266 DEEP BOREHOLE SURVEYS AND PROBLEMS 



from the core by observing the maximum inclination of 

 stratification planes in it. If A (Fig. 177) be the deepest 

 borehole and is h ft. deeper than B and 8 is the strata dip 

 observed from the core, set out a circle of radius h cot 8 

 and center A. Draw the two possible tangents from B to 

 A such as Ba and Ba' (Fig. 177). As the surface coordi- 

 nates of A and B are known we also know ^ba the bearing 

 of the line from B to A. The angle BAa, or BAa' = d, 

 is the strike angle sought. The contact point lines Aa 

 and Aa' of bearings ^a and ^d', respectively, are the possible 

 direction lines of the full dip of the stratum. We now get 



Ti' A " 

 h cot 5 = B'Ai" and A/,n, = cos d the angle required 



Hence 



or 



, . h cot 8 



cos i^d - ^ba) = ~Jb~ 



, . ]% cot 8 



cos {^BA - M = —Jb~ 



(50) 



The dip a in direction BA can now be found by the funda- 

 mental dip formula where a is any apparent dip A'B'A", 8 

 the true dip Ai'B'Ai", and d the angle Ai'B'A' between 

 them, i.e., 



tan a = tan 8 cos B (51) 



b. Given One Vertical and One Slanting Borehole and 

 the Angle the Core Makes with the Bedding to Determine 

 the Dip and Strike. — Say the vertical hole A cuts the 

 bedding at A' at 5 deg. (Fig. 1, Plate XVI), the slanting 

 hole dipping at a from B cuts the bedding at 5i deg. (The 

 point B may be moved up so that the apexes of the cones 

 about the A and B holes coincide at A', for this does not 

 alter the relative angular conditions.) 



Set off a cone at A' having the apical angle of 25 = CA'D 

 about AA' and another having the apical angle of 25i = 

 EA'F about BA' . The true dip is got from the vertical 

 hole as 90 — 8, since the beds make an angle of 8 with 

 the vertical. 



