhaps a more average case, assume that an excess or deficiency 

 equivalent to a unit mass is at depth 0.25 and another at depth 

 0.75. The following tabulation shows their influence upon the 

 surface of the earth at increasing horizontal distances. 



TABLE XVIII 



Attraction by Unit Masses at I and III upon Points on the Horizontal 



Line 



The data in this table are represented by the curves of Fig. 7. 

 It shows that for this arrangement of masses the influence on the 

 surface falls off rapidly at a horizontal distance between 0.25 

 and 0.75, which are also the vertical depths to I and III. When 

 the masses are of opposite sign the anomaly passes through zero 

 at a horizontal distance of about 0.6, and the deflection force for 

 opposite sign decreases to half the value of the sum at about o. 75. 

 The ratio between the effects of like and unlike masses becomes 

 more marked the greater the distance of the point, although the 

 actual magnitudes of the forces decrease. 



