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Re: Flat Bygrave alternative configuration
From: Hanno Ix
Date: 2014 Jun 28, 19:08 -0700

Robin,

I have made about 20 "sight reductions" using your alternative flat Bygrave.

Indeed, the larger cos() scale is quite helpful. Also, the range of the cos() in its present form functions well, however I did not quite understand your version that covers negative angles - it might indeed work better yet. So, I am looking forward to your more detailed demo of this idea.

There is one thing I do regret not having on your scales: Indexes for arcmins where possible. The scales are big enough to be inscribed, at least partially, with those. I believe you noticed that yourself. In my experience their missing introduces unnecessary errors . I compared errors using artificial examples based on existing marks vs. ones I had to interpolate. The difference is very noticeable: In the cases of "the first kind" my error was 2sm vs. 3.4sm. Admittedly, my skill to interpolate, my acuity, may patience etc influenced this error, so it might be different with different people.

I have started learning the use of your program. It does deliver great scales. However, my skill level has not advanced to the point where I could add those arcmin marks myself.

Would it be possible for you to revisit the scales and add arcmin marks where you can and when you can find time for doing so? I, for one, would greatly appreciate that.

Thank you for applying your skills for the benefit of us Bygrave fans.

On Thu, Jun 19, 2014 at 5:36 AM, Robin Stuart <NoReply_Stuart@fer3.com> wrote:

Hanno,

       To be clear; in the flat Bygrave, the cosine scale is printed on transparent material and laid over the cotangent scale.

       My Postscript code at http://fer3.com/arc/m2.aspx/Postscript-code-for-making-Bygrave-Scales-Stuart-mar-2014-g27398 is very flexible and it would be straightforward to produce 2 copies of the cosine scale on a single page. The variable CosScaleStartPosition controls the position of the cosine scale on the page. Your result could be achieved by generating 2 versions of the file BygraveAltFlat.prl and passing the cosine scale through the printer twice. The 2 cosine scales would not necessarily precisely align. I'm not sure I completely understand your explanation of how you plan to use it so it's not clear to me whether that would be a problem.

      As I said my code is pretty flexible and contains features that you might find useful. There is a switch that causes the cosine scale tick marks to be drawn pointing downwards which might improve clarity when reading the scales.

      It is also possible to have a cosine scale that runs from say -89°10' through zero to +89°10' rather than 0° to +89°10' as it does now. That way the division cot(z) = cot(x) / cos(y) can be achieved by aligning the zero pointer on the cosine scale with x on the cotangent scale and then finding y by moving right to left along the cosine scale and reading z off the cotangent scale. I will post an example with both features switched on to demonstrate these,

Regards,
Robin

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