246 Oil Corrections for Momeut-Goefficients 
(8) Illustration II. (b) We now propose to consider the moment-cocfficienta 
of a doubly truncated normal curve. We will take the portion of the above 1 ,000,000 
distribution with unit standard deviation from variate value 1"25 to vaiiate value 
3'75 and divide it into five groups, i.e. 
Absolute Relative 
frequencies frequencies 
65,591 -6213,5637 
27,834 -2636,7693 
9,245 -0875,7969 
2,402 -0227,5462 
489 -0046,3239 
Total 105,561 Total 1-0000,0000 
Using (iii) and (iv) which now involve all five groups we find 
(,, = -•8794,4917, 6, = - -0038,5527, 
a.,= -6084,9651, k= -0258,2393, 
03 = --2970,9362, 6, = - -0401,0477, 
a,= -0817,9157, b,= -0530,8779, 
= _ -0057,4076, b, = -0057,4076. 
From these results, since as = a"s and ^'s = b"s we have for the abruptness functions : 
«/ - 0*0 «:/ + 25V0".-; = - -8744,9989, 6/ - ^^6/ + ^^b^ - - -0031 ,8458, 
"/ -riu"/ = -6052,5081, b.: - j^j.b,' = -0237,1727, 
< - tt1j«/ + 2io«'/ =--8558,9423, V - tfli V + 2^0^./ =--0006,4843, 
«2'-8V«4' = -6013,3975, b.^-^^b; =-0211,7875 
About the first terminal we have for the raw moment-coefticients 
= 1-025,630, v.: = 1-668,535, v.; = 3-733,74;3, = 10-108,966, 
and by (xxii) — (xxv) the corresponding corrective terms are 
-•0731,4037, --0074,9994, +-0044,7459, --0981,1.557, 
leading to the Sheppard's correction moment-coefficients in actual units : 
yu/ = -512,815, yu,' = -396,300, /t^/ = -434,667, ya/ = -581,492, 
and the full correction moment-coefficients : 
/i/ = -476,245, fi.; = -394,425, fi,' = "435,226, /i/ = -575,360. 
We now transfer to the mean of the block and find 
yu/ = -476,245, /A., = -167,616, ytij = -087,7305, yu, = -128,691, 
while the values for the Sheppard's corrections only would be 
/i/ = -512,815, yUo = -133,321, = -104,701, = 107,714. 
The theoretical values for the normal curve block are 
yu/ = -476,930, ya, = -168,025, fi, = -089,730, /x, = -133,743. 
