(126.) The principle which renders the governor so perfect a regulator of the velocity of the machine is difficult to be [Pg212] explained without having recourse to the aid of the technical language of mathematical physics. As, however, this instrument is of such great practical importance, and has attracted such general admiration, it may be worth while here to attempt to render intelligible the mechanical principles which govern its operation. Let S (_fig._ 42.) be the point of suspension of a common pendulum S P, and let P O P′ be the arch of its vibration, so that the ball P shall swing or vibrate alternately to the east and to the west of the lowest point O, through the arches O P′ and O P. It is a property of such an instrument that, provided the arch in which it vibrates be not considerable in magnitude, the time of its vibration will be the same whether the arch be long or short. Thus, for example, if the pendulum, instead of vibrating in the arch P P′, vibrated in the arch _p p′_, the time which it would take to perform its vibrations would be the same. If, however, the magnitude of the arch of vibration be increased, then a variation will take place in the time of vibration; but unless the arch of vibration be considerably increased, this variation will not be great. 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.