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George, you wrote:
"A mathematician is what he was, but that denigration might be compared with
what Wikipedia has to say about Chauvenet, as follows-
"In 1841 he was appointed a professor of mathematics in the United States
Navy, and for a while served on Mississippi. A year later, he was appointed
to the chair of mathematics at the naval asylum in Philadelphia,
Pennsylvania. He was instrumental in the founding of the United States Naval
Academy at Annapolis, Maryland."
I've little doubt that his navigational experience on "Mississippi" far
exceeded mine, or Frank's."

The impression you may have gotten is that he was a naval officer in the 
normal sense of the word --that he sailed the seas and shot lots of sights 
with his sextant. Chauvenet was not the ship's navigator or even one of the 
officers. The steamship Mississippi was the newest ship in the fleet, one of 
the first steamers in the US Navy, launched at the very end of 1841. The 
Mississippi was employed in trials and training during 1842 rarely (ever?) 
out of sight of land. Chauvenet was a TEACHER aboard USS Mississippi with the 
title/rank of "professor of mathematics" (in an era when 'professor' was 
synonymous with 'instructor'). This was at a time when there was no Naval 
Academy, so they experimented with, what we might call, on-the-job training. 
For about a decade starting in the late 1830s, the US Navy had about a dozen 
"professors of mathematics" aboard ships at sea. The experiment failed. 
Chauvenet was so disgusted with trying to teach under such circumstances that 
he resigned his post after just a few months. 

A few years later, Chauvenet was indeed an important contributor to the 
founding of the US Naval Academy and out of great respect for his theoretical 
knowledge, he was appointed as a professor there. Chauvenet was an all-around 
scholar, a mathematician, a really brilliant guy. There are few better 
sources even today for some of the mathematical and theoretical underpinnings 
of celestial navigation than Chauvenet's books. But he was not a practical 
man or a man with direct experience of practical matters in navigation.

And:
"Here, Frank is making invalid assumptions, in thinking about a small craft
with one single "navigator", and in temperate climates, who observes a noon
Sun each day."

Even large vessels in the 19th century often had a single navigator or at most 
a couple of them, working together closely. The evidence is in the logbooks. 
My assumptions were not "invalid".

And:
"He might otherwise imagine himself as a second officer of a vessel in Winter
in high latitudes, working watch-and-watch. He has been dragged out of his
pit to go on watch for four hours, in pitch darkness and overcast weather.
With short daily sunlight, his previous watch might well have been the same.
In rough conditions, he hardly knows which way is up, to start with, never
mind what Greenwich Time it happens to be. "

It's not as if your poor second officer is utterly lost at sea. He knows his 
longitude. That knowledge is always imperfect, but even if you haven't seen 
the Sun for a week, and even if you're half asleep, you know your longitude 
within a few degrees. So if my DR longitude is 45 degrees west (+/-3 degrees) 
and it's 6 in the morning aboard ship, then of course the Greenwich Time is 
right around 9 in the morning. Then you make the change for the almanac's 
"astronomical time". They KNEW how to do this. It was a standard calculation, 
but different from today in terms of practical procedure. A modern navigator 
who shoots the Noon Sun knows that he needs to get the Sun's declination 
correct so he looks at his "chronometer" and with that GMT, to the nearest 
few minutes, he enters the Nautical Almanac and finds the correct 
declination. But in the 19th century (and well into the 20th), the DR 
longitude was converted to time and *that* was used to get the approximate 
Greenwich Time and enter the almanac for the correct declination (for Noon 
Sun).

Of course, there is still some logic in the idea of a chronometer with a 
24-hour dial, but it was apparently not sufficient to sell them in practice, 
at least not in overwhelming numbers. But as I said previously, and as you've 
noted, too, keeping track of the day could be a real problem. Maybe they 
should have made chronometers that showed the day of the week...

-FER



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