as deduced from Experiments made with the Pendulum. 101 



duce the length of the pendulum in M. Biot's experiments 

 from the mean ellipticity already found. Now, e — -00332, 

 L = 739*6885 mm. ; and, hence 



/Km \ mm " 



f- (^1. _ e \ x L = -00533 xL = 3-9425: 



mm. mm. 



consequently, I = 739*6885 + 3-9425 X sin 2 A. 



The following table shows the differences of the pendulums 

 calculated by this formula and the experimental quantities. 



Stations. 



Calculated 

 Pendulums. 



Excess of 

 Calculation. 



Formentera . 







mm. 

 741.2264 

 741-6331 

 741-6488 

 741-7134 

 741-9230 

 742-0720 

 742-3967 

 742-6901 



— -0256 

 4- -0208 

 + -0401 

 + -0082 

 + -0055 



— -0050 



— -0167 



— -0330 



Bourdeaux 

 Clermont . 







Dunkirk . . 







Leith Fort 

 Unst . . . 







M. Biot has investigated the general expression of the length 

 of the pendulum from the ellipticity adopted by Laplace, and 

 from the length of the pendulum observed by himself at Unst 

 which is assumed as free from error. The differences between 

 the formula and the experiments are given in the article al- 

 ready cited ; they are all on one side, except at Formentera ; 

 and they pass a little beyond the limit of the greatest error in 

 the table above. 



From the whole of this discussion it appears that the ellip- 

 ticities deduced from the three sets of experiments approach 

 to one another, and to the like quantities found by other me- 

 thods, nearer than could have been expected, considering the 

 irregularities to which the operations are liable. Capt. Sabine 

 has, however, inferred a much greater ellipticity, equal to 

 0-00346, from an extensive comparison of the same experi- 

 ments ; but as I have not seen his work, I can give no opinion 

 respecting the processes on which his conclusion is founded. 



Aug. 4, 1826. 



J. Ivory. 



XIII, Expert- 



