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    Re: Cylindrical Slide Rule tube poll
    From: Gary LaPook
    Date: 2010 Jan 22, 21:32 -0800

    Here are some links to photos of the Bygrave that I took in London and 
    previously posted:
    You can see the scales have a butt joint.
    I had written before that the Bygave cotangent scale went up to 89� 45' 
    but the picture shows it only goes to 89� 40' which may no seem like a 
    big difference but it takes an additional spiral to go that extra 5'.
    Richard M. Pisko wrote:
    > On Wed, 20 Jan 2010 01:57:16 -0700,  
    > wrote:
    >> The 'problem' is not parallax as the eye can look perpendicularly 
    >> onto the scales  on the tubes quite accurately; it is the difference 
    >> in scale lengths with different diameters of tube which I would 
    >> consider a potential problem.
    > I believe the sheet of paper wrapped around the innermost cylinder may 
    > be scaled smaller in one direction.  That way, the cut edge will meet 
    > the proper spiral exactly along a longitudinal butt joint (actually, I 
    > overlapped the join onto a quarter inch of blank space) while having 
    > the length untouched so as to match the outer scale.
    >> Theoretically they should be exactly the same scale factors and hence 
    >> same length wrapped around helically.
    > Yes, that would be true if the paper and tubes were infinitely thin.
    >> Different diameters necessarily means there will be slightly 
    >> different scale lengths if printed with the same scale factor.
    > Yes, and so the scale factor in one direction will be changed to match 
    > the diameter of each tube.  The scale factor in the other direction 
    > should be the same on both tubes.
    >> I have not worked out the errors introduced with a real Bygrave SR, 
    >> (I'm not sure of the exact diameters involved and the scale lengths 
    >> themselves)  but assume it cannot be too great or it would be 
    >> noticeable and would have been reported by now.
    > I think a little bit of trial and error in printing will give 
    > acceptable results.  If the spiral segment ends match up on each 
    > cylinder to within 0.01 inches, I doubt any of the calculation results 
    > would differ.  Since the real Bygrave has outside diameters of the 
    > tubes that differ by perhaps ten times that amount (say a tenth of an 
    > inch), the paper scale must have been reduced or enlarged in one 
    > direction accordingly; otherwise there would have been an overlap or 
    > gap of the printed part by about a third of an inch.

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