NavList:

 David,    you said:

These numbers tell me three things:

• The observations were accurate to <0.3'. This is to be expected given that they were taken on land by an experienced Extra Master who was Nautical Adviser to the NZ Government and also Examiner of Masters and Mates.
• There were errors in Blackburne's reduction method. This was acknowledged by Blackburne.
• The concept of a datum is meaningless when comparing observed  positions.

II think your third point is not valid.  When looking at your GPS to fix a place it is not the same datum as what was used back in 1902.  Even today, if you stand on the line in front of the Greenwitch Observatory the GPS will not show zero longitude.  Because the earth is not a ball but a squished grapefruit the equations used by navigators would have to be tweeked to compasate for the real shape.

You live near the antipode so my thinking is the difference would be more than other places.  So long as you use almanac data based on Greenwiitch for cel-nav and GPS, which is not based on Greenwitch, there will be built in error.

Also, rember the limitations of cel-nav.  Even if you had a perfect sextant it will only read to .1 minute.  The almanac, for the sun, is only accurate to .25 minutes GHA and because you record the time of the sight to only a whole second there will be a built in error of .25 minutes of GHA.  Sometimes, the errors cancel but you cannot count on it.

The sextant sight back in 1902 was excellent, but will never be GPS.

Thanks again for providing the problem and the data.  I enjoy working out sight reductions from real people from old.  I use sin-log-cosine tables and the law of cosine formulas for both time sights and St Hiliarie  Lots of fun.

John H.