ON SLATY CLEAVAGE AND ALLIED ROCK-STRUCTURES. 819 
placement of any two distant slices being proportional to the distance 
between them, and equal to s times that distance, where s is called the 
measure of the shear. A square (ABCD, fig. 1) would be distorted by the 
shear into a parallelogram (ABCD, fig. 2) ; and the ratio BE : AE would 
be the measure of the shear. The axes of the ellipsoid of strain would be 
in the ratios 
J/s?*ta4+s a: V/s? +4—s 
2 pie 2 ; 
One set of circular sections of the ellipsoid would coincide with the 
cleavage planes, and its major axis would make with these planes the 
angle whose tangent is 2 . The axes would be such that ac = b?, and there 
would be no change of volume in the rock during distortion. 
Fig. 2. 
A B 
M. Aug. Langel! also regarded cleavage planes as planes along which 
a shear (glissement) of the rock has taken place. It is easily seen, how- 
ever, that such an idea is entirely incompatible with the observed facts. 
For the kind of distortion described implies (i.) no compression of the 
rock in a direction perpendicular to the cleavage planes, and (ii.) no dis- 
tortion of plane objects lying in planes parallel to the cleavage planes. 
Moreover, as will appear in the next section, any mechanical theory of 
true slaty cleavage requires that the cleavage planes should be perpen- 
dicular to the least axis of the ellipsoid of strain. 
Accordingly the Rev. O. Fisher, who formerly endorsed the theory 
just mentioned,” was led to change his opinion, and, while still describing 
the distortion of slate-rocks as a shear, to suppose that the shearing has 
taken place, not along the cleavage planes, but in such a direction that 
ese planes are perpendicular to the least axis of the resulting strain 
ellipsoid. But if there be, as seems to be indicated by the facts of 
cleavage, a diminution of volume during the process, the distortion of the 
rock cannot be resolved into shearing ; and if, on the other hand, as Mr. 
Fisher maintains, there be little or no change of volume, it still seems 
‘simpler, as I have contended,‘ to describe the movement as a compression 
1 «Du clivage des roches,’ Bull. de la Soc. Géol. de Fr., 2° sér., t. xii. p. 363 (1855). 
2 «On Faulting, Jointing and Cleavage,’ Geol. Mag., 1884, p. 268. 
2 «On Cleavage and Distortion,’ Geol. Mag., 1884, p. 396. 
4 «On the Cause of Slaty Cleavage,’ Geol. Mag., 1885, p. 15; Reply, Zbid. p. 174. 
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