16 R. T. CHAMBERLIN AND W. Z. MILLER 
Hence the stress per unit area, or the intensity of stress, on 
section mnop is seen to be: 
P sin 6 aa 
(2) Normal stress (P72) = ar = 2) Sua (0). 
; P cos 6 5 
(2) Tangential stress (Pt) = Fae 1/2 ‘sin (4) COS (c) . 
For an oblique section at right angles to mnop substitute 90° —0 
for 6 and get 
P'n=P cos? 6. 
P't =P cos 6 sin @=Pi. 
Thus the intensity of tangential stress is the same on two oblique 
sections at right angles to each other. 
The value of P sin @ cos @ reaches a maximum for 6=45° 
when it equals $P. The intensity of the shearing stress is therefore 
greatest for planes at 45° to the line of propagation of the force. 
Since the intensity of the shearing stress is as a maximum when 
6=45°, it was natural enough to suppose that fracturing under 
compressive stress should occur normally along planes inclined 
4s. to the line of application of the force, and in the familiar prac- 
tice of crushing cubes of stone, cement, wood, etc., in testing 
machines to determine their strength for building purposes, experi- 
ence is that the blocks break at angles approaching 45°, though 
most frequently the angle is somewhat less than this. Forty-five 
degrees is the angle which is commonly stated to be the angle of 
fracture in the geologic literature which deals with faulting and 
jointing under compressive stresses. 
But, as has been noted, many thrust-fault planes are found to 
dip at angles much less than 45°, and short blocks in the crushing 
machine very commonly break at angles as low as 30°. F ractur- 
ing at 30 in our experiments has been commoner than at the 
higher angle of 45°. _ What is the meaning of this? Experimental 
error fails to satisfy the discrepancy, as an error of 15° is unlikely 
and the persistence of 30° and 35° breaks shows that there is some 
important factor, or factors, in operation which have not been con- 
sidered. Let us therefore consider some of the possible factors 
which may operate to reduce the angle of fracture from the theo- 
retical 45°. 
