# NavList:

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

**Re: Planisphere pour les Distances Lunaires**

**From:**Frank Reed

**Date:**2009 Jun 3, 18:33 -0700

I wrote previously: "His equation "(1)" with minor variations in grouping the terms had been well-known to nautical astronomers and mathematicians who studied lunars for the better part of a century. It consists of two linear terms and between one and three quadratic terms (depending on where the series was truncated). You can find the same equation derived in the rather long paper by Mendoza y Rios published in the Transactions of the Royal Society back in 1797. " Actually, looking it over further, Hue has made a bit of a mistake in evaluating the importance of the quadratic terms, and in fact this makes his solution slightly worse than what had been available to navigators since the early 19th century. Again, this strikes me as fairly typical of the period of obsolescence of lunars. Details: While deriving the series expansion, at the bottom of page 3, Hue has a remainder term R which is proportional to the product of the altitude corrections of the Moon and the other body and inversely proportional to the sine of the lunar distance. He demonstrates that this is small enough to ignore under many circumstances, but in fact it's comparable in magnitude to the cross-term in the "x squared" term which he has chosen to keep. The result is that his version of the quadratic expansion is no better than if he had kept the terms proportional to m squared only. This was acceptable in the late 18th and the very early 19th centuries, but most published versions of such series expansions had moved beyond this level of accuracy some four decades earlier (Thomson in 1824, Bowditch in 1826). I should emphasize that this is a SMALL issue for Hue's analysis, introducing errors on the order of a tenth of a minute of arc. It doesn't mean that the device doesn't work or that the approach is fundamentally flawed. But those errors were un-necessary. By the way, there's a footnote in the "Notice" that I didn't see before where Hue comments that his derivation of his equation (1) could have been done more easily by a straight Taylor series so he is at least aware that he is re-inventing the wheel here. -FER --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---