328 METHODS OF INTERPOLATION. 



If the assumed groups are consecutive and contain Wi terms eacli, the* 

 constants will be — 



(63) 



This properly commences not only the series of formulas (A), (B), (C), 

 &(i., but also the series (40), (41), (42), &g. 



Again, when formula (12) is extended so as to include nine constants, 

 it becomes — 

 S=«[A+ tV C n'-h^\B n'+jh^ n'+2ioT^ n'-{-(B+\D n'-\- j\¥ n' 



>(64) 

 + yV H n')x^ + (E+fGw2+|.I «V + (F " ~ ' ' 



F 4- ^ H if)j(^ i 



If we assume nine consecutive groups, containing Wx terms each, the 

 values of the constants are found to be — 



A=:.^^3^,^^^^^^^J11702134S5+125884(S3+S.)+1225(S,+S9) 



-80021G(S4+Sc)-17000(S2+S8)] 

 B=^j^gj|^^2[574G86(S6-S4)+33878(S8-S2)-170422(S:-S3) 



-3229(S9-Si)] 

 C =iT^JoUn?f ^^^-^^^(^^+ ^"^ + 4448^(^2+ Ss) -3260110 S5 



-323260(83+ S7) -3229(Si+ Sg)] 



S3) + 141(S9-Si) 



-1406(88-82)] 



D=^^3^j|^J6134(S:-S3) + 141(S9-8i)-8614(86-S4) 



E=^jy^^^5[15002 85+3908(S3+S,) + 47(Si+S9)-10840(84+SG) 



-616(82+83)] 

 r=jy^J-,[82(SG-S4)+26(S8-82)-74(S:-S3)-3(So-Si)] 



G=j=T7^.[752(84+Sc) + 80(82+88)-970S5-340(S3+8,) 



-7(8i+8„)] 



H=^f^^^^8[14(8;-S3) + (S9-S0-14(Sc-S4)-6(88-S2)] 



I=j(^3^9[70S5+28(83+8,) + (8, + So)-56(84+8c) 

 -8(82+ S«)j 



H^) 



