248 DETERMINATION OP THE LONGITUDE OP SEVERAL 



polation adapted to this subject does not appear to have been translated 

 into English, I propose to give the substance of it here. The grounds 

 of preference of it are, its rapid convergency, and its adaptation to com- 

 putation by logarithms. 



For the arguments, 



— 2, — 1, — 0, H- 1, + 2, H- 3, 



let the values of a function be 



a,„\ a,,', a,; a'; a"; a'". 



Denoting the differences as in the following scheme, 



: I II III IV V 



b c 



a ^ d 



a 



c c 



b . d f 



a ^ c e 



a 

 a 



A 



b 



c 



and making 



c = i (c, + c') 

 e =i(e,-i-e') 



then the value of the function for any argument t, expressed in parts 

 of the constant interval unity, 



= a-uLzJ 6 + ^-^ ~ ^ c 4- t .t — 1 .t — i ^ 

 ^ I 1.2 ^ 1.2.3 



