INTRODUCTION TO THE USE OF THE TABLES 



For this introduction to the use of the Tables I have largely drawn on the 

 prefaces to the original papers in Biometrika, and record here my acknowledge- 

 ments to the authors of the same. 



INTERPOLATION. 



(1) A word must first be said as to interpolation. Let a function u be tabled 

 for the argument x proceeding by differences A# = h. Then the scheme of such 

 a table with the differences of u is : 



A'-M_ 3 



A S M 



A'M_, 



A 3 M_, 



AX 



A*, 



A 4 H_, etc., etc. 



AX 

 A*, 



where: AH, = M + , M,, 



AX = AJ/.-H AM,, 

 AX = AX+I ^X etc., etc. 



Now there are throe interpolation formulae which it is desirable to remember. 

 If the function be required for the value x a +ffh and this value be termed M (0), 

 then we have : 



0(1-0) A1 _. , 0(l-0)(2-0) 

 3! 



.(i), 

 ("), 



where <^>=l-0. This is Everett's formula*. And lastly: 



K, ( 0) = M + 1 (A + Au_.) + ~ } A_, - g(I 3 "|^ i < A*!*., -1- A_0 - , . (iii), 

 where we work with the differences on or adjacent to the horizontal through x u . 



* .luiiriiiil <if the Institute of Actuaries, Vol. xxxv, p. 452. 



