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    Re: Bygrave Scale Lengths
    From: Brad Morris
    Date: 2013 Jan 30, 20:56 -0500

    Hi Gary

    In the excitement of the discovery of the official instruction to use the F-Tafel when the declination was close to zero, perhaps you missed my other post regarding the (co)tangent scale.

    While I'm positive you have Ronald Van Riet's excellent paper on the Bygrave Slide rule, others may not.  Consequently, here is a link to that paper in the NavList archives:


    If you closely examine Figure 29, zooming in on the left side of the image, you can indeed see the uppermost region of the scale.

    In that image, the highest numerical value I can make out is 89 deg 40 minutes.  Its clear from the mathematics that there cannot be an extension to 89 deg 59 minutes, I see that taking many meters more in scale length.  At 89 deg 40 min, the scale does not wrap around the cylinder even once more.  So that's the top of the scale.  I posit that the lower end of the scale will match the upper, with a 20' exclusion zone.

    This has been a real blast!  I feel like we have really extended the knowledge base of the Bygrave and variants.  We have official instruction of what to do in this case. 

    Thanks to everyone who participated so far.  The help is seriously appreciated!


    On Jan 30, 2013 6:36 PM, "Gary LaPook" <garylapook---.net> wrote:

    I wish I had spent more time examining the MHR-2 so that I could answer your questions. Next time you are in London you can see it, I can give you contact information to set up an appointment. I posted details about my inspections of the MHR-1 and 2 and the Bygrave back in 2009, you can search the archive.

    If I had taken pictures of the ends of the scales then we would know, but I didn't. I notice that the scale is marked every two minutes greater than 45 degrees but I don't have the ends of the scales. I can see using the magnifiers but a vernier would not work with a scale that is not evenly spaced such as the trig scales.

    Hi Gary

    Image 122161.img_2160.jpg tells the tale!

    In it, we see the rules for using the device. Within those rules, we see the standard admonishments for the MHR1, with one major and glaring change. In German, we have:

    Bei d nahe 0 oder t nahe 0 und 90 verwende F-Tafel

    Which I loosely translate to:

    Do not use the slide rule (F-Tafel) when declination is near zero deg or when the hour angle is near 0 or 90 deg.

    The is no longer any numerical prohibition like 0 deg 20 min or 89 deg 40 min. It just says "near" (nahe). This could be understood to say the same thing, since 20 min is near to zero.

    But given the precise directions of the MHR1, I would like to think that near now means that the scale has been extended downwards and upwards, as we have discussed, towards 0 and 90 deg. To what value? The images do not reveal this data point. Pity. I'd like to think that it went to within an arc minute, the trick of a tiny offset to include 0 deg 90 deg not withstanding.

    What do you make of the conversion table, the adjustment knobs and the magnifying glass? Magnifiers are typically associated with verniers and fine graduations.

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