A NOTE ON RATER’S REVERSIBLE PENDULUM 
L. P. SIEG 
In one of our laboratory classes recently, in connection with 
a routine experiment with Rater’s pendulum, certain of the stu- 
dents were confronted with the situation in which, although the 
periods of vibration from each of the two knife edges were prac- 
tically identical, the distance between the knife edges was by no 
means equal to the length of the equivalent simple pendulum. 
None of the treatises on dynamics available offered any help in 
their difficulty. In all the discussions it was virtually stated that 
when the periods from the two knife edges were equal the distance 
between knife edges was equal to the length of the simple pendu- 
lum of equal period. 
When their difficulty was presented to the present writer he 
was at once reminded of a study he had made some twenty years 
ago, but which at that time he had deemed unimportant enough 
for publication. In this study, a paper read before a Sigma Xi 
meeting, the writer pointed out that the shifting of a knif-e edge on 
any compound pendulum causes a variation in the period in which 
in certain cases it can pass through a minimum. In other words 
there are two positions of a knife edge with respect to the center 
of gravity of the system in which the periods of vibration will be 
the same. Some time later an article by Tatnall ^ appeared and 
covered almost identically the same ground. As neither of these 
treatments specifically deals with the present case it is thought 
worth while to publish a note on the question. 
In Fig. 20-A, let C denote the center of gravity (in future ab- 
breviated to c.g.) of the system, and 0^ and the two points of 
suspension. Further let and hz be respectively the distances of 
the c.g. of the whole system from and Og, and let and To be 
respectively the corresponding periods of vibration. Then we 
have the well-known expressions, 
( 1 ) 
( 2 ) 
1 R. R. Tatnall, Phys. Rev., 17, p. 460, 1903. 
