ON SLATY CLEAVAGE AND ALLIED ROCK-STRUCTURES. 817 
The exponents of such theories agree in referring the structure to the 
action of powerful lateral pressure, and in considering that such pressure 
operated simply by producing a distortion of the rock-mass upon which 
‘it was exerted. They differ to some extent, according to the special 
examples studied by each observer, as regards the precise kind of distor- 
tion produced, and the manner in which it has affected the intimate 
structure of the rocks in question. 
We consider first, then, the kind of distortion which the rock, 
regarded for the present as a homogeneous mass, is supposed to have 
experienced under the action of the lateral pressure. If we imagine a 
sphere traced in the rock previous to its distortion, the effect of any 
uniform strain upon the mass will be to distort this sphere into an 
ellipsoid. This latter surface, which may be called the strain ellipsoid, 
or ellipsoid of distortion, may conveniently be taken to express by its 
form and position the kind of strain or distortion undergone by the rock. 
We shall call its principal semiaxes, in descending order of magnitude, 
a, b,c. If the radius of the original sphere be &, it is evident that, in 
general, the distortion is accompanied by a change of volume in the 
ratio abe : k’. 
Mr. D. Sharpe’s? conclusions were drawn from an examination of the 
fossils in the cleaved rocks of Tintagel and South Petherwin, but he 
extended them to all rocks having slaty cleavage, and confirmed them by 
the slates of North Wales, Westmoreland, and Cumberland. He says: 
* It may be asserted as probable that all rocks affected by that peculiar 
fissile character which we usually call slaty cleavage, have undergone 
‘1. A compression of their mass in a direction everywhere perpen- 
dicular to the plane of cleavage. 
‘2. An expansion of their mass along the planes of cleavage in the 
direction of a line at right angles to the line of incidence of the planes of 
bedding and cleavage ; or, in other words, in the direction of the dip of 
the cleavage. No proof has been found that the rock has suffered any 
change in the direction of the strike of the cleavage planes. We must 
therefore presume that the masses of rock have not been altered in that 
direction.’ 
Assuming these laws, the strain ellipsoid would have its least axis 
perpendicular to the cleavage-planes, its greatest axis along the cleavage 
dip, and its mean axis along the cleavage-strike. Also the last clause in 
Mr. Sharpe’s results makes } =k, and therefore the change of volume 
would be represented by the ratio ac: b?. Mr. Sharpe speaks of the 
compression being ‘compensated’ by the expansion; if this is to be 
interpreted strictly, we should have ac = b?, and no change of volume ; 
but it is highly probable that in most cleaved rocks, ac would be less than 
b?, and the volume would be reduced in proportion. 
Dr. H. Clifton Sorby ¢ examined the slates of Penrhyn and Llanberis, 
and the cleaved limestones and dolomites of Devonshire, and drew con- 
1 Thomson and Tait, Natural Philosophy, vol. i. pt. i. § 160, new ed. (1879). 
: Minchin, Zyeatise on Statics, § 280, new ed. (1880). 
2 «On Slaty Cleavage,’ Quart. Journ. Geol. Soc., vol. iii. p. 87 (1847). 
8 The latter form of statement must be preferred ; the two expressions are clearly 
Not equivalent, unless the strikes of the cleavage and the bedding coincide. 
4*On the Origin of Slaty Cleavage,’ Edinb. New Phil. Jowrn., vol. lv. p. 137 
(1853). ‘On Slaty Cleavage as Exhibited in the Devonian Limestones of Devon,’ 
Phil. Mag., 4th ser., vol. xi. p. 20 (1856). 
1885, 3G 
