84 G. F. BECKER — FINITE STRAIN IN ROCKS. 



tion. In such a slate a fossil which lay in the cleavage plane would 



simply be flattened. From the observed fact that fossils are frequently, 

 though not always, relatively elongated to a sensible degree in one direc- 

 tion in the cleavage plane, Mr Sharpe inferred lateral confinement as well 

 as vertical pressure. 



On the theory of inclined pressure, a fossil would always be elongated 

 in the direction of the grain of the slate and contracted across the grain 

 in the cleavage plane, excepting when the pressure made no angle with 

 the fixed plane. A still greater elongation, however, would take place 

 in the direction of the major ellipsoid axis, called A in this paper, which 

 is at right angles to the grain and makes a large angle with the cleavage 

 plane. That such distortions do exist I have convinced myself by the 

 examination of specimens, but I have not had an opportunity of examin- 

 ing any large collection of fossils from slates with reference to this point. 



The relations of beds of hard grit occurring in slate bear a close rela- 

 tion to those of fossils. If such a bed were bounded by surfaces parallel 

 to the plane x y (or A B), the bed would behave either to a vertical or to 

 an inclined pressure as an independent mass. On the currently accepted 

 theory it would develop a horizontal cleavage. On the theory of inclined 

 pressure it would develop a cleavage in a direction between that of the 

 pressure and that of the fixed plane; and this would nearly coincide 

 with the cleavage of the surrounding softer mass, because the direction 

 of cleavage lies near that of constant direction and changes but little 

 during strain. The smaller the angle which the force makes with the 

 fixed support, the smaller would the divergence in the two cleavages be. 



" Steps " are produced when a grit bed cuts the cleavage across the 

 grain, the plane of the cleavage in the slate and the surface of the grit 

 bed making an acute angle. The grit is a harder material than the slate, 

 and the cleavage developed in the grit makes a larger angle with the 

 bedding than it does in the slate. 



To account for steps according to the theory of inclined pressure one 

 may consider the elementary stresses separately. It has been shown 

 that the shear in the plane B C does not tend to produce relative motion 

 on the cleavages. One may therefore suppose the stress, minus this shear, 

 to be applied to the rock first, and this shear to come into action later. 

 Figure 22, a represents a cube in the y z plane, with a layer of harder 

 material passing diagonally through it. If a shear and a shearing motion 

 or scission in the x y plane are impressed upon this mass, both portions 

 must yield simultaneously, because if the force were insufficient to strain 

 the harder layer, this would protect the surrounding mass from the action 

 of the force. Hence these strains would produce in both masses a cleav- 

 age, the traces of which on the y z plane would be parallel to o z, and 



