NavList:

Jim Rives, you wrote:
"I wonder how accurate one could actually be in trying to do lunars on a rolling ship using the peep holes in the sights of a 17th century quadrant.  I suppose anything within a degree of longitude was better than nothing."

We have some useful evidence on this question in logbooks. Navigators sometimes shot lunars near identifiable islands or points of land, which might not have had accurate longitudes 200-250 years ago, but if we can identify the landmark today, we can compare against the longitude they determined by lunar. In many other cases, primarily in later decades a lunars were winding down, navigators would record multiple longitudes, and we can compare their longitude by chronometer with the lunar longitude How good were longitudes by lunar? Obviously, it depends, and that's not meant to be funny. Some navigators did better than others. Within thirty seconds of Greenwich Time was not unusual. That corresponds to an error in longitude of 7.5 minutes of arc which is about 5-6 nautical miles in mid-latitudes.

You mentioned a "rolling ship". A key feature of lunars is that there is usually little urgency. Lunars were always used in conjunction with some other method of determining longitude. An early navigator would always keep a detailed longitude "by account" (understood as "dead reckoning" today). By the early/mid 19th century a navigator without access to a superior chronometer might be able to get a low-quality chronometer that could be relied upon for a week or two, and then lunars could be used to correct it. But in neither case would we need to get a lunar "right this instant". Anytime over a period of a few days would be useful, and that's a great thing because it means they could wait for good conditions. Ship rolling too much this morning? Try again in the afternoon (assuming the Moon is still up), or try again tomorrow. Only when a navigator had some unusual reason to doubt the other source of longitude would a lunar become a matter of some urgency. This did happen, but it was rare.

You also mentioned "the peep holes in the sights of a 17th century quadrant". That "17th" was presumably just a typo for "18th", but the idea of using an instrument with a peep sight is a case of imagining the worst possible choice of tool. The reflecting quadrant was immediately proposed as a tool for lunars even in th 1730s. Lunars weren't really possible then so it didn't matter much, but as soon as twenty years later, reflecting quadrants (actually octants) had been expanded to sextant range, and anyone who wanted to shoot lunars (only becoming practical in the early 1760s) was advised to ask the instrument-maker for a sextant equipped with a good telescope. The resolution of the human eye alone is about one minute or arc or a little better (so-called 20:20 vision is, by definition, the ability to resolve certain visual features with an angular separation of one minute of arc). If we assume a navigator with good eyes, the best one could expect from a well-adjusted sextant without a telescope is around +/-0.7 minutes of arc which would yield a time error of about +/-80 seconds of time or a longitude error of about +/-20 minutes of arc. Stick a scope on that same instrument with 7x magnification, and basically all of that error goes away.

The errors that I have mentioned in this post are strictly the observational errors from the capabilities of the instrument. On top of those errors, early lunarians from the 1760s through the first decade of the 19th century had to contend with errors in the predicted lunar distances themselves. Various prizes were offered starting in the late 18th century so this soure of error faded relatively early, but it's important to remember that it's there. A navigator at sea had no option to improve the tables. 

Suppose you had +/-0.5 minutes of observational error in your lunars. And suppose the tables introduced an additional +/-0.5 minutes of arc of error. The net error would be about +/-0.7 minutes of arc (that's 0.5·sqrt(2)). It's not the simple sum of 0.5 and 0.5, because with random errors, you sometimes get lucky and one source of error cancels the other.

Frank Reed