322 METHODS OF INTERPOLATION. 



ip ^ 1 ( 12288 g^ _ g^^ _^ 781.239210 (S5 - S3) - 1407.744414 (So - S^)] 

 G = ^ I (S3 + S5) + (Si + S,) - S4 - (S, + Se) I 

 The eight-group formula can be expressed without decimals : 

 %i = ng = 1 N(^l - cos^^ = I N (2 - V2 + V2) 

 M2 = ^i7 = JN^cos^-coS|J =iN ( V2 + V2 - V2) 

 %3 = 7i6 =-^lS /cos ^ - COS — - j r= 1 IS" ( -v/2 — ^/2 — 72) 

 W4 = ng = ^- N COS ^ = 1 N V2--/2 



_|la.2 72-2V2(2-V3)KS3 + S6)-(Si+S8) ] 

 B = ~(ll(S5-S4) + (7-4V2)(S,-S2)-(4V2-3)(Sc-S3)-(S8-S0} 

 C=^[|5+9V2-V2^^V2(4 + 7^/2)|(S3+Sc)+5(Sl4-S8) 



-1 V2=^V2(4 + 7V2)-5|(S2+S,)-{V2+V2(6+4V2) 



-(5+9^2)1(84+85)] 

 D=^,|3(l+2V2)(86-S3) + 5(S3-Si)-17(S5-S4) 



-3 (5-2 V2) (8,-82) I 



390 r _ 



E = -^[|V2-V2(6+7V2)-6KS2+8,) + 2{V2+V2(l+3V2) 



-(3+4V2)KS4 + 85)-6(8i+S8)-{2(3+4V2) 



-V2^W2(6+7V2)|(S3+S6)] 

 F = -^1 5(85-84) + (5- ^/2) (8,-82)-(3+ V2)(8e-S3)-3(8e-8i) ] 

 G = ^^[(8i+S8) + (l+ a/2- V2+VI) (S3+Sc)-( a/2+72-1)(S2+8,^ 



-^V2(2+V^)-(l+ V2)| (84+S5)] 

 H = I (Se— 83) + (88— 81) — (85- 84) — (S7 — 82) > 



This is SO complicated that, for practical purposes, we will employ 

 decimals, as follows: 



