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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Certaine Errors in Navigation Corrected
From: Gary LaPook
Date: 2007 Dec 10, 11:50 -0800
From: Gary LaPook
Date: 2007 Dec 10, 11:50 -0800
Gary adds: It is interesting to compare Wright's almanac with the modern one. The sun's declination today, December 7, 2007 at noon in England is 22� 35.7' south. If we were using Wright's almanac for the same day, which would be November 27th in the column for 1607 (found on page 118), we get his value of 22� 38' south and a modern almanac program gives it as 22� 39.0', only one minute differece! gl On Dec 10, 11:44 am, glap...@pacbell.net wrote: > Gary writes: > > It is interesting to compare Wright's almanac with the modern one. The > sun's declination today, December 7, 2007 at noon in England is 22� > 35.7' south. If we were using Wright's almanac for the same day, which > would be November 27th in the column for 1607 (found on page 118), we > get his value of 22� 38' south which is close enough for government > work. In comparing Wright's almanac with the modern one you must > subtract 10 days from his tabulation since England did not change to > the Gregorian calendar until September 25, 1752 while most Catholic > countries changed on October 5, 1582. (This caused me much confusion > when I first looked at his almanac almost thirty years ago since I > assumed that Wright was also using the Gregorian calendar since he > published 17 years after that calendar went into effect.) > > Also, comparing his value for the declination of the sun at the summer > solstice of 1597, he gives it as 23� 30' north while a modern almanac > program gives it as 23� 29.6' north, a difference within the limit of > precision of Wright's table! > > Remember that the letter "s" was printed in 1599 with a character that > looks like the modern letter "f" and that the letters "u" and "v" are > often interchanged. > > On Dec 8, 5:14 am, RS Petersonwrote: > > > I would like a copy. Thanks. -- Bob > > > glap...@pacbell.net wrote: > > >Gary LaPook writes: > > > >I now have a complete copy of "Certaine Errors In Navigation" in PDF > > >format and can email it off list to anyone who might want a copy. It > > >is a delightful book to read, Mr. Wright sounds like a thoroughly > > >modern man. > > > >gl > > > >On Dec 4, 8:03 pm, "Gary J. LaPook" wrote: > > > >>Gary LaPook adds: > > > >>What I meant by: " I suspect that the method was just forgotten in the > > >>mists of time" was that in Wright's time there was no reason to publish > > >>a method to calculate altitude as that need did not develop until St. > > >>Hilaire invented the "new navigation" almost 300 years later. After St. > > >>Hilaire, many methods were tried in an effort to reduce the work > > >>needed to calculate altitude including different mechanical devices such > > >>as the Bygrave slide rule (and many more), "short tables" and > > >>culminating in the precomputed altitude tables such as H.O 214, H.O. > > >>218, H.O. 229 and H.O 249. I suspect that nobody thought to look back at > > >>a book that had been published in the dim and distant past, 1599, and > > >>that didn't even include a method for calculating altitude, only great > > >>circle distance. > > > >>Gary LaPook wrote: > > > >>>Gary LaPook writes: > > > >>>You can look at his explanation yourself and you will see that is no > > >>>allowance for an elliptical earth so it uses the round earth > > >>>assumption used throughout celestial navigation. > > > >>>I would think his method could produce better accuracy with either > > >>>modern printing of the form to use, larger scale or precision > > >>>machining of a mechanical device to do the computation. One tenth > > >>>minute precision is not needed for flight navigation and many methods > > >>>and devices were used that produced accuracy that was attainable by > > >>>the Wright method. I suspect that the method was just forgotten in the > > >>>mists of time. > > > >>>gl > > > >>>Fred Hebard wrote: > > > >>>>Some naive comments/questions: > > > >>>>First, how much of the discrepency between Wright's calculated > > >>>>distance and the modern digital calculator is due to the elliptical > > >>>>shape of the earth, or were you using the same assumptions? > > > >>>>Second, one could guess that a graphical method would be good to 3 > > >>>>decimal places (about what you got for question 1). Five-decimal- > > >>>>place precision is needed to get 0.1 arcminute accuracy, more or > > >>>>less, so a graphical method would only be good to 10 arcminutes, more > > >>>>or less. Perhaps it's the lack of precision that led to Wright's > > >>>>method not being adapted to standard sight reduction. Certainly back > > >>>>in his time, simple reduction of noon sights for altitude was easy > > >>>>enough. By the period when time sights for longitude became > > >>>>prevalent, and especially by the point when intercept methods took > > >>>>over, 3 decimal places wasn't close enough anymore. > > > >>>>Fred > > > >>>>On Dec 4, 2007, at 4:18 AM, Gary J. LaPook wrote: > > > >>>>>Gary J. LaPook wrote: > > > >>>>>It is not surprising that nobody ever noticed this before > > >>>>>(considering that Wright published in 1599 almost 300 years prior > > >>>>>to Marc St. Hilaire) that Wright's method of calculating the great > > >>>>>circle distance on the earth using only a strait edge and a compass > > >>>>>could just as easily be used to calculate the altitude of a > > >>>>>celestial body. The great circle distance is simply 60 NM times the > > >>>>>number of degrees of the great circle between two points and this > > >>>>>is exactly the same as the zenith distance to a body having the > > >>>>>geographical position represented by the second point. The > > >>>>>formula is 90� minus zenith distance equals altitude. > > > >>>>>Wright's example of calculation of the great circle distance > > >>>>>between London and Jerusalem resulted in his calculated distance of > > >>>>>2325 NM and a modern digital calculator comes up with 2316.8 NM a > > >>>>>difference of only 8.2 NM or minutes of zenith distance or of > > >>>>>computed altitude for those coordinates! Using his method Wright > > >>>>>could compute altitudes to a precision of 8.2'. It is surprising in > > >>>>>light of the many devices invented later in an attempt to find a > > >>>>>mechanical method for this calculation that none (that I am aware > > >>>>>of) attempted to use Wright's method, a method that would seem > > >>>>>easily adapted to a mechanical device and that could provide much > > >>>>>greater accuracy using a larger scale and precise machining of the > > >>>>>parts. > > > >>>>>I would really like it if someone could explain why Wright's method > > >>>>>works since I have not been able to find such an explanation > > >>>>>anywhere. I am attaching pages 45-52 of "Certaine Errors" in which > > >>>>>he lays out his method. I am also including the errata sheet > > >>>>>showing that the corrections of typos I identified in my previous > > >>>>>posts were correct. > > > >>>>>gl > > > >>>>> > > >>>>> > > > -- > > Robert S. Peterson > > Great Lakes Compass > > 31 N Alfred, Elgin IL 60123 USA > > 847/697-6491 > > Compass Adjusting & Repair for Lake Michigan Navigators Since 1985 > > e-mail: rspeterson(at)wowway(dot)com --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---