_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 pendulum
required. Thus if the length of a pendulum were required that would make 70
vibrations per minute in the latitude of London, then SQRT(39.1393) x 60/70
= (5.363)^2 = 28.75 in. which is the length required.

37. _Q._--Can you explain how it comes that the length of a pendulum
determines the number of vibrations it makes in a given time?

_A._--Because the length of the pendulum determines the steepness of the
circle in which the body moves, and it is obvious, that a body will descend
more rapidly over a steep inclined plane, or a steep arc of a circle, than
over one in which there is but a slight inclination. The impelling force is
gravity, which urges the body with a force proportionate to the distance
descended, and if the velocity due to the descent of a body through a given
height be spread over a great horizontal distance, the speed of the body