VIII IX] 



/ittr<M(tn-tiint 



liii 



(e) Forward Difference Formula (compare Fig. 1, p. xviii). 



20, X = *0, + (*!, *0, o) + X (*0, 1 2o, D) 



+ $ [0 ((9 - 1) (* a , - 2^,o 4- *o,o) + 20% (*,,!-*( 



+ X(X- 1 )C*o, 2 -2*o. i + *o,o)] ........................ (iii). 



Linear interpolation will generally suffice for the final r interpolation if we are 

 seeking d/N, or for the final d/N interpolation if we require r. 



It must be remembered that in our standard table we suppose d to be the 

 contents of the quadrant for which the limits of integration are x = hto<x>,y = k 

 to oo , h and k being positive. It may be needful at times to find a, 6 or c from d, 

 or on the contrary d from a, b or c. Since h and k are supposed known the 

 connecting equations clearly are : 



(iv). 





Now let n st be the contents of the cell in the sth row and th column of a 

 correlation table. 



Y Y' 



C 



n 8t 



B 



D 



Let n u equal the total frequency or volume of the normal surface in the quadrant 

 standing on YAX^; n u ' that in the quadrant on Y'BX^\ n v that in the quadrant 

 on YCXi ; and n v * that in the quadrant on Y'DXJ. Then n v n u = n tt + V, where 

 V is the volume standing on XiBDXi'. But V= n v ' n u '. 



Accordingly n st = n v n u n v r + n u ' (v). 



Now it is clear that the hi, h t giving the lines YYi and Y'Yi, and the hi, k t 

 giving the lines XXi and X'Xi, will be known ; also r, the correlation coefficient, 



