FIG  7la


The  "curve  of  force"  in  Fig.  71a  has  ordinates  lepresent-
ing  successive  values  of  the  moment  of  the  impressed  forces
acting  on  the  ship.  For  example,  in  the  case  under  con-
sideration, the  moment  of  the  impressed  forces  at  any  time
includes  the  instantaneous  righting  moment  and  the  instan-
taneous moment  of  resistance.  During  certain  parts  of  the
motion  of  the  vessel  the  instantaneous  righting  moment  tends  to
add  to  her  angular  velocity,  while  the  moment  of  resistance  tends
to  diminish  it;  the  corresponding  ordinates  of  the  force  curve
then  represent  the  differences  between  the  moments.  During
other  parts  of  the  motion  the  righting  moment,  as  well  as  the
moment  of  resistance,  tends  to  retard  the  angular  velocity ;  and
the  corresponding  ordinates  of  the  force  curve  represent  the  sums
of  the  moments.  In  building  up  the  force  curve  it  is  necessary  to
know,  therefore,  instant  by  instant  the  inclination  of  the  masts
of  the  ship  to  the  wave-normal  and  her  angular  velocity,  because
the  instantaneous  righting  moment  depends  upon  that  incli-
nation, while  the  moment  of  resistance  is  governed  by  the
angular  velocity.    The  process  is  really  one  of  "  trial  and  error,"


CHAP.  VI.  OSCILLATIONS  AMONG   WAVES.  239

but  each  step  admits  of  a  complete  check  and  verification  in
consequence  of  the  inter-dependency  of  the  curve  of  inclinations
and  the  force  curve.  In  practice,  the  work  of  graphic  integration
can  be  rapidly  performed,  and  after  certain  preliminaries  have
been  arranged  in  any  particular  case,  the  remaining  steps  are
very  simple.
