METHODS OF INTERPOLATION. 321 



Formula (80). 



??2 = i?5 = -1 N r cos '. — COS .T J = 1 ]N" ( Vli — 1) 

 Wg = W4 = J ]sr cos !4-= ^ N 



^ = 3^ { (^^ - 4 V;5) (S3 + S4) + 3 (Si + Se) - (4 v/3 - 3) (S^ + S5) J 

 B = 3^ I 19 (S4 - S3) + 3 (Se - Si) - 5 (S5 - S^) | 



C = J^l (5 73"- 4) (S2 + S5) - 4 (Si + So) - (11 - 5 V3) (S3 + S4) | 

 D = |§j I 3 (S5 - S,) - 4 (S4 - S3) - 2 (So - Si) J 



^ = i^ 1^^^ + ®«) + (^ - '^'^^ (^= + S4) - ( V3 - 1) (S2 + S5) } 



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



When seven groups are assumd, we get the following: 



For inula (81). 



ni = n, = i^(^l — cos J J = .0495155660 I^ 



w.^ = «6 = J ]S[ Tcos ^ — cos ^ J = .1387395330 E" 



n^ = W5 = J N r cos ^ - cos -rfj= .2004844340 N 



»i4 = N cos ~ = .2225209340 K 



A 5= ^ I 5.244333412 S4 + .209118318 (S2 + Sg) - .525857833 (S3 + S5) 



-^(Si+S,)| 

 B = ^2 1 24.6748182 (S5 - S3) + ^ (S, - Si) - 16.4349544 (S^ - S^) | 

 C = ^3 1 138.5583290 (S3 + 85) + ?^ (Si + S,) - 194.1045503 S4 



- 59.2465387 (S^ + So) | 

 D = ^^ I 392.527327 (Sg -^,)-^ (S, - Si) - 286.517454 (S5 - S3) | 



E = ^3 I 1685.91223 S4 + 1189.67603 (S2 + Se) - 1533.08214 (S3 + S5) 



(Si + S,) j 



6400 



7 

 21 s 



