146 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
where 
y is the variable displacement of the earth particles, 
A the maximum displacement or amplitude, 
t the time, 
x the distance along the direction of propagation, 
P the period of vibration, 
»X the wave length. 
This represents a wave traveling in the positive direction of 2; the displacement y may be 
in any direction perpendicular to x, and in general it may be broken up into vertical and 
horizontal components. In figure 32, let x be the direction of propagation, and y may be 
either vertical or horizon- 
tal; since all the earth 
particles move parallel to 
y, a line in this direction is 
not rotated at all; whereas 
a line parallel to # is made 
to assume the wave form, 
and its elements experi- 
ence the maximum rotation. The tangent of the angle which an element of the line 
makes with the axis of 2x is given by the difference in the displacements of two neigh- 
y boring points divided by their distance apart, 7.e., by dy/dx; but 


Fig. 32. 
< § 
N 8 dy my odd em ay CE 2 
> —“ = —27r—cos2r/| —— — 
S) wh dx a (> *) ©) 
| i) A 
t 

and its maximum value is 27A/). If v is the velocity of propaga- 
tion, X=vP. The waves of largest amplitude have a velocity of 
about 3.3 km. per second, and a period of 15 to 20 seconds; and 
hence a wave length of from 50 to 66 km. If we take A=5 mm., 
which is a very large amplitude, and \=66 km., we find 2 7A/A 
= 6.3 x 5/66 x 10°= about 5 x 1077 or one-tenth sec. arc. As small 
as this angle is, the most sensitive instruments are capable of measur- 
ing it, provided the rotation is around a horizontal and not the 
vertical axis. If two horizontal pendulums were supported by the 
solid rock and placed one with the beam pointing in the direction of the propagation 
of the wave, and the other at right angles to it, then if the displacements were hori- 
zontal, that is, if the rotation was around a vertical 
axis, the first pendulum would suffer a slight relative 
rotation, but the second one would not. If, however, 
the displacements were vertical, and the rotation 
around a horizontal axis, the second pendulum would 
be displaced and the first would not. 
In the more general case where the direction of 
propagation makes an angle « with the direction of 
the horizontal pendulum we find the relative rotation of the pendulum for horizontal 
displacements to be cos? «-dy/dx, obtained by dividing cos a-dy by the length of the 
line; i.e., by dz/cos «, as shown in figure 33. If we had a second pendulum at right 
angles to the first, the amount of its relative rotation would be sin? « -dy/dz, and 
the direction of the 2 rotations would always be the same. In the case of vertical 
displacements the rotation of a horizontal line making an angle « with the direction of 


Faas, Maas 
& 

Fig. 33. 

Fig. 34. 
