152 Transactions of the Academy of Science of St. Louis 
tural axis continues from the Ordovician area, north to the 
Iowa line, as is evidenced by the trend of the majority of 
streams, 
Origin of Structures 
THE STRAIN ELLIPSOID 
Definition and. description(34). The strain ellipsoid rep- 
resents the form taken by a sphere after yielding to stress, pro- 
viding there is no dilation. The ellipsoid has three axes mu- 
tually perpendicular and of unequal length. The axis of great- 
est shortening is the axis of greatest stress, The axis of great- 
est elongation lies in a plane at right angles to the stress and 
parallel to the direction of easiest relief. The intermediate 
axis lies perpendicular to the other two and is intermediate in 
length but is not the arithmetical mean. As ease of relief be- 
comes equal in all directions in the plane normal to the axis of 
maximum stress, the intermediate and short axes approach each 
other in length. 
When the original sphere is superimposed upon the strain 
ellipsoid, it intersects the ellipsoid in four places. These inter- 
sections line on the planes along which there has been no dis- 
tortion. These planes represent the only spherical sections 
through .the ellipsoid and are the planes of maximum shear. 
The shearing planes parallel the axis of intermediate stress. 
When the intermediate and short axes become the same length, 
the planes are replaced by cones whose axis is the axis of max- 
imum stress. 
When stress is first applied, the shearing planes are at 45° 
to the stress but this angle increases as the object is deformed. 
According to Hartman’s Law, the angle between the shearing 
planes is acute toward the direction of compressive stress in the 
case of plastic material. 
Strain ellipsoid series. The strain ellipsoid is most com- 
monly represented on paper by an ellipse drawn in the plane of 
axes of maximum and minimum stress. This allows the shear- 
ing planes to be shown as they would not appear in sections 
