as deduced from Experiments with the Pendulum. 167 



At Port Jackson the pendulum determined by M. Duperrey 

 is less than the length found by M. de Freycinet, and ap- 

 proaches nearer to the pendulum at Paramatta, to which it 

 ought to be very nearly equal : and this proves the justness of 

 the remarks I made relative to this point at pp. 351, 352, of 

 this Journal for November 1826. 



Comparing the results obtained by M. Duperrey and M. de 

 Freycinet at the same stations and on the same spot, the pen- 

 dulum of the former observer at the Falkland Islands is longer 

 than that of the latter by '00233 ; and, at Port Jackson and 

 the Isle of France, the pendulums of the former are respec- 

 tively less than those of the latter by '00145 and '00095. We 

 may therefore conclude, that such experiments are liable to 

 an error amounting from '002 to '003 in the length of the pen- 

 dulum, or from two to three vibrations in a mean solar day. 

 We are sure that the error may amount to the quantity men- 

 tioned ; but it may be much greater. At Ascension the dif- 

 ference between the pendulums of Captain Sabine and M. Du- 

 perrey is very small. 



In deducing the ellipticity of the earth, M. Duperrey com- 

 bines his own experiments with M. de Freycinet's, exclusively 

 of those made by other observers. The results he obtains 

 vary between the limits ffa and ^o* Upon the whole he 

 concludes that the two hemispheres of the earth are similar, 

 and he fixes definitively upon g|^ or ^ m as the ellipticity 

 common to both. But on examining the calculations of M. Du- 

 perrey, it will be found that the ellipticity he adopts, depends 

 entirely on the equatorial pendulum determined by M. de 

 Freycinet at Rawak. If we suppose that the pendulum at 

 Rawak errs in excess, which is very probable, and diminish 

 its length by correcting the possible error, the ellipticities 

 will come out of less quantity in all the combinations in which 

 they were before equal to ^fa or y^j, Wherefore, although 

 M. Duperrey finds five combinations of his experiments in 

 which the ellipticity is 7 fa or -gfa ; yet, whether its real value 

 be equal to either of those numbers, or to a less fraction, will 

 depend entirely upon the error that may exist in the pendu- 

 lum at Rawak. Captain Sabine has deduced the same ellipti- 

 city, viz. -sin* D y man y combinations of his own experiments 

 and those made in England and France ; and I have already 

 remarked that this uniformity of result is occasioned by the 

 pendulums at the Islands of Ascension and St. Thomas, which 

 enter into all the computations. If these two stations be left 

 out in any, or in all, the combinations, the ellipticity will no 

 longer be the same as before, but a less fraction. The ar- 

 riving at the same result by a multiplicity of arithmetical ope- 

 rations 



