View Full Version : Galileo's pendulum

split system breaker
21st Feb 2015, 22:00
Just been watching a TV programme on the history of timekeeping. It restated the so often told story of Galileo's observation of a swinging suspended lamp; he noticed its periodicity was constant, and then proved this with a series of unstated experiments.

What I want to know is how did he notice this in the first place? And then how did he prove it?

The only true timepieces available were sundials or shadow clocks; water clocks or sand glasses could measure elapsed time to some extent, as could a burning candle, but how could you use any of these to prove, or even detect, constant periodicity of a pendulum.

Anyway, it's probably time I went to bed.

21st Feb 2015, 22:05
As the swinging lamp was, in fact, a chandelier (in Pisa Cathedral), he might have just 'counted' - and noticed that, regardless of amplitude, the time taken was constant.

Galileo discovered the crucial property that makes pendulums useful as timekeepers, called isochronism; the period of the pendulum is approximately independent of the amplitude or width of the swing.

From:- http://en.wikipedia.org/wiki/Pendulum#1602:_Galileo.27s_research

split system breaker
21st Feb 2015, 22:13
But that doesn't prove anything; how did he know his count was constant and equal, the same applies to breaths or heartbeats?

I'm not being difficult here, I think it's something we've all just accepted without questioning for, well, a long time...

21st Feb 2015, 22:18
By remarking that the swinging lamp was a large chandelier, I assumed (but didn't remark) that the period would be quite 'long' - therefore relatively easy to 'time' by counting (rather than a short 'clock' pendulum - which would be quite quick).

21st Feb 2015, 22:23
one over 2 pi times the root of l over g to a close approximation. Mass doesn't enter into it.

After etc...

Loose rivets
21st Feb 2015, 22:24
Indeed, henry, that's what the nice but dim bloke in the program said. BUT FOR ****'s sake. What a bizarre load of total bollox mixed with simplistic tat, overlaid with a sickening noise labeled as music background.

Phew, got that orf me chest.

It was thought that Galileo's father, a musician, taught his son such exact timing that he could time his experiments in his mind alone. Remember, dropping things off the Leaning Tower probably did not happen - apart from a public display or two - but timing balls running down curved troughs probably was the way it was done. That probably word keeps cropping up.

One and two and three and . . . Dad could better a candle anytime.

Vincenzo, in his study of pitch and string tension, produced perhaps the first non-linear mathematical description of a natural phenomenon known to history.[1] This was an extension of a Pythagorean tradition, but went beyond it. Many scholars credit him with directing the activity of his son away from pure, abstract mathematics and towards experimentation using mathematical quantitative description of the results – a direction which was of utmost importance for the history of physics, and natural science in general.


Oh, by the way, since it doesn't matter anymore. My space ship in The Perfect Code was named after Galileo's daughter. A big thanks to Dava Sobel who left me intrigued with the mystery of Galileo's missing letters.



split system breaker
21st Feb 2015, 22:30
Sorry guys, but your pulse isn't constant, neither is a count.

Yes, a large period of swing might help, but using the tools available, I don't see how you can prove anything.

If you had a second, exactly equal length and mass, pendulum you might be getting somewhere, but it's swing length would decay at the same rate as the subject, so you still can't really say you've done anything other than saying, "well it feels about the same length of time, so it must be"

21st Feb 2015, 22:31
Mass doesn't enter into it.

No, but length does, and a large chandelier would be long.

it's swing length would decay at the same rate as the subject, so you still can't really say you've done anything other than saying, "well it feels about the same length of time, so it must be"

The point is that the time taken is the same - regardless of the amplitude of the swing (at least at small amplitudes).

Galileo was moved to investigate the phenomenon having noticed the equal time period.

split system breaker
21st Feb 2015, 22:41
No, no , no, you can't time balls running down a curved trough, (beautiful image though it is), because you've got nothing to time them with, to confirm a constant transit.

You are all assuming a means of measurement, which itself cannot be measured as constant or consistent.

I like the idea of training someone to "perfect timing" but it still doesn't actually prove anything.

Um... lifting...
21st Feb 2015, 22:53

Easy peasy. Once the apparent variables are worked out (hmmm... seems that two pendula of identical length seem to have the same period. Let me test this...)

One tests this timing hypothesis by one of two ways:

1) Start two swinging simultaneously but with different amplitude.

2) Start one swinging, let it decay for a time, then start another.

If you've hit upon the appropriate variable or combination of variables, they should remain synchronized.

Of course, that's for your hypothetical pendulum. Your chandelier or censer or whatever introduces friction, air resistance, possible added forces, etc. into the mix. One suspects that over short periods, a keen observer might suspect that synchronizing these things might appear simple, but as the time of observation increases, errors start appearing due various factors.

split system breaker
21st Feb 2015, 22:55
Yeah; but I think that the honest burghers of Piza Cathedral might have a word or two to say about that.

You're probably right though.

