NavList:

A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

HOME

John Franklin lunar from 1818 and Mendoza y Rios method
From: Modris Fersters
Date: 2021 Jul 31, 09:04 -0700

Hi, everyone who is interested in historical lunars!

Here is link to J.Franklin lunar observations from 1818 (full calculations, original documents). Very interesting!

https://cudl.lib.cam.ac.uk/view/MS-FIS-00003/1

Calculations are made on printed forms. These forms were printed in 1814. Here is link to e-book:

https://books.google.lv/books?id=ZWpbAAAAQAAJ....

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 first method link to e-book is here:

https://books.google.lv/books?id=FzIAAAAAQAAJ&redir_esc=y

The second method link to e-book:

https://archive.org/details/b22007659

These methods are fundamentaly different. Tables are also absolutely different. Of course, the second method is most advanced: only addition operations are necessary, there are no half sums or differences which makes calculations liable to errors.

Franklin used the second method (that from 1809). This method is very convenient. I tried to use these Mendosa y Rios tables and found that the process of clearing lunars takes about 7…10minutes. Only Thomson method published later (in 1825) allows me clear lunars a little bit faster (6…9 minutes). But there is one advantage in Rios method: it is possible to clear distances larger than 120 degrees.

I am not surprised that Mendoza y Rios method was widely used in Royal navy and East Indian service (at least this is claimed in one letter from the beginning of 19. century).

I recalculated some Franklins lunar clearings by the same method he used and found some errors. For example May14,1818 (second set) Franklin makes mistake in corrected sum of altitudes. This yields to 1 minute error in cleared distance. Franklins cleared distance: 104 35 50; I cleared by Mendoza tables: 104 36 56; cleared by F.Reed lunar calculator: 104 36 54.

Besides Franklin always uses altitudes to nearest seconds, but this method needs input altitudes only to nearest minutes. I found that Franklin sometimes even unnecessarily interpolates logarithmic values from tables to match the seconds in altitude values.

Modris Fersters

What is NavList?

NavList is a community devoted to the preservation and practice of celestial navigation and other methods of traditional position-finding. We're a group of navigators, navigation enthusiasts and hobbyists, mathematicians and physicists, and historians interested in all aspects of navigation but primarily those techniques which are non-electronic.

To post a message, if you are already signed up as a NavList member, start a new discussion or reply to any posted message and use your posting code (this is a simple low-security password assigned when you join). You may also join by posting. Your first on-topic messsage automatically makes you a member, and a posting code will be assigned and emailed to you for future posts.

Uniquely, the NavList message boards also permit full interaction entirely by email. You can optionally receive individual posts or daily digests by email, and any member can post messages by email (bypassing the web site) by sending to our posting address which is "NavList@NavList.net". This functionality is similar to a traditional Internet mailing list: post by email, read by email, reply by email. Most members will prefer the web interface here for posting and replying to messages.

NavList is more than an online community... more about that another day.

© Copyright notice: please note that the rights to all messages and posts in this discussion group are held by their respective authors. No messages or text or images extracted from messages may be reproduced without the explicit consent of the message author. Email me, Frank Reed, if you have any questions.

Subject:
Author:
Start date:	(yyyymm dd)
End date:	(yyyymm dd)

NavList:

A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

NavList

What is NavList?

Join / Get NavList ID Code

Retrieve a NavList ID Code

Email Settings

Custom Index

Add Images & Files
Name or NavList Code:	Email:

Name:
	(please, no nicknames or handles)
Email:

NavList ID Code: