Moments,  Centre  of  Gravity,  Centre  of  Buoyancy,  etc.    61


Areas.
Simpson's
multipliers.
Functions  of
areas.
Number  of
intervals  from
forward.
Products  for
moments.
98

98

0

O

123
137
135

4
2

4

492
274
540

I
2
3

492

548
l62O

122

I                       122

1

4

488

1526


3148


Volume  =  1526  X  3  X  17^  =  8902  cubic  feet
moment  =  3148  x  \  X  i;£  X  17^

.*.  distance  of  centre  of  gravity  j  _  3*48  X  17*5  _    .^  ^^
from  forward  end  /  1526

It  is  always  advisable  to  roughly  check  any  result  such
as  this  ;  and  if  this  habit  is  formed,  it  will  often  prevent  mis-
takes being  made.  The  total  length  of  this  bunker  is  4  x
if  6"  =  70  feet,  and  the  areas  of  the  sections  show  that  the
bunker  is  fuller  aft  than  forward,  and  so,  on  the  face  of  it,  we
should  expect  the  position  of  the  centre  of  gravity  to  be  some-
what abaft  the  middle  of  the  length  ;  and  this  is  shown  to  be
so  by  the  result  of  the  calculation.  Also  as  regards  the  volume.
This  must  be  less  than  the  volume  of  a  solid  70  feet  long,  and
having  a  constant  section  equal  to  the  area  of  the  middle
section  of  the  bunker.  The  volume  of  such  a  body  would
be  70  x  137  =  9590  cubic  feet.  The  volume,  as  found  by
the  calculation,  is  8902  cubic  feet,  thus  giving  a  coefficient  of
=  0-93  nearly,  which  is  a  reasonable  result  to  expect.
Centre  of  Buoyancy.  —  The  centre  of  buoyancy  of  a
vessel  is  the  centre  of  gravity  of  the  underwater  volume,  or,
more  simply,  the  centre  of  gravity  of  the  displaced  water.
