PROCEEDINGS OF THE AMERICAN ACADEMY 



Fjx = G 



F T r = 5 



2^4 = 4 

 Fj:a = 3 

 Fzf2 = 2 

 F*i = l 



T 2^ + 42^16^ + 64^ 



+12-] 



+ 5 







— 3 



— 4 



— 3 J 



2? 2 =F 6 2? 3 + 28 2? 4 



+16 1 

 + 5 





 — 1 







+ 1J 





 —5 



fq=3 2? 3 + 36 2? 4 , 3 }ZB A + F». 





 —5 



This again may be transformed into the following form : — 



(6.) 



FW\ 



Fz^3 

 F^ 2 



+161 



+ 5 

 



+6 1 +121 



+5 | +5 



+2 — 4 



+1 ] — 3 J + 1 J 



01 

 -5 

 



\*QC+D)_^\fr D , 





 —5 



in which 



-(lio-7^) A -' } 



11 7 



B'= - B 4- — - A 4 — 



4 ' 2 o>" 36 a, 4 



} 



and in which the minus sign must be used for interpolated values of 

 F x preceding F , and the plus sign for those following F . In the 

 latter transformations no small terms have been omitted ; so that this 

 last form is of the same degree of accuracy as the preceding one, and 



