NavList:

Antoine, you wrote:
"I am just curious here because - just from looking up at this clearing computation method - I fail to see where and how he managed to take their (DR) Latitude in account in their Moon Clearing process.

I would think that some knowledge of the Observer's Latitude is an information absolutely required in any Lunar Clearing process, whatever the method actually used, would it not ?"

No. The altitudes are observed. This relates back to a short discussion we had off-list, which I suggested you should take on-list, about the issues of observed versus calculated altitudes. An interesting side-effect is that it's not directly possible to determine the error in these lunars since they are simply consistent. But you do have the option of using the resulting GMT and the measured altitudes as a standard two-body fix. Under the assumption of zero error in the lunar observation, you can then compare that against the DR position. A couple of nautical astronomers/mathematicians had figured out this possibility of getting a complete fix from the altitude sights in a lunar observation and they came very close to inventing the modern celestial fix. Unfortunately, their mathematical solutions were too convoluted, and it led nowhere.

You asked:
"And by the way, which Lunar reduction method is he using ? You said that it is not the one recommended by Bowditch."

Probably Witchell's or one related to it. The exact choice isn't actually important. It's a standard series solution or "corner cosines" solution, to use one of my catchy phrases with the triangles split in a way similar to some short modern sight reduction methods. Interestingly, he only works to first order in the corner cosines whereas nearly every navigation manual in this era already includes the first quadratic term. It doesn't matter as it turns out due to the geometry of the lunars he chooses to shoot during the voyage. Maybe he knew that, or maybe he just got lucky.

By the way, Witchell's method is included in Bowditch in this period, but it's last among the three choices available. Either Bowditch's Improved Method or his Original Method (known in England as the "method of Mendoza Rios" for various reasons) would have been more reliable.

-FER

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