296 W. J. MeGee—Origin and Hade of Normal Faults. 
and the hade will ever diverge from the normal. Conversely, 
if the stress be compressive the relation will become tan y= 
d the hade will 
ever approach the nor- 
mal; but if it become 
normal the tendency 
to movement will be 
(n—a+7 cos On)m or tan x=(n—b—7 cos On)m as the case may 
be, an 
d 
dragged fault or flexure will be engendered ; since the devel- 
opment of normal faults demands that the lateral extent of 
the faulted tract shall increase from T to T+(tan xd) where 
h is angle of hade and d the vertical displacement. 
(The case in which tangential thrust is predominant, and the 
tendency hence toward ordinary reversed faults, complex fold- 
ing and tumefaction, falls beyond the scope of this discussion.) 
It thus appears that the general disposition of differential 
radial strain, either singly or combined with tangential strains, 
is to form reversed faults. ; 
Let the case be farther modified by the introduction of sim- 
ple vertical stress apart from those due to the unstable equilib- 
rium. ere the stress tensile, its effect would be analogous to 
that of tangential tension; but since general vertical tension 
without predominant tangential thrust is inconceivable (whence 
the sum of tensile vertical stresses is always in defect), and 
since local vertical tension must equally react on adjacent 
couches, the effect of such stress is nugatory. But if the stress be 
compressive it will equally relieve AC and strain BD, and thus 
diminish 4; and since within the crushing strength of the ma- 
terial of the tract there is no limit to this stress, b will be re- 
duced to b—v cos 6m, where v is such vertical stress, and | the 
h noashm)m: 
Y¥v OUVUeyire } ¥ 
ag 
original expression for bade will beco (n 
when the fault may hade strongly to the down-throw. 
The natural case favorable to profound faulting arises 1» 
such an unstable tract as has been assumed within which exist 
vertical stresses due to its own weight and sufficient initial ee 
AC will progressively increase downward until the crushes 
strength of the material is reached ; whence the fault due to onan 
strain must originate with normal hade in a deep-seated hypoged 
c , and (since rupture if each couche will throw the strain 
on the next higher) must be upward with progres- 
_e propag i 
sively diminishing hade, which may eventually become nothing 
or even reversed ; while below the couche of origin the fracture 
