APPLICATIONS OF DIP SHOOTING 125 
which in a large number of cases is as often exceeded as not.”’ Since 
the area under curve 2 is directly proportional to the number of cases 
considered, the value of the horizontal co-ordinate (x) corresponding 
with half the total area will be the value of the probable error. This 
value was found to be about 87 feet. The mathematical solution of the 
problem follows. 
Differentiating equation (1), we obtain 
Equation (2) dx=—1.23 (d log y) = —1.23 dy/y 
The area under the curve is the integral of ydx. As, by equation (2), dx equals —1.23 
dy/y, we have for the area A 
Equation (3) A=—1.23 §)°ydy/y=—1.23 (¥.—3o) 
By equation (1) when x is equal to zero 
Equation (4) o=3.1—1.23 log y 
(5) log y=3.1/1.23 
(6) y=e? 4#=12.3 
Again by equation (1), when ~ is equal to , 
Equation (7) ~ =3.1—1.23 log y 
YI) Gti 
(8) log y= EF 20 
(9) y=e" =o 
Then by equations (3), (6), and (9), we have 
Equation (10) A=—1.23 (y,.—yo) = —1.23 (o—12.3)=15.1 
But the probable error is that value of x corresponding with half of the area, A. 
Let us designate this value of x as p. Then, substituting 7.55 for 1/2 A, yp for yo, and 
zero for y,, in equation (3) we derive 
Equation (11) 7.55=—1.23 (o—yp) =1.23 yp 
(12) vp=6.14 
Substituting p for + and 6.14 for yp in equation (1), we find, 
(12) p=3.1—1.23 log 6.14=0.87 
As this is the probable error sought, expressed in hundreds of feet, the probable 
misclosure deduced from the available data is about 87 feet. 
The probable error or misclosure here computed will serve as a 
measure of the accuracy to be expected from the dip-reflection method 
in the Coastal Plain series on the Gulf Coast. Some of the sources of 
misclosure, together with the conditions affecting the accuracy of the 
dip method will be considered next. 
CRITICAL ANALYSIS OF METHODIC ERRORS 
Probably the greatest source of error is in the drawing of profiles. 
The average length of the traverses in the group considered was 
27,500 feet. Dividing the probable misclosure by the average length 
of traverse we obtain the tangent of the probable angular misclosure, 
the net error being distributed over the entire length of the traverse. 
87/27,500=0.00316= tan o°.11’ 
This angular error is astoundingly small. Clearly in making up a 
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