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First, I'm glad I didn't throw stones at the guys from 100 years ago. Sure enough. I messed up in the triangle in the lower right. X should be =y/2 where 2 is the corresponding factor for 26d34m.

Robert, I started adding the left and right angles -trying to read something into those. Then lines "2" and "3" angles don't add up. "2" adds to 91d60m or 92d. Line "3" adds to the same.
The “T” scale on a slide rule has the same value. Arrrgh! They aren’t both Tangents.a The “DIV” side is CoTangent which is 1/Tan. On the slide rule T scale >45d, a value of 2 is Tan 63.45d and INV COT 2 is 26.55d. Really close to the numbers that should have been engraved on the sextant.

The rule for the engraved table should be: “On the left side of the table multiply (Mul) the distance to the object by the Mul number. On the right side of the table, divide (Div) the distance to the object by the Div number.”

The problem is that they meant this abbreviated table to come out to eight whole numbers that were tangent/cotangent values. The angle 65d26m or 65.43 has a Tan of 2.19. Tan of 73.56 is 3.39 instead of close to 3.00. The angles listed should have been 63d 26m and 71d 34m.

Tony, something about 3 km away is a problem. Unless it’s 3.00 km away. Then you pick the closest angle that includes the unknown length and move towards or away until the ends match on the sextant. I think it was meant to be more of a quick and dirty way to make an educated guess on things like tree height where moving 10 or 20 feet (or a few meters) would make things line up. Thinking about it, you’d have the same problem today with only optical instruments. You have three unknowns - distance from the object at a right angle, length of the object, and the angle between the ends. You need two of those to solve for the third.

I’m not sure if engraving was too expensive or if really fine engraving was not practical. I’ve attached a photo of the printed paper inside the cover of another box sextant. It’s messy.
Regards, Noell

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