Hannah Fry (a longstanding team member on Numberphile) had a lovely exposé about how the ends of the tunnel meet up:
Tunnelling through a Mountain - Numberphile
23rd Jan. 2022 | Numberphile
https://www.youtube.com/watch?v=kwrDX5qkwvA
She left however somewhat vague (though she offered suggestions) how they knew where E and S were, and that the elevations were equal on both sides, here I step in:
1) E, W and S, N:
5:54 Compasses - drawing tool, yes.
Magnetic tool for finding N, S, anything at right angles (E, W) and anything in between, no.
Marco Polo brought these latter ones from China. In his day magnetite was explained as:
- element earth
- under influence of Mars to make it iron
- and then under influence of Venus to make it attract.
Magnets worked even so, and as said, it was in China they were first used for compasses. In early modern times they were equipped with a paper that marked off not just quarters, not just eighth parts (NE, SW etc), not just sixteenths (NNE, ENE etc) but even thirtyseconds (E by N, ENE by N)* ... Belloc wrote an essay about a sailor who went mad as his captain or boatswain was explaining this.
Now - what did Polycrates (po-LEE-kru-TEES) use, as he lived before Marco Polo?
You might use the other type of compass or simply strings and pegs, in drawing straight angles, and that would include straight angles between a shadow marked at sunset and one marked at sunrise. At equinox these would be due W and E of what was throwing the shadow, and either way they would make a line due W-E, so that a straight angle would mark the exact time when the sun was in zenit, the shadow straight N.
Ensuing exchange:
- Mark Tillotson
- But the magnetic properties of iron were known the Greeks, its not a big stretch for them to have the compass - after all we get the word magnet from the greek region of Magnesia, so they had magnetic rocks and iron. Thales of Miletus described magnetic phenomenon (we only have second hand accounts of this apparently) - a lot of knowledge may have been lost to the ravages of time.
- Hans-Georg Lundahl
- @Mark Tillotson We have no direct reason to believe Greeks used magnets for compasses.
We have no reason to believe seafarers would have lost such knowledge if they had had it.
We have every reason to believe that Marco Polo got the magnetic compass from China. And that prior to him, it was unknown in the Mediterranean.
Greeks were not all that famous for practicality in using scientific discoveries. Nero used a lens as a magnifying glass, but corrective eye-glasses only came with the Middle Ages. Archimedes used a screw for elevating water slowly - around 1400, Europe had a practical push and lift pump and was attaching objects to each other with screws turned by screwdrivers. While screws for oil presses / wine presses already existed in antiquity, Europe added screws for woodcut pressing and printing with moveable types in the Middle Ages.
2) Elevation:
6:57 Build a momentary dam around the whole mountain or at least on one side the entrances need to have contiguity around the mountain.
Then fill that dam with water. Tada, entrance levels are equally high!
* Correction on these
"(in first quadrant) north by east (NbE), northeast by north (NEbN), northeast by east (NEbE), and east by north (EbN)"
Thank you, wiki:
https://en.wikipedia.org/wiki/Points_of_the_compass