Loose rivets
21st Feb 2015, 22:56
Well, it was about as good as it got in those days, and remember, you're dealing with the minds of a geniuses. They wouldn't be fooled by simplistic side effects.

Curved troughs? That's exactly what Galileo used. And yes, he adjusted for the curves. :rolleyes:

John Gribben. But he's written so much I can't find the specific subject in this forum timescale.

21st Feb 2015, 23:26
I agree with Henry.
All the evidence I'm aware of is that he used his pulse to time the pendulum swings. And if you've spend as long as he or I have in Cathedrals, you'll be aware that there's sod-all else to do as a scientist but look for patterns in the phenomena around you.

From the initial observation,with (inaccurate) pulses to give one the idea, one can then do matched experiments back home which develop the theory.

The timing troughs are in the Galileo museum in Florence, quite near the Uffizi (it's well worth a visit if you're in town). The balls rolling down trigger bells. The human sense of rhythm allows the bells to be spaced so that they are triggered at equal time intervals. I have replicated this in the school physics lab, and it's remarkably easy to be very accurate. What one cannot tell is how long the time interval is against the modern second, but this is not important for proving the theory.

22nd Feb 2015, 01:22
If the subject was a chandallier: Before electric light, those things was hanging in a crane mechanism to either lower to ground-level or rise to above loft-height where the candles or oil-lamps were lighted.
A chandallier in swing during this movement will change frequency remarkable enough to percieve it without time measuring. Once have had this experience, it's easy to compare two Chandalliers/pendulums side-by-side and start counting how many swings it demands to swing parallel again - quite like comparing Your cars turn signal with the one on the car in front of You: At some time they will blink at same moment whereafter they will differ for a time!

22nd Feb 2015, 02:46
My empirical evidence proves that its always a sunny day when stuck in a church. I would imagine the same to be true for Galileo.

So he could just have watched the Sun's shadow passing whole tiles or bricks and applied some trig if necessary. He might have used candles, but by arranging them in an arc at equal spacing or at proportional spacings in a straight line he wouldn't need to have lit them.

split system breaker
22nd Feb 2015, 07:14
Thank you gentlemen; I think that's another little mystery solved.

Personally I'm inclined towards the balls in a trough solution; although I suppose you could equally allow your balls to fall through a cylinder of honey, or perhaps have a friend drop then from a great height.

As an old instructor of mine once said about a fellow student, "give this man the job, and he'll finish the tools!".

joy ride
22nd Feb 2015, 07:17
Just because we now have very sophisticated time pieces and other equipment does not mean that we can discredit the abilities of previous generations. The Antikythera mechanism was made without the CNC lathes and milling machines which we would regard as vital to make such a fiendishly clever device.

The pulse varies slightly, but over the course of several observations a reasonably accurate average figure can be arrived at.

In the 1970s I saw an Open University programme about Galilleo and it showed the device he made for studying acceleration. I adapted it, added a chain and handle and chicks to make it into a mechanical toy, Gallinae Priemis (Spring Chickens)


tony draper
22nd Feb 2015, 07:36
To get back to that documentary,it appeared to be aimed at a audience of ten year olds,throwing in clips from cartoons and various other ruses and witticisms to keep the kiddies amused,more Channel Five or CBBC than BBC.

P6 Driver
22nd Feb 2015, 08:28
It's a good job I didn't view it then - way above my mental level.

A A Gruntpuddock
22nd Feb 2015, 08:32
Way back when I used to develop & print all my b&w 35mm stuff I found that I could eventually count up to 2 minutes or more just as accurately as a digital timer.

Always wondered after that how humans could measure time so accurately, but there is no doubt that it is possible.

joy ride
22nd Feb 2015, 08:59
AAG I too had my own darkroom and became pretty accurate in my counting (helped perhaps by being a drummer too). My college's darkrooms had an electronic beeper sounding every second and days after working in them I could still internally 'hear" a constant "beep... beep....beep" and used to walk in time with it!

22nd Feb 2015, 09:00
Talk of the rolling balls in troughs reminded of a jeweller's shop in Richmond, Yorks which back in the 60s had an old Congreve clock in the window. Always stopped to watch it - hypnotising


22nd Feb 2015, 09:07
What I want to know is how did he notice this in the first place?

I would have thought he would have noticed that swinging lamp kept in time with music. Musicians are used to keeping very strict timing.

Loose rivets
22nd Feb 2015, 09:13
I would imagine, but don't know, that a musician of that era would have had to try hard not to let his pulse interfere with his timing. As stated above, it is possible to get one's brain in tic mode and be reasonably accurate.

Over many years I have tended to time things using that method with fair success. For instance, we took our tea water from the filtered fridge dispenser. It was tediously slow, as was the 110v kettle, so I aimed to get the amount optimized. It wasn't long before I got it spot on the sight-gauge line every time. However, any stimulus, like the sheriff using my drive to turn in, could alter my perceptions. That Wadd-av-I-done syndrome gets one ready for fight or flight and totally resets our clocks.

