2U 
On Corrections for Momex f -Coefficients 
Using (iii) we determine from 
«/ = -6208,3294 
??/ = -2634,5480 
71/= -0875,0592 
= -0227,3545 
-0046,2849 
the values : a/ = - -878,708, 
aJ = -607,984, 
a/ = --296,843, 
«/= -081,723, 
a/= -005,736. 
Whence 
a,' 
- wo'-h' + «r.' = - -873,758, fl,' 
-(n5«/+ ^ioa/ = - -855,125, a,' 
l-ff,/ = + -604,741, 
/-a/ = + -600,833. 
The corrections due to these abruptness coefficients by (xxii) — (xxv) are for v^, v^'' 
v-i and Vi respectively 
-•072,813, --005,040, + -021,378 and + -004,769, 
while the corresponding Sheppard's corrections are 
0, --083,333, --257,378 and - -817,830. 
Thus we deduce for moment-coefficients about stump : 
"1 
"2' 
"3' 
Raw moment 
1-029,513 
1-693,994 
3-883,416 
10-974,937 
With Sheppard's 
corrections 
1-029,513 
1-610,661 
3-626,038 
10-157,107 
These values are in working units = '5 actual units. 
Full corrections 
•956,700 
1-605,621 
3-647,416 
10-161,876 
Hence in actual units 
we have 
"4' 
Raw moments 
•514,756 
-423,498 
-485,427 
-685,934 
"3 -4"! 
With Sheppard's 
corrections 
•514,756 
•402,665 
•453,255 
•634,819 
Ml' 
With full 
corrections 
•478,350 
•401,405 
•455,927 
•635,117 
True values 
•478,8131 
-401,4837 
•455,7714 
-634,7360 
"4 -^VO +7;|jJ 
It will be seen from these results that our full correction values for the moments 
about the stump are in every case accurate to 1 in the 1000, while, if Sheppard's 
corrections only are made, we may be out nearly 1 in the 100. The change in the 
moan, second and third moment-coefficients is very noteworthy. In the case of the 
fourth moment we are out '0004 in -6347, while the Sheppard's correction alone is 
out only -0001 in -6347. The cause of this irregularity we have not been able to 
detect, although we have examined carefully the whole of our arithmetic. It 
seemed accordingly worth while inquiring what differences would occur when the 
moment-coefficients were taken about the mean and not about the stump. 
"2 
"3 
»'4 
Raw moments 
about mean 
-158,524 
•104,226 
-149,090 
''2-,V(-5)- 
"3 
-4-2»'2(-5)Holo(-5)' 
With 
Sheppard's 
corrections 
-137,691 
•104,226 
•131,097 
M4 
With full 
corrections 
•172,587 
•098,801 
•156,767 
True values 
•172,222 
•098,612 
•156,405 ' 
