# NavList:

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

**Re: Mendoza's method for clearing lunars.**

**From:**Henry Halboth

**Date:**2004 Aug 2, 11:14 -0400

George: My 1839 edition of Norie's contains a Table XXXV - it is entitled "To correct the apparent distance of the Moon from the Sun, a Star & etc. for the effects of Paralax and refraction" with entries against Apparent Distance across the top and Paralax in Altitude or Distance down the side; this Table covers distances to 120-degrees. My 1889 edition of Norie's contains a Table XXXV, but only covers distances to 30-degrees. I will not open these books as necessary for copying, but would be pleased to provide specific entries - if you could copy the work forms indicated in your posting, I would also be glad to comment. Henry ps My 1902 copy of Norie's Tables alone no longer includes the XXXV On Mon, 2 Aug 2004 10:40:04 +0100 George Huxtablewrites: > This is a request for some help, please, because my own knowledge and > information has run out here. > > I am following the navigation practices of a captain in the > Greenland > Whaling, who accasionally used lunar distances to determine his > longitude. > > I have copies of a pamphlet he carried, dated 1816, which was > produced by > J.W.Norie, which had the usual extravagantly-long title of those > times, as- > "Formulae for finding the longitude, in which a method invented by > Mendoza > Rios is used for clearing the observed distances from the effects of > refraction and parallax, with rules for working the observations.". > > It seems that this consisted of a pad of blank forms for the > navigator to > fill in, preceded by a couple of pages of explanation about how to > do it. > I have copies of some of these completed forms from various whaling > voyages, and am attempting to work backwards to discover how the job > was > done, in detail. > > I have found no more than a mention of Mendoza's method in Cotter's > "History of Nautical Astronomy", and no details about that method. > From > Norie's explanation it appears to be an approximate method rather > than a > rigorous one (though that doesn't necessarily detract from its > accuracy). > > A footnote after the explanation states "N.B. In the above Rules, > the > numbers refer to the Tables in Norie's Epitome or Nautical Tables." > I have > my own copy of Norie's, but this dates from much later, 1900, while > its > bound-in tables date from as late as 1914. Even at such a late date, > this > includes tables for working a lunar distance, but unfortunately not > the > tables required for Mendoza's method, which had by then long been > superceded. Nor does my copy of Raper's (of 1864) seem to carry any > equivalent tables. So I'm stuck, rather. > > The vital table that's missing from that later Norie's is Table XXXV > (=35); > in my edition the tables go straight from XXXIV (=34) to XXXVI > (=36). A > handwritten note on the Mendoza explanation seems to imply that > Mackay's > table LXXII (=72) corresponds, but I don't have a copy of Mackay. > The > Mendoza-method explanation about using table XXXV states- "Enter > Table > XXXV. with the apparent distance at the top, and the Moon's > correction in > the side column, the corresponding number will be the third > correction; in > the same column, and opposite the difference in corrections, will be > found > the fourth correction." > > Another Norie table required was table XXX (=30), stated to > correspond to > Mackay table IX (=9). This was described as for the "proportional > logarithm > of the Moon's correction". In my more modern Norie's, table XXX has > become > simply a table of the Moon's correction, with no mention of > proportional > logarithms, but as proportional logarithms still remain, as table > XXXIV > (=34), by combining two lookups one can get the required answer. So > that's > a problem that can be bypassed. > > It's likely that the Bodleian Library will have copies of those > earlier > Norie's, but usually they are very stuffy about photocopying pages > from > their older texts. > > So here is my request. I'm asking any Nav-L member who may possess > (or have > access to) a copy of Norie's that's old enough to contain Table XXXV > if > they would kindly let me know how many pages it covers (to assess > the size > of the problem). If it's only a page or two, then if anyone is in a > position to make a scan and send it to me as a fax or off-list > attachment, > I would be most grateful. Alternatively, similar information about > Mackay's > table LXXII (=72) would be equally welcome. > > These difficulties exist only in the section of Norie's pamphlet > which > deals with clearing the apparent lunar distance, by Mendoza's > method; the > rest explains itself well. > > For those that are interested, here's a transcript of that section > from > Norie's pamphlet, about Mendoza's method- > > ============================== > > "To find the true Distance. > > 1. Add together the apparent distance and apparent altitudes, and > take half > their sum; the difference between the half sum and the Sun or Star's > apparent altitude call the first remainder: and the difference > between the > half sum and the Moon's apparent altitude call the second remainder. > > 2. Add together the log sine of the apparent distance; the log. > co-sine of > the Moon's apparent altitude: the log.secant of the half sum; the > log > co-secant of the first remainder; the proportional logarithm of the > Moon's > correction (XXX) and the constant logarithm 9.6990: their sum, > rejecting > the tens in the index, will be the proportional logarithm of the > first > correction. > > 3. Add together, the log. sine of the apparent distance (already > found;) > the log. co-sine of the Sun or Star's apparent altitude; the log > secant of > the half sum (already found;) the log. co-secant of the second > remainder; > the proportional logarithm of the Sun or Star's correction; and the > constant logarithm 9.6990: their sum, rejecting the tens in the > index, will > be the proportional logarithm of the second correction. [A footnote > states- > (The sun's correction is the difference of the refraction and > parallax in > altitude. (IV, VI) The star's correction is the refraction in > altitude > (IV)).] > > 4. The difference between the first correction and the correction of > the > Moon's altitude call the difference of corrections. > Enter Table XXXV, with the apparent distance at the top, and the > Moon's > correction in the side column, the corresponding number will be the > third > correction; in the same column, and opposite the difference of > corrections, > will be found the fourth correction. > > 5. Subtract the sum of the Moon's correction, and the second and > fourth > corrections from the apparent distance; to the remainder add the Sun > or > Star's correction, and the first and third corrections; their sum > will be > the true distance." > > =================== > > To me, Mendoza's appears to be a remarkably complex and long-winded > method, > even though it avoided the necessity for using long 5-figure or > 6-figure > logarithm tables. It's not surprising that it failed to survive, in > competition with (say) Thomson's Lunar and Horary Tables. > > In analysing these whaling journals, I could, of course, choose to > use > another method for clearing the lunar distance, one for which all > the > required information was readily available. But I would prefer to > follow, > if possible, exactly the same steps that were taken by this > navigator. > > George. > > ================================================================ > contact George Huxtable by email at george---.u-net.com, by > phone at > 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 > Sandy > Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. > ================================================================ >