28 DONALD C. BARTON 
The effect of the cap rock was then calculated. These calculations 
would have been simple, if the actual form and density of the cap 
rock had been known. But as a matter of fact, the form of the cap-rock 
mass along the southwest-northeast diameter is known only approxi- 
mately, and it is necessary to go through the whole tedious series of 
trial and error calculations to determine the most probable gradient 
profile of the cap-rock effect. The observed gradient profile is pre- 
dominantly the effect of the cap rock. The form of the cap rock was 
altered within the limits which were imposed by the drilling data; 
and the gradient profile for each form was calculated. The calculated 
gradient profile which most nearly fitted the observed gradient profile 
was assumed to be the actual effect of the cap-rock mass. 
Detailed calculations of the salt effect were then made. It was 
assumed that the edge of the salt core might have any of the forms, 
a,b c,d,e,f, g, of Figure 2. The form might take that of any com- 
bination of (a, b, c) with (d, e, f, g). 
Seventy-eight calculation points, 200 feet apart, were taken, cov- 
ering the whole length of the torsion-balance: profile. The gradient 
effect of the cap and the salt was calculated for every fifth station. 
The values for the intermediate stations were interpolated. The differ- 
ence between the calculated value at each station and the corre- 
sponding value of the smoothed observed curve was then recorded. 
The respective differences were then squared, the squares were added, 
and the mean square found. 
The mean square is taken to be the measure of probability of the 
particular set of assumptions used in the respective calculations. The 
less the mean square, the more probable is that set of assumptions. 
The set of assumptions which has the least mean square is assumed 
to be the most probable. 
Three unknowns have to be evaluated by the trial and error cal- 
culation of the least mean square: deviation of the calculated from 
the smoothed, observed gradient profile: 
A. The form of the salt and cap; 
B. The relative density of the salt and cap in reference to the 
sediments; and 
C, The regional gradient. 
Any one set of assumptions for a given calculation comprises: 
A. One of the forms (a—e), (a—/), et cetera. 
B. A net of assumptions regarding the density of the cap, the 
density of the salt, the respective density of the sediments at various 
depths. 
C. Some assumption in regard to the regional gradient. 
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