KATER’S REVERSIBLE PENDULUM 
101 
Fig. 21. Variationi of the period of vibration, /, with the distance, x, from knife 
edge to center of gravity of the whole pendulum. 
values of dr corresponding to the period A. To tevert for a mo- 
ment to the first paragraph of this article, my students had chanced 
in their experiment on the distance AB, when they should have 
employed the greater distance AC iov h-^. 
Let us assume now that the knife edges have mass, and let us 
refer to Fig. 20-B. We can assume, without any loss of gener- 
ality, that we can attain equality of periods by moving solely O^. 
Hence the mass of O 2 can be considered as merged with the re- 
mainder of the pendulum mass. 
Let ikf the mass of all the pendulum excepting O^. 
m = the mass of O^. 
Cx ~ the center of mass of the whole. 
Co = the center of mass of M. 
Cl = the center of mass of mi (assume Ci to be coincident 
with the near edge of Oi. The error will be only a small 
constant correction). 
X the distance of Oi from Cx. 
Then we have 
n=2.^ 
(M + m^g X 
= 2ir-\j- 
= 2 TT-y' 
l(M + m) T {M + ni)x^ 
(M + m)g X 
A2 + 
gx 
.( 8 ) 
where K is the radius of gyration about Cx, and / is the moment 
of inertia about Oi. 
The only difference between equations (8) and (6) is that in 
the former K is not a constant, but is a function of x. Now let 
CoCx ^ dr', then 
mx = M x' 
(9) 
