22 R. T. CHAMBERLIN AND W. Z. MILLER 
as those in which the principal directions of strain remain constant 
with reference to the principal axes of stress throughout the deforma- 
tion. Rotational strains are those in which the axes of strain are 
-being constantly rotated with respect to the axes of stress during the 
deformation. The behavior of a body deformed under each of 
these types of strain has been admirably set forth by Leith by the 
use of the strain ellipsoid and the wire-netting model. As shown in 
Figs. 5, 6, and 7 of his Structural Geology, the planes of no distortion 
are the planes of maximum shear, and are the planes along which 
fracturing should tend to take place in either rotational or non- 
rotational strain. But the inclination of these planes of shear with 
respect to the applied force is different in the two cases. Under 
non-rotational strain the shearing planes are seen to be located 
approximately at 45° to the direction of the applied force. Under 
rotational strain, on the other hand, while the relation of the 
shearing planes to the strain ellipsoid remains the same, the position 
of these planes with reference to the direction of applied force is 
steadily changed by rotation. In the extreme case (pure shearing) 
one plane of shear is seen to be parallel to the direction of the 
force, while the other commences at 9o° to the force and is gradu- 
ally lowered in angle as the deformation progresses. Fracturing is 
more likely to occur in the plane parallel to the force than in the 
one highly inclined to it. 
Thus the shearing plane inclined 45° to the force in pure non- 
rotational strain and the corresponding shearing plane parallel to 
the force in extreme rotational strain may be taken as the limiting 
cases. It is clear that between these two limiting cases of 45° 
and o° fracturing may actually take place at any intermediate 
angle, depending upon the relative strength of the rotational and 
non-rotational factors. This will perhaps be made clearer by 
Poze 
Ellipse A represents the cross-section of a sphere deformed by 
pure non-rotational strain resulting from a uniform, horizontal 
compressive stress. Shearing and fracturing may occur along 
either of the 45° shearing planes, but more likely along plane 6 than 
plane a. In ellipse B the force, though still horizontally directed, 
tC. K. Leith, Structural Geology, pp. 18-21. 
