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    Re: Certaine Errors in Navigation Corrected
    From: Fred Hebard
    Date: 2007 Dec 5, 00:11 -0500

    Thanks for the clarification.  I still believe the graphical methods  
    were just too imprecise by St. Hillaire's time.  You can work to  
    perhaps 0.3mm accuracy drawing (the resolution of the human eye is  
    about 0.1 mm).  So that's 0.3/50 cm error under the best of  
    circumstances.  Yes, perhaps Wright's method could have lent itself  
    to the use of mechanical tools like 3-arm protractors with verniers  
    so was lost in the mists of time, as you so nicely put it.
    Fred Hebard
    On Dec 4, 2007, at 11:03 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   
    > >
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