174 



H. F. REID GEOMETRY OF FAULTS 



ily be seen if we revolve the triangle about ta until it is vertical; tb will 

 then lie in the plane under consideration. The triangle atb will be called 

 the dip-triangle. From this triangle we see that ab is equal to ta tan 8 ; 

 therefore with a table of natural tangents we can immediately determine 

 the depth ab at any given distance, ta, from the trace; or we may deter- 

 mine it graphically from the dip-triangle itself. We shall use a heavy 

 line to represent the trace of a plane. 



Lines will be indicated by their projections on the horizontal reference 



plane, and for these projections we shall use broken lines. The lines 



themselves will be referred to as the originals of their projections. The 



, points where the lines 



X \ V i intersect important 



planes may be inclosed 

 in small circles. The 

 inclination of a line will 

 be indicated in the same 

 way as the dip of a 

 plane. The dip-triangle 

 of a plane will always 

 be drawn so that if it is 

 revolved about its hori- 

 zontal line until it lies 

 in a vertical plane, with 

 •£' the angle underneath, 

 the hypothenuse will co- 

 incide with the dip, 

 and a similar conven- 

 tion will be used for 

 lines. This will remove all confusion as to the direction in which lines, 

 or planes, slope. 



The line of intersection of two planes will pass through the intersec- 

 tions of their traces; by drawing contours at the same depth on the two 

 planes, their intersection gives a second point of the line, whose projec- 

 tion can then be drawn. We can determine the projection of the con- 

 tours from the dip-triangle, tab, figure 2 ; for ta equals ab cot 8, or 

 ab tan y ; and since y is the complement of 8, we can use our same table 

 of tangents ; or we may make ab and a! b' have equal values in the two 

 triangles and determine the horizontal distances at and a' t' graphically. 

 The original of the point a", the intersection of the two contours, ab and 

 a' b', will lie on both planes whose traces are T and T', and therefore on 

 their intersection; the projection of this intersection will then be cd. 



Figure 2. 



-Intersection of itvo Planes 



