20 Rk. T. CHAMBERLIN AND W. Z. MILLER 
where P is the limiting load which the column can support, E is 
Young’s modulus of elasticity, J is the least moment of inertia, and 
1 is the length of the column.t 
Increasing the length, therefore, weakens the resisting power 
of the column and increases the likelihood of fracture. 
Cubes and short blocks tend tc fracture at 45°, or somewhat less. 
But long columns, because of the preliminary flexure, split at a 
lower angle. In testing the strength of cast iron in engineering 
practice it has been found that, as the length of the longer dimension 
is increased while the other two dimensions remain the same, the 
angle of fracture becomes lower until it reaches 30°, beyond which 
there is no lowering with further increase in length. Experimenta- 
tion upon other materials has given analogous results. 
The lowering of the angle in the long column is a result of the 
development of rotational strain. The preliminary flexing of the 
column develops tensile stresses on the outer side of the bend, and 
at the same time develops shearing stresses by which the layers 
on the outer side of the bend tend to creep toward the crest of the 
fold. ‘This shearing of the layers may be illustrated by bending a 
pack of cards. If actual fracturing occurs, the effect of the rota- 
tional couple is to lower the angle of breakage. 
Earth deformation theoretically may partake of the nature 
either of the short block or of the long column. Except for the 
influence of the curvature of the surface, in most cases 1t would seem 
to parallel most closely the short block, for the dimension of the 
mass involved parallel to the direction of thrusting 1s, as a rule, less 
than five times the transverse dimensions of the block. The 
Appalachian Mountain chain is at the very least 1,800 miles in 
length, paralleling the Atlantic Coast. To be five times this, the 
northwest-southeast dimension (the length of the flexed column) 
would need to be 9,000 miles, or completely across North America 
and much of Asia. From Cincinnati to Charleston, South Carolina, 
on the coast, which is a most generous estimate of the distance 
across the deformed belt, is only approximately goo miles. The 
=R. J. Woods, op. cit., pp. 212-13. 
2 International Library of Technology and Mechanics (Scranton, Pa., 1909), 
