3o8 JOSEPH BARRELL 



variations in value and in direction. The resultants of the plotted 

 arrows point toward the centers of exceptional mass and their 

 rapid changes in value and direction point toward the existence of 

 many comparatively shallow masses. The epicentral points above 

 such masses are those where the gravity anomaly, Fv, is at a maxi- 

 mum. If a hidden mass may be regarded as approaching a spheri- 

 cal form and has its center at depth D, the following relations exist 

 between the value of the gravity anomaly and the distance x 

 from the epicenter: 



Fv = Maximum for x = o.ooD 



Ft) =.75 max. '' x = o.46Z? 



Ft; =.50 max. " x = o.']'] D 



Ft) =.25 max. " x=i.22,D 



If, for example, an approximately spherical mass has its center at 

 a depth of 32 km., .005 of the earth's radius, the anomaly Fv 

 will fall to half- value at a distance of 25 km. from the epicenter. 

 If the center is 64 km. deep, the anomaly will fall to half-value 

 at 50 km. from the epicenter. Between stations located 100 km. 

 apart by far the greater number of real maxima would be missed, 

 and in so far as they depended upon masses in the upper half of the 

 zone of compensation the indicated maxima would at most places 

 be less than one-half the real maxima. 



The stresses acting within the crust owing to excesses or defi- 

 ciencies of mass are not so concentrated and therefore not quite so 

 great as if those abnormalities of mass existed as surface loads of 

 rock of density 2.67 in the manner imagined for the interpretation 

 of anomalies.' Nevertheless to gain a conception of the meaning 

 of the gravity anomalies, imagine the present compensated topog- 

 raphy to be smoothed out to sea-level and the variations of mass 

 away from isostatic equilibrium to become variations of volume 

 upon its surface. The anomaly contours will then become topog- 

 raphy contours, the line of zero anomaly will become the datum 

 plane. The values in mass to be assigned to the successive anomaly 

 contours can only be given in mean figures. It has been shown 

 however in Part III that balanced vertical irregularities of density 



' The relations of mass and its distribution to the resulting stresses will be con- 

 sidered in a later part. 



