A Chance of a Lifetime

A maritime 'one in a lifetime chance'.

The passenger  steamer SS Warrimoo was quietly knifing its way through the waters of the  mid-Pacific on its way from Vancouver to Australia. The navigator had just  finished working out a star fix and brought the master, Captain John Phillips,  the result. The Warrimoo's position was LAT 0º 31' N and LON 179 30' W.   The date was 31 December 1899.
"Know what this  means?" First Mate Payton broke in, "We're only a few miles from the  intersection of the Equator and the International Date Line".  Captain Phillips  was prankish enough to take full advantage of the opportunity for achieving  the navigational freak of a lifetime.

He called his navigators to the  bridge to check & double check the ships position.  He changed course  slightly so as to bear directly on his mark.  Then he adjusted the engine  speed. The calm weather & clear night worked in his favor.

At mid-night the  SS Warrimoo lay on the Equator at exactly the point where it crossed the  International Date Line! The consequences of this bizarre position were many:

The bow of the  ship was in the Southern Hemisphere & in the middle of summer. The stern was in  the Northern Hemisphere & in the middle of winter.  

The date in the  aft part of the ship was 31 December 1899.  In the bow  (forward) part it was 1 January 1900.

This ship was  therefore not only in two different days, two different months, two different  years, and two different seasons, but it was also in two different centuries -  all at the same time.

According to this, there are only 4 possible positions the ship could have been on the equator, all relevant.