# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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The Bygrave Slide rule
From: UNK
Date: 2009 May 29, 02:46 -0700

```Brad's point is interesting - he points out that the reversed 90-180 degree
markings on both scales show that the scales are logs of abs(tan) and
abs(cos) respectively. Maybe this is just a 'kludge' for the annoying fact
that logs of negative numbers don't exist. It's left to the user to sort out
the signs when using logs to work with mixed-sign numbers.

However, I don't think Brad's point does impact on my postings, since it
applies whether or not the scales are 'thought of' as cotan/cos or
tan/secant.

In effect all I am saying is that I found the references to cotangent scales
in the papers by Ron and Gary were counter-intuitive, and the alternative
tangent/secant interpretation was easier to grasp, so I thought it worth a
posting. If no-one else agrees with me then I will go back into my cave.

I can't contribute an answer to Gary's puzzle about the apparent impossibility
of using the tangent/cosine method at the equinoxes (this puzzle is not
limited to the Bygrave solution). A quick look at the celestial triangle
tells me that if the sun is near the equator then the perpendicular from the
sun to the observers meridian is also near the equator, so the equation for
azimuth simplifies to tan(A)=tan(H)/cos(c), but this may already be what Gary
has rejected as not being very pretty. I wondered whether the discarded
azimuth in the alternative calculation might be a clue, but this is just
equivalent to swapping the observer with the sun. The altitude comes out the
same of course, but the discarded 'false' azimuth is then seen to be the
azimuth of the observer as seen from the sub-solar point, which isn't very
useful, even on March 21st.

regards
Peter M

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