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Of course if the scale was wrinkled it could cause an error but a 
distortion of the scale big enough to cause a problem I think would be 
noticed by the user so he would smooth it out to cure the problem.

One caution I neglected to mention is that it is important that both the 
cotangent scale and the cosine scale be printed to the same scale. The 
PDF files I provided do print to the exact same scale on my Hewlett 
Packard ink jet printer and on several printers I have tried. If you 
make a copy of the slide rule compare the cosine scale against the 
cotangent scale. The cotangent scale goes through two cycles on each 
line so the cosine scale should match up against one cycle, half of the 
cotangent scale. If it doesn't then change the printer scale slightly 
using your printer controls to make it work out.


I have made a half dozen of the cylindrical models and they are easier 
to use than the flat model because the scales are easier to read since 
they are separated and do not overlie each other. But they are much 
harder to make, getting the length of the scales just right and mounting 
the scales on the tubes, getting it exactly right, forming tubes of 
exactly the right size to fit tightly enough together to provide enough 
friction so they maintain their alignment but not too tight to prevent 
easy manipulation. I have often had to start over again when something 
went wrong during the construction.

So I think the flat one is quite useful. It can be printed off by 
anybody with an ink jet printer for pennies each and if you want to seal 
the cotangent scale in a plastic document protector it raises the cost 
to about a buck each.

Obviously I like the Bygrave and I think it is quite elegant in its 
simplicity and in its power to solve the navigational triangle, a 
computation that has involved the efforts of many of the great 
mathematicians over the centuries. One of my objectives was to make it 
available to a much larger audience of navigators so they can evaluate 
it for themselves.

BTW, does anybody know what became of Captain Bygrave after 1920?


Oh, and thanks for the compliment.

gl



bmorris@tactronics.com wrote:
> Hi Gary
>
> Just to be clear, I was not questioning the accuracy of the Flat Bygrave, 
WHEN FLAT.  Just as you have indicated, when flat, the device yields 
perfectly acceptable results.  Since the scales are a realization of the 
equations, unquestionably, they should work when used as directed.
>
> If, however, one scale was distorted by an out-of-flat condition, then we 
would see errors proportional to the error in flatness. One scale flat, with 
the other distorted will yield problems. That was my assertion and remains 
so.  Sharp as you are, you should see that as well.  
>
> My comments also indicated wrapping the scales around cylinders, which 
eliminates the distortion of one scale to another.  That solves the 
out-of-flat condition by making the surfaces stiff.  The follow-on problem, 
how to lock one cylinder to another securely, forces a mechanical solution.  
Bygrave himself didn't solve that properly.  There are a few mechanical 
arrangements I can think of to do that, all involving multiple moving parts.  
This would force your simple Flat Bygrave solution to a more complicated 
cylindrical Bygrave solution, and keep the device out of the hands of many 
who would try.
>
> Again: Nothing wrong with the Flat Bygrave when used properly.  You should 
be rightly proud of it.  Gosh knows I would be!
>
> Best Regards
> Brad  
>
>
> >
>
>   



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