16 Alfred Harlier — On the Cause of Slaty Cleavage. 



strains in question. The section of this ellipsoid by any plane 

 will be an ellipse whose ellipticity will indicate the degree of 

 distortion of an object situated in that plane. Further, the principal 

 diametral plane of the ellipsoid will determine the direction of 

 cleavage. Now the effect of a shear is to distort a sphere of radius 

 1) into an ellipsoid of semi-axes a, b, c, and it is evident that tlie 

 same distortion might equally be brought about by an expansion 

 which would increase the radius of the sphere in one direction from 

 h to a, and a compression at right angles to it reducing the radius 

 in another direction from b to c. 



Figure to illustrate the cause of Slaty Cleavage. 



It remains to inquire whether shearing can really account for the 

 appearances observed. There being no change of volume, we should 

 have, in the ellipsoid produced by shearing, a c = b'^, or in other 

 words the three semi-axes would be in geometrical proportion : 

 whereas in the actual ellipsoid of distortion, as calculated from ob- 

 servations of fossils, a and b are not very unequal, and often sensibly 

 equal, while c is much less than either, thus giving an ellipsoid very 

 like a flat oblate spheroid. This points not to a shear, but to a great 

 compression and a slight expansion, giving rise to a total condensa- 

 tion of volume in the ratio ac : b'^. 



Mi\ Fisher certainly strikes at the weak point of the received 

 theory, when he draws attention to the great amount of voluminal 

 condensation which it requires. Thus, if slate of specific gravity 

 2-64 has been reduced to half its original volume by the process 

 which impressed the cleavage-structure upon it, its former specific 

 gravity must have been only 1-32 ! Still it seems impossible to 

 escape from the fact of this compression. We have to face, for 

 example, the evidence of the crumpling and folding of resisting 

 gritty bands interbedded with more yielding rocks which show 

 cleavage, as in the now historic cliff-section at Ilfracombe figured by 

 Sorby. 



On the other hand, we may notice the great amount of shearing 

 demanded by Mr. Fisher's hypothesis in order to produce the degree 

 of distortion commonly observed in the fossils of cleaved rocks. The 

 proper measure of a shear is the relative lateral displacement of two 

 surfaces of shearing divided by the distance between them, or in 

 Mr. Fisher's notation, cot a. It can be readily proved that — 



, a — c 



V ac 

 If then a = 2c, we have cot a = -7071 and « = 54°- 44' ; or if a = Gc, 

 cot a = 2-0412 and a —- 26°- 6' ! 



Mr. Fisher has applied his theory to explain the disposition of 



