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



B has reduced the unit length to 0*344 unless the strain was 

 attended by diminution of volume, in which case the shrinkage 

 in this direction was somewhat greater. The product of the 

 other two axes is AC = 1/B for the case of incompressibility. 

 Some further relation must be exactly known to determine the 

 ratio of A to C. This the cut does not afford, but an approxi- 

 mation can be obtained without difficulty. The fixed plane in 

 the case of pure strain is in the direction of the major axis, 

 while in the case of scission on my theory, it coincides in 

 direction with the cleavage. When pure and rotational strains 

 are combined the resistance lies between the two extremes 

 noted, which in this case differ by J 9°. Now, as I shall point 

 out presently, the strain exhibited in the cut bears evidences 

 of a large amount of rotation and the fixed plane was probably 

 nearer the cleavage than the major axis. The assumption that 

 it made an angle of 6 degrees with the cleavage cannot be more 

 than a degree or two out of the way, and if this were the cor- 

 rect value, it easily follows that A = 2-36 and C = 1*23. 



I have drawn in to the cut, fig 6, the ellipse with these axes 

 and also shown the two lines representing the traces of the 

 planes of maximum tangential strain. One of them coincides 

 accurately with the cleavage while the other has exactly the 

 same direction as the joints. If this cut is compared with fig. 

 10 of my former paper, which was issued six years before Mr. 

 Dale's plate, it will be seen that the similarity is very great. 

 According to my theory, cleavage should develop in the acute 

 angle between the direction of the applied force and that of the 

 fixed resistance on one set of planes of maximum slide, while the 

 other set of such planes will be marked, if at all, by joints. 

 That appears to be exactly what has happened in the case under 

 discussion, and it is the great difference between the two struc- 

 tures which lead me to infer that the element of scission in the 

 strain is large. 



Having an approximation to the values of the axes, it is a 

 mere matter of detail to compute the component pure strains 

 and scission. The former are due to the vertical force com- 

 ponent, the latter to the horizontal component. To combine 

 them to a resultant applied force it would be needful to know 

 or to assume the relations between strain and stress. Hence I 

 merely indicate a pressure which must lie between the minor 

 axis and the cleavage, but an uncertain angle. 



It would appear that my theory throws far more light on 

 this occurrence than does Mr. Leith's, and affords a very satis- 

 factory explanation of an interesting occurrence which on a 

 natural scale covers only one square millimeter. 



While my theory of cleavage does not necessarily involve 

 the formation of new minerals, such as mica, it affords a means 



