PERMANENT DISPLACEMENTS OF THE GROUNDS. 17 
the western side and the compression on the eastern side. There may have been a more 
or less irregular distribution of compressions and extensions along the course of the fault 
due to differences in the amount of the movement, but these, according to Dr. Hayford, 
are slight except in the region just south of San Francisco. The question arises: How 
were these compressions and extensions taken up? Did the volume remain constant 
and the density change; or did the density remain constant and the volume change; or 
did both changes occur? We have not sufficient evidence to answer this question; 
but the general properties of matter would indicate that both changes occurred. To 
the north of San Francisco Bay there seems to have been, in places, a very slight eleva- 
tion of the land west of the fault, and the only satisfactory explanation so far offered of 
the action of the tide-gage at Fort Point (described in vol. 1, pp. 367-371) indicates a 
small depression of the west side of the fault opposite the Golden Gate. It is not im- 
possible, altho it is by no means clearly indicated, that the slight elevation of the western 
side along the northern part of the fault may be due to an increase in volume there, and 
that the probable depression opposite the Golden Gate may be due to a decrease in vol- 
ume, which must have taken place in that region, on account of the smaller displace- 
ment just south of it. 
Returning now to the curving of former straight lines at right angles to the fault as 
shown in fig. 5, the first analogy suggested by the lines is that of a bent beam. If a beam, 
which is long in proportion to its thickness, is supported at one end and a weight hung 
from the other, the beam bends into a curve very much like that shown in the figure; 
the under, concave surface is comprest; the upper, convex surface is stretcht; and 
between the two there is a neutral plane which is neither comprest nor stretcht. But 
when the thickness of the beam is great in comparison with its length, the distortion is 
due to the elastic shear of each layer over its neighbor. In this case the thickness of the 
beam would be 485 km. (270 miles) and the length probably less than one-twentieth as 
much; so that the distortion must have been due to shear and not to bending in the 
ordinary sense of the word. 
THE NATURE OF THE FORCES ACTING. 
We know that the displacements which took place near the fault-line occurred sud- 
denly, and it is a matter of much interest to determine what was the origin of the forces 
which could act in this way. Gravity can not be invoked as the direct cause, for the 
movements were practically horizontal; the only other forces strong enough to bring 
about such sudden displacements are elastic forces. These forces could not have been 
brought into play suddenly and have set up an elastic distortion; but external forces 
must have produced an elastic strain in the region about the fault-line, and the stresses 
thus induced were the forces which caused the sudden displacements, or elastic rebounds, 
when the rupture occurred. The only way in which the indicated strains could have 
been set up is by a relative displacement of the land on opposite sides of the fault and 
at some distance from it. This is shown by the northerly displacement of the Farallon 
Islands of 1.8 meters between the surveys of 1874-1892 and 1906-1907, but the surveys 
do not decide whether this displacement occurred suddenly at the time of the earth- 
quake, or grew gradually in the interval between them; there are valid reasons, however, 
for accepting the latter alternative, as the following considerations show: The Farallon 
Islands are far beyond the limits of the elastic distortion revealed by the surveys, so 
that we can not ascribe their displacement to elastic rebound; and we have seen that 
this is the only kind of force which could have produced a sudden movement; and what 



1 We use the words strain and stress as they are used in the theory of elasticity. A strain is an elastic 
change of shape or of volume caused by external forces; and a stress is a resisting force which the body 
opposes to a strain, and with which it tends to diminish it. 
Cc 
