264 DEEP BOREHOLE SURVEYS AND PROBLEMS 



D and A have had to be projected into the borehole plane) 

 we get the length for this case, where B is an upstream 

 derrick floor from outcrop A, by noting that 5 the strata 

 dip and 7 the surface slope are known, also a the borehole 

 dip. 



Thus A = y + 8 and 8 = 180° - 7 - a 



hence 



£ ^ sin (t + a) 

 L sin (7 + 5) 



.-.L^y^^^ ■ (48) 



sm (7 + 0:) ^ ^ 



When the borehole and strata dip against one another we 

 get 



L = ^^^^ ^ + f (49) 



sm (a — 7) ^ ^ 



and so on for all the other features such as displacement, 

 depth, etc., either normal to the stratum strike or at any 

 bearing therewith, by making the necessary lateral angle 

 addition to the formulae as in Eqs. (21 and 34). Therefore 

 it is scarcely necessary to add these variant cases which 

 will be left to the reader. 



2. To Locate a Specified Point in a Stratum, Vein, 

 Workings, etc., by Boring to It, i.e., to Find the Necessary 

 Starting Inclination and Bearing for the Borehole and 

 Therefrom Its Length, Displacement, etc. — This is merely 

 the converse of the above case. We now know the dis- 

 tances X and y and desire a and jS which are found from 

 Eqs. (46) and (47) as before. We solved x and y above as 

 a ratio of the known x -\- y, so here we may get a or jS 

 as a ratio of their sum which is also known since A and D 

 are known. 



It would be redundant to furnish a further example and 

 it may be added here that all variant forms of this problem 

 can be solved by either Eqs. (46) and (47) above or by Eq. 

 (20) on page 247. 



