1910-11.] Method of Finding Radius of Gyration of a Body. 517 
XXXIV. — Laboratory Note: A Simple Method of finding the 
Radius of Gyration of a Body. By W. G. Robson, A.RC.S. 
Communicated by Professor W. Peddie. 
(MS. received April 29, 1911. Read July 3, 1911.) 
In the course of some work in this laboratory a determination of the 
radius of gyration of an Atwood’s machine pulley was necessary. The 
radius was found by using a bifilar suspension. Having been unable to 
find any published record of the method, which is capable of giving fairly 
accurate results, and as the measurement of moment of inertia or of radius 
of gyration is a frequently occurring and ill-understood exercise in a 
physical laboratory, it seemed to me that the following details might be of 
interest. 
If a body be suspended by two threads of equal length, l, the distances 
between the threads being d 1 and d 2 at the upper and lower ends re- 
spectively, the time of a small oscillation about a vertical axis through the 
centre of gravity is given by 
16t 
yd-\d 2 
( 1 ) 
k being the radius of gyration. 
Now let the body be made to swing as a simple pendulum (using the 
same suspension threads). Then 
From (1) and (2) it follows that 
h = T Jd^d 2 (3) 
2T X 
— which reduces in the case of parallel threads to the simple form 
T d 
2Tj 
In (3) T and T x may, of course, be the times of any number of swings, and 
evidently the result is independent of the rate of the timepiece. 
A few typical results are given in the following table. The suspension 
threads were of thin copper wire about two metres in length ; d Y and d 2 
