nh 
ON SLATY CLEAVAGE AND ALLIED ROCK-STRUCTURES. 825 
to have been originally spherical, or perhaps slightly extended in the 
direction of the stratification so as to form a rather oblate spheroid ; but 
their present shape is that of an ellipsoid of three unequal axes, viz., the 
greatest axis in the plane of cleavage and along its dip; the mean axis 
in the plane of cleavage and along its strike ; the least axis perpendicular 
to the plane of cleavage ; thus indicating a compression perpendicular to 
the cleavage-planes, and an expansion along them in the direction of their 
dip. In fact, if the original form was spherical, the present form of these 
spots must give us the strain ellipsoid itself. If, however, as suggested 
by Mr. Fisher,! the formation of these spots be posterior to that of 
cleavage, we must account for their form by ‘ the chemical influence 
spreading most readily along the grain of the slate, and with greatest 
difficulty across its laminz,’ and in this case no quantitative conclusions 
can be drawn from the phenomena. 
The most valuable evidence of the nature and amount of the distor- 
tion of cleaved rocks is that obtained by noting the altered forms of 
contained fossils. The merit of first applying numerical calculation to 
this line of inquiry belongs to Professor Haughton,? whose work has 
already been alluded to. We are, however, not justified in assuming that 
the deformation of the fossils is invariably a correct measure of the dis- 
tortion of the rocks themselves. A hard substance imbedded in a softer 
matrix would evidently yield but slightly, or not at all, to any compression 
to which the mass as a whole might be subjected; and it is a matter of 
common observation that in many slate-rocks those fossils of more solid 
substance or stouter form are comparatively unchanged in shape, while 
those of slighter build exhibit a marked deformation. It might be 
possible by noting the degrees of distortion of different kinds of fossils in 
the same rock to form some idea of the consistency of that rock at the 
time of its deformation. Meanwhile, it may be remarked that the dis- 
tortion of the rock as deduced from the forms of its contained fossils will 
be in all cases an under rather than an over-estimate ; and where different 
kinds of fossils in the same rock exhibit deformation to the same extent, 
We may reasonably suppose that they have all shared to the full the dis- 
tortion of the rock itself. 
Taking this last case, it is clear that the degree of distortion of the 
fossils must be in direct relation with the form of the strain ellipsoid, so 
that with sufficient data the latter may be deduced from the former. It 
will be convenient to adopt the usual assumption that the bedding and 
cleavage have the same strike, and to regard the fossils as plane figures 
lying parallel to the bedding. 
Fig. 6 is taken in a plane perpendicular to the common strike of 
bedding and cleavage. The ellipse is the section by this plane of the 
strain ellipsoid, AOA’, COC’, are the greatest and least axes of the 
ellipsoid; POP’ is the trace of the bedding-plane, and the angle AOP is 
the angle between the planes of bedding and cleavage, which we shall 
call. If the radius OP be called p, then 
2 m2 
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wo t 
p2 a? a 
The plane of bedding cuts the strain ellipsoid in an ellipse whose semi- 
axes are p and b, and this may be called the strain ellipse for objects 
1 Geol. Mag., 1884, p. 402. 2 Phil. Mag., 4th ser., vol. xii. p. 409 (1856). 
