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THE  ARCTIC  REGIONS               45

           invisible  to an observer whose zenith is Z.  Corresponding to this
           total  disappearance  of the  sun  for  some  time,  the  luminary  will
           be  perpetually  above  the horizon  for  the  same  period during his
           northern course.  For instance, let the sun be at d,  then his diurnal
           circle  of rotation,  dH'  will  be  entirely  above  the  horizon  H' H,
           and  so  it will  continue to  be for all  the time  that the  sun moves
           from  d to E,  and  back again  from  E  to d,  in  his  annual  course.
           During this  time  the  sun will  neither rise  nor set,  but will  move,
           like  the  circumpolar  stars,  in  oblique  circles,  round  and  round
           the observer like a  wheel.  For all  positions between n and d,  and
           the  corresponding  portion  of the  ecliptic  on  the  other  side,  the
           sun, in his diu~nal course of twenty-four  hours,  would be partially
           above  and  partially  below  the  horizon,  producing  ordinary  days
           and nights,  as  with  us,  the day being  longer than the night when
           the sun is in the northern, and the night  longer than the day when
           the sun is in the southern  hemisphere. Instead of a single day and a
           single  night  of six  months,  the  year,  to  a  person  living  in  the
           Arctic  regions,  but not exactly at the  North Pole,  will,  therefore,
           be divided into three parts, one  of  which  will  be  a  long  night,
           one  a  long  day,  and  one  made  up  of a  succession  of  days  and
           nights,  a single  day and night of which will  together never exceed
           twenty-four  hours.  fhe  long  night  will  always  be  shorter  than
           six months  and  longer  than  24  hours,  and  the  same  will  be
           the case with the long day.  The long njght and the long day will
           mark  the  two  opposite  extremities  of the year,  the  middle  of the
           long day occurring when the. sun is at the summer solstic.e,  and the
           middle  of the  long  night  when  he  is  at the  winter  solstice.  This
           triple  division  of the  year  is  very  important  for  our  purpose,
           and I shall, therefore, illustrate it by a concrete example.  Suppose,
           for  instance,  that  the  observer  is  so  far  below  the  North  Pole
           that instead of a night of six  months,  he  has  a  night of 2 months,
           or,  in  other  words,  the  sun  goes  below his horizon only  for two
           months.  As  the winter  solstice will  fall  in the middle  of this long
           continuous night,  we  may say that the night will  extend  a  month
            before and a month after  December 21,  when the  sun  is at  the
            winter  solstice.  Corresponding to this  long  night,  there  will  be a
           continuous  day  of  two  months,  a  month  before  and  a  month
           after  June  21,  when  the  sun  is  at  the  summer  solstice.  If these
           four  months  are  deducted from  the  year,  there will  remain  eight
            nsonths, ant'  -:luring all these months there will  be days and nights,
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