282 OUTLINES OF NATURAL PHILOSOPHY. 



points, so as to be forced out of the straight line by 

 a small quantity, it will vibrate backwards and 

 forwards on each side of that line, and the curves 

 into which it will successively pass in the course 

 of these vibrations, will have their curvature at 

 every point proportional to the distance from the 

 straight line joining the fixed points ; the accele- 

 rating force at each point will also be proportional 

 to that distance, and the great and small vibrations 

 will be performed in the same time. 



It is usual to reckon the vibrations of a string differ- 

 ently from those of a pendulum ; the passage from 

 the highest point on one side, to the highest on the 

 other, is reckoned a vibration of a pendulum. The 

 passage from the farthest distance on one side to 

 the farthest on the other, and back again to its first 

 position, is accounted a vibration of a musical string* 

 It is properly a double vibration. 



r >'?ft 'f^rft (T f M\ r f MtTTf"* 



379. The figures which a musical string assumes 

 in its vibrations, constitute a series of elastic curves, 

 or elongated cycloids. 



The construction of these curves is easy. See the 

 Notes in LE SEUR, and JACQUIER'S Commentary on 

 the Principia, lib. u. prop* XLII. the Note 301. Al- 

 so SMITHES Harmonics. 



nwrnt & 



380. If 



