252 
On Correctious for Moment-Coetficients 
Now our scheriie of action is of the following kind : we shall obtain the abruptness 
coefficients at x = 1, or at the finite ordinate of the first trapezette, for here they 
will be finite. We shall then trust to our auxiliary curve to give the moments of 
this trai)ezette about J' = 1, using the integral 
X = — (,f — 1)'' dx. 
dx 
And lastly we shall determine the moments and the corrections of the remainder of 
the cur've by the process already discussed as if it had to be applied from x = l 
onwards*. The moments for the trapezette before x = 1, and for the remainder of 
the curve, must then be added together to get the total moments and so the moment- 
coefficients about X = 1 . The transference to the centroid then proceeds in the usual 
manner. 
Moments of first trapezette ??i about non-infinite ordinate 
(XXIX ) 
Again remembering that 
E). 
we find 
a, = \{A+^B + bG+1D + 9E), 
«, = i (-A+SB + 15G + S5D + Q3E), 
(xxx) Ia, = l{A-B + 5G+35D + 105E), 
a, = -a (- 5A + SB - 50 + S5D + S15E), 
, a, = ^ {S5A - 155 + 150 - S5D + S15E). 
If we now substitute (xxviii) in (xxix) and (xxx) we shall obtain the moments 
of the first trapezette and the abruptness coefficients at x = 1 in terms of the first 
five sub-frequencies. We have 
p;i/^/'=--S12,7818H,-l--677,06yi«,--660,5497»;, + -347,1889/!4--073,7827«5, 
//,/i,"= ■706,7407«i--824,1137«., + -830,5586«;--441,5218«,4--094,3572?ia. 
^ " ' ^«,^/' = --(;34,7502H,-l--857,2689«,--880,7900n3 + -47l,4747H4--101,1083?i5, 
„j^;'= -581, 4517«, --8.54,1 1.49H„-f--888,8688«3--478,0407»4 + -102,7607n5, 
* The abruptness coefficients in the previous case were determined from the five frequencies following 
the initial ordinate; here they are found from the four frequencies following and the one preceding it. 
