must be slow in proportion to the greatness of that distance. It is clear,
therefore, that as the length of the pendulum determines the steepness of
the arc, it must also determine the velocity of vibration.

38. _Q._--If the motions of a pendulum be dependent on the speed with which
a body falls, then a certain ratio must subsist between the distance
through which a body falls in a second, and the length of the second's
pendulum?

_A._--And so there is; the length of the second's pendulum at the level of
the sea in London, is 39.1393 inches, and it is from the length of the
second's pendulum that the space through which a body falls in a second has
been determined. As the time in which a pendulum vibrates is to the time in
which a heavy body falls through half the length of the pendulum, as the
circumference of a circle is to its diameter, and as the height through
which a body falls is as the square of the time of falling, it is clear
that the height through which a body will fall, during the vibration of a
pendulum, is to half the length of the pendulum as the square of the
circumference of a circle is to the square of its diameter; namely, as
9.8696 is to 1, or it is to the whole length of the pendulum as the half of
this, namely, 4.9348 is to 1; and 4.9348 times 39.1393 in. is 16-1/12 ft.
very nearly, which is the space through which a body falls by gravity in a
second.

39. _Q._--Are the motions of the conical pendulum or governor reducible to
the same laws which apply to the common pendulum?

_A._--Yes; the motion of the conical pendulum may be supposed to be
compounded of the motions of two common pendulums, vibrating at right
angles to one another, and one revolution of a conical pendulum will be