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



If, on the other hand, either condition fails to be fulfilled, 

 the position of the strain ellipsoid will not be indicated by the 

 elongation of the pebbles and the divergence may amount to 

 any angle. In a general way, this conclusion may be arrived 

 at in a moment, for the ellipticity of the strain ellipsoid will be 

 superposed on that of the pebbie and the resultant figure will 

 coincide with neither, either in amount or in attitude. 



Specific examples are perhaps more convincing than general 

 principles, and I have therefore computed some cases which 

 are illustrated in figure 3.* In diagram a are shown a circle 

 and three ellipses in a square which are to represent the sections 

 of a sphere and three plastic ellipsoids within a cube. In b the 

 mass is supposed to be strained by a force acting at 30° to 

 the resistance, and this is assumed to be horizontal. The strain 

 is the same as that represented in two other diagrams in this 



3 



paper and some further details concerning it will be given 

 presently. The sphere is of course distorted into the strain 

 ellipsoid and the major axis of this figure Mall stand after 

 strain at an angle of 22° 37' to the horizontal. The greatest 

 axes of two of the ellipsoids originally coincided with the direc- 

 tion of the resistance, but after strain they make with the 

 horizontal angles 8° 45' and 6° 5 r , showing how the original 

 ellipticity affects the final orientation. One of these elongated 

 pebbles makes an angle of about 14° with the strain ellipsoid 

 and the other about 16-|°. No ellipsoid which is originally 

 parallel to the resistance can have a negative inclination after 

 strain, but the third ellipsoid illustrated dips at minus 11° 42' 

 in the unstrained state and after strain at minus 6° 5', thus 

 standing at an angle of nearly 29° to the strain ellipsoid. Had 

 either its ellipticity or its attitude in the unstrained mass been 

 different, its final inclination would be more or less than 6° 5'. 

 This last ellipsoid was computed with a secondary purpose, 

 for, in its final position, it coincides exactly with the direction 

 of the cleavage which, according to my theory, would be de- 

 veloped in the mass by strain. Either of the other pebbles if 



*The angles given in the diagram are v = 22° 37', c?i = 8° 45', J 2 = 6° 5'. 

 tf 3 = -6° 5', <A=-11°42'. 



