NavList:

Modris Fersters, you wrote:
"The method used by Franklin is that of Mendoza y Rios. I found two different methods from him: one published in 1801, other in 1809."

The method that you're referring to from 1801 (I'm sorry to say I don't have time today to follow your link and check) is probably a variant on the standard series method that was published by him in an article in the Transactions of the Royal Society in 1797. It's a terrific article which will give you insight into MyR's capabilities and interests and also insight into some obscure aspects of clearing lunars using the tools available at the end of the 18th century. In an appendix he displays his simple variant of a series method. As far as I have determined, MyR never really cared much about this method, and the attachment of his name to it has as much to do with tearing down that "upstart" American, Nathaniel Bowditch, as anything else. Bowditch published a nearly identical method just a few years after MyR, and Norie, in particular, characterized this as near plagiarism so he insisted on referring to any versions of this method as the "Method of Mendoza Rios". 

The other method of Mendoza y Rios was apparently his pride and joy which he spent years compiling and setting in type. It was a well-constructed "direct method". I have a copy of those tables in their original binding in excellent condition sitting on my bookshelf a few feet from here. Their popularity is unclear, but a fairly large print run was supposedly funded by subscription. Unfortunately it's a big book whose only function is to clear lunars. Many navigators preferred the series methods because those volumes were compact, and the tables were often general purpose.

You added:
"Besides Franklin always uses altitudes to nearest seconds, but this method needs input altitudes only to nearest minutes."

That's always fascinating. The confusion over mathematical precision in the 19th century was an interesting phenomenon. One little clarification: the altitudes are required to the nearest few minutes (+/-5' is generally acceptable) in all methods of clearing lunars. It's a property of the geometry of lunars rather than any specific clearing method. 

Thank you for finding and writing about these lunars by Franklin. They're new to me at least. :) 

Frank Reed