g6 Capt. Kater’s experiments for determining the 
spheres, the result of which it may not be useless for a 
moment to dwell upon. 
It is known, that if two curved surfaces be ground together 
in every possible direction, they will become portions of 
spheres ; and thus a perfect sphere may be formed by grind- 
ing a ball in a hemispherical cup. If a pendulum vibrate on 
such a sphere, working in a conical aperture, it is evident 
that the centre of the sphere will be accurately in the axis of 
vibration. In trying this method, however, it was found, that 
the friction was so considerable, as to bring the pendulum to 
a state of rest after a few vibrations ; and when the friction 
was sufficiently diminished, by a contrivance which it is un- 
necessary to describe, the lateral force of the pendulum in an 
arc of two degrees and a half, was sufficiently powerful to 
carry the ball entirely out of the socket ; and it was conse- 
quently evident, that though the arc of vibration might not 
be large enough to effect this, it must necessarily cause the 
ball in some degree to ascend the inclined plane of the aper- 
ture ; and this consideration induced me to abandon at once 
a mode of suspension which I should otherwise ha ve esteemed 
the best that could have been employed. 
The principal objections to the use of a knife edge, ap- 
peared to be, the difficulty of forming it perfectly straight, 
and the possibility that it might suffer a change of figure 
from wear, during the experiments, which might introduce 
an error not to be detected. The first of these objections I 
found to be perfectly groundless, as a knife edge can be made 
so as not to deviate sensibly from a right line. The second 
objection would indeed be of weight, were the usual method 
of determining the time of vibration resorted to, by coin-*. 
