7i6 WALTER H. BUCHER 



A complete analysis from these data involves the following 

 steps. Find 



1. The actual position of the two planes in space. 



2. The direction, in space, of the line of intersection of the two 

 planes which corresponds to the position of the intermediate princi- 

 pal stress. 



3. The position of the plane normal to this line. 



4. The location in this plane of the other two principal stresses 

 bisecting the acute and obtuse angles respectively. 



The stereographic projection is admirably adapted to the 

 demands of problems of this kind. By its use, the position of the 

 principal stresses in space can be obtained in the field from any 

 given set of joints within a few minutes. In the following brief 

 description of the construction of Figure 4, a working knowledge 

 of the stereographic projection is assumed."^ 



1. Draw the line Ex-Ex, trending N 23 E, to represent the 

 vertical plane of the exposure. On it, mark the point c, 27° south- 

 ward from O, and c' , 35° northward from O. The planes ach and 

 a'c'h' represent the two joint planes and can now be drawn. 



2. Since the two points O and d are common to both planes, 

 Od is the line of intersection of the two planes, that is, the direction 

 of the intermediate stress. 



3. On the great circle ach mark point e, and similarly point e' 

 on a'c'h\ both 90° from d. Through e and e' draw the great circle 

 fee'g, representing the plane normal to Od. On it we can read 



directly the true value of the acute angle of the shearing planes, 

 which in this case is 72°. 



'^ For a detailed discussion of the stereographic projection see A. Johannsen, 

 Manual of Petrographic Methods, p. 17. McGraw-Hill Book Co., 1914. For most 

 purposes a protractor giving great circles and vertical small circles 10° apart, such 

 as is given (after Penfield) in A. F. Rogers, Introduction to the Study of Minerals 

 (McGraw-Hill Book Co., N.Y., 1912, pp. 82-86), is perfectly sufficient. It can 

 readily be copied and carried in the notebook for use in the field. Greater accuracy 

 can, of course, be obtained by the use of Wulff's net, a large copy of which is con- 

 tained in E. E. Wright, "The Methods of Petrographic-Microscopic Research," 

 Carnegie Inst. Pub. ij8, PI. III. 



The reader who has had little practice in the use of the stereographic projection 

 will find it easy to visualize Fig. 4 by remembering that the great circles must be 

 imagined to be drawn on the surface of a hemisphere resting on the circle NESW 

 with at its center. A line such as dO, therefore, represents a radius extending 

 from the surface of the hemisphere, at d, downward to the center O. 



