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Re: Flat Bygrave alternative configuration
From: Hanno Ix
Date: 2014 Jun 30, 17:15 -0700

Robin,

I've spent some more time with your flat Bygrave scales. I had them printed on a B-size cardboard by a professional printer. Let me just say, I am amazed at the accuracy!

The version with the neg. angles does make the reasoning for the dual zero pointers clear. They work well but once one understood them the inclusion of the neg. angles per se isn't rally adding much - unless I am missing something here.

Returning to the additional arcmin marks: There is no reason I can see why they needed to be labelled. Their meaning would be perfectly clear simply by their location. As to the shape to the tick marks: I have used just small dots for a similar purpose. The dots simply straddle the base line and attract attention by their contrast in shape: circles v.s. bars. I am attaching a picture to convey the concept. Here I used MATLAB for those scales, and including the dots was very easy with it. I don't know if that would be so in a PS program, though. PS, however, seems to produce sharper lines and characters. See if you like such a scheme.

I just feel presently one cannot fully take advantage of the excellent accuracy of your scales by lack of resolution. My interpolation by eye introduces needlessly errors of +/- 1' or more. What a shame. I truly think additional armin marks would significantly enhance the utility of your scales

Anyway, Robin, I have had much pleasure using your fine work.

Hanno

On Sun, Jun 29, 2014 at 4:31 AM, Robin Stuart <NoReply_Stuart@fer3.com> wrote:

The text in my previous post doesn't seem to have wrapped correctly so here it is again with line breaks inserted

=============================================
Hanno,
As promised I attach pdf files in which the cosine scales are
printed high and low on the page. The programs that generated them differ

by a single statement
/CosScaleStartPoint { 2.3 cm 11.5 cm } def
for the upper scale and
/CosScaleStartPoint { 2.3 cm 1.5 cm } def
for the lower. They can be printed together by passing the page twice but

as noted previously they will not then be precisely aligned.

I also attach a version of the flat Bygrave in which the cosine scale runs
from -89°15' through zero to 89°15' with signs omitted on the negative angles.

This extended scale makes it fairly obvious why the dual zero pointers work.
As I alluded to in an earlier post, with this scale multiplication is performed
by aligning a zero pointer with a number on the cotangent scale and reading left

to right. Division is performed by aligning a zero pointer with a number on
the cotangent scale and reading right to left. The CosScaleTicksDown flag has
been set to true in this scale which allows calculations to be performed by

aligning the cosine and cotangent scales baseline to baseline which may enhance
visibility.

The code to generate the scales requires explicitly listing how each and every
scale tick is drawn and labeled. Inreasing the number of ticks just requires

expanding that list. Where do you think the additional ticks should be added?

Regards,
Robin

Note: in generating the last scale I found that not all signs were being omitted
from the lables of negative angles and also that the program would fail for

certain combinations parameters. These bugs have been fixed in the attached
Postscript file and I will post the new version of the code for other Bygrave
types in due course.

File:

Subject:
Author:
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