98 Mr. Ivory on the Ellipticity of the Earth 



Thus we get, L = /■•+ g -/sin 2 a' \ . . 



x = /(sin 2 A-sin 2 A') - (I -I 1 ). J K ' 



Taking the whole of Captain Sabine's experiments, except 

 those at St. Thomas and Ascension, suppose that V and A' 

 are the experimental quantities at Maranham, and for I and 

 A substitute successively the experimental quantities at the 

 several stations in the order in which they stand in the fore- 

 going table ; then, observing that we have before found 

 /sin 8 A' = '00039, we shall get these equations, 



L = 39-01175+ s 



#0)= -01985/— -00783 



x^ = -03220/- -00670 



x {3) - -04857/— -01211 



x {i) = -09288/— -02296 



x (5) = -42349/— -08954 



x {6) = -61085/- -12696 



d?( 7 )= -79800/— -16242 



x w — -87827/— -18305 



x^= -92698/- -19121 



^(10) _ -96689/- -20255 



As these equations of condition are different from those 

 usually employed in this research, it is necessary to explain 

 the reason of departing from the common method. The aim 

 is to find a value of L and one of/ that will give the observed 

 length of every pendulum exactly if it can be done, otherwise 

 as nearly as possible. Now, we should be able to find values 

 of L and/ that would satisfy the case of every pendulum, if 

 all the quantities x^ l \ x<- 2 \ x^ &c. were evanescent, so that 

 every one of the equations gave the same value of/; for then 

 the expression of L would contain no unknown quantity, ex- 

 cept s, which would be determined by the particular case of 

 any one of the pendulums. But, on account of the irregu- 

 larities to which the experimental quantities are liable, the 

 equations do not all give the same value of/ and the quan- 

 tities x^\ x [ ~\ &c. are not all equal to zero; and we must 

 therefore proceed in the usual way to find the most advantage- 

 ous value of/ by making the sum of the squares of x^\ x^\ 

 &c. a minimum. When / is found, the expression of L will 

 still contain the arbitrary quantity s, which may be determined 

 by a particular pendulum, or by any other consideration 

 deemed preferable. In the usual method of proceeding the 

 quantities L and /are found by investigating the minimum of 

 the expression, 



that is, by making the sum of the squares of all the errors a 



minimum. 



