Antikythera Mechanism

[Neil WyattModerator @neilwyatt]

I've just come back from a talk at my new local Astronomy Society, by Mike Edmunds, President of the Royal Astronomical Society.

He was talking about “Mechanism and Error in the study of the skies”.

He heads the Antikythera Mechanism Research Project and when I said I was interested in the engineering aspects of the device, he asked me what was a reasonable estimate of the errors in hand drilling holes, diameter about 0.3 mm?

His 'guesstimate' is about 0.1 mm.

This matters because they are trying to calculate the diameter (and hence the number of holes) in an incomplete ring. On the face of it 360 or 365 seem right, but measurements of the hole spacings suggests 354 holes. Errors of ~0.1mm in hole placement in radius would be sufficient to account for this error (because a randomly wandering sequence of holes around the circumference would always appear to be longer distance).

Personally, I think the right way to solve the diameter question would be to measure the chords across widely spaced pairs of holes.

But with regard to the issue in hand, how accurately do you think you could drill a ring of small holes? Probably using a spade bit with a pad and a small bow to spin it. You could use some sort of jig (say a radial bar or strap with a hole).

Bear in mind that the makers will be aiming for 'good enough' not working to any pre-conceived or measured tolerance.

Neil

[Neil WyattModerator @neilwyatt]

A question about manufacture

[not done it yetParticipant @notdoneityet]

I would imagine the problem, in hand, would have been ‘spotting’ the ring of dots before starting to drill. How they determined where the holes should be positioned wrt each other is the answer to the question I would be interested in.

[Ian PParticipant @ianp]

Not really answering Niel's question but 'Clickspring' on YouTube has some videos showing his build of the mechanism using tools and technology that the original maker might have used.

Apart from showings the marking out of the parts he actually made the files and other tools totally from scratch.

The videos and presentation are among the very best of the Youtube

Ian P

[Ian PParticipant @ianp]

Not really answering Niel's question but 'Clickspring' on YouTube has some videos showing his build of the mechanism using tools and technology that the original maker might have used.

Apart from showings the marking out of the parts he actually made the files and other tools totally from scratch.

The videos and presentation are among the very best of the Youtube

Ian P

[Ian PParticipant @ianp]

Double post!! That's the first time it happened to me and I did nothing different than I ever do

[Ady1Participant @ady1]

Depends on the maker IMO

Was he a dabbler or a Harrison

[Neil WyattModerator @neilwyatt]

These are the holes, only visible on an X-ray so not possible to measure directly.

[Neil WyattModerator @neilwyatt]

[Ady1Participant @ady1]

Looks like a dabbler to me

The holes look like they are following a series of straight lines to me too, 6 to 8 holes a pop

So he probbly did a series of 60 round the entire circle, and then filled in the other 5 between each hole kinda thing

p

 

Edited By Ady1 on 04/10/2021 23:22:24

[Neil WyattModerator @neilwyatt]

Very perceptive Ady!

[duncan webster 1Participant @duncanwebster1]

Measure the chord from 41 to 79,and the offset to the middle hole 60, then you can work out the radius and the angle subtended, which then let's you work out how many holes in a full circle. Absolute dimensions don't matter as long as there is no distortion of the image.

I'd probably import the image into cad to do the measure but there might be a better way

[Michael GilliganParticipant @michaelgilligan61133]

What an interesting forensic puzzle, Neil

I would will certainly start by getting my best estimate of the radius of that pitch circle.

To inform that exercise, we obviously need to identify the centre point of each hole

… So the obvious question is :

Do you have access to a higher-resolution image of the X-ray, or is that all we have ?

MichaelG.

.

P.S. __ Your second image shows a radius … but on what basis was that defined ?

Edited By Michael Gilligan on 05/10/2021 07:14:18

[OldironParticipant @oldiron]

Posted by Neil Wyatt on 04/10/2021 23:05:25:

These are the holes, only visible on an X-ray so not possible to measure directly.

Who ever drilled the holes had a pretty good set of number stamps. "hides under table.

regards

[SillyOldDufferModerator @sillyoldduffer]

Posted by Neil Wyatt on 04/10/2021 21:48:01:

…

On the face of it 360 or 365 seem right, but measurements of the hole spacings suggests 354 holes. Errors of ~0.1mm in hole placement in radius would be sufficient to account for this error (because a randomly wandering sequence of holes around the circumference would always appear to be longer distance).

…

As the Lunar Year is 354 days possibly the mechanism is based on, or predicts, phases of the moon rather than earth years and days. In which case the hole placement and accuracy looks reasonable for hand methods.

