PROBLEMS 251 



B"B' = Hcota 



B"E = B"C sin (a - 8) 



^, ^ B^E^ ^ AB" sin 5 



sin (a — b) sin (a — 6) 



AB" = if (cot 7 + cot a) 



rr A T>f/ 



BC = BB" + B"C = L = -^^ + 



sm a cot 5 sm a — cos 



a 



i = // (^ + ''"t ?- + ""*" ) (23) 



\Sin a cot 5 sin a — COS a/ ^ ' 



If the borehole is downstream of the outcrop the first 

 term in the bracket is negative; on a level surface B. van- 

 ishes, also 7, and since then AB" = AB' = AB, the above 

 form is not applicable, a modification of either Eqs. (216), 

 (21c) or (21c^) being then most suitable, which will yield 

 the length, thus 



BC = L = 4^^^ (24) 



sm {8 — a) ^ ^ 



and so on for other dimensions which need not be repeated 

 here. 



16. The Displacement of the Borehole.— This is the shift 

 of the hole and will be in the full dip direction here (Fig. 

 168). 



Displacement = DC = B'B" + FC. 



= H cot ex + B"C cos a 



= n cot a + 77 :r~r. tt 



(tan a cot 5 — 1) 



DC^H (cot a + ;«tT+COta \ 



\ tan a cot 5 — 1/ ^ ^ 



Wherein the first term on the right is negative if the bore- 

 hole is downstream of the outcrop; and if the surface is 

 level 



DC = BC cos a (26) 



