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Gary,
Thanks very much for your in-depth explanation. I find that it was the 
declination giving me trouble, and I finally realized I was subtractng 30' 
for the "d" correction, not 0.5' as I should have. (Half a degeree instead of 
half a minute!) So for the time of the sight I (eventually) got a declination 
of 18d 59.8'S and the correct latitude of 55d 37.8'S.  Whew!

As an aside, you asked why I thought there was a 12-minute time span between 
the time of the shot and LAN for the DR longitude.  I converted his DR 
longitude of 68d 25' to time, and got 4h + 32m + 100s, or 16:33:40.  I 
figured that meant that the sun would be over his meridian at that time.  The 
shot was made at 16:46:20, which is 12m and 40s later.  Did I go wrong on 
that reasoning? Did the navigator make his shot when he did, rather than when 
I would have advised him to had he asked me, simply because he recognized 
that his DR was not likely to be close enough to make the difference 
significant?   

Or, as another reader suggested, was this perhaps meant to be an "ex-meridian" 
sight?  In that case, as I eventually found in Jeff Toghill's "Celestial 
Navigation," the observed altitude should be corrected for the time 
difference by factors found in Bowditch.  (The tables referred to were 29 and 
30, though in the 2002 Bowditch they are now 24 and 25.)  I plan to rework 
the problem from that perspective and see what I get.

Thanks again for your patience and thoroughness.  This list is like having 
dozens of expert tutors on call!

John


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