PROBLEMS 



255 



its bearing that of the seam dip plus 180 deg., say ,8 + 180 

 deg., where jS is the direction of full dip of the stratum and 5 

 its amount. 



Substituting in Eq. (21) we get for the shortest connection 

 at a bearing 62 between hole and stratum strike directions 



5C = i7 cos 5 + AB' cosec 5 sin di (34) 



/. THE SHORTEST OF ALL POSSIBLE BOREHOLES TO THE STRATUM 



Here the vertical plane holding point A in the stratum 

 and B on the borehole 

 mouth must have the 

 direction ^ + 180 deg., 

 so that 62 = 90 deg., 

 and we get (Fig. 171) 



BC = H cos b + 



AB' cosec 5 (35) 



This is similar to E'E 

 of Figs. 168 and 169 



„!„„ Fig. 171. — Borehole dipping against the beds. 



We shall not deal with upward holes, since these do not 

 come under deep boring ; also we will not go into the variant 

 forms of Eqs. (21a), (216), (21c) and {2ld) above, which arise 

 with contrary senses of hole and strata dips. Varying 

 these, as we have done in the cases of vertical and inclined 

 normal holes, will give the reader no difficulty and preserve 

 the space at our disposal. 



II. Boreholes Not at Right Angles to the Strike of the 



Strata 



All the cases are covered by Eq. (21) for length, i.e., 

 H ± AB' tan 8 sin 62 



L = BC = 



sin a + sin d\ tan 6 cos a 



(36) 



and it appears needless to draw the upstream and down- 

 stream cases, since the previous examples are particular 

 cases of these problems. The related displacement and 

 depth problems will need no further embellishment here 

 either. 



