by the Method of the Least Squares. 53 



This is also corroborated by Mr. Ivory's value of it, de- 

 rived from some extensive series of pendulum experiments de- 

 tailed in several numbers of the Philosophical Magazine, in 

 which he finds from 



Captain Sabines's experiments, e = 0*00333 



Captain Kater's = 0-00329 



M. Biot's = 0-00332 



Mean of the whole ... = 0-00331 

 or, a little greater than that obtained above. 



This is the more remarkable, as the result deduced by Mr. 

 Airy from Captain Sabine's series of experiments by an ap- 

 plication of the method of the least squares, according to de- 

 ductions from his analysis, gives s = 0-0034.74, and from the 

 measures of arcs, e = 0-003589. Mr. Airy concludes that if 

 the Indian and French arcs are supposed to be qjiite accurate, 

 E = 0-003269 — A X 2-139. 



Now, from a previous analysis, he finds A = — 0-000157, 

 which, if applicable here, would give e = 0-003269 ± 0-000336, 

 a result (in whatever way we take the sign), he observes, that 

 cannot be reconciled with the values of e and A, which were 

 s = 0-003474., and A= 0-000064*, as deduced from the pen- 

 dulum experiments. However, if A in this case were nothing, 

 or very small, the compression, as I have also found it from 

 these arcs, would very nearly agree with that deduced from 

 various sources by Laplace. 



He remarks, that " the measures of arcs of the meridian 

 which have hitherto been made are, I imagine, insufficient for 

 the determination of the figure of the earth." Now, from the 

 consistency in the various measures of the compression which 

 1 have found above, it seems hardly possible that by increas- 

 ing the number of the measures of arcs, a more near coinci- 

 dence can, on the whole, be expected ; and therefore it can- 

 not be supposed that a better agreement among individual de- 

 terminations could take place. 



But still the question occurs. How does it happen that there 

 is such a discrepancy between the method I have employed 

 for individual observations, and that of the least squares, which 

 connects the whole ? Is it possible by any means to reconcile 

 them ? And which deduction is most worthy of credit ? Is 

 there any peculiarity in the application of the method of least 

 squares to the present question, that makes it deviate so far 

 from the other ? I am disposed to think that there is, and 

 that it consists in this : that there is not any regular series ot 



• I have supposed this to be the real vahic in page ."iGfi, Phil. Trans. 

 1826, though the decimal point has been from some oversight onnttcd. 



observations 



