These arrangements being comprehended, let us suppose that, either by reason of a diminished load upon the engine or an increased activity of the boiler, the speed has a tendency to increase. This would impart increased velocity to the grooved wheel A B, which would cause the balls I to revolve with an accelerated speed. The centrifugal force which attends their motion would therefore give them a tendency to move from the axle, or to diverge. This would cause, by the means already explained, the throttle-valve T to be partially closed, by which the supply of steam from the boiler to the cylinder would be diminished, and the energy of the moving power, therefore, mitigated. The undue increase of speed would thereby be prevented.
If, on the other hand, either by an increase of the load, or a diminished activity in the boiler, the speed of the machine was lessened, a corresponding diminution of velocity would take place in the grooved wheel A B. This would cause the balls I to revolve with less speed, and the centrifugal force produced by their circular motion would be diminished. This force being thus no longer able fully to counteract their gravity, they would fall towards the spindle, which would cause, as already explained, the throttle-valve to be more fully opened. This would produce a more ample supply of steam to the cylinder, by which the velocity of the machine would be restored to its proper amount.
Fig. 42.
(126.)
Now let it be supposed that while the pendulum P P′ continues to vibrate east and west through the arch P P′, it shall receive such an impulse from north and south as would, if it were not in a state of previous vibration, cause it to vibrate between north and south, in an arch similar to the arch P P′. This second vibration between north and south [Pg213] would not prevent the continuance of the other vibration between east and west; but the ball P would be at the same time affected by both vibrations. While, in virtue of the vibration from east to west, the ball would swing from P to P′, it would, in virtue of the other vibration, extend its motion towards the north to a distance from the line W E equal to half a vibration, and will return from that distance again to the position P′. While returning from P′ to P, its second vibration will carry it towards the south to an equal distance on the southern side of W E, and it will return again to the position P. If the combination of these two motions or vibrations be attentively considered, it will be perceived that the effect on the ball will be a circular motion, precisely similar to the circular motion of the balls of the governor already described.
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.