100 



Mr. Ivory on the Ellipticity of the Earth 



good reason for expecting to better the formula by seeking a 

 more advantageous value of s. With regard to the ellipticity 



resulting from this combination of the experiments, we have, 



e = -00865 — -£ = '00333 



which is precisely the mean quantity we found by the first 

 method. 



If we join Captain Sabine's experiment at Maranham to 

 those of Captain Kater, taken in the order in which they are 

 set down in the foregoing table, and proceed in the same man- 

 ner, we shall get these equations, viz. 



L — 39-01175+ e 

 xW.= -75942/- 

 ir (2 )= .71225/- 

 #(3)= -68500/ — 



,(4) 



= -64360/- 



■15932 

 •14945 

 •14340 

 •13386 

 •13036 

 •12715 

 •12400 



x^ = -62265/- 

 x^ = -61085/ — 

 x'^- -59557/- 



o — 3-08299/— -64451 

 /= 0-2091, 

 I = 39-01175 + e + 0-2091 sin 2 *. 

 The following table contains the comparison of this formula 

 with observation, s being supposed equal to zero. 



And hence, 



Stations. 



Calculated 



Excess of 



Pendulum. 



Calculation. 





inches. 







39-17088 



- -00058 





39-16103 



— -00056 



Leith Fort . . . 



39-15532 



— -00022 





39-14668 



+ -00068 



Arbury Hill . . 



39-14230 



— -00020 





39-13983 



+ -00054 



j Shanklin Farm . 



39-13663 



+ -00049 



Here the errors are very small. And it appears from both 

 methods of calculation that, in this set of experiments, the 

 discrepancies are contained within very narrow limits. The 

 resulting ellipticity is -00329, which is exactly the mean quan- 

 tity found by the first method. 



As this second method of calculation has been found to 

 agree exactly with the first in two sets of experiments, we 

 may presume that there will be the same perfect agreement 

 in the third set. To save calculation we may, therefore, de- 

 duce 



