820 REPORT—1885. 
perpendicular to the cleavage-planes accompanied by a compensating ex- 
pansion along the cleavage-dip, for to this his shearing, with the neces- 
sary rotation concurrent with it, may be reduced. In this case the strain 
ellipsoid, having b a mean proportional between a and c, differs both from 
that of Dr. Sorby, in which 6 is greater than that mean proportional, and 
from that of Professor Haughton, in which a = b. 
Finally, it seems reasonable to suppose that the precise kind of dis- 
tortion produced in a rock by powerful lateral pressure depends on the 
nature of the rock itself and on the intensity and duration of the pressure. 
We may perhaps distinguish, as I have elsewhere suggested,! three stages 
of the process, at any one of which it may be arrested. In the first stage 
the rock-mass yields by a simple lateral compression with no considerable 
expansion to compensate it; the volume is accordingly diminished, this 
being effected by the closer packing of the constituent fragments and the: 
expulsion of the greater part of the interstitial water. In the second 
stage the limit of this packing has been reached, and further lateral com- 
pression is therefore compensated by expansion along the cleavage-dip, 
there being no diminution of volume. In the third stage the intense 
pressure facilitates chemical changes in the rock, involving a further 
diminution of bulk, and so a lateral compression only partially com- 
pensated by expansion along the cleavage-dip. The strain ellipsoid of 
Professor Haughton would characterise thé first stage, that of Dr. Sorby 
the latter stages of the process. 
A rock may, of course, be operated upon, either successively or 
simultaneously, by pressures in two or more directions, and the cleavage- 
structure will be determined by the resulting distortion. For instance, 
there may be compressions in two directions and an expansion in the 
direction perpendicular to both, producing a very prolate strain ellipsoid, 
in which } and care nearly equal and a considerably greater. In this 
case the rock would have the fibrous structure which Professor A. Heim? 
denominates linear cleavage as distinguished from ordinary plane cleavage, 
and which has been artificially imitated in the well-known experiments: 
of MM. Tresca* and Daubrée.t Instead of a plane of cleavage there is: 
an axis of cleavage. K 
III. The Mechanical Theory of Slaty Cleavage: the Intimate Structure 
of Cleaved Rocks. 
The direct evidence for the distortion of cleaved rocks and the 
methods of arriving at a numerical estimate of it will be treated in the 
next section. At present we have to consider what effect such distortion 
has upon the intimate structure of these rocks, and how slaty cleavage is 
only a logical consequence of it. 
Mr. Sharpe,® examining certain coarse brecciated bands in the slate 
quarries of Langdale and Patterdale, noticed that the included large 
fragments, of which the rock was to a great extent made up, were com- 
pressed perpendicularly to the cleavage-planes and elongated along the 
cleavage-dip, thus approximating, when allowance was made for their 
’ *On the Successive Stages of Slaty Cleavage,’'Geol. Mug., 1885, p. 266. 
* Mechanismus der Gebirgsbildung, Ba. ii. s. 59 (1878), Basel. See also Dufet, 
Ann. de V Ecole Norm. Supér., sér. 2, t. iv: p. 184 (1875). 
’ Sur écoulement des solides, 1872, Paris. 
‘ Htudes Synthétiques de Géologie Expérimentale, 1879. 
* Quart. Journ. Geol. Soc., vol. v. p. 112 (1849). 
