A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2016 Sep 1, 11:03 -0700
Robin Stuart, you wrote:
"The problem is that the raw lunar distances in the Almanac have been rounded to the nearest 0.1' "
In which almanac?? The historical almanacs always listed the distances to the nearest second of arc. In my modern tables, this is an option. For example, you can select seconds of arc (normal precision), or decimal degrees (2.8 times higher precision than seconds), or minutes and tenths (6 times lower precision than seconds). Historians should select the first. Modern navigators should prefer decimal degrees, always. Traditional navigators prefer decimal minutes.
I think the attraction of proportional logarithms is that they sound exotic and novel when we first encounter them... "A whole new type of logarithms?? Wow. Why didn't anyone tell me about these proportional logarithms?! They must be really cool!" But they're trivial and barely different from common logarithms, and their entire purpose was to so solve a basic division problem in an era before slide rules and before cheap handheld calculators. Again, as I mentioned in a previous post, the math problem that they help us solve is no more complicated than this:
T = 40.1*180/93.7.
That's fourteen keystrokes on the cheapest calculator you can find. Proportional logarithms (defined as Plog(x) = log(3/x) which equals log(3) - log(x)) were useful tools two centuries ago. If you're interested in historical computation, you should definitely try them out once or twice just to see the work. But pretending they're practical in any way today is antiquarianism --not quite jousting with wooden swords at the Renaissance Fair, but getting close! ;)