METHODS OF ATTAINING SENSITIVENESS, ETC. 9 
is due to Zollner and is shown in the diagram (fig. 3). The 
pendulum rod CD is supported by wires AC and BD both 
under tension on account of the mass M, and clamped to fixed 
points A and B so that AB is the axis of rotation. 
This method is used by Galitzin in his aperiodic pendulums. 
In all these cases the angle z is practically very small, and 
clearly we may regard the system as a compound pendulum 
controlled by “reduced gravity” of amount of gsinz or gz. 
In this way periods of 20 seconds or more can readily be 
attained implying a large increase of magnification. 
If Mé? represents the moment of inertia of the system 
about AB, 
h = distance of the C.G, from AB 
and @ in the apparent angular motion, we get the equation 
M#6+ Mghi0 = —- Mhi 
while if we introduce a frictional term proportional to @ we 
may reduce the equation to the form 
6 +266 +220 = -£/1 
wherein 2*=ghz/k?, and /=k?/k is as before the length of 
the equivalent simple pendulum. CM the axis of the pendulum 
is very nearly horizontal, and we have to observe that the 
pendulum will record not only horizontal motion of the 
ground represented by x but also tilting represented by rota- 
tion yy about a horizontal axis coinciding with CM and rotation 
represented by y about a vertical axis. 
It is easy to show that the complete equation is 
6+ 2664+ 70= -z/l+gpll+x (2- Al 
but in obtaining the equation it is important to remember pre- 
cisely what the quantities are, viz. :— 
@ is the apparent angular movement. 
# is the acceleration that would have been experienced by 
a point coinciding with the C.G. of the pendulum 
but rigidly attached to the earth. 
yy is the angular rotation about the horizontal axis through 
the C.G. coinciding with the nul position of CM 
and 
x is the angular rotation about the vertical axis through 
the C.G. 
