150 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
THE HORIZONTAL PENDULUM. 
There are three points of the pendulum on which forces act, namely, the center of 
gravity and the two points of support. We shall call the line joining the two latter points 
the axis of rotation. The forces at the points of support may be replaced by a single force 
F, acting at the point of intersection of the axis of rotation with the perpendicular on it 
from the center of gravity of the pendulum, and acouple. In the Zollner form of suspen- 
sion this point is not fixed relatively to the pendulum, and therefore the theory here 
given does not apply to the Zdllner suspension; see further, page 179. The force at the 
center of gravity is simply gravity acting vertically downwards. 
Let us refer the position of the pendulum to a set of rectangular codrdinates fixed in 
space whose origin is at 0 and whose positive directions are shown in figure 36. When 
(3) ~vert 
Ly 
Ox x 

Fia. 36. 
the pendulum is at rest, let it lie in a plane parallel to the plane of yz, and let it point 
in the direction of y. Let CG, refer to the original undisturbed position of the center 
of gravity of the pendulum; CG, the position which this point would take during the 
disturbance if it were rigidly connected with the support, and CG its actual position at 
any time. 
In figure 36, let 
%, be the inclination of the axis of rotation to the vertical in the undisturbed 
condition; 
