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Stark Tables for lunars- an old friend reappears
From: George Huxtable
Date: 2010 Dec 12, 20:24 -0000
From: George Huxtable
Date: 2010 Dec 12, 20:24 -0000
Back on 11th November, some nice words were written about Bruce Stark's Lunar Tables by Frank, Andres, and Jeremy, and now I would like to add some of my own. First, though, I should mention that Andres' post referred to some words of a publisher's "blurb", as though they came from me, but my own contribution to that extract was no more than "Captain Cook would have relished using these tables, had they been available to him then." - George Huxtable, FRIN". Not that I would disagree with the publisher's assessment. 1995 and 1997 editions of the Stark Tables being now out-of-print, this new edition of Bruce's Tables comes from a different publisher: from Starpath Publications, indeed, run by that respected navigator, David Burch. I'm pleased to note that its contents are basically unchanged from the previous, 1997, edition. What is very different is the format. Instead of a bulky spiral-binding, on heavy paper, which occupied a formidable space on a bookshelf, it's thickness has been roughly halved, now having a standard paperback binding. This has allowed its price to be kept in check: including delivery, it's within �23 in UK, $30 in US. But something has been lost; the convenience, for a set of tables, of lay-flat opening. I recommend, instead, that one or two narrow ribbons can be usefully attached to the spine, as place-keepers, to lie in the cleavage between in-use pages. The first twenty-odd pages are explanatory, with useful hints about lunars and their observation. There are only a few pages given over to explaining how to use the tables themselves; no more than absolutely essential. The way to learn is to carefully follow the examples provided, using photocopies of the form templates that are provided. Bruce suggests that a few tags be attached to the page edges, as guidance to find the various sections of the numerical tables, which occupy the next 315 pages. Like any volume of tables, these, when first opened, look rather unprepossessing: just pages and pages of numbers. It's when you start to use them that you appreciate how carefully, and how cleverly, they have been thought out. Over the 17th and 18th centuries, mathematicians and astronomers vied to minimise the number of steps needed to compute a lunar distance, but Bruce, with a complete rethink, has beaten them all. As a source of data, the Nautical Almanac, for the year in question, is needed, but Bruce's tables take the place of any log-trig tables that would otherwise be called for. It just requires additions and subtractions, in a process that does the job by logs, but in such a way that you are hardly aware of it. The tables are expanded enough to avoid need for interpolations. The intermediate numbers are always greater than 1, so none of the awkwardness of negative-logs arises. The smartest bit is the introduction of "Gaussian logs". These have nothing to do with any other Gaussians you might have come up with, except as the product of the same mind. These "addition and subtraction logs" cleverly allow for an addition to take place, without "coming out of logs", something that I had previously thought impossible. All necessary corrections are accounted for, such that any error in your final result will depend on the precision of your lunar distance observation, not the precision of the processing. A procedure is given for deducing the predicted true-lunar-distance at an integral-hour of GMT, from Almanac data, or you could use another source, such as Steven Wepster's website, or that of Olav Soft. So, who are Bruce's Tables aimed out? Well, for those who are wedded to computers, the same job can be done by pressing a few buttons, which is what I do some of the time. They're for those who get a bit of extra satisfaction out of "rolling their own", as I do, some of the time. But not for purists who want to follow the exact procedures that early lunarians had to adopt: if you insist on authenticity, it will be a much harder job. It's for those who wish to try steering a middle course between those two. In his introduction, Bruce discloses little about how his tables actually work, and I would have liked to see a bit more. For those that wish to understand in more detail, Bruce has published a paper in The Journal of Navigation, vol 40 (1987) No 3, pages394 to 396, "Resurrecting the Lunar Distance". And I have tried doing a bit of reverse-engineering on the tables in the book, which I can offer for what it's worth, for the curious-minded that like to know such things- The most extensive table, for the quanity K, as a function of angle A, is given by- K= - log hav A, which is the same as log (1 / (1-cos A)) The table of "Gaussian logs" of the quantity x, is given by log ((10^-x ) +1), or log (to the base 10) of [(10 to the power of -x) +1) The table labelled "log Dec" is actually - log (cos dec) Table 7 provides, as a function of A, log (4/A), where A is in degrees. Table 8 provides log ( 60 / T) where T is time in minutes. But there's no reason, at all, why you should need to know such things. George. contact George Huxtable, at george{at}hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.