NavList:

Don S, you wrote:
"Of these entries, two were made within two days of the first quarter moon, and four were made within one day of the last quarter moon."

That confirms it then: those longitudes aboard USS Constitution in 1814-15 "by obs" were almost certainly "by lunar". Lunars at sea in common use were mostly Sun-Moon distances (something like 80% of the cases I've seen), and of those the most common were shot within a day or two of first or last quarter. There are good reasons for this. They're visually easier. A half moon shows nice contrast in the daytime sky. 

There are also mathematical simplifications that occur when the distance is near 90°. When using a series method, the quadratic terms go to zero for distances near 90. Also, something they did not necessarily know in the era (see PS) was that the altitude of the Moon did not matter much for distances near 90. You could be off by a whole degree, and it might not matter. Despite having likely direct knowledge of these mathematical aspects, I suspect that navigators were taught (in actual classes or by other navigators) that they could get better results near first and last quarter. It was certainly common practice.

As for DR longitudes, the expression DR comes up now and then, but as in the case you described, they referred to this as "longitude by account" especially in the first half of the 19th century. This was often shortened to "lon by acct" (obvious) or "lon per acct" or "lon ac" or even "lon a/c" (not so obvious!).

One other expression that we haven't discussed (recently) was "lon in". I've seen this label especially in the late 18th and early 19th centuries. It's an oddity. Apparently the "in" adds nothing. It meant "the longitude the vessel was in" apparently and writing just "lon" or "long" would have been sufficient. Does anyone know (or can anyone suggest) an alternate meaning for "lon in"?

Frank Reed
PS: The dependence of lunars on the accuracy of the altitudes was described in vague terms in most navigation manuals in the era. They might say something like "no great accuracy is required" unless the altitude of the Sun is also used to "regulate the watch" (get local time). The mathematical dependence does not appear to have been widely understood until I posted about it right here on NavList fourteen years ago on Halloween: Lunars: altitude accuracy. That same Halloween night fourteen years ago, I first described the 90 degree miracle which I have also outlined in this message.