NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Bissaker Sliderule
From: Nicolàs de Hilster
Date: 2008 Mar 31, 16:05 +0200
From: Nicolàs de Hilster
Date: 2008 Mar 31, 16:05 +0200
Dear Group,
I cross-post this message to Rete and NavList, so some of you will get
this message twice.
Last January I was contacted by Werner Rudowski with questions about the
Bissaker sliderule. Rudowski is currently writing an article about the
Bissaker sliderule. Robert Bissaker was a Mathematical Instrument Maker
who worked between 1642 and 1664 and created this sliderule, which is on
display at the Science Museum in London, in 1654.
Rudowski contacted me with several questions, one of which concerned one
of the scales: This scale, the so called 'm-scale' (after a description
by Baxandall from 1914), has a, yet unknown, purpose. The divisions have
been measured using a modern metric ruler (which I post here with his
permission):
degrees on m-scale
90 85 80 75 70 65 60 55 50 45 40 35 30 28 26 24 22
mm 0 10 20 32.5 46 61.5 80 99 124 154 189.5 -
-
331 366 406 454
The origin (90 degree mark) is located at 111mm from the start of the
sliderule.
From these values I was able to reconstruct the following two formulae:
1) 154/(TAN(degrees)^1.2)
2) 154/SQRT(2) * ((1/TAN(degrees/2))-1)
I attached an image with both formulae in a more clearer notation. The
constant 154 was taken from the 45 degree measurement and might be
slightly different.
Although the first formula gives a better fit, it seems to me that the
second is more likely as I am not sure whether or not they were able to
solve the power 1.2 in those days.
Would any of you be able to explain the purpose of this scale based on
the figures and formulae given? The part 1/TAN(degrees/2) of the second
formula is known from stereographic projections, so perhaps there is a
link?
on behalf of Werner Rudowski
best regards,
Nicolàs de Hilster
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