PROBLEMS 



269 



kept on the dipping surface the point would be displaced, 

 giving two solutions for the strike. 



C. THREE-BOREHOLE PROBLEMS 



These are the most favored and oldest of borehole com- 

 putations because they provide a convincing proof and 

 can be applied also to three given altitudes like outcrops 

 at different heights above sea level. 



Three Boreholes Not in Line 



First Solution. — If the holes are not put down from a 

 level surface, first reduce the surface level to a given datum 

 such as sea level or that of 

 the lowest borehole mouth. 

 From the survey of the lines 

 connecting A the deepest 

 hole (Fig. 178) to C the 

 shallowest and also from the 

 depth yielded in each hole we Fig- i78. 



know the plan length of CA which is CiA, also of CB which 

 is EB. We know the respective dips of these lines, 

 i.e., a and j8 since AdBiD is on the horizontal plane, 

 D being where CB produced meets CiBi produced; 

 therefore we also know the plan angles Bi, 6 and 62 between 

 these lines, by construction for di and 62 while d is given. 

 From the two vertical triangles CCiA and CCiD and base 

 triangle ACiD note that 



tan a sin di 



tan 18 sin 62 



= m 



and 



therefore 



61 + ^2 = 180 - = n 



n — 



(52) 



(53) 

 (54) 



Substituting m and di in Eq. (52) we get 



sin {n — 62) 



m 



which expands to 



tan 02 



sin 62 



sin n 



m + cos n 

 thus giving 62 for obtaining the strike. 



(55) 



