as deduced from Experiments with the Pendulum, 169 



e being the error of observation, and^a quantity which is the 

 same at all points of the earth's surface. The equation (1) 

 being general, if we add all the like equations at the 34 sta- 

 tions we propose to include in our investigation, we shall get 



34 A + fX (sin 2 K) =. 2 (8) + 2 (e). 



Now I have found, 



2 (sin 2 A) = 15*9316, 

 2(8) = 3-72872; 



and hence by dividing all the terms by 34, we get, 



A + -4686/= -10966, (2) 



neglecting the term containing e 9 which must be very small, 

 both because the errors must in some degree compensate one 

 another, and on account of the great divisor 34. The equa- 

 tion (2) must be very exact, provided we take care not to en- 

 hance its error by introducing small divisors. 



Again, when the ellipticity is ^ F , we havey = -202 nearly, 

 as appears from the calculations of Captain Sabine ; and, when 

 the ellipticity is tof^/ is nearly -208, according to my formula 

 in this Journal for October 1826. The mean is -205, which 

 cannot err from the true value of f more than + -003. Now 

 it is evident that this small error will not affect the product 

 jfsin 2 X near the equator, and so long as sin 2 \ is less than 0*2. 

 I have therefore computed the values of A by means of the 

 formula, A = 8 — f sin 2 A, 



on the supposition that fz=. -205, for all the stations in the 

 table where sin 2 K is less than 0-2, as follows: 



A 



Maranham -01173 



Bahia -01398 



Rio Janeiro -01264 



Trinidad -01188 



Madras -01289 



San Bias -01066 



6)-07378(-01230, mean of 6. 



Rawak -01479 



Sierra Leone... -01550 

 Jamaica -01560 



9)-11967('01330, mean of 9. 



The inequality of the several values of A is very remarkable ; 

 in particular the three stations placed last, greatly exceed the 

 mean of the first six. But whatever be the cause of the irre- 

 gularity, it cannot arise from the approximate value assigned 

 New Series. Vol. 3. No. 15. March 1828. Z to 



