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



This explanation differs from that proposed in the last para- 

 graph more than might be supposed. It is analogous to Sharpe's 

 theory, but is more general ; for Sharpe supposed cleavage de- 

 veloped by an external pressure perpendicular to the induced 

 cleavage, or to a pure strain, usually accompanied by lateral 

 constraint ; whereas Mr. Leith's second hypothesis is that, 

 whether the strain is pure or not, the cleavage is normal to the 

 least axis of the strain ellipsoid. 



I entirely share Mr. Leith's opinion that pure strains are rare 

 in nature. Some idea of their rarity may be gained by a little 

 reflection. The direction of a force with reference to a resist- 

 ing plane may be regarded as fortuitous. If so, the chance 

 that the direction will be exactly 90° is infinitesimal, but if a 

 variation of plus or minus half a degree is tolerated, the chance 

 will rise to one in 20,626, which is the number of square de- 

 grees on a hemisphere of unit radius, or 360 radians. On the 

 other hand, a zone one degree in width on a sphere at a polar 

 distance of 45° has an area of 255 square degrees, so that the 

 chance of a force having an inclination of 45° ± 30' to a fixed 

 plane is 255 times as great as that it should be normal to the 

 plane. The average value of all possible inclinations is an 

 angle of one radian (57° 18') to the normal. Thus pressures 

 at less than 45° to the plane are more probable than those at 

 higher angles and normal pressure is least probable of all. 

 Hence a pure strain is a highly improbable limiting case of 

 rotational strain. Unmodified scission is also a limiting case, 

 but is 360 times as probable as a pure strain. 



It has been assumed in the preceding paragraph that rock 

 masses undergoing deformation may be regarded as resting 

 against a fixed support, and this is only partially true. Any 

 supporting masses must yield by rotation to some extent, though 

 the amount of such yielding must usually be exceedingly small 

 as compared with the amount of deformation. When a dis- 

 location occurs between the Ancles and the basin of the Pacific, 

 the trend of the range is not sensibly changed to accommodate 

 the rocks adjacent to the fault system. Ho w ever, so far as the 

 supporting resistance does rotate, the probability of a pure 

 strain is increased by the diminution of the rotational strain 

 component. I shall assume that the probability rises to one in 

 10,000, though in my opinion this is a gross exaggeration. 



Sharpe's theory is that cleavage is clue to pure strain. The 

 many geologists who are content with this theory ought to tell 

 the rest of us what happens in 9999 cases in which the strain 

 is not pure. 



In the vast exposures of the Archean and early Paleozoic, 

 millions upon millions of cases of dynamo- metamorphism are 

 exposed to examination and when such numbers of instances 



