238 On Corrections for Momeid-Coe§iclents 
where v-^ = moment about the origin of the subrange frequencies concentrated at 
their mid subrange points. Similarly 
1 
iTr S \{ic„ + {u - i) h)" - Ih- - x^} Vu 
iV „ = i 
= v^-lli'-x,- (xi); 
\ {sG.-,%^, = ~ |- ^' (.^„ + nhf + (.r. + f + I (.'.0 + nh) - ,v - |" 
= V:'-i/;-7V-P'a'o-^o' (xii); 
^ (sC, .0.^4 = ^' I - (.T„ + '»7/,)^' + {x, + «// )^ + /r + f 
= 4 + - I) )' - 2 (•'•o + ( " - i) ^')' + tV^'^ - ^'-^"'! 
= v: - ^ /(=7'o' + ^yh' - x,-> - h?x,^ (xiii) ; 
1^ + {x„ + vhf + (.ro + 
, \ {sC,^,\^, = 4 S {- {x„ + uhy + (x„ + vhf + ^h^ {X, + uhf 
= ~ s {{x„ + (n-^)hy-^hHx, + (u-h)hy 
+ ^^//^ (.r„ + (m - i) /O - - S/'W + 
= 4 § {(.'^^o + ("-i)/')"-f/i^'(*o + ("-i)/0^ 
+ j^i* {x, + {u - 1) hy - ^\ A" - x,^ - p.^T,,^ + l//^^o'') nu 
= i^; -^)vv,' + j^jjh'v.;/ - j?jh' - V - ^h-x„' + Vi'x,r (xv). 
(5) We can now put together the complete formulae for the corrected moment- 
coefficients about any origin from the values we have obtained for the component 
parts of (ix), but we may first simplify our notation slightly so as to abbreviate 
somewhat the lengthy resulting expressions. We write pp — h/hp, p„ = h/lia ; these 
will very frequently be unity. Next we put Z>/ = 6sp/, «/ = fls/5,/, and Xp/h = Xp, 
ii-^^jh = x„' : thus for terminal units the same as for the bulk' of the frequency we 
