3 Sir G. Greenhill, Note on Dr Searle’s experiment, etc. 135 
| Note on Dr Searle’s experiment on the harmonic motion of a 
rigid body. (Proceedings of the Cambridge Philosophical Society, 
November 24, 1913.) By Sir GEorGE GREENHILL. 
[Received 20 February 1914.] 
The experiment provides an instructive exercise in measure- 
ment for the student of mechanical physics, and the practical 
details are useful for anyone who wishes to repeat it. 
But as the experiment is carried out in a gravity field, and the 
calibration of the wire torsion is made (fig. 2) by weights in a 
scale pan, it would be more genuine and instructive, in my opinion, 
if the torsion couple 4@ was recorded as it is measured, in gram- 
centimetres. 
This makes 7’ = 27 Jz in formula (1), and then iE is the 
length of the equivalent simple pendulum, 44°42 cm in the 
experiment, with 
K = 10! x 9894 g-cm’, and Sp ANOLE 
: 10 x 1428 
per radian ; and when this pendulum length is measured, beating 
time alongside with the torsional vibration, like a metronome but 
with invisible oscillation, the experiment is complete. 
No need for a clock or a watch, in this the method of 
Galileo. 
And the factor g, required for the conversion into absolute 
measure of force, cannot be measured directly by experiment with 
any accuracy approaching the determination of the length Z of 
the pendulum which beats the second; so that g is always 
calculated indirectly through the formula 
g=wL. 
The formula for the beat ¢ of a pendulum of length / is thus 
more properly 
Pee l 
t=4/7. instead of my /-. 
Thus if we take the length as 25 cm, in round numbers, of the 
half second pendulum for which 7'= 1, then 7'= 1337 would have 
an equivalent pendulum length 
: 13:37\? : 
1 =25 x (1337) = = = (6685)? = 44-69 om. 
But with / = 44°42 cm, the length of the half second pendulum 
would be 44°42 = (1°337)? = 24°85 cm, making the length 99:-4cm 
of the pendulum which beats the second. 
= 10° x 2:227 g-cm 
