SIMULTANEOUS JOINTS 27 1 



therefore, that those features of experiments are observable in 

 nature which depend on great differences in strength between 

 the material tested and the apparatus used in testing. 



In cases of uniform lateral resistance then, at least 4 systems 

 of joints may form simultaneously as the result of the action of 

 a single force, separating the rock into octahedrons and tetra- 

 hedrons. Very minute differences in resistance would of course 

 modif}^ the development of the octahedral faces, but the 4 sets 

 of planes at least would be, and often are, perfectly distinct. 



In experiments the 4 surfaces are so oriented as to be readily 

 distinguished, but in nature such orientation is relatively rare. 

 Tectonic forces are not usually exactly horizontal or exactly 

 vertical, and the exposures due to erosion or other causes are 

 generally inclined surfaces. Now, granting the simplicity and 

 symmetry of the fissuring, it is not at once evident how the 

 joints would be distributed on a plane taken at random through 

 the jointed mass. It is really an easy matter to project the fis- 

 sure systems onto a random plane, and requires only the appli- 

 cation of rudimentary descriptive geometry ; but the step has 

 not heretofore been taken, while it is interesting to compare the 

 results of the process with natural examples. The plots also 

 indicate how observations on a random plane may most simply 

 be dealt with when it is desirable to reduce field data to a sym- 

 metrical orientation and to find the line of force. 



On account of its bilateral symmetry the octahedron gives a 

 convenient starting point for constructing a random section. 

 This octahedron will not be a regular one, inasmuch as the 

 angle between 2 planes taken over the coign will be a right 

 angle, and the 8 triangles of the octahedron will therefore not 

 be equilateral. 



Fig. 4 shows such an octahedron so drawn as to expose 

 to view only 2 of the triangular faces. Fig. 5 shows the 

 same octahedron in plan and Fig. 6 in elevation, 4 faces being 

 visible. 



In order to display the fissure systems of the jointed mass 

 taken on a random plane, any 3 points on the edges of the 

 octahedron may be selected in Fig. 6, such as /, in, n. These 

 points of course fix the plane. By evident and familiar methods 



