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On 3 May 2006 at 0:30, George Huxtable wrote:

> Ken Muldrew wrote, responding to a posting from Jim Hickey-
>
> | > My personal preference, assuming I had only a choice of a graphical
> method | > like Margetts, a tabular method or a slide rule type method. I
> would choose | > the slide rule method first, graphical second and the
> tabular last. Clearly | > I would be out in left field compared to the
> norm. | | Compared to the 1790 norm, anyway. I would choose the same order
> as you | (if there was a slide rule type method to choose from).
>
> ====================
>
> Well, there was, it seems. One such method appears to have been available,
> from Margetts himself.
>
> This is what Eva Taylor had to say about Margetts, in "The mathematical
> practitioners of Hanoverian England, 1714-1840".
>
> 868 Margetts, George, M.I.M. (1789-1803)  [presumably, these were they
> dates between which he flourished].

I think you are correct; that is a common suffix for clock and watchmakers
(presumably to make it easier to date clocks and watches).

> 42, Penton Srtreet, Islington ~(1789),
> London ; 21 King Street, Cheapside, London (1792) 3 Cheapside, London
> (1801).
>
> 1789-90. Horary & Longitude Tables. These were accompanied by engraved
> plates, or Rotulas which allowed graphical solutions of nautical problems:
> 1. A Logarithmic sexagesimal Rotula for giving proportional parts. 2. A
> Rotula containing the Line of Numbers, Sines, Tangents,  etc., equivalent
> to a 6-foot Gunter's Rule. 3. A Decimal Rotula for Mensuration & Gauging.
>
> 1790-3. Tables for correcting the effect of Parallax and Refraction.
> Thomas Lynn [1009] said he had used Margett's tables for thirty years at
> sea, and Mackay [866] praised his 4-foot slide rule for navigation, while
> Patrick Kelly [736] describes his rotulas, which could also be used for
> solving surveying problems.
>
> The rest of Taylor's entry refers to Margetts' timepieces.
>
> Taylor is frustratingly vague about what Margett's slide rule actually did.

I think the "slide rule" is really just Margetts' graph containing the
parallactic proportional table, the duodecimal proportional table, the
three hour proportional table, dip table, parallax in altitude table,
lunar semidiameter, and augmentation of lunar semidiameter. This is a fold-
out graph at the front of his book. I printed mine out at 20 inches and it
seemed adequate, but perhaps the original was 48 inches to increase
accuracy. One would have used a separate ruler to slide across the graph
to take various points out to the horizontal and vertical axes. The word
"rotula" seems to refer to a graph that is used for interpolation (cf.
James Ferguson's Astronomical Rotula).

> There were other such instruments, it seems, I copied to the list a similar
> account from Taylor, about David Thomson and his brass instrument for
> correcting lunar distances,  under threadname "Lunars: Thomson's tables",
> on 19 April. Again, it's short on detail.

Thanks, I'll look it up.

> There may be an interesting project awaiting someone, to search out any
> such instruments in museums, and discover how they were used.

Indeed. The ingenuity of these "mechanics" never ceases to amaze me.

Ken Muldrew.

   

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