4 G. F. B< ch r — Current Theories of Slaty Cleavage. 



are to be dealt with the laws of probability become exact. 

 Again, wherever there are evidences of dynamo-metamorphism, 

 cleavage appears in the rocks, not always good cleavage, but 

 still a fissile structure which should be accounted for. " With 

 every possible allowance for yielding of supports, it appears to 

 me conclusively shown above that the average direction of de- 

 forming force to the resisting plane cannot have exceeded some- 

 thing like 45°, and hence also that schistosity is brought about 

 as a concomitant Of strains in which the rotational element is 

 large. It follows to my mind that Sharpe's theory is inade- 

 quate, for if it were a sufficient explanation, not more than a 

 ten thousandth part of the strained rocks ought to show cleavage 

 or foliation. 



The hypothesis that crystallization takes place in surfaces 

 perpendicular to the resultant stress is attractive, but it must 

 be tested first of all by determining for the simplest cases what 

 the direction of resultant stress really is. Mr. Leith evidently 



c c 



D £>' 



supposes that in the case of pure or ir rotational strain in a 

 homogeneous mass, the resultant stress coincides in direction 

 with the least axis of the strain ellipsoid. Such a coincidence 

 will truly exist between the external stress or surface traction 

 and the axis in question when the strain is pure, but there is 

 no such agreement between the resultant internal stress at an 

 arbitrarily selected point and the local orientation of the strain 

 ellipsoid. In pure strains the resultant stress acting on any 

 material particle is in the direction of the motion due to this 

 action. The paths traced out by the particles are called the 

 lines of displacement or the "lines of flow" and the surfaces 

 which are perpendicular to these lines are the elastic or plastic 



