THE PENDULUM. 



thirty teeth, and if "the pendulum take one second to make a 

 single swing, it will allow the escapement-wheel to make a 

 complete revolution while it makes thirty swings from right to 

 left, and thirty from left to right, that is, in sixty seconds, or one 

 minute ; so that, if the axis of the third hand were in this case 

 fixed upon the axle of the escapement- wheel, that hand would 

 make one complete revolution in a minute, and consequently the 

 second would make one complete revolution in one hour, and the 

 third in twelve hours. The required conditions would therefore 

 be in this case fulfilled. 



To render this explanation of the regulating property of the 

 pendulum complete, it will be sufficient to show 1st, that the 

 time of vibration must be always rigorously the same with the same 

 pendulum ; 2nd, that this time can be made shorter or longer by 

 varying the length of the pendulum, so that a pendulum can 

 always be constructed which will vibrate in one second, or in half 

 a second, or, in short, in any desired time ; and 3rd, that the 

 connection of the pendulum with the escapement-wheel can be so 

 constructed, that the motion of the latter shall be governed by 

 the vibrations of the former, in the manner already described. 



A pendulum consists of a heavy mass attached to a rod, the 

 upper extremity of which rests upon a point of support in such a 

 manner as to have as little friction as possible. Such an in- 

 strument will remain at rest when its centre of gravity is in the 

 vertical line immediately under the point of suspension or support. 

 But if the centre of gravity be drawn from this position on either 

 side, and then disengaged, the instrument will swing horizontally 

 from the one side to the other of the position in which it would 

 remain at rest, the centre of gravity describing alternately a 

 circular arc on the one side or the other of its position of rest. 

 If there were neither friction nor atmospheric resistance, this 

 motion of vibration or oscillation on either side of the position of 

 equilibrium would continue for ever ; but in consequence of the 

 combined effects of these resistances, the distances to which the 

 pendulum swings on the one side and on the other are continually 

 diminished, until, after the lapse of an interval, more or less 

 protracted, it comes to rest. 



12. It is related that Galileo, when a youth, happening to 

 walk through the aisles of a church in Pisa, observed a chandelier 

 suspended from the roof, whose position had been accidentally 

 disturbed, and which was consequently in a state of oscillation. 

 The young philosopher, contemplating the motion, was struck 

 with the fact, that although the range of its vibration was 

 continually diminished as it approached a state of rest, the times 

 of the vibration were sensibly equal, the motion becoming slower 



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