VIII IX] 



Introduction 



Ixix 



S a 2 ,o 



S a 



If we proceed by the forward difference formula, we find r 0545, again a 

 result slightly in excess of the true value. As our value of d/N does not fall into 

 ,i lini.il panel, formula (/3) applies, and we proceed to calculate the additional terms. 

 We find: 



r=-05 



'000,614 



-000,756 



-000,558 



-000,687 



000,063 



-000,053 



8'%j -000,201 



S%! -000,175 



Substituting in the formula in a manner suitable for a nearly continuous operation 

 we obtain the upper figures in curled brackets referring to r = '05, and the lower 

 to r = '10 interpolation : 



S3) 



r=-10 



-000,552 



-000,703 



-000,496 



-000,634 



--000,010 



- -000,017 



-000,130 



-000,107 



- as + - 



[ f -001,0520) 



= - -0400,4963 [{.000,9574} + 



n^fi QA9^ F J 00 ' 0996 t , ('000,2498 

 3356,9425 [^|_ ^^j + {. oo,1583 



_ (-000,0757) _ (-000,0125) _ _ f'000,0882) 

 {000,0686} |-000,0049j = |-000,0735j ' 



Accordingly : 



For r = -05 : dfN = -155,0218 - -000,0882 = -154,9336, 



r = 10: d/N= -162,2162 --000,0935 = 162,1227, 



and finally for d/N= '155,5556, 



The result is thus in excellent agreement with that found by forming the 

 high order tetrachoric equation and solving it. We conclude that formula (a) will 

 suffice for three and formula (yS) or formula (7) for four-figure accuracy. We shall 

 give further illustrations with greater brevity as the method of arranging the work 

 will now be clear to the reader. 



