G. F. Becker — Current Theories of Slaty Cleavage. 11 



the included mass were relatively very brittle, it would be cracked 

 at the iuception of strain, and would therefore exhibit a be- 

 havior of its own. On my theory of cleavage, this behavior 

 can be fairly well followed up. Fig. 4 is a diagram supposed 

 to represent a quadrangular surface of a plastic mass including 

 a cube of a different character. I suppose this cube to be made 

 of some substantially isomorphous material, such as glass or 

 quartzite or some very fine-grained eruptive rock, and that this 

 cube is also brittle. Then at the inception of strain, it will be 

 cracked at angles of 45° to the axes of the initial strain-ellip- 

 soid. It may crack in two directions, or only in one, and I 

 shall suppose that the direction in which it yields is that which, 

 according to my theory, is characteristic of the master joints 

 in slates. Now, these lines of fracture will during continued 

 strain change their inclination, precisely as if they were mere 

 geometrical lines in the plastic mass. The several slices will 

 slip over one another and be rearranged. Doubtless at the 

 edges of these slabs there will be a certain amount of disturb- 

 ance of the surrounding material, but there appears to be no 

 reason to suppose that these disturbances will not so balance 

 one another that the centers of inertia of the several slabs will 

 behave with simple regularity. If so, these centers of inertia 

 will also remain on a material line which will be deflected pre- 

 cisely as if the cube were absent altogether. It is then possible 

 to compute for certain displacements the position which these 

 centers of inertia will take, and therefore to exhibit the relative 

 position of the slices after deformation is complete, and this is 

 done in the second figure of the diagram. 



In constructing this diagram, advantage has been taken of a 

 little problem solved in my former paper on this subject. I 

 have there shown that, provided Hooke's Law holds and Pois- 

 son's ratio is assumed at one-fourth, a force inclined to the 

 surface of the mass at an angle of 30° will bring about just this 

 distortion. Now, there are substances for which Poisson's 

 ratio is equal to one-fourth, especially the glasses. Hooke's 

 Law is applicable to small strains with perfect accuracy ; for 

 large strains it affords only a first approximation. The diagram 

 may therefore be. erroneous to some extent, but the only error 

 which it can contain is in the direction of the applied force, and 

 this error probably does not exceed one or two degrees at most. 

 It is impossible to draw such a diagram without assuming some 

 law between stress and strain.* 



It thus appears that my theory of cleavage completely explains 

 the slicing of a pebble and the inclination in the position of the 



*If x, y is the position of a point in the unstrained mass, and as', y' the 

 point to which it is brought by strain, then x' =1*0577 x + y ; y'=0 - 7691 y. 

 It follows that v o =m° 58', y=22° 37'. 



