BELLE ISLE TORSION-BALANCE SURVEY 1341 
The results of the field survey with the torsion balance, therefore, 
qualitatively verified the prediction of a large unexplored area of cap 
rock. The next task was to make a quantitative calculation of the 
amount and depth of the cap rock and the position of its edge. 
Cap-rock calculations.—The calculation of the amount, depth, and 
edge of the cap rock was made by a series of trial and error calculations, 
profile by profile. A trial cross section of the dome along the selected 
profile was sketched; its gradient profile was calculated and then com- 
pared with the observed gradient profile; the trial cross section was re- 
molded or replaced by a new sketch cross section; the gradient profile 
was calculated and compared with the observed gradient profile; the 
cycle was continued until a cross section was found whose calculated 
gradient profile fitted the observed gradient profile move closely than 
did the gradient profile of any of the other trial cross sections. 
The calculations in connection with the torsion-balance survey at 
Belle Isle were made graphically by means of one of the writer’s graphic 
charts (8).t The principle of these charts is that space is divided into 
rectangular prisms at right angles to the vertical plane of the section; 
the length of the prisms is calculated so as to vary by some simple law to 
approximate the dimensions of the structure at right angles to the plane 
of the section; the cross section of each prism is so calculated that each 
prism produces a gradient of 1E at the origin; if the cross section of a 
structure is sketched on transparent paper and superimposed on the chart, 
it is necessary only to count squares and multiply by the specific gravity 
in order to obtain the gradient at the origin. The actual calculations in 
connection with the Belle Isle survey were made by the writer’s assistant, 
Mrs. Elizabeth B. Summers. 
The specific gravity relations which were used were those which 
seemed geologically the most probable on the basis of the laboratory 
determinations of the specific gravity of cores from the cap rock at Bryan 
Heights, Hoskins Mound, and other domes and from cores of sediments 
from depths less than 3,500 feet and on the basis of experience in previous 
calculations in connection with other domes. Those assumed density 
relations are given in Table I. 
For the purposes of checking, several other sets of assumptions were 
tried. Two of the more important sets of those assumptions are given 
in Table II. 
tNumbers in parenthesis refer to list of references at end of article. 
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