94 Mr. Ivory on the Ellipticity of the Earth 



V = L + 0-2 sin 2 A' = L + 0-00039; 

 and hence, L = 39-01175. 



But if we are not in possession of any experiment near 

 enough to the equator for finding L, we may still derive a 

 value of e from any two experiments made at a sufficient di- 

 stance from one another in latitude. Let A' and A be the two 

 latitudes ; I' and I, the two pendulums ; then, we have 



esin 3 A'=l + 4r sin 2 A' 



e sin ~ A = 1 + — sin - A =-\ 



2 • L 



f sin-A- T 



and hence we readily get, 



e - -00865 ^- — ^ r . (2) 



sin " X — r sin 2 X' v 



It is evident, that (1) is only a particular case of (2), namely, 

 when A' = 0. But it is of more importance to notice that no re- 

 liance can be safely placed on either of the two formulae, when 

 the denominator on the right-hand side is a small number. 



Let us now take the experiments of Captain Sabine, which 

 give us the lengths of the seconds pendulum at thirteen 

 stations from the equator to 80° of latitude. They are con- 

 tained in the following table. The inspection of the table will 

 show that the results it contains are very irregular near the 

 equator, and we may extend this observation so as to include 

 Jamaica. It must be remarked here, that there is no inten- 

 tion of throwing any discredit on the operations of Captain 

 Sabine, by what is now said, or may hereafter occur in the 

 course of discussion. I have not even seen the Captain's own 

 work ; his experiments are taken from the 39th Number of the 

 Journal of Science ; and in reasoning upon them, it must not 

 be understood that the causes of the discrepancies occasionally 

 noticed, are in any way alluded to. In order to have a just 

 idea of the irregularities we may assume the equatorial pen- 

 dulum as determined at St. Thomas, and 0-2 in. for the total 

 increase from the equator to the pole, which is the least and 

 most favourable supposition that can be made ; then, having 

 calculated from these data, the pendulums at the other stations 

 in the table including Jamaica, the observed pendulums are 

 uniformly short of calculation, the errors being all very great 

 except at Ascension, and amounting to the enormous quantity 

 of -008 in. at Maranham and Trinidad. On the other hand, 

 if we assume 39-01175 for the equatorial pendulum, which is 

 the length deduced from the experiment at Maranham ; and 

 take 0*2 in. for the total increase as before, this being now the. 



least 



