Page 116 - statbility for masters and mates

104 Ship Stability for Masters and Mates
The volume of this wedge 12 y y2 dx
The moment of the wedge about the centre line 12 y y2 dx 23 y
13 yy3dx The total moment of both wedges 23 y y3 dx
about the centre line
The sum of the moments of all such wedges
But
L O
of the wedges
Butthesumof v gg1
the moments
where v is the volume of the immersed or emerged wedge.

I
I
L
23 y y3 dx L
y 23y3dx O
O
or
Now: and
or
Substituting in (I) above:
BM V I ; BM VI
The second moment 23 y3dx ofthewater-plane0
area about the ship s centre line ;Thesumofthemoments I y
; I y v gg1 I v gg1
y
BB1 v gg1 V
BB1 BM y ; BM y v gg1
V BM V v gg1
y