NavList:

George wrote:

"Frank Reed quoted the following interesting letter (which had little
connection with Jefferson, except as the recipient)."

 

There's more connection if you read further (I don't think there was any need to bother with a new thread title!)

 

First things first. The LOC web site behaves a little oddly, and I don't think the previous link I gave will work directly. So let's try this web link:

 

At that address, enter "lunar Dunbar" (without quotation marks) in the "Search all collections" box. That will call up the letters back and forth between Dunbar and Jefferson on this topic. Jefferson was personally interested in longitude observations, as we've discussed previously with respect to the Lewis & Clark expedition.

 

Here's another snippet you'll find if you visit this site:

"We shall I hope soon be able to make Satisfactory lunar observations for the ascertainment of the Longitude if not at this place, in its neighbourhood; I have a most excellent instrument for this purpose, being a Circle of reflection Supported upon a pedestal, which last facilitates greatly correct observations on land; this is wanting to the Sextant brought by ..."

 

Lots of interesting little details like that.

 

George you wrote:

"This accords with a suggestion Frank made recently, (in a posting that I've
inadvertently deleted), that changes in Moon declination, rather than in
lunar distances, might in theory be used to determine Greenwich Time."

 

Just to clarify, I wasn't suggested anything like that, in the sense of advocating it. I did bring it up once before in reference to this same web site just to see if anyone might find it interesting, but no one bit the bait on that first pass --hence the longer quotation this time.

 

And:

"But first, there seems to be an error on Dunbar's part, or a transcription
error since, that makes Dunbar's proposal seem more impractical than it
really was."

 

There are certainly transcription errors, especially on numerical matters, but the original scans are available on the web site so you can check for yourself.

 

And:

"Twice in the month the declination stops
changing, and anywhere near those times Dunbar's method would be quite
useless."

 

Indeed. As he says! But this once again points up the differences between terrestrial surveying and navigation. On land, you can wait a week.

 

And George wrote:

"He doesn't go into the details of this calculation; with the
Moon's dec. changing so fast, there can be a large interval between the
moment of max altitude and that of meridian passage, which has to be
carefully allowed for, in a way as yet unexplained."

 

Quite so. Do read those letters on the LOC web site. You'll find that Dunbar discusses this very issue in yet another of his letters to the busy President.

 

And George wrote:

"Well, it seems clear, with hindsight, why Dunbar's proposal failed to
"catch on". One of those ingenious methods which might be all right in
concept but which fails to do the job in practice."

 

You really should read the letters. There's plenty to be learned about the practice of practical astronomy in the early 19th century in those letters --plenty that is wrong along with plenty that is right. Understanding the common misconceptions of the era is every bit as important as understaning the common good sense.  For example, go to pages 1319 and 1320 of the scanned image versions of the correspondence. There you will find a complete observation of the Moon's max altitude worked out (for longitude!) in excruciating detail. He gives altitudes measured to the nearest quarter of a second of arc. In his conclusion he gives the longitude (in time units) to the nearest hundredth of a second. And then, for comparison, Dunbar gives a lunar eclipse-based longitude to the nearest half-second of time. We know that those extra digits have no significance today --they're garbage. But in the early 19th century, this was a common misconception. They had little appreciation for the difference between accuracy and precision and the concept of significant digits.