SGATS TOSI AND SEATY CLEAVAGE 431 
parallel to them however great the distortion may be. If hori- 
zontal edges of the unit cube are extended in the ratio aso 
that these edges in the strained mass have a length a, then the 
vertical edges are contracted in the fanionza,. leis usual to 
define the quantity a za as the ‘amount. of shear. If the 
ee ea 
ee ee | 
Fic. 1 —Pure Shear. 
unstrained cube contained a sphere, this in the strained mass 
would become an ellipsoid with axes a, I, 7a." 
Since a is greater than unity, and za less, there must be 
radii of the ellipse in the plane of forces which are of unit 
length, and which are therefore of the same length after strain 
as they were before. Since the lines perpendicular to the plane 
of forces are also of unchanged length, it is evident that the 
circular sections of the ellipsoid pass through the radii of 
unchanged length in the ellipse. These circular sections of the 
strain ellipsoid are of as much importance in the theory ot 
deformation as are the corresponding sections of the ellipsoid 
of elasticity in the theory so familiar to most geologists of the 
effect of crystals on polarized light. 
All planes parallel to the central circular sections are also 
circular sections. In the plane of any such section there is no 
distortion when the strain is a simple shear. Any two such 
"If the equation of the sphere is +®-++-y?-++z?—1, and if x,, y, and 2, are 
the values which the same points have after strain, +; =a x, 7, —ya ands2a—2e 
Substituting in the equation of the sphere evidently x, 2a *+-a® y? + g® =I, repre- 
sents the sphere after deformation. The volume of this ellipsoid is 7a, 1. 7a@= 
which is also the volume of the sphere. 
