286 
On Corrections for Moment-Coefficioits 
s = 4: 
s = b 
d'Z' 
d-'Z'' 
dx^ 
'd'Z'' 
'dZ^~ 
dx _ 
d'Z' 
dx' 
d'Z' 
dx^ 
d-'Z'' 
dx"' 
d^Z^ 
dx'-' 
6, 7- -a, 
X. 
= 0, g>4; 
3024(-(|\ + |i))iV 
ftp /io 
d^'i+'Z'' 
~diif-'i+^ 
- 60 (b, "f- + a, - 60*-o^) N, 
' ' + 2100 ( 6, % - a, 5l 
-42Oo(6,i+<..g) + 252o(A_0))i^. 
15120 f-'^+a, 
= 0, g > 4....(vii). 
(4) We have now to see the relation of the present integral I Zx^'dx to the 
moment-coefficients. Integrating by parts we have 
Zx^da 
1 
+ 
yx 
dx 
Nxo' 
+ 
N 
s+1 s+1 
s+1 
where /Lt'^+i is the (s + l)th moment-coefficient about the arbitrary origin. Accord- 
ingly we have, changing s to s - 1, 
^ j ' Zaf'^dx (viii). 
