XIII. On a Correction requisite to he applied to the 

 Length of a Pendulum consisting of a Ball sus- 

 pended by a fine Wire. 



By GEORGE BIDDELL AIRY, MA. 



MEMBER OP THE ASTRONOMICAL SOCIETY, FELLOW OP TRINITY COLLEGE, AND OP THE 



CAMBRIDGE PHILOSOPHICAL SOCIETY, AND PLUMIAN FROPESSOR OP ASTRONOMY 



AND EXPERIMENTAL PHILOSOPHY, IN THE UNIVERSITY 



OF CAMBRIDGE. 



[Read Nov. 16, 1829.] 



In the deduction of the lengih of the simple pendulum 

 vibratinj^ .seconds from the time of vibration of a compound pen- 

 dulum, con.sisting of a metallic ball suppoited by a wire, it has 

 always been supposed that the diameter of the ball which in its 

 position of rest was vertical, continues during the whole vibration 

 to be in the same straight line as the wire. This at least was 

 tacitly assumed in the experiments by Borda, Cassini, Arago, and 

 Biot, (the corrections in the Jiase du Systeme Metrique, Tome III. 

 J). 358, and Biot, Astrouomie Physique, Tome III. Additions 

 p. 173, are calculated on that supposition,) and in the only account 

 which I have seen of the experiments lately made by Mr. Be.s.sel, 

 the same thing is tacitly suppo.sed to be correct. Yet it is per- 

 fectly certain that, during the vibration, the wire and the diameter 

 which was vertical will make an angle, except in one position 

 which will in practice be the same as the position of rest. I pro- 

 pose in this paper to investigate the motion of such a pendulum, 



Vol. in. Pari II. Z z 



