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    Re: The Sun does not stop for anyone
    From: Gary LaPook
    Date: 2016 Dec 26, 22:14 -0800

    Frank wrote:

    ----------------------------------------------------------------------------------------------------------------

    " What you have described here is the Bowditch directions for making a homemadeMercator chart of a region of the world covering some several degrees --not a standard plotting chart! That's what meridional parts are required for."

    -------------------------------------------------------------pp

    But that is not what is written in Bowditch. What is written is :

    "324. Small area plotting sheets.-A Mercator plotting sheet can be constructed by the method explained in article 307. For a relatiely small area a good approximation can be more quickly constructed by the navigator by either of two alternative methods based upon a graphical solution of the secant of the latitude, which approximates the expansion." Bowditch, HO 9, 1962 ed. The exact same wording is found in the 1977 ed.  (Article 307 explains the use of table 5, Meridional parts.)

    "224. Small area plotting sheets. A Mercator plotting sheet for a relatively small area can easily be constructed by the navigator. Two alternative methods based upon a graphical solution of the secant of the latitude the approximate degree of expansion are explained below." Air Navigation, HO 216, 1967.

    As I said in my previous post, "a good approximation of what" obviously a Mercator chart. 

    "317 Plotting sheets are designed for use by the navigator at sea where no large scale charts are available. They are basically Mercator charts showing only the graticle of meridians and parallels with a compass rose, without any other chart data." Dutton, 12th ed., 1969

    What Frank has objected to is naming these small area plotting sheets, constructed using the graphical method, as MERCATOR plotting sheets because they are not constructed using Mercator's method of Meridional parts. Apparently the graphical methods approximate Mercator's method well enough that the U.S. Navy Hydrographic Office believes that it is appropriate to give them that name. Dutton, the standard navigation textbook used at the U.S. Naval Academy, also agrees with this naming convention. 

    As I said before Frank, I believe you may be being overly pedantic on this naming issue. You appear to be the only one who has a problem with it. And, again, as I said before, a Mercator chart constructed using the standard table 5 of Bowditch of Meridional parts only approximates a true Mercator chart. 

    So, here is a test. What say I construct two small area plotting sheets covering 34 to 35 degrees of latitude, one using the graphical method and one using Meridional Parts. Frank would have to admit that the second one is truly a Mercator chart. Now, could you tell which chart was which, which one was constructed with the graphical method and which one was made with Meridional Parts? If you could not tell them apart then you must admit that both were Mercator charts, including the one made graphically.

    So, how would we test them, what characteristic would tell them apart?

    Well, the expansion of Meridional parts, and charts constructed with them, show an uneven latitude scale, constantly expanding the spacing of one minute latitude lines as you move away from the equator so the chart that has a constantly explanding latitude scale would be the Mercator chart and the other one would be the imposter. 

    Looking now at table 5. The Meridional parts for latitude 34-00 is 2158.5 and for 34-01, 2159.7 a difference of 1.2. Looking at the top of the plotting sheet, 34-59 is 2229.7 and for 35-00, 2230.9, again a difference of 1.2. This means that the spacing of the parallels one minute above 34 degrees and one minute below 35 degrees have exactly the same spacing. In fact, all the lines up to 34-25 will be spaced 1.2 and all the lines from 34-55 to 35-00 will also be spaced 1.2 units apart, the same as at the bottom of the plotting sheet. In fact, 56 out of the 60 spaces will be drawn 1.2 units apart and 4 will be drawn 1.3 units apart intersperced randomly, but will not be expanding continuously towards the top of the plotting sheet. 

    The standard universal plotting sheets have the one degree parallels of latitude three inchs apart making a scale of 20 minutes of latitude per inch so the one minute lines are spaced 0.05 inches apart. Doing the same computations for a chart constructed with Meridional parts, keeping the same three inch spacing for degrees of latitude, makes the spacing of 1.2 units equal 0.04972 inches, just 0.00028 inches different from the standard universal plotting sheet constructed with the graphical method. Do you think you could spot a spacing difference of about three ten-thousanths of an inch? (3/10,000 inch) 

    So if I constructed these two plotting sheets Frank would not be able to tell which was which using normal plotting tools, he would need a micrometer and a microscope to do it, so, I submit, that a plotting sheet constructed using the graphical method IS a Mercator chart. 

    gl

       
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