rest to it, the momentum cannot be supposed to be
concentrated at the centre of gravity, but at a point further removed from
the central shaft, and that point is what is called the centre of gyration.

33. _Q._--What is the centre of oscillation?

_A._--The centre of oscillation is a point in a pendulum or any swinging
body, such, that if all the matter of the body were to be collected into
that point, the velocity of its vibration would remain unaffected. It is in
fact the mean distance from the centre of suspension of every atom, in a
ratio which happens not to be an arithmetical one. The centre of
oscillation is always in a line passing through the centre of suspension
and the centre of gravity.

THE PENDULUM AND GOVERNOR.

34. _Q._--By what circumstance is the velocity of vibration of a pendulous
body determined?

_A._--By the length of the suspending rod only, or, more correctly, by the
distance between the centre of suspension and the centre of oscillation.
The length of the arc described does not signify, as the times of vibration
will be the same, whether the arc be the fourth or the four hundredth of a
circle, or at least they will be nearly so, and would be so exactly, if the
curve described were a portion of a cycloid. In the pendulum of clocks,
therefore, a small arc is preferred, as there is, in that case, no sensible
deviation from the cycloidal curve, but in other respects the size of the
arc does not signify.

35. _Q._--If then the length of a pendulum be given, can the number of
vibrations in a given time be determined?

_A._--Yes; the time of vibration bears the same relation to the time in
which a body would fall through a space equal to half the length of the
pendulum, that the circumference of a circle bears to its diameter. The
number of vibrations made in a given time by pendulums of different
lengths, is inversely as the square roots of their lengths.

36. _Q._--Then when the length of the second's pendulum is known the proper
length of a pendulum to make any given number of vibrations in the minute
can readily be computed?

_A._--Yes; the length of the second's pendulum being known, the length of
another pendulum, required to perform any given number of vibrations in the
minute, may be obtained by the following rule: multiply the square root of
the given length by 60, and divide the product by the given number of
vibrations per minute; the square of the quotient is the length of pen