SPECIAL DIFFICULTIES 193 



tance b" b"' above the plane, and therefore the translation parallel with the 

 axis consists in raising /' through the difference of these distances. 

 Rotating everything down around T" T" through angle, <f, to come back 

 to the original position, o goes to the original of o', whose depth is o' o" ; 

 and if at o" we draw the line o" P, making the angle ^ with o" o' , the 

 point of intersection of o" P and o' o will be the point where the axis of 

 rotation intersects the horizontal plane, o o' will be its projection and its 

 positive direction, 8 will be its dip, and <p its amount; b" b"' — /' /" will 

 be the translation. If this latter quantity should come out zero, then the 

 whole displacement would be a simple rotation; but in general it would 

 be impossible to assume in the beginning that this condition held. 



We have treated this case as though the strata were plane, but this is 

 not at all necessary. If the fault were diagonal to the strata, we might 

 be able to construct the geological section on opposite sides of the fault, 

 and we could determine the rotation by considering the displacement of 

 a plane tangent to the apex of an anticlinal, and the line of tangency ; or 

 if a dike cut the strata, the plane of the dike and a line in this plane tan- 

 gent to the apex of an anticline could be used equally well ; the intersec- 

 tion of the dike with the apex of the anticlinal would furnish a point 

 whose displacement would determine the translation. 



Special Difficulties 



There are two kinds of accidents which may materially interfere with 

 the determination of the actual movement of a fault. The first of these 

 is an unconformity. This may be entirely covered on the downthrow 

 side, so that only the strata above it are exposed, and on the upthrow side 

 all the strata above the unconformity may have been eroded away. The 

 strike of the strata will in general be different on opposite sides of the 

 fault, but this, of course, will have nothing to do with a rotation. We 

 must reconstruct, if possible, the position of the strata below the uncon- 

 formity on the downthrow side; otherwise we can only determine at best 

 a limit to the amount of the vertical throw. 



The second kind of accident that may interfere with consistent results 

 is due to the fact that the whole movement at a fault may have been made 

 up of a series of steps, and it is quite possible that dikes or veins may 

 have been formed at a time between the steps; their displacement would 

 not then represent the whole movement on the fault. Moreover, it is by 

 no means necessary that the direction of movement of all the steps should 



