BULLETIN OF THE GEOLOGICAL SOCIETY OF AMERICA 

 Vol. 21, pp. 737-740 December 31, 191o 



ADDITIONAL NOTE ON THE GEOMETRY OF FAULTS' 



BY HARRY FIELDING REID 



(Presented for publication to the Society March 3, 1910) 



In a recent paper simple projective methods were given for deter- 

 mining the displacement of a stratum at a fault. ^ It was pointed out 

 that any displacement of a stratum could be represented by a linear dis- 

 placement and a simple rotation. The rotation was determined by 

 rotating the stratum first around a horizontal axis until it was hori- 

 zontal, and then around a vertical axis until a line on it was properly 

 oriented; these two rotations were then combined by the ordinary 

 method of combining small rotations, namely, by representing the rota- 

 tions by lines drawn in the directions of their axes, and Avith lengths 

 proportional to the amounts of the rotations. The resultant axis is in 

 the direction of the diagonal of the completed parallelogram, and its 

 amount is proportional to the length of this diagonal. The positive 

 direction of the axis is that in which the rotation appears right-handed . 



This method, although correct for very small rotations and leading to 

 no important error in most practical cases, is not accurately applicable 

 except to very small rotations. It is desirable to give an accurate 

 method which can be used in all cases. We must, therefore, find a 

 simple method for determining the axis and the amount of a single 

 rotation which will be equivalent to a rotation around a horizontal axis, 

 followed by one around a vertical axis, however great these rotations 

 may be. 



In figure 1 let OA and OS represent the directions of the axes respect- 

 ively, the rotation around these axes being right-handed when looked at 

 from 0. The simplest way to represent and combine the rotations is to 

 consider a sphere of unit radius around and determine the positions 

 on it of certain points of the stratum before and after rotation. We 

 suppose that the stratum passes through the horizontal axis OA and 

 intersects the sphere in the great circle ADB. Let PDS be a great circle 



1 Manuscript received by the Secretary of the Society March 3, 1910. Not read at a 

 meeting. Published by vote of Publication Committee. 



2 Geometry of faults. This Bulletin, vol. 20, 1909, pp. 171-196. 



(737) 



