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 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?

A.—­Not in the least; each ball may be supposed to be made up of a number of small balls or particles, and each particle of matter will act for itself.  Heavy balls attached to a governor are only requisite to overcome the friction of the throttle valve which shuts off the steam, and of the connections leading thereto.  Though the weight of a ball increases its centripetal force, it increases its centrifugal force in the same proportion.

THE MECHANICAL POWERS.

45. Q.—­What do you understand by the mechanical powers?

A.—­The mechanical powers are certain contrivances, such as the wedge, the screw, the inclined plane, and other elementary machines, which convert a small force acting through a great space into a great force acting through a small space.  In the school treatises on mechanics, a certain number of these devices are set forth as the mechanical powers, and each separate device is treated as if it involved a separate principle; but not a tithe of the contrivances which accomplish the stipulated end are represented