NavList:

Hello Francis,

You wrote:
"I realise the 1' accuracy of the Bygrave is probably not good enough for regular lunars, but, I'm getting very accurate results so far using John Karl method page 93, if I start with known Relative Bearing angle(RBA), declination (ho moon),lat (Ho sun.I basically do the "great circle" calc and get accurate LDo."

You say you start with the known azimuth difference (John's expression "RBA" here is un-necessary, and in fact, his whole methodology is idiosyncratic). This is a step halfway through the standard "direct triangle" methods of clearing lunars. How do you get that azimuth difference? Well, of course, you calculate it from the observed lunar arc and the observed altitudes of the two bodies. So if there's any error in that process, it feeds into the second half. Once you have the difference in azimuth, you run the calculation again with the corrected altitudes (corrected for azimuth and parallax just like any common celestial sight) and then calculate the corrected lunar arc. So you're really doing that "great circle" calculation twice. If there is a "standard deviation" error (or some other error measure) of one minute of arc in each great circle calculation, then you could expect about 1.4 minutes of arc s.d. error doing it twice, as in the lunar clearing calculation. That's big, and historically it would have been unacceptable. That error would be in addition to any other errors in the whole process. An error of 1.4' in the clearing corresponds to an error in Greenwich Time of about 168 seconds or about 42 nautical miles at the equator. Not very good! Of course, though, this is all a matter of degree. There are circumstances where an error that large might be acceptable. For example, if you work the process on paper, clearing it on the slide rule might be provide a nice "sanity check".

I had mentioned before in a message to you that you wouldn't normally get acceptable accuracy for lunars working them on a slide rule. Later that day, it dawned on me that this isn't true at all ...IF we clear lunars using one of the "series methods". I presume you've read my "easy lunars" essay (and/or NavList post) describing how to clear lunars with a series method on a simple calculator. I note there that the calculation only needs to be accurate to three or four significant digits, and that should be well within the range of your Bygrave slide rule.

And you wrote:
"As an intellectual challenge, could anyone help me work out a method to calculate [azimuth difference] on the Bygrave?"

It's still completely analogous to the great circle problem except you're solving for the difference in longitude instead of the distance on the circle. I don't have much interest in slide rules personally so I wouldn't know how to set it up. But it should be straight-forward, right?

You concluded:
"2)There was a lot of discussion on Bygrave replica manufacture over the last few years. Any updates on status from anyone? I have an original MK11A circa late 1920s, but no serial number and a homemade replica, both work perfectly, if anyone interested in details."

I haven't heard from any of the other would-be Bygrave replicators, but Gary LaPook built a nice working replica and also developed his "Flat Bygrave system" which allows anyone with a printer and a few sheets of printer transparency to use the same calculational processes as the original Bygrave. Transparency film is rather pricey these days ($75 for a box of 50 sheets is not uncommon).

And yes, I would love to see some photos of your original Bygrave and also your homemade replica. I'm sure others would, too.

-FER

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