DEFORMATION OF ROCKS 1 87 



angle. That is to say, the highest possible dip which a cleavage 

 can have as a result of simple shearing is 45°. The greater 

 diJEferences between the positions of the rotated vertical lines 

 and the major axes of the flattened ellipses result from the 

 smaller rotations and the largest or limiting value is 45°. The 

 differences between the positions of the rotated verticals and 

 the corresponding major axes of the flattened ellipses rapidl}- 

 diminish in amount with the increased rotation of the verticals,, 

 and for rotations of 75° and above the differences are less than i°. 

 The last column (7) shows the relative efficiency in the produc- 

 tion of cleavage of simple shearing, as compared with shortening 

 in a single direction with consequent elongation in another 

 direction. From this column it is seen that shearing which 

 rotates the vertical by 10° is equivalent to a shortening of some- 

 what less than one-tenth ; that a rotation of the vertical of 20° is 

 equivalent to a shortening of about one-sixth ; that a rotation of 

 the vertical of 30° is equivalent to a shortening of about one- 

 fourth ; that a rotation of the vertical of 45° is equivalent to 

 a shortening of a little more than one-third ; that a rotation 

 of 60*^ is equivalent to a shortening of a little more than 

 one-half; and that a rotation of 75° is equivalent to a short- 

 ening of about three-fourths. Of course the ratios between 

 the minor and major axes of the ellipses are the same for short- 

 ening and corresponding shearing. 



In the actual production of cleavage, shortening and rota- 

 tion are combined in various proportions. It would be inter- 

 esting to know certainly the amount of simple shearing and 

 of shortening which is necessary to produce ordinary slaty 

 cleavage. I have pointed out in another place' that cleavage 

 develops more largely from the formation of new minerals 

 than from the flattening of the old mineral particles, and I am 

 inclined to believe that a very moderate amount of shearing or 

 shortening is sufficient to produce the structure imperfectly — 

 possibly as little as that represented by a shortening of 10 per 

 cent., or a rotation of the vertical of about 10°. Upon the other 



' Loc. cit., (A), p. 635 ; (B), pp. 451-453- 



