The Pre-Cambrian Structure of Missouri 133 
parallel to the other two axial planes. Plate IXa shows the ser- 
ies of ellipses produced by decreasing the stress until it has as 
strong a negative value as it formerly had positive. The same 
series is obtained by rotating the forces through 180° as is shown 
by the dotted arrows. This is due to the fact that strain occurs 
only where stress is resisted so that the only component or each 
Stress that results in deformation is the component directly op- 
posite in direction to the opposing stress. In this series, the 
forces are considered as acting in couples, each member of which 
is Of equal strength and acting parallel to the other but in the 
opposite direction. Each force is considered as acting at a 
single point which is indicated by the heads of the arrows. 
The above series shows that the direction of stress does not 
control the orientation of the strain ellipsoid, but governs the 
intensity of strain. The orientation of the ellipsoid depends on 
the location of the stresses relative to the object being deformed. 
Application of strain ellipsoid to structure. All tectonic 
Structures are parallel to either the shearing planes or to the 
axes of the strain ellipsoid. When several structures of the 
Same age are present in a region, it is possible to orient the 
Strain ellipsoid for the forces producing the structures. It is 
necessary to know that the strucures used in orientation are 
of the same generation because structures of other periods of 
deformation may demand different orientations. A later stress 
may act along pre-existing structures although it is acting from 
a different direction than the original stress. In the latter 
Case there may be minor structures which indicate that a second 
Stress was active. Major stresses may lead to secondary struc- 
tures which require a different orientation of the strain ellip- 
Soid than the primary structure. 
Folding is caused by compressive stress and the axis of the 
fold parallels the intermediate stress axis of the strain ellip- 
soid when the axial plane of the fold is parallel to the inter- 
mediate and long axes of the ellipsoid. Cleavage may also lie 
’ this plane or may parallel the shearing planes (14). 
