60 PROFESSOR C. V. BOYS ON THE 
The moment of inertia of the counterweight is directly obtained from its dimen- 
sions. The moment of inertia added to the beam requires more explanation. When 
the balls are hung on to the beam in the manner already described, they add to its 
moment of inertia, both on account of their distance from the axis, and on account 
of their own moments of inertia, about their own axes. Besides the balls the small 
wire hooks and the quartz fibres produce their own effects. These are found in the 
four lines bracketed B. In the first line the mass of the balls is made up as 
follows :— 
Mass of gold balls + wire holders, corrected for” 
buoyancy as against brass weights, but not 
absolutely, + 3} mass of displaced air. . . . 5°302204 
se Mass Old Marva tbKeS)\ eae. ane ene aa eee ‘00060 
5°302804 
this is multiplied by the square of the radius +. 
In the second line the radius of the support of the hook is obtained by direct 
measurement of the beam itself. It is relatively unimportant. In the third line the 
mass of the balls does not include the ball-holders or fibres or (perhaps wrongly) that 
of any surrounding air. The radius of the ball is found by a screw micrometer. The 
fourth line needs no explanation ; it is infinitesimal. 
U is found from the formula placed next to it. This is the moment of inertia of 
the mirror. It is not required in the calculation, but is found for the purpose 
of comparison, It should be constant. 
S represents the stiffness of the torsion fibre, 7.c., the couple that must be applied 
in order to twist it through unit angle (57°:296). 
If the unknown moment of inertia had been eliminated by the usual method, that 
is by supposing the torsion constant while the mirror was made to swing either with 
or without a known added moment of inertia (in this case, that due to the balls) then 
T°’ and T,” would have been required. Taking T,” from the previous experiment 
when it was found to be 116800, 
a Br? i 
U becomes ——*— = ‘035396 
PT? 
and 
= 4B 
S becomes oe = °001196375. 
eee 
Since the torsion is not the same when T,” and T,? are being found, as in one case 
the fibre is much more strongly stretched than in the other, and is therefore longer 
and thinner, and is not necessarily made of a material having the same rigidity, the 
above figures are spurious.. They differ from the true figures found in the previous 
page, but U, which is eliminated differs far more than S$, which is made use of. The 
