The  two  triangles  formed  by  one  diagonal  are  first  closed  by
correcting  the  four  angles  of  each  b}^  one-fourth  of  the  closure-error
for  the  triangle.  One  of  the  other  triangles  is  then  closed  by  cor-
recting each  of  its  four  new  angles  by  one-fourth  of  its  closure-
error,  which  correction  is  also  applied  to  the  remaining  four  angles
(of  the  fourth  triangle),  with  the  opposite  sign,  so  that  all  four
triangles  are  thus  satisficnl  exactly.     Taking  the  pole  for  the  side

1  Due  to  Prof.  T.  W.  Wright.
ADJUSTMENT  OF  TRIANGULATION  119

equation  at  the  intersection  of  the  diagonals,  each  of  the  eight  new
angles  is  corrected  by  one-eighth  of  the  error  of  closure  of  the  log-
sines  divided  by  the  algebraic  mean  of  the  eight  differences  for
1",  the  angles  on  the  right  being  corrected  with  the  opposite  sign
to  those  on  the  left,  so  as  to  bring  the  sums  of  their  logsines  closer
together.  If  the  eight  angles  were  equal,  the  side  equation,  also,
would  be  exactly  satisfied  by  this  method ;  in  this  case  the  figure
would  be  a  square.
