44 DEEP BOREHOLE SURVEYS AND PROBLEMS 



hole and L + I oi the wire. The azimuth of CB is easily 

 taken from 



y2 - yi 



We first detect contact of the wire in the hole by m becom- 

 ing constant, but, as already stated, it may vary again if 

 the hole diverges back to its former direction later on. 

 If this latter contingency arises it can be demonstrated 

 as follows: Each deviation of the hole gives a new value 

 in amount and azimuth for m, thus giving in a crooked hole 

 a series of values, ai, a^, as ... a„ at different points 

 1, 2, 3 ... n. At each of these points trace the bore- 

 hole cross sections as shown in Fig. 4. Here the circles 

 representing the circumference at the said points \ . . . n 

 are projected downward on to a Une ai . . . n which is 

 the continuous horizontal traverse of the deflections ai 

 . . . (Zn in bearing. The centers of the circles are corre- 

 spondingly subscript figured 1 . . . n. If the line SA 

 do not touch the borehole sides, i.e., it is straight, we 

 find it on the projected plan as the line can. That is to 

 say, that if we make a vertical section of the borehole 

 through can and draw in SA, it must not touch the sides. 

 The points must be inside the borehole section circumfer- 

 ence circles at the corresponding levels. If one or more 

 do not obey this requirement, point S may be shifted 

 for a new suspension and therefore new plan point C. 

 Failing any agreement with the above demands, on moving 

 S to the limiting lateral positions, the method ceases to be 

 of utility any further. 



When point C has been retreated a distance d to C 

 (Figs. 1 and 5) and the projection completed, the new 

 deviation w is got from the new suspension and hole lengths 

 a and h. Thus 



w = ^{a-Yh) ±d (6) 



Other but perhaps more troublesome methods have been 

 adopted as modifications of the above method.^ 



1 F. Schmidt, op. cit., p. 180. 



