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    Re: How Many Chronometers?
    From: Frank Reed
    Date: 2009 May 12, 13:37 -0700

    Henry Halbot, you wrote:
    "Although again probably past the prime era of the method, it reinforces my 
    often stated opinion that, given more time, innovation, and practice, it 
    would have been significantly perfected in its accuracy and consistency. "
    
    Well, the methods described in that article were not new, and I don't think 
    they represent any approach to perfection. In fact, I see rather the 
    opposite: advancing decadence.
    
    I read this article some three or four years ago, and if I remember correctly, 
    someone wrote a follow-up letter to the MNRAS pointing out that this was a 
    known method for rating chronometers --known for decades. Indeed, a decade 
    earlier, one T.N. Were related his experiences rating his chronometer by 
    lunars and even then he referred to lunars in that decade as "too much 
    neglected". The interesting change in the time elapsed between those two 
    articles is that Were's results were published in the "Nautical Magazine" 
    while Toynbee's results were relegated to the MNRAS --"Monthly Notices of the 
    Royal Astronomical Society". I say "relegated" because the Nautical Magazine 
    was a publication aimed at practicing navigators while the Monthly Notices 
    were targeted to astronomers. The method had gone obsolescent, and its 
    remaining advocates were primarily rediscovering aspects that were relatively 
    common knowledge in the heyday of lunars.
    
    By the way, I remember three or four follow-up letters to the MNRAS regarding 
    Toynbee's article, so at least the astronomers enjoyed it!
    
    And you wrote:
    "We are also not advised as to whether or not the Captain had access to the 
    newly calculated Lunar Tables which came out about the time of the published 
    observations - I know only that the American Almanac first contained the new 
    tables in 1855, but that does not necessarily mean that they might not have 
    been available elsewhere before that date."
    
    I consider it highly unlikely that he had any updated tables. But be advised 
    that there are two separate improvements here. The improvement which was made 
    in the American Ephemeris (and which somewhat surprised the Europeans) was 
    due to a very simple revision. They took the established model of the Moon's 
    motion, which had been in use since the early 19th century, reduced more 
    recent observations, and re-generated the basic tables (for a modern analogy, 
    they effectively re-calculated the "coefficients of the time series" used in 
    the algorithms for calculating the hourly positions of the Moon). This had 
    not been done in Britain in decades so the errors in the predicted positions 
    were slowly building up. If lunars had mattered to any significant degree to 
    British shipping at this point, they easily could have done the same thing. 
    
    If you examine the first American Ephemeris and compare the lunar distance 
    tables with the standard British Nautical Almanac for the same year, the 
    American tables are moderately more accurate. The average errors are 
    something like 30% smaller. When I compared these a few years ago, I found 
    that one could get even better results, surprisingly, by averaging the 
    British and American predictions. 
    
    Just a few years after the first release of the American Ephemeris, the models 
    of the Moon's motion were significantly improved, and these improvements were 
    rolled out in later years in the various almanacs in Europe and the US. But 
    it was too little, too late. By 1860, there were very few practitioners of 
    lunars at sea.
    
    I've posted it before, but for reference, here is T.N. Were writing about his 
    experience with lunars in 1842:
    "CHRONOMETERS AND LUNARS.
    
    [After a preamble offering some revised positions for islands and points in the Indies...]
    
    I would now beg to offer some remarks relative to chronometers, and the 
    fearful consequences that may arise if we place too much confidence in them, 
    which from their beautiful and improved construction we are now too apt to 
    do, and neglect those observations of the Heavenly bodies (which can only be 
    of use by their being in constant practice) when you may have confidence in 
    them. 
    
    On my outward voyage, I had a beautiful watch of Murray's, which differed only 
    nine seconds, in my run from Portsmouth to the Great Ladrone (on the coast of 
    China). I placed great reliance on this watch during my homeward voyage, 
    after leaving the coast of Java, and as soon as the moon came in distance I 
    obtained a few sets of sights which gave the watch a considerable error, 
    nearly three minutes. At this time I imagined my distances must have been 
    incorrect, but the day previous to getting on the L'Agulhas bank, and in a 
    run of about thirty days from Java Head, I was fortunate enough to get the 
    mean of some thirty or forty distances, and I was much astonished that they 
    gave the watch an error of ninety miles to the westward. I also carefully 
    observed the sun's semi-diameter, and this corresponding with the Nautical 
    Almanac, gave me confidence in my sights, and shook my confidence in the 
    chronometers. It also fortunately placed me on my guard, and as on rounding 
    the land, I was in a position to make Cape L'Agulhas at daylight I did not 
    bear away. I was running nine knots at the time, with a strong S.S.W. wind, 
    and did not see the Cape until 2 P.M., having run since daylight about 80 
    miles departure, which made the lunar sights as near correct as I could take 
    the bearings of the land, at about four leagues distance in hazy weather. Had 
    I been by chronometer, near the longitude of the Cape in the evening, I 
    certainly should have borne away before morning, and had I done so, the 
    melancholy fate of the ship which I commanded would, I fear, have been 
    similar to the Arniston, Northumberland, and various others. 
    
    How to account for this error in the watch has quite bewildered me, excepting 
    it arose from magnetic attraction, as from some cause or carelessness a brace 
    of pistols was placed close to the watches, which I had removed, directly I 
    found the watches had altered their rates. The chronometer has since remained 
    stationary, and retains the same rate as when I was off the Cape. 
    
    On my passage towards England, after rounding the Cape, I took every 
    opportunity of obtaining lunar distances ; and two days before I reached St. 
    Helena, I spoke a ship which had also seen Cape L'Agulhas, and we differed 
    seventy miles in our longitude. This startled me. But when I found my brother 
    mariner had not taken any lunar sights, and having confidence in my 
    instrument, I steered boldly for the island, and made it ahead about an hour 
    before daylight. 
    
    I was at St. Helena two days. Each day I got the Greenwich time from the 
    observatory, and in taking the mean of my lunars about 100 distances, I was 
    much pleased to find we only differed one second from each other. 
    
    I would from these circumstances caution mariners, not to be too confident in 
    their chronometers, and to lose no opportunity of obtaining lunar 
    observations when practicable, and which I fear is now too much neglected, 
    and which unless they are constantly practised can be of little avail, and 
    can give no confidence to the observer. I have generally rated my 
    chronometers by lunars, and have hitherto been fortunately correct in doing 
    so, as they seldom retain the rate given by their constructors, and having 
    two sextants, one of which being Troughton's, which as an instrument of 
    confidence for navigation, is worth to me all the chronometers that were ever 
    constructed. 
    
    I have once before made some small contribution to your work, and am a 
    subscriber from its commencement, and many an agreeable hour, I spend at sea 
    in conning over its pages. Should yon think this worth inserting, or any part 
    of it in your publication, I beg you will do so. 
    
    I have the honour, &c., 
    T. N. WERE, 
    Commander of the Ship City of Derry. "
    
    -FER
    
    
    
    
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