ccxx Tables for Statisticians and Biometricians [XLV XLVI 



We have now two series of interpolations to make : 



First, for the six incomplete normal moment functions for x = 1*291,02, we 

 shall content ourselves with the central difference formula 



^ = ^o + ^i-^</>{(l + ^)^o + (H-<9)S 2 ^} (xi). 



Secondly, for the six coefficients from Table XLV, it will be adequate to use 

 linear differences, n being 168*34, 



First, we need m (x), ra 4 (x), m 6 (x), m 8 (x), m 10 (x) and m-^ (x). 



1 f x 

 Now T??O(#) = -F= e ~* fl dz = ka x . 



A/g / - 



This can be found from Table II of Part I of this work. 



6 --= -102, <f> = -898, 6$ = -01 5,266, 

 z = '901,4747, zi= -903,1995, 



2~ _ _ 904, 2- _ _ OOQ 



O o <iiAjTr, O ^5j Zi-jO, 



^=0-5 + m (1-291,02) = '9016,5063 - '015,266 {1-898 (- 223) + 1'102 (- 224)} 



= -9016,5063 + -0000,0102 = -9016,5165, 

 and 77io (1-291,02) = -4016,5165. 



m 4 (x), w 6 (x), m s (x) and m w (x) are to be found from Table IX of Part I. We have 

 m 4 (x) wj 6 (#) m 8 (x) m 10 (x) 



z -040,0559 -007,8427 -001,2160 -000,1558 

 *! -054,9214 -012,5028 -002,2617 '000,3386 

 S 2 ^ 28524 14699 4391 928 



&Z-L 28872 18265 6503 1628 



Here = '9102 and </> = '0898 and #</> = '0136,2266. 



Then Wi 2 (#) must be found from Table XIII of the present volume (Part ll). 



We have 



Z Q = -000,0170, *! = -000,0432, 



Substituting in the central difference formula (xi) above, we have* 

 rw (as) = -4016,5165, m 8 (as) = '0021,4436, 

 4 (a?) = '0534,6900, m w (x) = '0003,1657, 

 m 6 (x) = -0120,1497, m 12 (x) = -0000,398. 



Secondly we proceed to determine the c's by linear interpolation from Table XLV. 

 Here = *17, < = "83, since the argument of n proceeds by two units. 



We find 



c = 1-004,4477, c 8 = -000,1136, 



c 4 = -004,4752, CM = '000,0082, 

 c 6 = -000,0886, c 12 = -000,0057. 



* The eight figures are only kept for ease in continuous working. 



