SCHISTOSITY AND SLATY CLEAVAGE 435 
It is very easy to calculate and illustrate the position of the 
planes of gliding ina pure shear. If the unit cube is reduced by 
a pure shear to a height = (or elongated at a right angle to this 
direction to a length a) then the tangent of the angle which 
the circular planes make with the greatest axis of the ellipsoid is 
—, which it is worth while to note is also the smallest semi-axis 
a 
of the ellipsoid. Ifa differs insensibly from unity, the angle in 
question differs insensibly from 45°, and for the values a= 4 
2, 4, the respective correspondiny angles are to the nearest degree 
SV 2 n Was 
By way of illustration, consider a cube of homogeneous mat- 
ter subjected to pure shear such that its height is ultimately 
reduced to one-half and let the elastic limit be so small that flow 
sets in when deformation is very small. Then the first lines to 
flow will stand at 45° (sensibly) to the direction of greatest 
elongation while at the close of the experiment the last lines to 
flow will stand at 27° to this axis. The material surfaces on 
which flow first took place of course acquire greater and greater 
inclination as the deformation increases, but their position is 
determinable in any state of strain because they connect the 
diagonal corners of the strained cube. 
This case is illustrated in Fig. 3. The broken lines in the 
distorted cube answer to the directions in which flow begins ; the 
dotted lines are those along which flow takes place at the close 
of the operation; the short broken or dotted lines in the square 
representing the undistorted cube show the original positions of 
the two sets of lines before strain. For strains intermediate 
between the initial and final states the lines of flow are also inter- 
mediate in position. } 
For comparison with other strains the two wedges in the 
unstrained cube marked Randy are of much importance. Each 
of these wedges is bounded upon one side by the line of particles 
which are the first to undergo flow and on the other side by the 
last line of particles which undergo flow. In pure shear R =, . 
