88 G. P. BECKER — FINITE STRAIN IN HOCKS. 



The conclusions reached are then applied to cases such as may arise 

 in geology. Large masses of rocks, it is assumed, may be considered as 

 homogeneous. Were it necessary to take into consideration the minute 

 texture of rocks, any general conclusions as to their behavior under 

 orogenic stress would be impracticable. Simple irrotational .pressure is 

 first taken up. It is shown that such a pressure will produce two sets 

 of fissures crossing one another at angles approaching 90° if the rock is 

 brittle. If it is plastic, two sets of schistose cleavages will replace the 

 fissures. The line of force bisects the obtuse angles of the cracks or 

 cleavages. Use is made of the theory of this case to prove in a very 

 simple manner why mica scales and flat sand grains tend to arrange 

 themselves parallel to the bedding of sedimentary rocks, and why flat 

 pebbles in water-channels " shingle up stream." 



A mass resting on a yielding foundation and subjected to an inclined 

 force is briefly discussed. This case closely approaches that of the 

 simple irrotational pressure. It seems to account for unsymmetrical 

 schistosity. 



The most interesting case is that of a mass resting upon a rigid founda- 

 tion and affected by a force inclined to the foundation at any angle. It 

 really includes the case of the simple irrotational pressure. If the mass 

 is brittle and is strained so gradually as not to bring viscosity into play, 

 the material will rupture in columns, the axes of which are parallel to 

 the fixed plane of support and at right angles to the force. If the strain' 

 is so rapidly produced as to excite viscosit}^, only one set of fissures will 

 form, and these will be intermediate in direction between the line of force 

 and the projection of the force on the fixed plane. If the rock is plastic 

 (or if it is kept strained between the elastic limit and the breaking point 

 sufficiently long to undergo considerable deformation) the fissures inter- 

 secting the angle between the line of force and the fixed plane will be 

 replaced to a greater or less extent by cleavage planes; and if the force 

 • does not approach the vertical to the fixed plane, these cleavage planes 

 will preserve a nearly constant direction and have a slaty character. In 

 this case the second set of planes of motion, if they receive expression at 

 all. will cut sharply across the cleavage planes as master joints. This 

 seems to be the only way in which slate-like structure can result from 

 the action of force on homogeneous matter. 



The spacing of fissures formed, by inclined pressures is discussed on 

 the hypothesis that they are so disposed as to lead to the greatest depo- 

 tentialization of energy. This leads to an exceedingly simple formula 

 for the thickness of a column in a direction perpendicular to either pair 

 of bounding planes. The formation of a single system of parallel fissures 



