e
compounded of the motions of two common pendulums, vibrating at right
angles to one another, and one revolution of a conical pendulum will be
performed in the same time as two vibrations of a common pendulum, of which
the length is equal to the vertical height of the point of suspension above
the plane of revolution of the balls.

40. _Q._--Is not the conical pendulum or governor of a steam engine driven
by the engine?

_A._--Yes.

41. _Q._--Then will it not be driven round as any other mechanism would be
at a speed proportional to that of the engine?

_A._--It will.

42. _Q._--Then how can the length of the arms affect the time of
revolution?

[Illustration: Fig. 1.]

_A._--By flying out until they assume a vertical height answering to the
velocity with which they rotate round the central axis. As the speed is
increased the balls expand, and the height of the cone described by the
arms is diminished, until its vertical height is such that a pendulum of
that length would perform two vibrations for every revolution of the
governor. By the outward motion of the arms, they partially shut off the
steam from the engine. If, therefore, a certain expansion of the balls be
desired, and a certain length be fixed upon for the arms, so that the
vertical height of the cone is fixed, then the speed of the governor must
be such, that it will make half the number of revolutions in a given time
that a pendulum equal in length to the height of the cone would make of
vibrations. The rule is, multiply the square root of the height of the cone
in inches by 0.31986, and the product will be the right time of revolution
in seconds. If the number of revolutions and the length of the arms be
fixed, and it is wanted to know what is the diameter of the circle
described by the balls, you must divide the constant number 187.58 by the
number of revolutions per minute, and the square of the quotient will be
the vertical height in inches of the centre of suspension above the plane
of the balls' revolution. Deduct the square of the vertical height in
inches from the square of the length of the arm in inches, and twice the
square root of the remainder is the diameter of the circle in which the
centres of the balls revolve.

43. _Q._ Cannot the operation of a governor be deduced merely from the
consideration of centrifugal and centripetal forces?

_A._--It can; and by a very simple process. The horizontal distance of the
arm from the spindl