268 DEEP BOREHOLE SURVEYS AND PROBLEMS 



The bedding planes make an angle of 8i with the slant 

 hole and the locus of all planes satisfying this demand 

 is found by the surface of the cone EA'F constructed as 

 above. The right cone of the vertical hole A A' is cut by 

 the horizontal surface in a true circle and the cone about 

 the slant hole of axis BA' is cut by the same surface plane 

 in an ellipse as shown. Use any of the well-known methods 

 for getting the section of a cone cut by a slanting plane. 

 Here the plane slants at a to the cone axis BA'.^ 



Any tangential plane to the right cone CA'D of the verti- 

 cal hole will be cut by the vertical hole A A' at 5 deg., 

 the angle at which this vertical borehole cuts the bedding. 

 Therefore the tangent to both circle and ellipse satisfies the 

 demands of both holes. This tangent XX can be drawn 

 on both sides, making the problem ambiguous. 



1. The problem has many possibilities dependent on the 

 relative sizes and positions of circle and ellipse. Thus 

 in Fig. 1, Plate XVI, we have the two possible strikes 

 XX and XiXi. Therefore we have only two possible 

 strikes when circle and ellipse cut each other. ^ 



2. If however the minor axis of the ellipse equals the dia- 

 meter of the circle as in Fig. 2, Plate XVI, we also get a 

 definite dual strike solution. Indeed the line connecting 

 their centers is also a strike elevated or depressed, but the 

 dip may be in either direction. 



3. When the cones do not intersect, as in Fig. 3, there 

 are four possible solutions to the problem. 



4. When the cones are externally tangential there are 

 (Fig. 4) three possible solutions, and the tangent strikes 

 need not be parallel. 



5. When the cones are internally tangential there is 

 only one tangent (Fig. 5), we get only one strike and the 

 problem is therefore solvable. 



6. Another single solution case arises when the slant 

 hole follows the true dip of the strata and is therefore a 

 point in plan. If it did not follow the true dip but still 



1 Haddock, M. H., "Disrupted Strata," p. 19, Crosby, Lockwood & Sons, 

 1929. 



^LoBECK, A. K., "Block Diagrams," p. 134. 



