272 BECKER 



the random plane can now be brought into the plane of the paper 

 as shown in Fig. 7/ where also the direction and amount of 

 dip of the 4 surfaces is shown as determined by an easy con- 

 struction. Finally from the data of Fig. 7 and the hypothesis 

 that the fissures are evenly distributed in space, it is possible to 

 display the traces of the joints on the random plane as shown 

 in Fig. 8. 



Every observer who has paid attention to systematic joint- 

 ing, will recognize the similarity between Fig. 8 and certain 

 field occurrences ; it is noticeable, too, that the effect produced 

 by Fig. 8 is much more complex than the indications of Figs. 



1 and 2 might lead one to expect. Such a joint system as is 

 displayed in Fig. 8 does not ordinarily extend over any large 

 region of country and the reason is that in nature, as a rule, 

 the unequal support afforded by surrounding rock masses is 

 sufficient to suppress one or more of the joint systems. As 

 pointed out above, it is only when the resistance perpendicular 

 to the line of force is the same in every direction that all 4 

 systems of joints will appear. On the other hand, even more 

 complex systems are sometimes found locally developed for 

 reasons which will be set forth a little later. 



The process of construction outlined can be reversed, so that 

 if the spacing and dip of the fissures on the random plane were 

 given, the quadrangle of Fig. 7 could be drawn and the posi- 

 tion of the octahedron, or the line of force, determined. There 

 are natural cases in which this reduction would be instructive. 



In the construction of Fig. 8, it has been assumed that the 

 permanent strain at rupture was insignificant and, on this 

 hypothesis, the faces of the octahedron are isosceles triangles 

 with one angle of 70° 32' (cos"' 1/3) and 2 equal smaller angles. 



'Transfer the intersections of the random plane from Fig. 6, PI. XII, to 

 Fig. 5, PI. XII; draw also in 5 a square (parallel to the plane of 5) which 

 will contain the point at which the random plane intersects the axi& of the octa- 

 hedron. Then the line rs is common to 5 and 7 and rotation of 5 about the line 

 rs yields 7. 



In constructing Fig. 7 it is necessary to have a vertical section through Fig. 

 5 perpendicular to rs. In finding the spacing for Fig. 8 it is convenient to have 



2 other vertical sections of 5, one along the line /;« and the other along /«. It 

 is unnecessary to state that computation might be substituted for construction 

 if a high degree of accuracy were called for. 



