Now the time of vibration of the pendulum S P between east and west will not in any way be affected by the second vibration, which it is supposed to receive between north and south, and therefore the time the pendulum takes in moving from P to P′ and back again from P′ to P will be the same whether it shall have simultaneously or not the other vibration between north and south. Hence it follows that the time of revolution of the circular pendulum will be equal to the time of similar vibrations of the same pendulum, if, instead of having a circular motion, it were allowed to vibrate in the manner of a common pendulum. If this point be understood, and if it also be remembered that the time of vibration of a common pendulum is necessarily the same whether the arch of vibration be small or great, it will be easily perceived that the revolving pendulum or governor will have nearly the same time of revolution whether it revolve in a large circle or a small one: in other words, whether the balls revolve at a greater or a less distance from the central spindle or axis. This, however, is to be understood only approximately. When the angle of divergence of the balls is as considerable as it usually is in governors, the time of revolution at different distances from the axis will therefore be subject to some variation, but to a very small one. [Pg214] The centrifugal force (which is the name given in mechanics to that influence which makes a body revolving in a circle fly from the centre) depends conjointly on the velocity of revolution, and on the distance of the revolving body from the centre of the circle. If the velocity of revolution be the same, then the centrifugal force will increase in the same proportion as the distance of the revolving body from the centre. If, on the other hand, the distance of the revolving body from the centre remain the same, the centrifugal force will increase in the same proportion as the square of the time of vibration diminishes, or, in other words, it will increase in the same proportion as the square of the number of revolutions per minute. It follows from this, therefore, that the greater is the divergence of the balls of the governor, and the more rapidly they revolve, the greater will be their centrifugal force. Now this centrifugal force, if it were not counterbalanced, would give the balls a constant tendency to recede from the centre; but from the construction of the apparatus, the further they are removed from the centre the greater will be the effect of their gravitation in resisting the centrifugal force.