1348 DONALD C. BARTON 
The error in the predicted thickness of the cap probably indicates 
that the assumed relative density is too small. The relation holds very 
roughly that if the relative density times the reciprocal of the area of 
cross section of a very long horizontal body is a constant, the gradient 
is constant. If, in the present calculations of the Belle Isle survey, too 
small a relative density were used for the cap rock, the predicted thick- 
ness of the cap would be too great. The cap proved on the whole to be 
tight and to have little of the porosity commonly present in the lime 
rock of the cap. The assumed specific gravity of the sediments also 
may have been slightly too high and actual specific gravity of the sed- 
iments may be 1.9 to a depth of 700 feet and 2.0 from 700 to 1,200 feet 
instead of 1.9 from the surface to 300 feet, 2.00 from 300 to 700 feet, and 
2.1 from 700 to 1,200 feet, and the relative density might be 0.8 instead 
of 0.6. A difference between an actual relative density of 0.8 and the 
assumed relative density of 0.6 would be sufficient, substantially, to have 
caused the error in the prediction of the thickness of the cap. 
Irregularities of mass at right angles to the plane of the section can 
not be detected by this type of calculation. The gradient profile is 
essentially the same, whether the mass is concentrated in the vertical 
plane of the section, or a slightly greater mass is uniformly and 
symmetrically disposed at right angles, or a certain mass is symmetrically 
concentrated at two points on opposite sides of the plane of the section. 
The upper part of the Belle Isle dome does not have a simple geometric 
form; several centers of uplift seem to be present; two are reflected in 
the topography by the north hill and by the west hill. The drilling re- 
veals another on the southwest radius, and the torsion-balance data sug- 
gest another on the east-southeast radius. The flank of the cap is scal- 
loped correspondingly, convex around the centers of uplift and concave 
between. The scalloping is reflected in the topography of the northwest 
flank of the island. The west radius lies in the concavity between the 
respective areas of the northwest and southwest centers of uplift. In the 
effect on the gradient, the excess of mass in the convexity of the area of 
these centers of uplift partly compensates for the deficiency of mass in 
the intervening concavity. The calculations, therefore, predict too 
much cap rock in the area of the concavity. Conversely, the calculations 
predict too little cap rock for a line of profile down a convex zone. 
CONCLUSION 
The Belle Isle torsion-balance survey affords an example of an 
average successful application of the torsion-balance method to the 
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