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In describibg Halley's method for lunars, I referred to the

>> [... ]line though the horns continues sweeping through the
>> stars at constant speed.

and Herbert Prinz asked-

>This line is not necessarily perpendicular to the ecliptic. Does Halley correct
>for this or confine himself to cases where it is?

The Moon can indeed be 5deg or so off the ecliptic, and as long as the Sun
is well-spaced, that line through the horns can deviate from being
perpendicular to the ecliptic, by up to 5 deg, perhaps a bit more. That
would have given rise to an error in the difference between ecliptic
ecliptic longitudes of Moon and star, which would be greater as the
passing-distance increased. Whether Halley had any way to correct for this,
I just don't know (but rather doubt it). He has left us little information
about the details of how he worked.
>
>> Even parallax matters little
>> if a star can be chosen which passes the horn-line near the time of Moon's
>> meridian passage.
>
>If the Moon passes through the meridian you can still have considerable
>parallax in longitude. The question is whether the ecliptic is perpendicular to
>the vertical through the Moon. If this is the case alone, the parallax in
>altitude affects only the Moon's latitude and does not interfere with the
>observation of the conjunction.

Herbert is right. But I doubt if Halley was expecting to get his Moon
ecliptic-longitudes to within a minute. It's hard to tell how accurately
his longitudes turned out. They enabled him to plot a point in mid-ocean
where he could measure variation. Bat as he wasn't carrying a GPS receiver,
it's hard for us (or him) to know how accurate his positions were.

George.

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