PARALLEL DISPLACEMENTS 183 



up the fault-plane to the original of f, or a point of the stratum, t, has 

 moved in the opposite direction. The horizontal line at right angles to 

 the fault-trace has therefore been shortened by the amount equal to ff", 

 the horizontal projection of the line ff', at right angles to the fault-trace. 

 If the stratum and the two dikes meet on the undisturbed side of the 

 fault, they will not meet again on the displaced side; but their virtual 

 meeting point can be determined by finding the meeting point of the 

 three displaced planes produced. 



Case II: Given, the traces, dips, and offsets of a stratum and of two 

 dikes. Suppose we have not found the fault itself, but have found the 

 traces of the disrupted stratum, T, t, figure 8, and have also found the 

 parts of two dikes which have been disrupted by the fault. We proceed 

 as in the former case ; we find the projection, /, of the meeting point of 

 the stratum and the two dikes before the disruption, and the projection 

 /' of the point where their displaced parts meet. The line ff' will be the 

 projection of the total shift ; fg and /' g' will be the depths of the orig- 

 inals of / and /' respectively; gg' will be the total amount of the shift, 

 and 8' will be its inclination ; /" /' will be the lengthening of a horizontal 

 line at right angles to the fault-trace. 



Although we have determined the direction, inclination, and amount 

 of the total shift, we have not determined the fault-plane, for there are 

 evidently an indefinite number of planes which can contain a line par- 

 allel with the original of ff'. If we have found one point of the fault- 

 plane where, let us say, dike 1 has been disrupted, we can still pass an in- 

 definite number of planes through that point which would contain a line 

 parallel with the original of ff', but if we have also found a second point 

 where, for instance, the stratum has been disrupted, the fault-plane can 

 be immediately determined. We shall suppose these two points to be 

 the originals of a and b, and that they are not in the horizontal plane, 

 but, on account of the topography, the original of a lies above, and that 

 of b below, this plane. The altitudes of the originals of a and b would 

 naturally be determined in the field; but, since one lies on dike 1 and 

 the other on the stratum, we can find the altitude each must have by the 

 ordinary method of the dip-triangle. We thus find that the original of 

 a lies a distance ae above the horizontal plane, and that of b at a distance 

 b d below it. The fault-plane must pass through the original of ab and 

 contain a line parallel with the original of ff' ; therefore it must contain 

 a line through the original of a parallel with the original of ff' ; ah will 

 be the projection of this line. The trace of the fault-plane must pass 

 through the points k and c, where the originals of ah and ab intersect 

 the reference plane. Moreover, the fault-plane contains the original of 



