FISSURING BY INCLINED PRESSURE. 57 



Partial Theory of the Spacing of Fissures. — When a slab of rock resting 

 broadside against an inflexible support ruptures under the influence of 

 a pressure inclined to the supporting plane, it is easy to see that the 

 pressure can be relieved only by several cracks, which must divide the 

 mass into sheets bounded by planes of maximum tangential strain. 

 Such a division is extremely common on a large scale in granite and 

 other relatively homogeneous masses ; on a small scale it is frequent in 

 the pebbles of conglomerates which have been subjected to pressure. It 

 is therefore very desirable to ascertain the conditions which determine 

 the thickness of the sheets. 



A slab of rock must evidently rupture in such a manner as to relieve 

 the pressure upon it, and this relief must be accompanied by a readjust- 

 ment of the fragments. This consideration at once assigns a superior 

 limit to the spacing of the cracks. Suppose, for example, that in a case 

 illustrated by the following diagram cracks were to form only at a and c 5 

 then, since a perpendicular from the upper end of a falls between a and c, 



a lr c 



Figure 7. — Widest possible Spacing of Fissures. 



the fragment a a c c cannot rotate without increasing its vertical dimen- 

 sion, and the pressure cannot be in any way relieved by the ruptures. 

 But if a third crack, b b, is so placed that its lower end is perpendicularly 

 below the upper end of a, the fragment a a b b can be rotated so as to 

 decrease the vertical dimension, and thus to relieve pressure. Hence 

 the cracks must be at least so near to one another that the terminations 

 of adjacent cracks are in vertical lines, and the higher the angle which 

 the cracks make with the fixed plane, the nearer must they be to one 

 another. This, however, is an extreme case; for an infinitesimal rota- 

 tion of the vertical line a b about any point of it would not diminish the 

 thickness of the mass. The actual distance between fissures must there- 

 fore be less than that assigned by this limit. 



When the process of straining is so slow that the mass can fully adjust 

 itself at each instant to the external forces (an important limitation) it 

 seems impossible to avoid the conclusion that the actual spacing will be 

 such as to depotentialize the greatest possible amount of energy for a 

 given length of fissure. In other words, the cracks will be so disposed as 



