RATER’S REVERSIBLE PENDULUM 
99 
% 
(“•"•a 
-c, 
•C. 
. o 
r— 1 
rz] 
□ 
r 
B 
Fig. 20. Kater’s pendulum. A, with weightless knife edges; B, with actual knife 
edges. 
where / denotes the moment of inertia of the system about C, M 
is the total mass, g the acceleration of gravity, and K the radius 
of gyration of the system about C. Denoting by and Eg, re- 
spectively the lengths of the equivalent simple pendulums in the 
two cases, we have 
= ^ ( 3 ) 
L2 = 
R 2 + /?,2 
( 4 ) 
Let us first, to avoid confusion, make the assumption that the 
knife edges have no mass, so that their movement will not affect 
the location of the center of gravity of the system. Later this 
assumption will be avoided. Let be at such a distance, x, from 
C that we have again the same length of the equivalent simple 
pendulum. Then from (3), 
R2 + /?i2 ^ 
hi X 
Solving for x, we have the two values 
x = hi aT 
Thus the knife edge 0^ can be either at a distance from C, as in 
the figure, or — from C, and we shall have in both cases the 
