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    Re: Blackburn's C2 table...a ramble
    From: Jackson McDonald
    Date: 2016 Dec 4, 11:47 +0000
    Great post, Frank.  We're eagerly awaiting your authoritative history of navigation and hope you are contemplating such a chef d'œuvre. 

    JMcD




    On Dec 3, 2016, at 2:19 PM, Frank Reed <NoReply_FrankReed@fer3.com> wrote:

    David C, you wrote:
    "Did Captain Norton really do two ex-meridians five hours after LAN?"

    Thank you for a fascinating post. I think the honest answer to your question here is "yes and no". I would say that the problem here is that the terminology "ex-meridian" is not fixed in stone. To us today, it applies to sights taken near noon that are worked up using a short quadratic approximation of the spherical triangle to yield latitude, as in the recent posts by Greg Rudzinski. This computation produces junk at any siginficant distance from the meridian. But the word "ex-meridian" is quite broad, and etymologically it means nothing more than "out of the meridian" or "away from the meridian" which could then apply to any sight whatsoever except an actual meridian sight. 

    Navigators in the late 19th century were aware of, familiar with, and comfortable with the expression "ex-meridian" as it applied to sights near noon --those cases where the noon latitude was missed due to clouds or bad timing but the latitude could be worked up anyway as long as there was a reasonable estimate of the time from noon (implying a good longitude). Many navigators were also aware of the generalization of sights to any time of day, but it was a hard sell. The original publication by Charles Sumner came out in 1843, but it was a commercial failure and an educational failure, too. While many light histories talk about the instant success of Sumner's methodology, they are invariably quoting the advertising material from the first few pages of the second edition of the tables. Sumner's method did not become genuinely popular until decades later, taking off circa 1880. Even so, lines of position would not become the overwhelmingly popular method of navigation computation until after the Second World War. But by calling these sights "ex-meridian" a conservative navigator could be lured into experimenting with the new methodologies. The language may have helped sell the concept.

    You added:
    "Studying the explanation I concluded that the C2 table allows Sumners (and presumably intercepts) to be plotted on a plane rather than mercator chart. It is based on the A B C tables."

    I'm not familiar with the C2 table specifically, but it may be worth noting that there were quite a few hybrid tables available in the early 20th century.

    Also, regarding plotting, one of the major misconceptions created in Sumner's original work was the idea that Sumner lines had to be plotted on "Mercator's chart". This was wrong. True Sumner lines (not the later hybrid methods involving azimuth tables) can easily be plotted and crossed for a fix on common "graph paper". They require no longitude scaling. The conformal or "shape-preserving" property of the usual line of position plotting sheets is not required unless azimuths are plotted. Lines of position plotted from two points on each line never reference azimuth and do not require any scaling in the plot. This is a big advantage! And it's an advantage that I emphasize in my Modern Celestial classes (see PS). A navigator who has learned to plot lines of position on standard plotting sheets is helpless without them. This is a significant weakness of the intercept method as it is commonly taught. Finally, be aware that navigators routinely abuse the label "Mercator" on their plotting sheets. A true Mercator projection (as the expression is used in neary every other field that employs cartography) is a rather complex thing. The simple scaling of latitude and longitude found on ordinary plotting sheets is an element of any conformal mapping projection, of which there are many examples. Common plotting sheets are "conformal" or "shape-preserving". Plotting sheets for lines of position that do not depend on azimuth (true Sumner lines, e.g.) can be simple graph paper or "plane charts".

    You also wrote:
    "Glancing through the text in Blackburn's book I conclude that at the beginning of the 20th century Sumners and Mark St Hilaire methods were used interchangeably. Sometimes one sight would be worked as a Sumner, the other as an intercept. Why I do not know."

    Yes. As for the explanation, you could equally well ask "why not?" The market was huge and diverse. Many navigators, even a majority in the first decade of the 20th century, used noon sun for latitude and morning or afternoon time sights for longitude. They didn't use lines of position at all --because they offered no significant, perceived benefit. Meanwhile there was a community of experimental navigators, many interested in methods that could ring maximum information from sights taken in difficult circumstances, and in this community new methodologies were developing and growing. Both of these communities were collapsed by the crisis of the Second World War. Navigation education was militarized, codified, and regulated, and an entire generation of navigators grew up knowing nothing but the laws and rules decreed by committees. Fortunately for the curious, experimental navigator, the old books remain, and there's fascinating variety to be discovered. I agree completely with your conclusion at the end of your message, "Those who just study intercepts and 229 do not know what they are missing!"

    You mentioned Cotter's "A History of Nautical Astronomy." I would warn you to be cautiously skeptical of Cotter's History. Cotter was extremely knowledgeable in the science and math of navigation, one of the experts of his era fifty years ago, but some of the material was clearly beyond him (the chapter on lunars in this book is a trainwreck), and most importantly, he was not a historian. Cotter did not understand how history is researched and discovered, or perhaps he did not find pleasure in real historical research. His "History of Nautical Astronomy" is a compendium of library research. It's a history of the mathematical works and the textbook compilations. He made little or no effort to explore primary source documents to discover how navigation was actually practiced. This is a huge, lingering problem with histories of navigation. Articles by mathematicians in journals tell us nothing about practicality, and textbooks tell us very little about usage in the real world (though they do have their moments: first editions of popular textbooks tend to be close to the metal). Navigation is what navigators do --not what they read.

    You wrote:
    "I discovered that (in theory) latitude can be found when the sun is on the prime vertical."

    Yes. Latitude can be found from any pair of sights when the Sun is far from the meridian. This is an example of "latitude by double altitude" often known historically as the "Douwes problem". It was an object of great fascination to mathematicians in the early days of scientific navigation, inspiring almost as many mathematical techniques and tricks as the process of clearing lunar distances. Latitude by double altitudes depended on measuring the altitude of the Sun or some star when well away from the meridian as well as the time interval between the two altitude observations. Today we can see it as a special example of a running fix. The time interval could be measured with a common watch. Watches good enough for this purpose were widely available long before chronometers became common which probably helps to explain the popularity of the concept. It potentially gave the navigator something useful to do with his watch! As I say, this method was very popular with mathematicians, and no doubt there were some mathematically-inclined navigators who used it regularly, but they seem to have been few and far between. I have seen no actual examples of latitude by double altitudes in logbooks or other practical records. The indirect influence of the method may have been more important --inspiring the general concept that latitude and longitude can be determined from any pair of altitudes, which is the essence of fully-developed celestial navigation.

    Frank Reed
    ReedNavigation.com
    Conanicut Island USA

    PS: When I teach modern "Sumner lines", I absolutely never call them Sumner lines. There are enough students who are familiar with, or later become familiar with, some of the light histories of navigation who will hear "Sumner" and immediately think "obsolete, antiquated, bad!". I have recently called this a "two-point line of position" methodology. Like the intercept method (which might be called in parallel the "intercept-azimuth line of position" methodology) the output is a line on a plot.

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