420 The Incomplete Moments of a Normal Solid 
Transposing and integrating 
1 r^' fi^' 
+ '-^ ^, r . / (*■', k') dx' - ^ . z' {x', k') (96), 
1 — ^\ • ^ • ^ = — ^ "-M + — ■ ~ ^ »,» ^- ■ -(97), 
that is 
2/1 9\ • ■ n+1,0 ■;(— 1,0 I /I „v • -O n 0 
a^Hl-r^) ay • ay ' o-^o-,^ (1 - r^) ay. o-^^oj^ 
where % = ^ (A, ^;), see equation (10). 
KB 
Reducing by one degree and dividing out by — r , 
^l/^X \^ f ) 
5',,o = ^ + (n - 1) (1 - r=) ajB',_,,, - ^'—^^f^ (1 - r^)...(98). 
ay AiJ 
Hence = - ^| (1 - .■^) (99), 
and we may write 
5'„,o = „ + („ - 1) ( 1 - r^) a,^B',^,^, + f ^',0 - . . .(100). 
Divide throughout by cr^"(Vl — ?•")" and write 
ay^l^f^ = Sy, 
-BVo^rF i?^„_,,o ^'„-.,o B\, rk' A'»-^ .^^^ 
then ^„ = + (n - 1) /3„_2 + t«-iySj - ri**-' « (103) 
Putting n = \ in (81), 
o"x Vl — r~ ay Vl - -^-S 
/ /( — rk \ 
...J 
Vl - 
r„ Vl - 7-2 \/l - ^^,k-rk 
o-yVl-r^ ^ fh ja^-rJc I 
- (t - r/e) 
o";/ Vl — r- S (i — r/t) 
= + (104), 
where is the centroid of the face B. See equation (16). 
