Antikythera Mechanism

Blown glass bottle with water in it?

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Not an estimate, Neil but possibly relevant … Have a look at the section about John Bird : **LINK**

https://www.academia.edu/5340304/Dividing_to_Rule_Precision_Mathematical_Instruments_in_mid-18th_Century_England

MichaelG.

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Thanks, Neil … it also answers the question posed in my P.S.

MichaelG.

Unfortunately that site will only let me in if I allow it to download my contacts!

Neil, I'm registered with Academia.edu, I just emailed you a copy to your mytimemedia address.

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Sorry … forgot about that little scam, and the iPad didn’t mention it

… and I did not need to log-in to just read the paper

I’ve been warning people not to use it for a while now.

MichaelG.

Edited By Michael Gilligan on 05/10/2021 17:30:43

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But, unfortunately, I am not entirely convinced by their Least Squares Fit

… see the substantial deviation from the circle within my green Region of Interest :

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MichaelG.

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If we are trying to decide how many holes there must be in the full circle, then we need a good estimate of its radius.

That also looks like an area of damage, I suspect that without all the corrosion it would no longer be attached to the rest.

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Good point, Dave

… so we’re down on valid hole locations

MichaelG.

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Taking Neil’s best available image : **LINK**

https://www.researchgate.net/figure/Fragment-C-showing-degrees-of-longitude-on-the-zodiac-scale-as-well-as-the-holes_fig5_252678779

They have obscured the hole numbered 1, so I suggest we need to start at 2

The presumably-displaced group starts at 73 … so realistically we have 2 to 72 available for investigation.

I plan to measure the angle subtended by various groups of holes and do some simple statistics

… The big problem is the low resolution of the image, and therefore the difficulty in locating centres of holes !

360/355 is difficult to distinguish from 360/354 when you are measuring fog. …

MichaelG.

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Edited By Michael Gilligan on 05/10/2021 23:13:40

The paper mentions the fracture.

On the plus side, i measured the distances from hole 1 to 41 and 41 to 81 as being the same.

(They shouldl have numbered the holes 0-80 IMHO).

Neil

Thankj John,

Neil

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(a) True, but [rather worryingly] they appear to be using those displaced holes

(b) What were you measuring ? … chords and/or subtended angles ?

(c) Agreed

MichaelG.

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Note: The white dots at [or near] holes1, 9, and 81 are theirs, not mine.

… and I don’t think they are sufficiently accurately placed to decide between 354 and 355

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The angular difference between those two counts is less than 0.003° per step

MichaelG.

My random 2P's worth:

They knew about gears and ratios at that time so could they have made some kind of 'rotary table' out of the parts they had already made?

Tin hat now on

A very tentative thought, would it be more accurate to mark out the holes on a much larger radius and then follow the radial lines towards the centre until the required diameter is met?

David

Excellent idea in principle, but its implementation raises questions of its own, such as how to get a reliable straight radial line to mark from - a simple tight cord might not be easy to use.

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Well … I’ve had a go, and it’s even worse than I anticipated

First I scaled the photo up by 500% and then drew lines from the marked centre to [my best estimate of] the centre of various holes, and recorded the angle subtended by each five steps.

Tabulated and calculated:

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The result is, to say the least, unconvincing !

It is, however, reasonably predictable when we remember that tiny angular difference between 355 and 354 holes.

If anyone would like to repeat the exercise, as a check on my work … Please Do

MichaelG.

Here’s a ferinstance of the fog which we are attempting to measure:

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MichaelG.

Regarding the deviation from circular. There are two reasons that the holes are non circular (assuming they were to start with). Firstly as has been mentioned that there is a physical distortion/fracture etc or that the XRAY image was not exactly normal to the plane of the hole circle. In the second case there will be some projection errors at right angles to the rotation axis. I assume that the images were obtained by 3D XRay scanning and reconstricted to show the relavent slice. It would be nice to know the origin of the data.

regards Martin