2 WALTER H. BUCHER 
acting upon the sphere are those due to outside matter. Since 
we assume that the stress distribution within the body is continuous, 
the stresses that correspond to the two surface elements at the 
end of a diameter of the sphere are therefore numerically equal - 
and opposite in sign, except for negligibly small quantities. 
FIG. 10 
We shall now obtain the relation between the unit stresses px, p2 
at the two surfaces r;, 7. Form a parallelepiped with three pairs 
of planes tangent to the sphere, one pair normal to 7,, another to 
72, while a third pair is normal to a radius 7; which is perpendicular 
to both r, and 7,. Figure to shows the projection of this parallele- 
piped upon a plane through P normal to 7;. Both faces normal 
to 7; project into a rhombus. The other four faces are rectangles 
of equal area, dA, and project into lines. Now resolve the stresses 
px: into three components: parallel to 7,, parallel to r,, and normal 
