What  is  the  shortest  distance  from  the  point  left  to  the  point
reached  ?

Solve  the  same  problem  for  latitude  45°,  60°,  etc.
Traverse  Sailing.
135.  Traverse  Sailing  is  the  application  of  the  principles
of  Plane  and  Middle  Latitude  Sailing  to  cases  when  the  ship
sails  from  one  point  to  another  on  two  or  more  different
courses.  Each  course  is  worked  by  itself,  and  these  inde-
pendent results  are  combined,  as  may  be  seen  in  the  solution
of  the  following  example  :

136.  Leaving  latitude  37°  16'  S.,  longitude  18°  42'  W.,  a
ship  sails  N.E.  104  miles,  then  KN.W.  60  miles,  then  W.  by
S.  216  miles.  Find  the  position  reached,  and  its  bearing  and
distance  from  the  point  left.
We  have,  for  the  first  course,  difference  of  latitude  73.5  N.,
departure  73.5  E.
We  have,  for  the  second  course,  difference  of  latitude,
55.4  K,  departure  23  W.
We  have,  for  the  third  course,  difference  of  latitude  42.1  S.,
departure  211.8  W.
On  the  whole,  then,  the  ship  has  made  128.9  miles  of  north
latitude,  and  42.1  miles  of  south  latitude.  The  place  reached
is  therefore  on  a  parallel  of  latitude  86.8  miles  to  the  north  of
the  parallel  left ;  that  is,  in  latitude  35°  49.2'  S.
The  departure  is,  in  the  same  way,  found  to  be  161.3  miles
W. ;  and  the  middle  latitude  is  36°  32.6'.     With  these  data.
MISCELLANEOUS    EXAMPLES.  99

and  the  formula  of  Example  123,  we  find  the  difference  of
longitude  to  be  201',  or  3°  21'  W.  Hence  the  longitude
reached  is  22°  3'  W.
