CHAP, i.] OSCILLATIONS OF THE PENDULUM. 



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The time of oscillation of the pendulum depends on its length, 

 and this length is determined for each clock by the connection or train 

 of wheels between the minute hand and the scape-wheel. It will thus 

 be seen that the function of the pendulum is to regulate the move- 

 ment of the wheelwork by changing this continuous movement into a 

 series of oscillatory movements in equal times. But as it receives its 

 momentum from this wheelwork, the force of which may vary from 

 different causes, it follows that the arcs of these oscillations are 

 liable to decrease : their duration is then shortened, even though the 

 length of the pendulum is not altered, and the clock would go faster. 

 Huygens sought for and found the means oi; solving this difficulty by 

 an admirable discovery which, unfortunately, cannot be adopted on 

 account of the difficulties which the application presents. We refer 

 to the cycloidal pendulum, thus named because it is based on the 

 principle of the geometric curve called a cycloid. 



FIG. 7. Huygens' cycloidal pendulum . 



The rod of this pendulum is a flexible metallic plate, suspended 

 between two solid cheeks taking the form of two cycloidal arcs tan- 

 gent to the starting-point. In oscillating, the flexible rod bends and 

 rests on each of these arcs by turns., and the length of the pendulum 

 thus diminishes in a degree which depends on the extent of the oscil- 

 lations. Huygens found that, if the diameter of the generating circle 

 of the cycloidal arcs has a length equal to half that of the oscillation 

 of the pendulum, the centre of the bob describes an arc (r" p p') which 

 is itself a cycloidal arc. 



Now a heavy body which moves by gravity in an arc of this kind 

 takes the same time to reach the end of its path at P, whatever may 



