NavList:

John Howard, you wrote:
" Patterson had developed a method of Lunars where you do not need to measure the altitude of the moon and the star or sun."

Also, such methods were well known. I haven't looked at Patterson's own approach, but there's nothing exotic in this. Of course, a method like this is of no use if there is no recent altitude of the Sun available. Longitude by lunars depends on a recent "time sight" (an altitude of the Sun for local time) just as much as longitude by chronometer depends on a recent time sight. If there's a good watch available, it can be "set" (or its error on local time determined) by a sight in the afternoon, and then lunars can be recorded in reference to that watch's local time.

You added:
"Hassler could not do the lunars thinking information was missing and declared that the two explorers messed up. Hassler apparently did not know Patterson's methiod #4."

But there's more to it than this. Clearly the longitudes were not considered terribly important. There were hundreds, perhaps thousands of people in the USA who could work lunars, especially in New England, but it appears that no effort was made to seek out any other expertise on the matter. Latitude and longitude coordinates aren't really that critical if you're travelling along a river, or several rivers, between known locations. When rivers are the primary highways, the branching network itself is the only map you need. Lat and lon have only academic interest (so long as you stay within agreed international boundaries).

Getting back to those lunars for longitude, this revisionist history, which claims that L&C actually did just fine, unfortunately doesn't go far enough in examining their observations. In fact, their lunar observations were rather poor, even if you give them the benefit of the doubt on the components of the data that they collected. The team members were not adequately trained in celestial methods. 

Frank Reed