24 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
An element of the surface a, on the eastern side of the fault, has been displaced to a’ and a 
vertical line, aa, thru a has been distorted into a’a’ by an elastic shear. The forces parallel 
with the fault acting on the element in its new position are: a shearing force to the south- 
east on its northeastern face, one 
to the northwest on its south- 
western face, one to the north- 
west on its under surface due to 
the shear in the vertical plane; 
for equilibrium the sum of these 
must be zero, therefore the shear- 
ing force on the northeastern face 
must be greater than that on the 
southwestern; this relation holds 
for the whole length of the line 
D’C’; the shearing stresses there- 
fore must become greater as we 
leave the fault-line. As the 
strains are proportional to the 
Fie. 11. stresses, the curvature of the 
line D/C’ must become greater 
the further we go from the fault, until we reach the boundary where the forces are 
applied. This is true whether the forces are tangential forces applied along a boundary 
parallel with the fault, or a general north-south compression and an east-west tension. 
The surveys, however, on the east side of the fault, where alone they are sufficiently com- 
plete, show that the curvature of the distorted line was greatest near the fault-line; they 
could not, therefore, be due to a general compression and extension nor to simple tangential 
forces, but the distorting forces must diminish with distance from the fault-line; this could 
only hold if they were applied at the under surface, which brings us back to the conclusion 
already reached. 




Go 
a w 
Let us suppose the straight line WOE in fig. 12 to represent a line at right angles to the 
fault in the unstrained condition ; let this line be slowly distorted by the applied forces into 
the full line WAOCE just before the rupture. We have heretofore only considered the 
region between A and C, that is, between Mount Diablo and the Farallon Islands, but we 
now extend our consideration to the whole region moved. It is evident that the displaced 



Fia. 12. 
area must have some limit; the surveys only covered the region between A and C, and 
therefore throw no light on what occurred at greater distances from the fault. There is 
no reason whatever to believe that other ruptures and slips occurred outside the region 
between A and C; there is a gradual diminution of the intensity of the felt disturbance 
as the distance from the fault increases, with the exception of the Sacramento Valley, 
where the slight increase is entirely accounted for by the alluvial character of the ground, 
thus indicating that the whole disturbance originated in the one fault. The great intensity 
in the San Joaquin Valley may possibly be due to a local rupture; but this lies only 
opposite to the southern part of the great fault and does not affect the general argu- 
ment, which is especially applicable to the region north of San Francisco. We conclude 
therefore that the displacement gradually dies out to the west of A and to the east of C, 
tho it may continue for a very great distance; and we assume that the line of displace- 
ment becomes asymptotic to the undisturbed line WOE at some distant points, W and E, 
which would be characteristic of any displacement gradually dying out. The shearing 
force at any point of this line is proportional to the shear, which equals the angle at that 
