Title ~ Physical Properties of Gases, Liquids and Solids
Author ~ R. P. W. Scott
Section ~ The Measurement of (G).
The Measurement of (G)
There are many methods of measuring (G) most of them involving the use of a torsion balance. As an example the Boys’ method will be briefly described here. The torsion balance employed by Boys consisted of a central quartz fiber that carried a horizontal glass beam from the ends of which hung two further quartz fibers of unequal length with a gold sphere attached to each end. The whole system was hung inside a glass tube to protect it from draughts that could, if required, be evacuated. Outside the tube hung two large spheres of equal weight made of lead, the centers of the lead spheres being situated on the same horizontal plane as the gold spheres.
Let (M) and (m) be the masses of the individual different spheres. Consider the situation depicted in figure 6, which portrays the situation after equilibrium has been achieved.
Figure 6. Plan of the Boys Torsion System After Equilibrium had been Established
A and B
represents the position of the gold spheres and C and D the positions of the
lead spheres. The attraction between the spheres at different levels is
neglected. The forces exerted along BC are 
and the moment of this
force about O is 
where (
) is the perpendicular from projected onto the line of
action of the force. Thus, including the same force along AD the total moment is 
.
Now, 
Where 
Thus,
the total displacement moment is given by,
The
moment of the restoring force will be (c
) where (c) is the torsional constant of the quartz fiber and () is the angle of
deflection.
Thus, 
The torsional const (c) is determined from its period of oscillation in the
absence of the large lead masses,
i.e. 
Where (I) is the moment of inertia of the torsion system that can be calculated from its mass and dimensions.
Boys found a value for G of 6.658 x 10-8 c.g.s. units and the mean density of the earth as 5.527 g/cc.