METHODS OF INTERPOLATION. 



337 



meteorology uiakiug it convenient to have the nnniber of gronps a 

 divisor of 24. With six groups, the constants are — 



A=^(Si+S.4-S3+S,+S5+So) 



Ci=| sin GOO[(S3+S4)-(«i+!So)] 



B3=i[(S4-S3)-(So-S,)] 



C2=f sin G{)o[(S,+ S,) + (Si+S,)-2(S,+S.)J' 



B3 = l|Bi-(S5-S2)] 



(^) 



With eight groni)s — 



A=^(S,+S,+ 



+ ^8 



B,=i(2 sin 45o+l)[(S,-S,,) + (S,-a)l+i{(S.-S,) + (^^.-S.)]i 

 C,=i(2 sin 45o + l)f(S,+ S,)_(S, + .S,)] + i|(S3+S,)-(a+S,)]' 

 B,=i[(S,-S4) + (S«-S3)-(S,— S,)-(S,-S,)] ) (.7) 



0,=i[(S,+ S,) + (S, + S3)-(S,+ SJ-(S,+S,)] 

 B3=B,- sin 45o[(S«-S3) + (S;-S,)] 



c,=c,+i[(a+s,)+(S,+s,)-(S3+s,)-(s,+s,)] 



+ S,,) 



\ 



And witli twelve gronps — 



A=^-(s.+a+ 



B,=i(«iii OOo+l)[(S,_SJ + (S,o-S3)]+i(sm 60o+i)[(S,-S, 



+ («u-S.)]+M(Sr-So) + (S,,-S.)] 

 C,=i(sin G0o+l)[(S,3+S,-)-(S.+S,)]+i(>sin GOo+^)[(S,+ a 



-(a+Sn)]+M(S.+s,)-(«3+s,,)]- 



B,=i[2(S,-S,) + (S;-So) + (So-«.)-2'(S„-S,)-(S.„-S3) 



-(S..-S,)J 

 C,=i sin G(P[(S,+ S,-) + (S.+S,,)-(S,+ S,)-(S3+S,„)] 



B3=M(S;-s.)+(Ss-y,)+(Sn-a)+(S„-so-(S,-«,) . 



-(«10-S3)] /('') 



C3=M(S«+S;) + (S3+S,o) + (S.+S„)-(.S,+S«)-(S,+ S,) 



-(«l+s,,)] 



B,=i[(S,-S,)+(S,o-S3)-(S,-S,)-(S.,-S0] 

 0;=i sin G0o[(Se+S,-) + (S,+ S,) + (S3+S.„) + (S, + S,,) 



-2(S,+S,)-2(a+Sn)j 

 B, = (S,-S,) + (S«-S,) + (S„-a) + (S,,-S0-B,-4B3 

 C,= (S,+ S;)-(S, + S„)-0,-2 03 



Bo=TV[(S,-S,0 + (S,-S,) + (Sn-S,)-(Ss-S,)-(S„-S3) 

 -(S.2-S1)] 



To illustrate the use of these formulas by an example, let us tali;e the 

 series employed in illustrating Cauchy's method of interpolation in the 

 22 S 71 



