I4 WALTER H. BUCHER 
the angle changed from 100° to values as low as 84° and event 70°. 
These values remained the same, whether the compressive stress 
acted longitudinally or as hoop stress. 
Here, then, we have a substance which normally shears under 
compression at an angle of 100° changed to one shearing at 80° 
through the action of tension in all directions normal to that of the 
axial compression, or, using the word in the sense defined above, we 
may say, the substance has been made more brittle. 
III.’ THE ELLIPSOID OF STRAIN 
The attempt to correlate joint planes with stress-strain relations, 
to which the first part of this paper was devoted exclusively, is by 
no means new. Steidtman’s splendid paper on ‘‘The Secondary 
Structures of the Eastern Part of the Baraboo Quartzite Range, 
Wisconsin’ is well known, and Leith, in his lectures and in his 
Structural Geology’ has impressed on the younger generation of 
geologists the importance of shearing planes in the mechanics 
of rock fractures by the use of a wire-netting model. 
Unfortunately, however, the model as well as the earlier dis- 
cussions by other writers, give expression only to that case in which 
the planes of shearing form an obtuse angle in the direction of 
compressive stress. 
The outstanding characteristic of the strain ellipsoid illustrated 
by Leith’s wire-netting model, is the fact that the elongation in 
the direction of one principal stress equals the shortening in the 
direction of the other principal stress, or, that the area of the 
strained surface remains unchanged. A simple mathematical 
consideration shows that when a circle is changed into an ellipse 
of equal area, the angle of the lines of no distortion facing the direc- 
tion of shortening, must always exceed 90° (Fig. 14). To reduce 
this angle to the smaller value characteristic of all brittle materials, 
we must assume the longitudinal shortening to be smaller than 
t 'W. Mason, “‘The Liiders’ Lines on Mild Steel,” Proc. Phys. Soc. of London, Vol. 
XXIII (1911), Table D, bottom of column (complementary angle). 
2 Jour. Geol., Vol. XVIII (1910), pp. 259-70. 
3 New York: Henry Holt & Co., 1913, pp. 18-20. 
