194 H. F. REID GEOMETRY OF FAULTS 



be the same, and therefore striae which may be found may only represent 

 the last step, and if their direction were taken as the direction of the 

 whole motion, we should be led to erroneous conclusions. It is difficult 

 to say just how these various accidents may be avoided; each case must 

 be treated by itself ; but in general, if we have more observations than are 

 necessary to determine the movement, we can compare the results ob- 

 tained by combining them in different ways, and if the results are all 

 accordant we may feel pretty sure that we have determined the full move- 

 ment. For instance, if we have given, not only the offsets of three inde- 

 pendent planes, but also the direction of the stria?, we have several 

 methods of determining the total shifts. If they do not give the same 

 results, we may be sure that the offsets of the planes were not wholly due 

 to the movement which produced the striae. 



Possible Displacements 



When faults extend over very long distances they are usually not very 

 straight, and sometimes they curve considerably. The form a fault will 

 take will depend on the strength of the rock along its course and the dis- 

 tribution of the forces which produced it. It is hardly probable that 

 where the curvature is great the displacement could have a strong hori- 

 zontal component ; but it might be either a translation or a rotation. In 

 the former case the intersection of the surface with the plane containing 

 the movement would be a straight line : in the latter it would be a circle. 

 If both a translation and a rotation existed in not too unequal propor- 

 tions, it is probable that the fault surface would become nearly a circular 

 cylinder, and its course along the earth's surface would not be far from 

 straight. These surmises must not be applied too vigorously: it is only 

 in small masses that the rock may be considered rigid, and the displace- 

 ments might be very different in the different parts of a long fault as a 

 result of plastic deformations. 



Where two faults intersect and neither suffers an offset, we must con- 

 clude that the blocks in the four angles have suffered displacements par- 

 allel with the line of intersection of the two faults. 



Sometimes the rock is found to be broken up by numerous faults into 

 a series of blocks. If the blocks defined by three or four faults do not 

 have their edges parallel, but are wedge-shaped, we may be sure that the 

 movements on the different faults occurred at different times, and we 



