NavList:

Hi Robin,

It's been four days since you posted this, and I'm sorry I haven't gotten back to you sooner. 

First, I have to say, this guy sounds like a typical late 19th century self-important and slightly delusional "lunarian dabbler". There are too many of these clowns, all doing the same dance, singing the same song... "at last, thanks to my brilliant invention, the math of lunars is finally rendered easy-peasy, and so, at long last, lunars will be practiced regularly at sea... and aren't I great for doing this?" But they're wrong. They're wrong because the math was already easy. The problem was already solved. And lunars are (already) no longer necessary. 

:)

All that out of the way, the math in Saxby's machine appears to be a simple variant on Thompson's classic short method (or Elford's or Turner's or various others in that family), which was an evolution of the standard series method. Saxby's device mechanically, graphically solves the "easy part" of the method, which was historically a trivial logarithmic calculation [for anyone reading along who has attended my "Lunars and Longitude" workshop, this is the calculation of P1 and P2]. By the nature of his computation method, he assumes a fixed, standard value for the HP and then scales that up or down by the actual HP. That's ok, but it's a long way to go to replace a very short logarithmic calculation.

But there's something missing...

The clever part of those short lunar methods is not the logarithmic computation or the computation done by the device in Saxby's approach. The clever part is the table of the remaining small correction --the "everything else" table. Where is that in Saxby's method? Is there a missing page in the patent declaration? Or is the "secret sauce" in his method just another copy of Thompson's "everything else" table (his "Third Correction" table), which was not included in the patent because it was directly imported from an earlier publication? This other table must exist. The method demands it!

Why didn't his method succeed in the navigation "marketplace"? Surely it's because the lunars problem was already solved and had been solved for decades. Too little; too late.

Another oddity in the patent papers: As inputs, he lists the "apparent distance corrected for semi-diameter(s)" and the "Moon's altitude corrected for semi-diameter and dip" [yes, this is the standard pre-clearing step for those quantities], but then he lists "Sun'n's altitude corrected for semi-diameter, dip, and refraction". That serves no purpose that I can see. Why create an asymmetry between the Sun and Moon in this process? Yet another sign that Saxby is simply confused.

Frank Reed