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 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