XV111 



Tables for Statisticians and Biometricians 



we are content with the terms in the z's alone. The chief formulae required for 

 the body of a table, i.e. when we are not interpolating on its boundaries, are 



(a) z e<x = <^o,o + <to>,i + 0^1,0 + %*i,i. 

 We term this the Hyperbolic Interpolating Formula. 



o, o 



i, o + 



This is the Midpanel Central Difference Formula. 



-_i-<J>-J 



e,x 



Tz 



v. 



T 





(y3) 



ORDINARY WOW-PINIAL PAWBL 

 (NEITHER h NOR k LimrrED) 



Fig. 1. 



The diagram above indicates what entries in the table of double argument it 

 is needful to extract, and formulae (i) and (ii) provide the requisite S 8 2 and 8' s 2 . The 

 reader should convince himself by a use of (/3), that the additional terms beyond 

 (a) are or are not requisite for the purposes he has in hand. 



But the formula (ft) cannot be used if with regard to either h or k we re- 

 quire a value on the boundary of our table, for then we cannot determine one or 

 more of the values of S 2 and 8' 2 . To meet these cases we require three additional 

 formulae according as our k falls into the space between the first and second argu- 

 ments for k recorded in our table, as our h falls between the first and second values 

 of h entered in the table, or as both h and k do this at the same time. 



