NavList:

Gary,

I have finally read through this thread but rather superficially, so I apologize if this is repetitive. In one post you asked:
"Were the Itasca's officers simply wrong and they should have also calculated the new value if they had been accurate? "

Yes, I think that's the correct analysis. It's only a minute of arc. Without details on their methodology, there's no way to figure out the exact source of such a small error. The earlier 19th century position is also not an atypical error, five miles, for that era. Would Noonan have been surprised by a one mile error in the position? Surely not. Would he have planned for some margin of error in the island's position? Did their lives really depend on an accurate position of the island --accurate to the nearest mile??

You also asked:
What would a celestial navigator determine the longitude of the island to be if he took the observations tomorrow? "

Yes, within a fraction of a mile in both latitude and longitude the astronomical fix would match the WGS84 position.

Richard Langley already mentioned the 5 arcsecond offset of the Prime Meridian. After that, the deflection of the vertical is on the order of 10 seconds of arc in level terrain. Near mountain ranges or other large changes in local mass distribution which have not isostatically "evened out", deflections of one minute of arc or more are possible. If I remember correctly the maximum difference found on the ocean is something like 1.5 minutes of arc (off the coast of South America near the Peruvian Andes?). In mid-Pacific, away from the great deep sea trenches which have significant gravitational anomalies, the deflections should be almost always less than a tenth of a nautical mile. There's nothing that I can see in the gravity maps indicating anything out of the ordinary near Howland Island. It's flat out there.

Thinking aloud now... The low values of the deflection of the vertical on the Earth's surface are to some extent a pre-requisite for useful celestial navigation. Imagine if we lived on a lumpy asteroid where the vertical was deflected by several degrees at different locations. With luck, we would probably still have a one-to-one correspondence between astronomically-derived fixes and points on the surface, but it would be no simple picture: the latitude and longitude lines derived from celestial navigation sights would be wavy lines on the surface.

By the way, I agree with Alex (I think he made this point), as for early reported positions of Howland Island, these would have been necessarily actual astronomical latitudes and longitudes. It would not have been possible or desirable to reference them to any of the early ellipsoids.

-FER

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