STEPS IN SLATE. 85 



the appearance of the mass would be that shown in figure 22, b, where 

 the fine horizontal lines represent mere cleavage, not partings. Now let 

 the final shear at right angles to the x y plane be applied. It will elon- 

 gate the mass in the direction o z and contract it in the direction o y. But 

 since the more rigid layer yields to this stress less freely than that in 

 which it is imbedded, the grit bed will rotate more nearly as if it were a- 

 rigid mass, and will assume such a position as is shown in figure 22, c 

 In short, the hard layer will be deflected in just the same way that an 

 imbedded scale of mica parallel to it would be deflected. Thus the 

 cleavage in the hard layer will not be parallel to that in the adjoining 

 mass and will form a larger angle to the bed planes. 



It thus seems sufficient to suppose the grit bed to have a greater coef- 

 ficient of rigidity to account for the phenomena of steps.* 



*Dr Sorby's theory of this phenomenon, as stated by Mr Harker, is as follows: "Since the grit 

 yields less than the slate to the compressive force, the total voluminal compression is greater for 

 the slate than for the grit. Hut near the junction of the two rocks the change of dimensions in the 

 direction parallel to the bedding must be the same for both. Consequently, in the direction per- 

 pendicular to the bedding, the slate undergoes a less expansion (or greater compression) than the 

 grit; and the cleavage planes, which are in each rock perpendicular to the direction of greatest 

 compression, will therefore be less inclined to the bedding in the slate than they are in the grit.' - 



This is a very ingenious explanation, but I have not been able to convince myself that it is sound. 

 It depends primarily upon the hypothesis that a large cubical condensation is involved in the 

 production of slate. This certainly docs not seem to be the case when slaty cleavage is produced 

 in moist clay or wax, for such substances are probably compressible only to a very minute extent. 

 It also implies that there is a very great difference between the cubical compressibility of the grit 

 and the shale. I know of no good reason to suppose that such a difference exists. The difference 

 in hardness does not imply such a relation, for cast iron, though so much harder than gold, is 

 nearly three times as compressible ; but even if it be granted that the relations of compressibility 

 are those demanded, it is not clear that any means is provided of changing the direction of the force 

 in the manner required by Sorby's theory of cleavage. 



One may suppose a cubical portion of a rock mass to undergo the pressure needful to develop 

 slaty cleavage without change of volume, and that cubical contraction takes place subsequently. If 

 the mass contains a stratum of smaller compressibility than the remainder, the cleavage on the 

 theory now under consideration would be perpendicular to the direction of the force throughout 

 the mass before cubical contraction occurred. In this stage the mass would have the appearance 

 of figure 22, b. The effect of the shrinkage would then be to deflect the slaty laminae close to the 

 contact in curves with points of inflection at the contact, but to leave the direction of the cleavage 

 at a little distance from the contact unchanged. The appearance after cubical contraction would 

 would then resemble that illustrated in the following diagram : 



Figure 21. — Effects of Compressibility. 



But this does not represent the phenomenon to be accounted for; so thai although the hypothesis 

 of varying cubical compression would explain a change of direction in the surfaces of cleavage al 

 the contact with a gritty bed, it does not, so far as I can see, account for steps. 



