of  the  strip  B'C  is ,  and  the  area  of  this  strip  is


35


The  area  of  the  curve  will  be  the  area  of  all  such  strips,  or —

fA  .  a .  dz

35

The  moment  of  the  volume  of  displacement  about  the  L.W.L.
is  given  by —

and  the  distance  of  the  C.B.  below  the  L.W.L.  is  found  by  dividing
this  moment  by  the  load  displacement  in  cubic  feet,  or —

[A.x.ds


J  WL  x  35
The  area  of  the  curve  divided  by  the  load  displacement  in  tons  is —

/"A  .  s .  dz


35


which  is  the  same  thing.
WL


Appendix.
249


Normand's  Approximate  Formula  for  the  Position  of  the
Centre  of  Buoyancy. — This  formula  was  given  on  p.  63.
-T-  is  known  as  "  Rankine's  mean  depth,"  and  we  may  for  con-
A

venience  say —


V


=  D


The  formula  then  becomes —

Distance  of  CB  below)
the  LWL  in  feet      )

In  Fig.  105,  let  ABC  be  the  curve  of  water-plane  areas,   DC
being  the  mean  draught  d.     Draw  the  rectangle  AFCD.    Make  DE

A.  D.
E.
FIG.  105.
=  D.  Draw  EG  parallel  to  DA,  cutting  the  diagonal  FD  in  H.
Finish  the  figure  as  indicated.  The  assumption  made  is  that  the
C.G.  of  the  area  DABC,  which  will  give  the  vertical  position  of
the  centre  of  buoyancy,  is  in  the  same  position  as  the  C.G.  of  the
area  DAHC.  This  is  seen,  on  inspection,  to  be  very  nearly  the
case.  These  two  figures  have  the  same  area,  as  we  now  proceed
to  show.
