35 
time of vibration (ti) against tlie force of torsion Qi) of the 
wire was observed. The moment of inertia of the stirrup 
being S we have 
ti = 7T^S 
fX 
The time of vibration (ti) was then observed when a cylin- 
drical brass bar of known moment of inertia B was inserted 
in the stirrup. We now have 
ti = 7T 2 (S + B) 
The bar was then removed and the balance beam inserted 
in its place, and the time of vibration (tf 3 ) gives 
ti = 7T 2 (S + MI 2 ) 
From these three equations eliminating S and fx we obtain 
M p_ B fe 2 -^ ) 
iVJ ~ L “ / 2 / 2 
Now Bg was calculated from the weight and dimensions 
of the bar to be 6332.83 (in centimetres and grammes). The 
observed times were t x = 3.6792 // ; U = 4.495" ; t z -l.\ 483" ; 
From these values we find 
My I 2 = 35651.6* 
To measure 6. The angle of deflection was measured by 
the number of divisions of the scale which the pointer 
moved over. As the length of the pointer is 32T006 centi- 
metres, while 20 divisions of the scale measure 2*5658 
centimetres, a tenth of a division, in terms of which the 
deflection was measured corresponds to an angle of 0’0003996. 
The oscillations were observed from a distance of 6 or 8 feet 
by a telescope. The resting point (i.e. the point where the 
balance would be in equilibrium) was found in the usual 
way by observing the three successive extremities of two 
swings and taking the mean of the second and the 
* To this a small correction should be added if the adjusting bob is not in 
its lowest position. This amounts to 7.6 for each turn of the screw and may 
therefore in general be neglected. 
