12 WALTER H. BUCHER 
When rocks are subjected to deformation in nature, the question 
whether they will break or bend depends largely on the degree of 
brittleness they possess under the given conditions and not on their 
hardness. ‘This explains why geologists have been justified in the 
attempt to reproduce in the laboratory the various structures 
exhibited by the hard materials of the earth’s crust by the use of 
soft clay, mixtures of clay and plaster of paris, and even wet sand. 
The use of the angle of shearing as an index of brittleness opens 
up new possibilities for standardizing the materials used in such 
experiments to accurately reproduce definite actual conditions. 
Mohr’s formula could be quantitatively correct only, if the curve 
Tm=f(o) were practically a straight line between the circles of 
ultimate tensile and compressive stress. This, however, is not 
true. The form of the curve, therefore, must first be determined 
experimentally for each substance. From it the variable 6 can be 
computed, from point to point by analogous formulas. 
This was carried out for the first time, as far as the writer knows, 
in a series of excellent experiments by Karman.? 
He used an apparatus in which small cylinders of rock could 
be subjected simultaneously to hoop and longitudinal pressures in 
such a way that either pressure could be controlled without changing 
the other. The results of his experiments are embodied in stress- 
strain diagrams which in the most striking way show the fact that 
the materials used—marble and sandstone—change step by step 
with increasing hoop pressure from a state of perfect brittleness 
to one of perfect ductility. In this respect Karman’s experiments 
supplement beautifully the brilliant investigations of Adams. 
With low hoop pressures shearing occurred in the rock cylinders 
resulting in the formation of Liiders’ lines on the polished surfaces 
and, with lowest hoop pressures, leading to rupture. 
In the following table? the observed values of the angles of 
shearing at various hoop pressures are placed side by side with the 
values computed according to Mohr’s graphic construction. 
t The angle of shearing can readily be determined for many substances by means 
of an ordinary vise, if small cubes (x cm3) are used. 
Th. von Karman, “Festigkeitsversuche unter allseitigem Druck,” Zeitschr. des 
Vereins deutscher Ingenieure, Vol. LV (10911), pp. 1749-57. 
3 Tables 1 to 4 of K4rman’s paper. 
