A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2014 Jul 1, 10:30 -0700
Glad to hear that you are finding the Bygrave scales useful.
My thinking with the negative angles on the cosine scale is as follows: When you do multiplication you line the zero pointer up against a number on the cotangent scale which you interpolate by eye. When you perform division you have to line up 2 numbers both of which are interpolated by eye. Without a cursor that you would have in a normal slide rule this can be a bit tricky to do. With the negative angles you can calculate cot(z) = cot(x) / cos(y) by lining the zero pointer on the cosine scale up against x on the cotangent scale and then looking for y in the negative side of the cosine scale.
I can certainly add additional minute marks on the scales but of course that can only be done up to a certain point near the zero end of the cosine scale before things all merge together towards zero. For the flat Bygrave I found personally that having too many markings introduces a fair amount of visual confusion so I followed Gary Lapook's marking densities. It would be a simple matter to turn the cylindrical scales found at http://fer3.com/arc/m2.aspx/Postscript-code-for-making-Bygrave-Scales-Stuart-mar-2014-g27398 into flat versions and I can do that for you. Of course that would require the supplementary angles to be removed.
Regarding your printing of scales on B size paper; I assume you did some printer scaling. This will have a couple of effects that may be or may not be advantageous. The scale tick marks will be thicker and the labels will be larger than in the original. Finer scale marks presumably make for more precise readings. Also the spacing between scale cycles will increased and that would mean the area available on paper is not be used as efficiently as possible. It should be straightforward to produce a version of the scales that are optimized for B size paper and can be printed directly without scaling by the printer. Would that be of interest?