AVe  now  have  to  consider  the  portion  we  have  left  out  below
No.  6  water-plane.  Such  a  volume  as  this  is  termed  an
"  appendage."  The  sections  of  this  appendage  are  given  in  the
body-plan  at  the  several  stations.  The  form  of  these  sections
are  traced  off,  and  by  the  ordinary  rules  their  areas  .are  found
in  square  feet.  We  have,  therefore,  this  volume  divided  by  a
series  of  equidistant  planes  the  same  as  the  main  solid,  and  we
can  put  the  areas  of  the  sections  through  Simpson's  rule  and
obtain  the  volume.  This  calculation  is  done  on  the  left-hand
side  of  the  sheet,  the  areas  being  placed  in  column  3,  and  the
functions  of  the  areas  in  column  4.  The  addition  of  these
functions  is  49*99,  and  this  multiplied  by  ^  x  7*1  gives  the'


Moments,  Centre  of  Gravity,  Centre  of  Buoyancy,  etc.    69

volume  of  the  appendage  in  cubic  feet,  viz.  118-3;  and  this
volume  divided  by  35  gives  the  number  of  tons  the  appendage
displaces  in  salt  water,  viz.  3*38  tons.  The  total  displacement
is  thus  obtained  by  adding  together  the  main  solid  and  the
appendage,  giving  91  '3  6  tons  in  salt  water.  The  displacement
in  fresh  water  (36  cubic  feet  to  the  ton)  would  be  88' 8  tons.
