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 spindle divided by the vertical height, will give the amount
of centripetal force, and the velocity of revolution requisite to produce
an equivalent centrifugal force may be found by multiplying the centripetal
force of the ball in terms of its own weight by 70,440, and dividing the
product by the diameter of the circle made by the centre of the ball in
inches; the square root of the quotient is the number of revolutions per
minute. By this rule you fix the length of the arms, and the diameter of
the base of the cone, or, what is the same thing, the angle at which it is
desired the arms shall revolve, and you then make the speed or number of
revolutions such, that the centrifugal force will keep the balls in the
desired position.

44. _Q._--Does not the weight of the balls affect the question?