respecting the Ellipticity of the Earth. 209 



By substituting '01605 for A in the foregoing equation, we 

 get y= '2014. We now have, 



a = -01605, A m a + s, 



b = -2014, f = b + r: 



and the equations (B) and (C) will give us, 

 5 + -40627 t = 

 3-869 t = (sin* A (8 — a - b sin 2 X)). 



Computing now the sum on the right-hand side of the last 

 equation, which sum consists of 40 terms, we shall find, 



3-869 t = + '00307 ; 

 wherefore, r = -f -00079; s = — -00032; 

 /= -2022; A = '01573: 



And we hence obtain this general formula for the length of 

 the pendulum, viz. I - 39-01573 + '2022 sin» A, 



•2022 I 



ellipticity = -00865 - ^^ = -00346 =^. 



This result coincides almost exactly with what Captain Sa- 

 bine has deduced from his experiments. We have next to 

 examine, how the formula agrees with the phaenomena. Be- 

 ginning with the six anomalous stations, there is still an ex- 

 cess of gravity at them all, as will appear by the following 

 errors which must be applied to the observed pendulums to 

 make them equal to the calculated lengths ; viz. 



errors. errors. 



Galapagos . — -00144 

 St. Thomas - -00500 

 Ascension.. — -00427 



Guam —'00355 



Mowi — 00599 



Isle of France —'00746. 



The error at Galapagos is now very small, and, in all pro- 

 bability, smaller than the actual error of observation. At the 

 other five stations the excesses of gravity are still great ; and, 

 with respect to the like errors in my table, they appear to be 

 reduced nearly in the proportion of 3 to 4. But if some ad- 

 vantage be gained at the anomalous stations, there is a disad- 

 vantage at all the other stations within 50° of the equator on 

 either side. Within these limits all the observed pendulums 

 are uniformly short of the calculated ones, except at Port 

 Jackson and Jamaica, where there is a very small difference 

 of an opposite kind, which may be neglected ; and even, with 

 respect to these two stations, there is great reason to think 

 that the observed pendulums are both too long. Nor are 

 the deficiencies trifling, as will appear by the following list of 

 New Series. Vol. 3. No. 15. March 1828. 2 E errors, 



