ISOCHRONISM. 



arrived at A, the ball, being again brought to rest, will fall once 

 more from A to B, and so the motion will be continued alternately 

 between A and A'. 



The motion of the pendulum from A to A', or from A' to A, is 

 called an oscillation, and its motion between either of those 

 points and B is called a semi-oscillation, the motion from B to A 

 or from B to A' being called the ascending semi-oscillation, and 

 the motion from A or A' to B, the descending semi-oscillation. 



The time which elapses during the motion of the ball between 

 A and A' is called the time of one oscillation. 



It is evident, from what has been stated, that the time of 

 moving from either of the extremities A, A', of the arc of oscillation 

 to the point B, is half the time of an oscillation. 



If, instead of falling from the point A, the ball had fallen from 

 the point c, intermediate between A and B, it would have then 

 oscillated between c and c' ; two points equally distant from B, 

 and the arc of oscillation would have been c c', more limited 

 than A A'. 



But in commencing its motion from c, the declivity of the 

 arc down which it falls towards B would be evidently less than 

 the declivity at A ; consequently the force which would acce- 

 lerate it, commencing its motion at c, would be less than that 

 which would accelerate it, commencing its motion at A. 

 The ball, therefore, commencing its motion at A, would be 

 more rapidly accelerated than when it commences its motion 

 at c. 



The result of this is, that, although the arc A B may be twice 

 as long as the arc c B, the time which the ball takes to fall from 

 A to B will not be sensibly different from the time it takes to 

 fall from c to B, provided that the arc of oscillation A B A' is not 

 considerable. 



It was at first supposed, as we have just stated, that, whether 

 the oscillations were longer or shorter, the times would be 

 absolutely the same. Accurately speaking, however, this is not 

 the case : but if the total extent of the oscillation A A' do not 

 exceed 5 or 6, then the time of oscillation in it may be con- 

 sidered, practically, the same as in the lesser arcs. 



14. This important principle may be easily experimentally veri- 

 fied. Let two small leaden balls be suspended from the same point 

 of support, but one being in advance of the other, so that in oscil- 

 lating the two balls shall not strike each other. This being done, 

 let one of the balls be drawn from its point of rest through an 

 angle less than 3, and let it be disengaged. It will oscillate 

 as described above. Let the other ball be now drawn from 

 its point of rest through a much less angle, and let it be so 



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