W. J. McGee—Origin and Hade of Normal Faults. 295 
: 
Now manifestly, before fracture supervene- the strain will be 
distributed over a considerable horizontal zone, and will be 
propagated vertically through the tract; whence the resultant 
of stresses at any point in the plane of imminent faulting will 
bisect a parallelogram similar to that whose base and perpen- 
dicular are respectively the width of the stressed zone and the 
thickness of the homogeneous tract. Make such parallelogram 
equilateral; denote base and perpendicular by 2n and 2m 
respectively; and let BO be the depressed side. The strain 
will then be resolved into stresses of opposite sign acting in the 
directions of the diagonals. : 
_If now fracture relieve tensile strain only, it will occur at 
right angles to the tension-diagonal AC, or in BD; and the 
fault will hade to the up-throw. Such indeed is the direction 
actually taken by ice-stream crevasses (to which the diagram 
will equally apply) as shown by Hopkins;* for in slowly 
moving ice the crushing strength must be nearly nd and the 
compressive-elasticity infinite, while tensile stress probably in- 
creases rigidity and brittleness, and thus diminishes the tensile 
elasticity.+ And were the antithesis of ice existent its fracture 
Denoting these in their order by ¢, ¢, ¢' and c’, the values (x? 
and exe’ are obtained for the moments of fracture orthogonally 
s 
€ readily computed. ae 
If the case be modified by the introduction of initial tan- 
gential stress, such stress will operate through mO with inten- 
sity 2, and tend to produce fracture in nO. If the stress be 
tensile it must be less than a, and will at once relieve BD and 
Strain AC proportionally to its intensity by the cosine of the 
angle formed by its direction and that of the latter diagonal, 
and thus (denoting such angle by @) reduce a by ¢ cos On; when 
the expression for hade will become tan y=(n—a—7 cos On)m, 
* Tans. C; Cte Cpe 
t Vide ting mind cate heat any peste Thr 1, 2; Proc. A. A. A. S,, 
XXix, 1880, 497, 
