254 DEEP BOREHOLE SURVEYS AND PROBLEMS 



d. THE SHORTEST BOREHOLE FROM A GIVEN POINT TO A STRATUM 



These are not strictly normal to the strata but are best 

 dealt with here. 

 We have already shown in Eq. (21) that this length is got 



by 



^ H ±AB' tan a sin e. 



sin a + tan 8 sm di cos a ^ ' 



the signs depending on the relative dipping senses of the 

 stratum and borehole. 



If we consider the point B of the borehole mouth fixed, 

 then the length of the hole is a function of a and ^i, its dip 



'ir|iiiiji || ii| || |TiiirnT 



_™^ 



Fig. 170. — Horizontal borehole. 



and bearing; it is thus dependent on two variables. The 

 number of connections is thus infinite. 



e. THE SHORTEST POSSIBLE CONNECTION, AT A GIVEN BEARING, 

 BY A BOREHOLE TO A STRATUM 



We might get, with the aid of the calculus, the values of 

 a and 02 to meet this case, but the same result is obtained 

 by stereometry, wherein we note that the line falling at 

 right angles to the stratum dip line is the shortest in the 

 said direction. That is to say, the hole hitting the stratum 

 face ''square on" (not perpendicular) is the shortest at a 

 given bearing. Thus the dip of this hole will then be 90 — 5 

 and its bearing that given. 



The shortest of all possible boreholes will be in the plane 

 at right angles to the strata dip, and its dip will be 90 — 6, 



