A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Longhand Sight Reduction
From: Hanno Ix
Date: 2014 Jun 12, 11:06 -0700
of course, Doniol did work out!
It is the same old basic formula cast, without any loss of info, into a very convenient form.
Long hand multiplications have become hard for us because we didn't do them for so long.
One could test oneself, though, by cross checking with a slide rule. Errors would be distributed over all digits and therefore a discrepancy will most likely show up immediately. This combination, hand and slide rule, would give you both: 4 digit resolutions AND confidence in the results. Or perhaps, Francis will come up with a practical Fuller for Doniol. Might be simpler to make than the Bygrave and end up with better results yet.
Peter did not answer my request for a more detailed discussion of his multiplication-by-hand technique. Fortunately! Forced me to think about it! His method must be based on the fact that only certain combinations of the digits of the multiplicator and the multiplicand affect a particular digit of the result. He memorized the correct combinations and only executes the ones that make up the digits he seeks. The rules are simple and can be easily reconstructed should you not have them in your memory.
Think Napier's bones. As you observed, the process can be awkward. One way or the other, you will sum along a diagonal list, not a column, or start out with the multiplicator and the multiplicand written in a diagonal form to begin with. Peter does that in his mind. The wikipadia article on Napier's bones is quite entertaining.
Since this issue came up I am tempted to learn it myself.
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