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    Re: Watch error, watch rate: some problems to solve?
    From: Frank Reed
    Date: 2018 Dec 23, 11:00 -0800

    Chronometer error and rate is one of the easiest, most trivial issues in celestial navigation (apart from a very small class of specialty users who existed historically --see below). You compare your chronometer with a known exact source of time on two separate days, typically 5-10 days apart. The error is simply the difference in time between your chronometer and the exact time source on either date. The rate is just the difference in the errors on the two days expressed as some number of seconds per day.

    Sample problem: You're a modern celestial navigation enthusiast preparing for an ocean crossing, and you have a basic quartz watch that you intend to use as your chronometer. You find a good time-standard website like the USNO Master Clock Time (ignore the security warning) or perhaps you listen to a shortwave signal like WWV. You watch or listen for the top of the minute (that makes the arithmetic simpler) and when the minute mark hits exactly, you read and record the time on the watch. So let's suppose on Monday morning (near 10am UT) your watch reads 10:05:13 when the time signal indicates 10:03:00 UT exactly. Obviously your watch is 2:13 fast. That's your chronometer error. You repeat this process on Saturday (near 4pm UT) and this time your watch reads 16:02:29 when the exact time was 16:00:00. Obviously your watch is now 2:29 fast. The error has increased by 16 seconds in 5.25 days. So what's the rate? That's easy. Just divide: 16/5.25 = 3.0476 seconds per day. The number of significant digits here is much lower (you could call it 3.0), but there's no harm done to the subsequent calculation by including extra digits. Using the rate and error is trivial. You work out the error on each succeeding day by adding 3.0476 second every day. So 20 days after that Saturday when you did the second time check, the chronometer error is 16s (the original error) plus 20 times 3.0476 or... drum roll... 77 seconds. So if the chronometer reads 12:05:27 on that date, the correct UT is actually 77 seconds earlier or 12:04:10.

    As I say, it's child play.

    But when is it not child's play? Historically there were other markets, other users, other issues. For normal celestial navigators, it was just as above -- a trivial math problem. But there were also scientific users such as those explorers who carried dozens of chronometers. For them there were clever schemes developed for detecting chronometers which had become deranged and separating them from the "trustworthy" collection whose time would be averaged. There were also schemes for attempting to control for temperature variation in circumstances where that could not otherwise be managed. None of this is relevant in any way in the modern world.

    And finally, there was a whole industry of science mixed with lore for the professional chronometer-raters. This was a thriving, dependable business. Since practical navigators in the 19th century (e.g.) did not have time signals or other sources of exact UT, they relied on rating shops who frequently had a telegraph connection to a nearby observatory for exact time determinations. A ship's chronometers would be dropped at the rating shop upon arrival in port and picked up a week or two later with a freshly determined error and rate. It was up to the ship's master (or other navigator) to prepare a daily error table from the determined initial error and rate, and you'll often find these tables written out on the end-papers of old books (or at least you'll find tables which have all the required properties and one may assume that they are daily error tables).

    In the earlier periods, before 1850, it was also possible to determine chronometer error by shooting lunars. This was not often done in practice in any "formal" sense, but you'll find circumstances where navigators are keeping an extra longitude. They'll list a DR longitude and a Chro longitude (or T.K. for "Time Keeper" or some other name in the period before the word "chronometer" caught on) and alongside they'll list a daily Lunar longitude. This can create the misleading impression that lunars are being shot every day, but you can usually see by inspection that the "lon by chro" and "lon by lun" are synchronized, changing by the same value from day to day. Thus the "lon by lun" is really a longitude by chronometer with the error determined by the initial lunar at the beginning of the sequence. It's another "lon by chro" but "initialized" with a lunar longitude at the beginning of the run.

    When I'm writing "lon by chro" here I am referring to the original usage and not the later "decadent" usage in some British sources in the 20th century.

    A note on the word "chronometer": Apart from one satirical usage in the 18th century, sea-clocks were only referred to as chronometers starting around 1810, almost fifty ears after Harrison's H4. And in that period, it seems to have been the case (I'm still investigating this) that the word was, at first, reserved for seagoing time-keepers of exceptional quality. A "chronometer" was a class above the rest.

    A seagoing clock that could cross the Atlantic and keep excellent time for the few-weeks duration of that voyage was an "ordinary" time-keeper (Harrison's original H4 would have fallen into that category despite being miraculously accurate when first exhibited). To be classed as a "chronometer" --no mere "clock" but a machine that records the passage of time with scientific exactness-- implied that a clock could maintain absolute time on a global voyage lasting months without error. Naturally, any maker wanted all clocks to be counted as chronometers so it seems that the word's meaning crept outward and soon included all clocks that were used to carry absolute time for navigation and other position-finding applications.

    Frank Reed
    Clockwork Mapping / ReedNavigation.com / HistoricalAtlas.com
    Conanicut Island USA

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