260 DEEP BOREHOLE SURVEYS AND PROBLEMS 



hence 



V 1 — COS- i cos^ d 



Case 3. — Case 3, Plate XV, shows that in this case the 

 form is 



5 = (GO - iS) + (90 - a) = ISO - 13 - a 



consequently 



5 = 180° - ( /i"' + «i"^i_ \ (39) 



Vvl — cos^ i cos- 6/ 



Case 4. — The form assumed in this case is shown in 

 Cases 4, Plate XV, to be 



5 = (90 - iS) - (90 - a) = a - iS 



which gives 



5 = Z'"^'-^^"' - (40) 



V 1 — cos^ i cos^ d 



When the hole is at right angles to the strike of the 

 bedding, the above four formulae become : 



Case 1.— 6 = ^■ + 5i (41) 



Case 2.-5 = i - di (42) 



Case 3.-5 = 180° - i - 8i (43) 



Case 4. — 8 = 8i - i (44) 



2. To Find the True Thickness of a Bed Knowing Its 

 Dip and the Direction of a Borehole in It, also the Distance 

 Through Penetrated by the Hole.— Let A2B (Fig. 174 

 plan) be the plan of the borehole AB, and A2C2 the direction 

 of the strike on this plane (all lines parallel to A2C2 are in 

 the direction of strike). A2-D1 is the direction of full dip, 

 and AiDi and AD are in the same vertical plane as shown 

 also in Fig. 174, end view. The angle d between the directions 

 of full dip and of the borehole is shown in its different super- 

 imposed positions in the right or projected figure. The 



