INTO THE STRENGTH OF WROUGHT-IRON PLATES. 
I=I,-AX^ 
W/(Di-X) 
S= 
4l 
717 
(9.) 
( 10 .) 
and 
Z(Di-X)* • • 
. . . . (11.) 
0,-2 A2, (I3 A3, 
then 
X=0, I, = I, 
and 
I=yA,D;-2A,Di-2A,D”|, 
S: 
W/Di 
■ 41 
and 
SWTP, 
~4{A,Dl-2AJ)l-2AsDl} ' 
_ 4S ( A. D? - 2A,Bl - 2 AM) 
3/Di 
(12.) 
(13.) 
which expresses the breaking weight when S is given. 
Let D'l, D 2 , ..., A', A„ ... &c. be the corresponding dimensions of a beam in all 
respects similar, and let r be the ratio of the linear dimensions, then 
D',=rD,, &c., A'=r^Ai, &c., A 2 D 2 =r®A 2 D 2 , &c., A'iD'7=r^AiDi, &c. 
By equation (6.), 
"V ' X 2 D 2 + A 3 D 3 — 
~ 2A' 
+ r® AgDg — — r^%d^ 
~ 2^ 
2A 
By equation (8.), 
=rxX. 
i;=i{A;D;-A;D?-A;D?-a;rf?-«;rf;4 
=r‘ X A,D; — AjDI — A,D| — — ajrfsj 
By equation (11.), 
W'= 
=r^Xli. 
4sr 
z'(d;-x') 
4S X 7-^1 
?A^Di — rX) 
2 4SI 
=r^xW . . 
(14.) 
