192 H. F. REID GEOMETRY OF FAULTS 



point to the horizontal plane, we find it must be rotated through the angle 

 <p lt which immediately appears if we consider the triangle a' id" as verti- 

 cal. When the rotation through the angle <p x is accomplished the two 

 planes coincide, and the original of a' c' becomes a" c". On rotating 

 a" c" about a vertical axis through the angle <f 2 , it coincides with bg'. 

 We have rotated T' T' through an angle <p x around a horizontal axis T' x\ 

 and then around a vertical axis through an angle <p 2 . We can combine 

 these two into a single rotation, just as we can two simple translations. 

 At i lay off a distance towards i' proportional to <f 1} and vertically down- 

 ward a distance proportional to <f 2 ; on completing the parallelogram 

 the diagonal will give the direction of the resultant axis, and its length 

 will be proportional to its amount. In representing a rotation by a 

 length of its axis we measure the length positively in the direction in 

 which the rotation would carry a right-handed screw. By measuring 

 <P 1 = d id" and <P 2 = 9' nc " , we find them respectively 15° and 10.3°; 

 and <p becomes 18.2° ; ii' will be the projection of the axis, which will dip 

 down from i. 



We must now bring our whole mass to its original position by rotating 

 back through angle 8 2 about it. The original of i will be brought to the 

 original of e, that of %' to that of e', and the axis of rotation will become 

 the original of ee' ; its dip, 8, is readily found by laying off, at right angles 

 to ee', at e, and e' respectively, the depths of their originals and joining 

 the ends of the lines thus drawn. As this line does not meet ee' within 

 the limits of the figure, we find 8 by drawing an auxiliary line parallel 

 with it, and which intersects ee' at a convenient point, p. We have found 

 the direction of the axis of rotation ; that is, its projection is ee', its posi- 

 tive direction is from e towards e', its dip is 8 ; its amount is 18.2° ; but its 

 actual position may be anywhere ; and if we choose a position for it we can 

 then determine what translation is necessary, in addition, to make the un- 

 disturbed stratum coincide in all respects with its displaced part. In par- 

 ticular we may choose the proper position of the axis in order that the 

 translation shall be along it. For this purpose let T" T" be the trace of a 

 plane at right angles to the axis; its dip will be if/ = 90° — 8. Eevolve 

 everything up through the angle, <//, about this trace ; the axis of rotation 

 (original of ee') will become vertical and / will go to f, and b' to b". 4 

 point, o, can now be found on the perpendicular bisector of f b" at which 

 /' b" will subtend the angle of rotation, <p ; this then will be the position 

 of the axis, for /' will be brought to b" by a rotation, <p, around this point. 

 The original of /' is at a distance f f", and the original of b" is at a dis- 



