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

    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.


    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



            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



    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?





    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.



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