NavList:

Greg,

>>Step 2. is 90°- X + Latitude<<

I noticed this in my inbox late last night when I looked at my cellphone just before bed.  I got so excited that I got up and tried it out.  Lo, and behold, like a flower opening before me, all of the Bygrave equations started working great.  Thank you so much for helping me on this!!

>>Y> 90° Y= 180° - Y<<

Would I be correct in inferring that if Y < 90°, then Y = Y?

Ageton and Bygrave appear to manage azimuth angles the same way.  Different from Pub. 249, but similar in method to each other.

I thought I would do a comparison of the Ageton equations (formulated to use sines and cosines) with the Bygrave equations (using cosines and tangents) using the calculator on my cellphone.  In testing two cases only so far, both methods have agreed with the USNO site at http://aa.usno.navy.mil/data/docs/celnavtable.php to within 0.1' of altitude and have matched exactly the USNO on azimuth.

More surprisingly, when working through a sight reduction where the USNO says Hc should be 48° 40' and another where the USNO says Hc should be 23° 43', I find that the Ageton equations and the Bygrave equations yield *precisely* the same azimuth and Hc (to the nearest tenth of a minute of arc for both types of value).

This leaves me a question in my mind when I read things like this:

From: Gary LaPook
Date: 2009 Jul 7, 22:06 -0700

The rms of 1.8 minutes using the Bygrave method is much better than
the 4.7' error level you found using the standard sine-cosine formulas
and confirms what everyone has written about the accuracy of the
Bygrave.

So then several NavList members have tested Bygrave against Ageton and found Bygrave more accurate.  I presume this means "more accurate within these particular ranges of Ho or of meridian angle".

What would be some of the conditions under which the Bygrave equations would demonstrate their greater accuracy?

Oh, and what does "rms" mean in the quote above?

Thank you!  I am having a ball with Bygrave equations.  The next thing will be to sort out how to do them with my dad's old 10" K&E slide rule.

____________

I wish my teachers back in 1970 had given the first HINT that sines/cosines/tangents had some USE in the wide, wide world.  As far as I could sort out then, I was engaged in abstract exercises whose only purpose was to pass an exam.  My HS math teachers suffered from an appalling lack of curiosity about the world...which made them not very engaging instructors.  NavList people are a lot more fun folks to be around, even if from afar.  Bygrave equations are like magical incantations that make a positional fix appear, almost (so it seems) out of nothing.

Thanks again!

Bob