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Here are some links to photos of the Bygrave that I took in London and 
previously posted:


http://www.fer3.com/arc/imgx/IMG_2095.JPG
http://www.fer3.com/arc/imgx/Copy-of-IMG_2100.JPG
http://www.fer3.com/arc/imgx/IMG_2097.JPG
http://www.fer3.com/arc/imgx/IMG_2098.JPG

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'.

gl



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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