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    Re: Lunar stuff (was: Calculating accurate apparent-angles between stars)
    From: Jan Kalivoda
    Date: 2003 Jan 9, 10:29 +0100

    ----- Original Message -----
    From: "William Allen" 
    Sent: Wednesday, January 08, 2003 9:35 PM
    Subject: Re: Lunar stuff (was: Calculating accurate apparent-angles between stars)
    Jean Charles de Borda lived in 1733 -1799. He did honorable military service 
    ashore and at sea. He improved the reflecting circle for measuring "the 
    lunars" (invented by Tobias Mayer, famous for his lunar tables, the first 
    ones that made the use of lunars practically possible) by adding again (after 
    Mayer's proposal, which was neglected by instrument makers) the repeating 
    mechanism to it . Hence an observer could only mark the values and the times 
    of the first and last distances in the set of observations and the average 
    error of measurement was less. But only the most competent and the richest 
    navigators used the "circle" in addition to an ordinary sextant.
    In his work "Description et usage du cercle de r�flection" from 1787 (or 1778 
    - my data waver; can anybody check it?) Borda published his method for 
    clearing the lunar distance you have asked about.
    Dunthorne's (1711 - 1775) method, very popular in Germany and Scandinavia, was 
    published by Maskelyne in the Nautical Almanac for 1772 (according to 
    And from that moment, the number of methods invented grew incessantly. In 1797 
    a list of 40 direct and many indirect methods was published. And as 
    M.D.Wright says in his sharpwitted history of the early air navigation ("Most 
    Probable Position", 1972; in another context), teachers of navigation and 
    navigators probably adored the method they had known the first in the youth.
    You assess the time of glory of lunars correctly. Up to the fifties of the 
    19th century, chronometers were very expensive (cca 200 - 400 pounds). They 
    were common only on great men-of-war, where the governement paid the bill. 
    The lunars were much more affordable, of course, but very difficult to use. 
    And owing to their inherent inaccuracy of 30 - 60 minutes of longitude, they 
    served only as a check of the latitude sailing, very common on sailing ships. 
    Nevertheless, the fraction of merchant masters that really used it frequently 
    can only be guessed.
    From 1850, the price of chronometers began to drop. And slowly emerging 
    steamers (although with sails till 80's) could not afford to spend the coal 
    for widely easting / westing the point of arrival, as sailing ships did. 
    Simultaneously, their trips last less than one month at sea in the most 
    cases. And till one month, a chronometer was able to give much more better 
    time than lunars even before the corrections of chronometer rates for 
    temperature differences were commonly used. Only after two months without a 
    check sunk the reliability of chronometer to the level of lunars.
    From cca 1870 the temperature rate corrections were usual. Therefore, even 
    after several months at sea a chronometer was more reliable than lunars, that 
    could provide only a gross time check from then. Simultaneously, in main 
    ports the optical and acoustic time signals, operated by telegraph, were 
    widely established, so that the tedious astronomical checking of chronometer 
    errors and rates (made with the help of the artificial horizon ashore) became 
    superfluous. In 80's, the price of a brand new chronometer sank to 30 pounds.
    The efect was that at the end of the 19th centure lunars became only a fetish 
    for "lunarians". The precomputed lunar distances were dropped from French 
    Connaissance des temps in 1905, from the Nautical Almanac in 1907 and from 
    German Nautisches Jahrbuch, hear, not until 1925!
    The first radio signals were transmitted in 1904 -1905 for the first time and 
    from 1908 regularly. From WW I they were commonly used. With their shift to 
    the short radio waves before WW II (they became wordlwide by then) the 
    chronometer began to follow the path of lunars into oblivion.
    And astronavigation is the third in the line. Or not?
    Jan Kalivoda

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