NavList:

Francis, you wrote:
"Slocum says his old tin clock remained asleep. He estimated local time from LAN noon LAT? Correct?"

No! He got local time from the altitude of the Sun, which was measured anyway as part of the lunar sight process. The time sight came directly from the altitude of the Sun simultaneous with the lunar (at least that would be the normal process).

This was daily bread-and-butter navigation right through the middle of the 20th century. Latitude was determined by the meridian passage of the Sun at noon, the standard noon sight. Local time was determined by an afternoon or morning time sight, typically taken three hours from local noon (so 9am or 3pm) or at some other fixed time on the schedule. This was just an altitude of the Sun converted into local time. In effect, the time sight treats the sextant as an accurate sundial. The result of this observation is a time. If the observation was taken when the shipboard (local time!) clock said 3:00 pm, its result might be something like 3:06:40 --the difference from exactly 3:00 arising primarily from the change in longitude since the last time the local time had been determined. This local time would then be compared with Greenwich time which could come from a chronometer or from a lunar (after 1850, in 99% or more of cases at sea, GMT came from a chronometer). And then, assuming we've dealt properly with mean time versus apparent time issues (details varied depending on the decade) longitude follows very simply as the time difference converted to degrees at the usual rate of 15 degrees per hour.

You wrote:
"How did he "advance" the noon LAT to the time of the lunars without any clock?"

He didn't need to. From the earliest use of lunars, this basic concept was standard, essential, even trivial. The Sun-Moon distance yields Greenwich time, and the Sun's altitude (if it's not too close to noon) yields local time. Actually the tricky part was when navigators went beyond this basic technique and realized that they didn't necessarily need the local time to get something useful out of lunars, but that's another story.

And you wrote:
"Even Cook on Endeavour needed a reasonably accurate watch to advance time sights"

It helps, and pocket watches were common and accurate from the middle of the 18th century, but it wasn't necessary. If you had a common watch, then you had more options. Slocum was playing "old timer" and maybe "curmudgeon" and definitely "cheap Yankee" by not bringing along a decent pocket watch. If you had one, you had more options; you could take the time sight when convenient and take the lunar when convenient. The altitude of the Sun for the lunar clearing process only needed to be accurate to +/- 5 minutes of arc --no problem. But if you were also using it for local time, then, of course, you want it to the nearest minute of arc (since the logic that a minute is a mile is true no matter what). But only a bit more work and care in the sight timing was required to get the local time from the Sun's altitude without a pocket watch.

You added:
"My "no clock" method uses "simultaneous" :LDs, and moon and sun alts. I then do classic St Hilaire moon and sun LOP using the lunar GMT to get a 2 body fix. But I think Slocum did not use this, correct? "

Your two-body "fix" yields latitude and local time. If you vary GMT, that just shifts the fix east or west in longitude. It's the same thing, right? Since modern navigation methodology uses GHA, you never see the local time, but it's in there, naturally. I'm sure you're thinking right now, "Of course!! I should have seen that."

You concluded: "See attached paper."

That paper from 1997 is ancient history. It's a nice example of the illusion of "journals of navigation". That seemingly scholarly "paper" is really no more significant than any of a hundred NavList messages in the past dozen years. And he's got it all wrong with his focus on mathematical theory. Like too many "math geeks" who have attempted to understand lunars, he treats it as a math problem that has to be "solved" with a trigonometric analysis (and a bad one, at that), failing miserably to understand that the problem had been long solved and converted into multiple simple cookbook recipes --bearing NO RESEMBLANCE to the pedantic math that he includes in the paper-- over a century before Slocum shot his single lunar on that circum-navigation. That paper is wrong-headed in almost every way --not wrong on factual details, but seriously misleading in its emphasis and analysis. Slocum didn't do any trig. Or putting it differently, he didn't know he was doing any trig.

Slocum's single lunar observation and his account of it in his memoir "Sailing Along Around the World" was a fine epitaph for lunars, but it's a real shame that people continue to treat it as an object for historical navigation study. Slocum was not a math genius, not an "expert" in lunars. He jjust knew how to work 'em. Slocum was a throwback, an anachronism... and he knew it, too. Lunars had been irrelevant for decades when Slocum wrote his story. Studying Slocum's lunar observation in 1997 (or 2015) as an example of "traditional lunars" would be like someone in the 22nd century studying the altitude observations of one of the backyard enthusiasts on NavList today as examples of "traditional celestial navigation" (and for you 22nd century navigation historians reading this a hundred years from now, don't make that mistake!!).

Frank Reed