I like Ady's method, but would expect the reference holes to be more accurately set than intervening holes and don't see much sign of that – they're all a bit random. If I was making it, I'd try marking out a much larger circle, and using a long rod to scale down to the instrument's circle. The outer end of the rod could be moved a fixed distance from the previous point to step out the angle, or moved between pre-made marks.

Not sure how I'd mark out the outer circle because the lowest factor of 354 is a prime number (59) which can't be made easily by dividing by two. However, as 60 is easily divided by two, maybe it was done by marking out 60 divisions on the big outer ring and then losing one by eye.

A long rod being a little bendy coupled with a 60/59 approximation might explain why some of the holes are noticeably off, see the wide gap between 55 and 56.

The mathematics of the day were fairly advanced, making the theory available to the builder. What's surprising is the use of gears in an instrument this ancient. Most impressive.

Bow driven drill seems likely, but not obvious to me how very a largish number of fine drill heads could be made to the same diameter. They weren't ordered off the internet!

Dave

[John HaineParticipant @johnhaine32865]

Not quite to Neil's question, but there is an open-access copy of two papers on the mechanism on the BHI website, where they present the evidence and arguments for 354 holes. Clickspring, a/k/a C. Budiselic, is one of the authors.

**LINK**

https://bhi.co.uk/wp-content/uploads/2020/12/BHI-Antikythera-Mechanism-Evidence-of-a-Lunar-Calendar.pdf

Edited By John Haine on 05/10/2021 12:29:31

[Neil WyattModerator @neilwyatt]

Posted by Michael Gilligan on 05/10/2021 07:05:45:

What an interesting forensic puzzle, Neil

I would will certainly start by getting my best estimate of the radius of that pitch circle.

To inform that exercise, we obviously need to identify the centre point of each hole

… So the obvious question is :

Do you have access to a higher-resolution image of the X-ray, or is that all we have ?

MichaelG.

.

P.S. __ Your second image shows a radius … but on what basis was that defined ?

Edited By Michael Gilligan on 05/10/2021 07:14:18

There are much better images here, this links to the best. You can also download the full paper:

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

[Neil WyattModerator @neilwyatt]

Posted by SillyOldDuffer on 05/10/2021 12:11:00:

Bow driven drill seems likely, but not obvious to me how very a largish number of fine drill heads could be made to the same diameter. They weren't ordered off the internet!

Dave

Agreed, I pointed out that iron and bronze are fairly close in hardness. I wonder how many holes per drill?

That said, there was some knowledge of electricity Baghdad_Battery, so p[erhaps the Greeks had an early spark eroder

Neil

[Neil WyattModerator @neilwyatt]

Much as I find this discussion fascinating, has anyone got any estimates for the accuracy of setting out and hand drilling small holes?

I seem to recall Tubal Cain/Tom Walshaw did some experiments in his academic role at Loughborough University, that he recounted in ME. Getting toolmakers and apprentices (I think) to mark out and drill holes.

Any practical tests welcome as well as theoretical.

I suspect that you could achieve a high degree of accuracy by making a large enough jig. I expect the radial placement was done by marking out a strip and wrapping it around the device (or a larger circular object) – you would expect such a simple arrangement to be standard kit for marking out the many gears.

The limit of accuracy could be a pilot hole used for drilling and its wear, but I suspect marking a line off of the edge of the 'pointer' might have been the approach.

[Neil WyattModerator @neilwyatt]

Next thought… Prof Edmunds pointed out some of the measurements would have had large cyclical errors, e.g. it would have predicted lunar months accurately well into the future, but moon phases could have been many days out.

He suggested it may have been a teaching aid, rather than a calculator per se. as they had the capability to calculate astronomical events manually to far greater precision.

Neil

[Mick B1Participant @mickb1]

Do we know whether the maker(s) might've had magnifying lenses? Could make a lot of difference to marking-out precision.

[Dave HalfordParticipant @davehalford22513]

Posted by Mick B1 on 05/10/2021 14:18:43:

Do we know whether the maker(s) might've had magnifying lenses? Could make a lot of difference to marking-out precision.

Blown glass bottle with water in it?

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Neil Wyatt on 05/10/2021 14:14:32:

Much as I find this discussion fascinating, has anyone got any estimates for the accuracy of setting out and hand drilling small holes?

[ … ]

.

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.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Neil Wyatt on 05/10/2021 14:02:25:

.

P.S. __ Your second image shows a radius … but on what basis was that defined ?

There are much better images here, this links to the best. You can also download the full paper:

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

.

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

MichaelG.

[Neil WyattModerator @neilwyatt]

Posted by Michael Gilligan on 05/10/2021 15:01:31:

Posted by Neil Wyatt on 05/10/2021 14:14:32:

Much as I find this discussion fascinating, has anyone got any estimates for the accuracy of setting out and hand drilling small holes?

[ … ]

.

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.

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

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