25.  The  shade  of  an  opaque  plane,  or  plane  figure,  is  the  whole
of  one  side  of  such  plane  or  plane  figure.     The  former  being  of
indefinite  extent,  can  have  no  line  of  shade.     That  of  the  latter
is  its  perimeter.
26.  The  line  of  shade  of  any  plane-sided  body,  as  a  pyramid,
consists  of  those  edges,  collectively,  which  divide  its  illuminated
from  its  unilluminated  surfaces  (12).     This  line  of  shade  can
often  be  determined   by  inspection,  having  given  the  relative
position  of  the  body  and  the  rays  of  light.
The  two  following  problems  will  show  the  method  of  finding
lines  of  shade  on  plane-sided  bodies,  when  they  cannot  be  deter-
mined by  inspection.
8  GENERAL   PROBLEMS.
PROBLEM  I.
To  determine,  first,  ivhether  the  line  of  intersection  of  two  oblique
planes  is,  or  is  not,  a  line  of  shade  ;  and,  second,  to  determine,  by
inspection,  the  compound  line  of  shade  on  a  given  plane-sided  body.
First: — Principles. — After  finding  the  projections  of  the  line  of
intersection  of  the  given  planes,  by  Prob.  V.,  Des.  Geom.,  assume
any  point  on  that  line,  and  draw  the  projections  of  a  ray  of  light
through  it.  If  the  ray,  thus  given,  pierces  either  plane  of  pro-
jection between  the  traces  of  the  given  planes  on  that  plane,  it
shows  that  both  planes  are  illuminated,  both  being  pierced  by
rays,  and  hence  that  their  intersection  is  not  a  line  of  shade.  On
the  contrary,  if  the  ray  pierces  either  plane  of  projection  outside
of  the  traces  of  the  given  planes  on  that  plane,  it  shows  that  the
intersection  of  the  given  planes  is  a  line  of  shade.
