[ 246 ] 



XXXVII. Disquisition concerning the Length of the Seconds 

 Pendulum, and the Ellipticity of the Earth. By J. Ivory, 

 Esq. M.A. F.R.S.* 



T N this Journal for August last, I endeavoured to show that 

 -fi the three principal sets of experiments with the pendulum 

 concurred in giving to the earth very nearly the same ellipti- 

 city as that found by other methods. It must be allowed that 

 the results I obtained agree with observation even to an un- 

 expected degree of accuracy in two sets of the experiments ; 

 and although, in the third set, the errors are greater, yet they 

 are warranted by the undeniable irregularities of the experi- 

 ments. But the article alluded to can be considered as no 

 more than a preliminary inquiry. The great importance of 

 the subject requires a more definitive discussion. My pre- 

 sent purpose is to investigate a general formula for the length 

 of the seconds pendulum in all latitudes ; to compare it with 

 all the tolerably exact experiments that have fallen within my 

 notice ; and, by this means, to lay before the reader a precise 

 account of the present state of this research. 



In another article accompanying this, I have proved that 

 the method of investigation I followed in this Journal for Au- 

 gust last, is free from the objections to which the method of 

 the least squares is liable when it is employed to deduce a 

 mean result from a number of pendulum experiments. At 

 p. 100 of the Journal cited, the method in question is applied 

 to Captain Kater's experiments at the stations of the Trigo- 

 nometrical Survey, joined to the experiment of Captain Sabine 

 at Maranham, the result obtained being, 



= 3-08299/- -64451: 



and if to this we add the value of A deduced, not from any 

 single pendulum, but from the combination of all the pendu- 

 lums, we shall get, 



A + 0-58062/- 0-13314 = v. 

 And hence, / = -20905 



A = -01177 + <r 

 L = 39-01177 + <r, 

 <r denoting an unknown error of the same order with the errors 

 of the pendulums. 



In the Philosophical Transactions 1824, we find an account 

 of experiments made by Captain Hall, R.N., and Mr. Henry 

 Foster, with an invariable pendulum at Rio de Janeiro, and 



* Communicated by the Author. . 



other 



