168 Mr. Ivory on the Ellipticity of the Earth 



rations is in reality a play of calculation caused by one common 

 datum, or several common data; and therefore it does not 

 furnish independent proofs in favour of the number in question. 

 There must, in all probability, be some error in the pen- 

 dulum at Rawak ; and we know that the two pendulums of 

 Captain Sabine are anomalous, involving an irregularity much 

 greater than usually occurs in such experiments ; from which 

 considerations we must conclude that the evidence for the el- 

 lipticity 2^ rests but on slender foundations. 



It is reasonable to think that every new set of experiments 

 with the pendulum should be joined to the stock we already 

 possess, in order to add to the number of unexceptionable ex- 

 periments, and to correct such as are of doubtful authority. 

 By proceeding in this manner our data for obtaining an exact 

 knowledge of the figure of the earth and of the distribution of 

 gravity on its surface, would continually increase and improve 

 in accuracy ; and, by applying proper methods of calculation, 

 we might hope to bring this great question to a satisfactory 

 solution. But if every new set is to be taken by itself, we 

 may, by making arbitrary combinations of the experiments, be 

 led into great error, and to entertain speculations that have 

 little foundation in nature. 



The number of experiments made with the pendulum by 

 good observers at present amounts to 40, contained in the 

 subsequent table ; but of these, six, placed last in the table, are 

 -decidedly anomalous, and must be separated from the rest. 

 In setting aside these six experiments I do not now proceed on 

 my own opinion ; I follow the example of M. de Freycinet 

 and M. Duperrey. There remains 34 experiments which may 

 be compared together; and we have now to inquire, What 

 mode of calculation must be adopted in order to obtain a re- 

 sult entitled to the greatest confidence the case will admit of. 

 On reflection it will appear that we cannot expect to attain 

 what we wish for by the method of the least squares as usually 

 applied, nor by the modification of that method I used in 

 this Journal for October 1826. These more direct methods 

 are useful in bringing out a first approximation ; but it seems 

 necessary to correct the approximate elements thus obtained 

 by the methods used with success in so many problems of 

 astronomy. It is on these principles that the following inves- 

 tigation is conducted. 



If we put 39+ I for the pendulum in English inches at any 

 station ; K for the latitude ; and 39 + A for the equatorial pen- 

 dulum; we shall have this equation, 



A+/sin 2 A = 8 + f, (1) 



e being 



