34 PROFESSOR C. V. BOYS ON THE 
In the first place it is supposed that the mirror does not change its axis when 
swung alone or with the balls or counterweight suspended, for, if it does, its unknown 
moment of inertia will not be a constant, as assumed. Secondly it is supposed that 
when the gold balls are suspended from the beam mirror, they are rigidly connected 
with it, or that the mobility of suspension or torsion is so minute as to be equivalent 
to a rigid suspension. Thirdly, that the counterweight, when suspended from the 
beam mirror, is rigidly connected with it, and that it rotates about its geometrical 
axis. Jt is obvious that however carefully the parts have been made, the suppositions 
cannot be rigidly true. It is necessary, therefore, to find what order of error is intro- 
duced by any possible or observed want of perfection. 
It is evident that the axis of rotation of the mirror must always pass through the 
point at which the quartz fibre leaves it, and that, when it is unloaded, its axis passes 
through its centre of gravity. As the construction is intended to be symmetrical 
with respect to this axis, and is so, as far as observation enables one to judge, and as 
such an axis is an axis of maximum or minimum moment of inertia, the uncertainty 
in the moment of inertia, due to a small angular displacement, is proportional to the 
square of the angle, and is altogether beyond the region of experimental certainty. 
When, however, the balls or counterweight are placed in position, if the construction 
is not truly symmetrical, the beam mirror will now rotate about an axis which does 
not pass through its centre of gravity. In an experiment made for the purpose, this 
displacement, when the larger balls were suspended, was found to be ‘0068 inch, an 
amount considerably larger than I had expected. In this case the moment of 
inertia, added to the whole combination on this account, is, weight of beam 
X 0063? = 844 X 0063 = 0000335 inch® gram. The corresponding increase, when 
the counterweight was added, was 844 X 0012? = :0000012 mch* gram. Applying 
these small differences to the observations of Experiment 12, if I may so far antici- 
pate, the torsional rigidity of the suspending fibre is changed from ‘0012577 to 
001257736, so that if this had been overlooked, the error introduced would have 
been 1 in 35,000. It was not, as a matter of fact, observed until after the conclusion 
of Experiment 12, and then I placed one of the microscopes so as to see the edge of 
the lower hook of the beam, and measured the unexpectedly large deviations in the 
plane of the mirror; those perpendicular to the plane I had always known to be 
practically inappreciable by the very small change in the position of the observing 
telescope needed to again see the scale reflected centrally. This insensible correction 
which tends to make G seem greater, can only be applied to Experiments 10, 11, and 
12, as the fibre met with an accident after Experiment 9, and was re-fastened to the 
beam, As it cannot be applied to the others, and is far smaller than the uncertainty 
of the experiment, it is not taken account of in the table. 
The rigid attachment of the gold balls to the mirror might seem to be purely 
imaginary, seeing that they hang from fibres 5 and 11 inches long, and so can lag 
behind when the mirror is subject to angular acceleration, that they must fly out 
