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    Tables Requisite: 1781
    From: Frank Reed
    Date: 2013 Jan 12, 12:19 -0800

    The Royal Astronomer Nevil Maskelyne himself wrote the introduction and many of the explanations and instructions in the Nautical Almanac in the late 18th century and also in the "Tables Requisite". Though less well-known today, the latter was really an indispensable companion to the annual almanac. The modern Nautical Almanac includes many tables which do not change from year to year. In the late 18th century, this would have made the annual book too expensive. So the actual Nautical Almanac included only the ephemeral data and occasionally an extra articles on some new method of working a site. The Tables Requisite included tables of refraction, dip, logarithms, trig functions, etc. It also included some basic advice on instruments and sight-taking which should sound remarkably familiar. You can read our download the 1781 edition of the Tables Requisite at Google Books here:

    Here are the first few paragraphs with some comments:
    "THE observer must be furnished with a good Hadley's quadrant, and a watch that can be depended upon for keeping time within a minute for six hours. But it will be more convenient if the instrument be made a sextant, in which case it will measure 120°, for the sake of observing the moon's distance from the sun, for two or three days after the first and before the last quarter."

    Notice here that the expression "Hadley's quadrant" includes a sextant as a sub-category. Maskelyne is recommending having the instrument manufactured as a sextant specifically for its value in observing lunars. Nearly every feature of the modern sextant that distinguishes it from an octant from 250 years ago follows from the needs of lunars. It's also interesting that Maskelyne considers a good watch a necessity even in 1781. Of course, he's not talking about a "time-keeper" of chronometer --just a good watch that can keep track of local time for an hour or two.

    Maskelyne continues:
    "The instrument will be still more fit for the purpose, if it be furnished with a screw to move the index gradually in measuring the moon's distance from the sun or star; an additional dark glass, lighter than the common ones, to take off the glare of the moon's light in observing her distance from a fixed star, and a small telescope, magnifying three or four times, to render the contact of the star with the moon's limb more discernible. A magnifying glass of [1.5] or two inches focus will assist the observer to read off his observation with greater ease and certainty."

    The additional shades and the telescope that are common features of the modern sextant were recommended by Maskelyne, again, specifically for the needs of lunars.

    Wooden octants from this period often have a big knob behind the index mirror which allowed the mirror to be rotated. Modern sextants have tiny adjustment knobs or adjustment screws. Small knobs are for careful adjustment in a shop or in the 'comfort' of a ship's cabin. A big knob was intended for live adjustment on the spot. And that was the common practice for index error in the early period. Before a round of sights, the navigator would simply remove any index error, zeroing it out, by rotating the index mirror. Maskelyne advocated correcting for index error instead of zeroing it out, as is the standard modern practice, as follows:
    "The greatest care must be taken in having the quadrant carefully adjusted before the observation, or, which I should rather advise, in examining the error of the adjustment, for it is liable to alter, and allowing for it. The method of doing it is this: turn the index of the quadrant till the horizon of the sea, or the moon, or any other proper object appears as one, by the union of the reflected image with the object seen directly; then the number of minutes by which 0 on the index [the zero on the vernier of the arm] differs from 0 on the arch is the error of adjustment. If 0 on the index stands advanced upon the quadrant before, or to the left hand of 0 on the arch, that number of minutes is to be subtracted from all observations; but if it stands off the arch behind, or to the right hand of 0 on the arch, it must be added to the observations. But the sun himself is incomparably the best object for this purpose: either the two suns may be brought into one, or, which is a still better method, the sun's diameter may be measured twice, with the index placed alternately before and behind the beginning of the divisions: half the difference of these two measures will be the correction of the adjustment, which must be added or subtracted from all observations, as the diameter measured with the index upon the arch, that is to say, before or to the left hand of the beginning of the divisions, is less or greater than the diameter measured with the index off the arch, behind, or to the right hand of the beginning of the divisions. Thus, suppose I had measured the sun's diameter with the index upon the arch or to the left hand of the beginning of the divisions, to be 30', and the contrary way to be 33'; I should conclude that the correction of adjustment is [1.5], or half the difference, 3', additive to the observations. In the practice of this method the telescope must be used, and a dark glass must be applied at the eye, or at least on the hither side of the little speculum [horizon mirror], to darken both suns at once. It will also be convenient to provide an umbrella of pasteboard, about six inches square, with a hole in the middle to receive the telescope, in order to defend the eyes from the direct light of the sun, as well as from the ambient brightness of the sky, which would otherwise render this practice in many cases too painful and difficult."

    And that, of course, is a standard method of measuring the index correction which we have also discussed recently. By the way, Maskelyne's idea of making a cardboard "umbrella" or shade around the telescope is a good one.

    Maskelyne continues:
    "It will conduce to greater exactness to take two or three measures of the sun's diameter each way, half the difference of the means each way will be the correction of the adjustment, to be applied as before. Thus I have often assured myself of the exact quantity of correction of my quadrant within a quarter of a minute."

    So he says that if you average two or three of these observations (using a sextant with a telescope of 3x to 4x magnification), you can expect to get the index correction within a quarter of a minute. And that, of course, agrees very nicely with observations that I have reported as well as observations by Greg Rudzinski and others.

    This all confirms something that Alex Eremenko and Norm Goldblatt both noted recently which is that things really haven't changed much in 230 years. I would only add that there have been eras when the practice of celestial navigation has atrophied in one way or another. It's not that the knowledge was ever lost really, but it was less important in some periods. For example, in the late 19th century, lunars were a rare novelty at sea. The level of accuracy required for latitude by Noon Sun and common time sights was considerably less than that required for lunars. It seems likely that the reduction in quality of sextants in this period (Lecky talks about this in his "Wrinkles") was due to these more relaxed requirements in the accuracy of observations. Similarly in the recent precipitous decline of celestial navigation in the past 25 years, entropy has taken its toll. Fortunately for us today, the Internet gives us access to nearly all the great reference works of the past, as well as primary source documents, to confirm that we're doing things right and to help us decide what we should expect from our instruments and our observations.


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