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    Re: Impossible lunar example
    From: Frank Reed
    Date: 2010 Aug 29, 08:54 -0700

    These letters were sent to the London Gazetteer in late 1785:

    Dec 20, 1785

    "I Am a seaman, and can say I have seen many sights, sailed at all seasons, studied the situations of ths Sun, Saturn, and satellites; and have stated, in several simple schemes, the best methods of determining the longitude. But, of all the sights I have seen, I never saw the solution of an impossible triangle, till, in my last voyage, I was reading the new Requisite Tables, published by order of the Commissioners of Longitude. The preface of this useful book is larded with the names of many mighty men, who have assisted the astronomer-royal in the compilation of the work, sed mirabile dictu! -We there see wonders! Two miracles Wrought! (examples 3d and 4th, pages 35 and 36!) Two triangles solved, in which the observed distances are considerably greater than the respective zenith distances of the objects observed. In the first, one side is greater than the other two by above three degrees; in the other, nearly six degrees. This would have heen laughed at two thousand years ago. Surely we are not to have mysteries in the mathematics, as well as in mythology; but perhaps without them the mystic ministers of M---- will miss the money taken for the passport into the wooden world, long the habitation of ...
    NAUTICUS."

    Dec 26, 1785

    "In the Requisite Tables, published by the authority of the Commissioners of Longitude, I have since discovered a more egregious error than the two before mentioned, viz. in page 31, example the IVth, the sun's zenith distance is given above 71 degrees, the moon's 19 degrees, and the apparent distance of their centres 103 one-hale degrees, consequently impossible; for one side of the triangle is longer than the other two by above 13 degrees. Shame! Shame! How degraded is the dignity of a British astronomer!
    NAUTICUS."

    How like the modern Internet they were... posting under "handles" and all...

    I'll post Maskelyne's replies shortly. I could not find my digitized copy so I am stuck typing from a paper copy. Fortunately, they're short letters.

    Maskelyne DID soon after make notice of these in the "errata" for the Tables Requisite as follows (from the Nautical Almanac for 1791 which was, in fact, published at the end of 1786):
    "The Observations, which Ex. III p.30 and 35, were taken from, must have been
    erroneous, since the Numbers will not consist in a spherical Triangle. Also Ex. IV p. 31 and 36, is in the same Situation, owing to a Mistake in transcribing
    the Moon's Altitude 71d 6'2" instead of 41d 6'2". But the Rules on p.28 and 32, having been exactly followed in the Calculations, no Person can be puzzled or misled by these Mistakes. However, to avoid Cavils, let the Moon's Altitude in Ex. III p.30 and 35, be taken 84d 46' instead of 88d 46' [etc.]"

    Note his words: "NO PERSON CAN BE PUZZLED OR MISLED"... That's true, unless the student gets carried away by the details. He doesn't seem to recognize yet that it's just plain bad pedagogy even if there's no real error here. Anything that might confuse the student should be avoided or explained somewhere (e.g. in a footnote). He offers alternative altitudes to use in the problems "TO AVOID CAVILS"... That word, cavils, is largely obsolete in modern English. According to the Oxford English Dictionary, it means "quibbling or frivolous objections". I agree with him that the objections of "Nauticus" are cavils.

    -FER

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