176 



H. F. REID GEOMETRY OF FAULTS 





intersection of the projections of the line and of the contour will be the 

 projection of the point sought. To find the depth at which a vertical 

 line cuts a plane, find the depth of the contour immediately under the 

 line. 



If three points of a plane are given, we can readily find its trace and 

 dip. Let a, b, c, figure 4, be the horizontal projections of the three 

 points on a plane, and let these letters also represent their depths below 

 the reference plane. Draw ac and lay off the depths of a and c at right 

 angles to it; if dg is the depth, b, then the original of d will have th\e 

 depth, b; d can be found from the proportion ad; ac = a-b:a-c. The 

 line bd will be the projection of a contour on the plane. Draw ah per- 

 pendicular to bd; lay off the 

 depths, eg' and al, at e and a; 

 draw the line lg' intersecting 

 ae in k; 8 will be the dip of 

 the plane, and a line through 

 k, parallel with bd, will be 

 the trace. 



If one point of a plane and 

 the direction and amount of 

 the dip are known, we can 

 easily determine the trace on 

 the reference plane. We pass 

 a line through the point in 

 the direction and with the in- 

 clination of the dip and find 

 its intersection with the 

 reference plane ; through 

 this intersection draw the 

 trace at right angles to the dip. This is the method which will 

 be frequently followed in finding the trace of a stratum or other plane 

 on the reference plane ; for, on account of irregular topography, obser- 

 vations will rarely be made directly on the horizontal reference plane 

 itself. On the other hand, it is easy to determine the outcrop of any 

 plane on an irregular topographic surface when we have given the 

 trace of the plane on the reference plane and its dip. We draw the 

 projections of the contours on the plane and on the surface, and inter- 

 sections of the projections of contours having the same altitude will be 

 points on the projection of the outcrop. 3 



X u- - - l£ 



Figure 4. — Plane determine.} from three Points 



3 Many examples of the determination of the locations of outcrops are given in Pro- 

 fessor Konrad Keilhack's Lehrbuch der praktischen Geologie, second edition, pp. 174 — . 



