34 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
equivalent to saying that s must be small in comparison with Ec. It is evident that if 
the line had the position Hc’, where a’ = a, it would be lengthened by the same amount 
that Ec is shortened. 
Suppose we stand in the acute angle between the shearing zone and a line crossing it; 
if the line is on our left, as in the position a (fig. 19), we say it crosses the. zone from 
left to right; if it is on our right, as in position b, we say it crosses from right to left. 
For the same line it makes no difference whether we are in the position a or a’. With 
this convention we can state that if a line crosses the sheared zone from left to right, it 
will be shortened; if from right to left, it will be lengthened; and this is true without 
any compression of the sheared zone at right angles to the direction of the movement. 
The total change in length is zero when the line is at right angles to the direction of the 
shift, and is greatest when it approaches parallelism with it. 
To determine the change in length per unit length of the line we must divide s cos a 
by Ec or l/ sina, which gives (s/ 2 1) sin 2 a; this isa maximum when a equals 45°; there 
is therefore a tendency to form open cracks crossing the zone from left to right and mak- 
ing an angle of 45° with its direction. This direction would be modified by pressure or 
tension at right angles to the sheared zone; compression would make smaller cracks 
more nearly at right angles to the trend of the fault-zone; tension would make them 
larger and more nearly parallel with it. The very general existence of cracks making an 
angle of about 45° with the direction of the fault-trace shows that there was neither 
compression nor expansion at right angles to the fault for at least a large part of its 
course. 
If the sheared zone is so narrow that a line crossing it is broken and the two ends 
separated, as in fig. 20, it is shortened or lengthened by an amount s’ cos a. 
It may happen that a part of the movement is concentrated along a narrow crack and 
a part is distributed over a zone on the sides of the crack; so that the straight line / in 
/ fig. 21 is changed into the two broken lines, 1’, /’. 
A line crossing the zone from left to right will 
be shortened by an amount equal to the sum 
of the shortenings at the crack and in the zone 
of distributed shear, that is, by (s, + s, + s’) 
cos a, and a line crossing from left to right 
would be lengthened by an equal amount. 
But s, + so + s’ =s, the total shift of the 
boundaries of the sheared zone, so that we 
can say in general, a line crossing the sheared 
zone from left to right ts shortened, and one 
crossing from right to left 1s lengthened, by an 
amount equal to the total relative shift of the 
boundaries of the zone multiplied by the cosine 
of the acute angle between the line and the direction of the shift. If therefore we measure 
the shortening or lengthening of a line crossing the sheared zone and the acute angle 
we can calculate the amount of the shift, whether the shift be concentrated in a narrow 
crack or distributed over a wider zone. 
CRACKS IN THE GROUND. 
Let us apply these simple results. When the shift is concentrated in a narrow zone, 
only a few feet wide, there is more or less demolition, within the zone, of a fence or other 
object that may cross it, and the broken ends of the fence receive an offset which gives 
a measure of the shift. The turf in such a narrow zone is torn in a characteristic way ; 
at the beginning of the movement the turf is rent into strips by cracks formed at right 
angles to the line of greatest stretching; that is, the cracks and the strips of turf between 

Fie. 20. Eiaw2i. 
