respecting the Ellipticity of the Earth, 207 



pendulums when thus compared are excessively irregular, we 

 never can deduce from them, by any mode of investigation 

 whatever, any conclusion respecting the figure of the earth, 

 in which much confidence can be placed. On this ground I 

 always rejected such of the experiments as were irreconcile- 

 able with the rest ; and I thought this proceeding the more 

 justifiable, both because the experiments set aside were al- 

 ways very few in comparison of the whole number, and be- 

 cause those that remained were brought within the compass 

 of inequality to be expected in experimental quantities. The 

 results obtained on this principle, are already before the 

 public, and therefore need not be particularly mentioned. 

 My present intention is to solve the problem, by taking in all 

 the 40 experiments we at present possess, in the expectation, 

 that by this means some light will be thrown on this subject, 

 although my former mode of solution still appears to be 

 founded on sound principles. 



In order to abridge, I shall begin with laying down the 

 general formulas of the mode of solution I follow. Put 39 + 5 

 for the pendulum in English inches at any station ; A, for the 

 latitude; 39+ A, for the equatorial pendulum; and/ for the 

 difference between the pendulums at the pole and the equator: 

 then A +/sin«A = 8. 



Further, let G = 2 (&), 



H = I (sin 2 a), 

 K = 2 (sin 4 A), 

 the sums being extended to all the stations of which the 

 number is n : then, by taking the sum of all the like equa- 

 tions at the n stations, we get, 



±+"f=l (A) 



Next, a being an approximate value of A, find an approxi- 

 mate value of / namely b, by substituting a for A in Equat. 

 (A) ; or, if b be an approximate value of / find, by means of 

 the same equation, a corresponding value of A , namely a : 

 then, if we put, A = a + 5 



we shall have, 5 + 5 T = . (B) 



Again : Multiply all the terms of the first equation by the 

 coefficient of f: then 



A sin 2 A + /sin 4 A = 8 sin 2 A ; 

 and, by substituting the values of A and/ 



$ sin 2 A + t sin 4 A = sin 2 A (8 — a — b sin 8 A) ; 



and, 



