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I wrote:
> The discrepancy is due to the deflection of the
> vertical, given by angles ξ (xi) and η (eta). The reference direction is
> the normal (perpendicular) to the datum's ellipsoid. If a plumb line
> intersects the celestial sphere north (east) of the ellipsoid normal, xi
> (eta) is positive.
>
> Another way to look at it: if astronomic latitude (longitude) is north
> (east) of the geodetic coordinate, xi (eta) is positive by that difference.

Correction to second paragraph: the longitude difference depends on eta
and latitude, due the convergence of the meridians. For example, if eta
= +10″ at latitude 34°, astronomic longitude is 10″ / cos 34° = 12.1″
east of geodetic longitude.

This can be ignored at Howland Island since it's practically on the equator.

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