208 Mr. Ivory's additional Discussion 



and, by adding the like equations at all the stations, 

 Hs + Kt = 2 (sin 2 A(8 — a — &sin ~A)); 

 and, by exterminating s, 



(K - S!) t = 2 (sin 2 A (8 - a - b sin 2 A)). (C) 



If sin 2 X had exactly the same value at all the stations, the 

 coefficient of t in this last formula would be evanescent. In 

 reality this can never be the case : but if all the stations were 

 in higher latitudes than 45°, the coefficient would be so small 

 that a minute variation in the sum on the right-hand side, 

 would produce a great alteration in the values of s and t; 

 and, considering the uncertainty of the experimental errors, 

 the problem would be in a great degree indeterminate. Were 

 we in possession of no other experiments than those north of 

 Formentera, the figure of the earth would be very ill deter- 

 mined ; because all the pendulums might be sufficiently well 

 represented at the same time that the equatorial pendulum is 

 made to undergo considerable variations. The practical so- 

 lution of this problem requires many accurate experiments 

 between the tropics for finding the exact length of the equa- 

 torial pendulum; and likewise many experiments from the 

 tropics to the poles for ascertaining the value of the other 

 element,/ with the requisite precision. 



Now taking all the 40 experiments in the table of my 

 former paper, I have found, 



G = 3*91529 

 H = 16*25069 

 K = 10-47158: 



hence, n being 40, by equat. (A) 



A + -40627/ = -09788. 

 In order to find an approximate value of A, the six ano- 

 malous experiments must be reduced to the equator on the 

 same supposition as before ; namely, f — -205 : Then 



A 



Galapagos -01717 



Ascension -01995 



St. Thomas -02073 



Guam -01912 



Mowi -02136 



Isle of France '02277 I 



Sum ......... -12110 



9 equatorial values of A in my former paper -11967 mean 



15)" : 24077(-01605 

 By 