I wonder if the same is true for Sir Simon Rattle. I'll wager he'll have a darn nigh-on perfect internal clock.

22nd Feb 2015, 09:34
Remember reading and interview with an F1 driver (Jackie Stewart?) years ago. He claimed that he could tell his lap time within a couple of tenths of a second. Of course, that may have been because he knew roughly what his time would be, and knew if he had done a fast or slow lap.

Galileo wasn't the only one who used his pulse as a timer. Leonardo da Vinci did so when investigating water flow.

joy ride
22nd Feb 2015, 09:48
Sir Simon Rattle started his career as a percussionist and can keep excellent time as well as knowing how to "bend" time for maximum musical effect without loosing touch with the original tempo.

cockney steve
22nd Feb 2015, 09:50
I would imagine the drip of water from a slightly -leaking container, would give a pretty good time-constant.

They could have proved that with a stop- watch ;)

flying lid
22nd Feb 2015, 10:24
Foucault had a different one !!

Foucault pendulum - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Foucault_pendulum)

One at Preston, Lancashire in the Harris museum.


tony draper
22nd Feb 2015, 10:35
Anybody know offhand when and where the minute was first divided into sixty parts ie the second?
Finding a actual date on google has proved elusive,one might have to start trolling through actual books.

22nd Feb 2015, 10:42
Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day? - Scientific American (http://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/)

22nd Feb 2015, 11:38
that documentary,it appeared to be aimed at a audience of ten year olds,

That programme, and the previous one in the series, struck me as being 'Made for US consumption'. His reference to standardised time being introduced in 1865 in the US 'and adopted a year later in the UK' ignored the fact that the GWR started using it in 1840 and it being taken up by other railway companies in the next 2 to three years. The cartoon clips reinforced that image.


joy ride
22nd Feb 2015, 11:53
Worth bearing in mid that musicians of Gallileo's time would not have had Metronomes to practice to! They had to wait until Winkel made the first one:

Dietrich Nikolaus Winkel - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Dietrich_Nikolaus_Winkel)

Later a better version was designed by Maelzel and this is the pattern used until electronic ones, interesting to read about both men's work:

Johann Nepomuk Maelzel - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Johann_Nepomuk_Maelzel)

Groundgripper, in my experience there are sometimes contrived "definitions" or warping of facts or even Time itself to ensure that US precedence can be claimed in their programmes!

22nd Feb 2015, 12:22
Anyone remember Foucault's Pendulum which used to hang in the Science Museum London and which proved the rotation of the earth was taking place ? I was aghast when it was taken out and replaced with a lift/elevator, needed because fat parents and fat kids couldn't walk to the existing lift shafts near the back of the main hall.

joy ride
22nd Feb 2015, 13:01
I used to love watching the pendulum there, in front of the Atmospheric engines. After a few hours of looking around the museum I would return to see how it had progressed. Hope to visit their large object store some time.

22nd Feb 2015, 14:59
Anyone remember Foucault's Pendulum which used to hang in the Science Museum London and which proved the rotation of the earth was taking place ? I was aghast when it was taken out and replaced with a lift/elevator, needed because fat parents and fat kids couldn't walk to the existing lift shafts near the back of the main hall.

Whaaaaaattt?? You're kidding! Gone?


joy ride
22nd Feb 2015, 15:53
Yup, sadly it went quite a few years ago. The lifts there are quite nice, with transparent panels and fascias so that you can watch all the workings, but I do miss the pendulum and looking up to its top.

22nd Feb 2015, 21:26
You mean there's Foucault there?

22nd Feb 2015, 22:24
G-CPTN, it takes a lot to make me laugh, but that did!

Loose rivets
22nd Feb 2015, 23:07
:ok: Concur.

There's a vast iron chandelier in Biltmore, the largest privately owned home in the US. (beautiful in the extreme) It hangs in a large and very tall area with the stairs to one side in the wall. When they took it down to electrify it, the bolt, in shear, was almost worn through. I wonder if cyclic movement caused it to wear because that might have fooled the designers.

The darn thing weighed 1,700lbs if I remember correctly.

22nd Feb 2015, 23:38
I like this at the end of the link from post#32
' Interestingly, in order to keep atomic time in agreement with astronomical time, leap seconds occasionally must be added to UTC. Thus, not all minutes contain 60 seconds. A few rare minutes, occurring at a rate of about eight per decade, actually contain 61....'

Anuvver interesting fact is that atomic clocks in TV satellites in geostationary orbit (but still whizzing rapidly round earth) go out of sync with their 'stationary' brothers on earth due to a relativity effect and have to be tweaked occasionally.

Um... lifting...
23rd Feb 2015, 00:19
This the boy, LR? Word around the estate was there was great wailing and gnashing of teeth when they let the chandler and the lamplighter go.


23rd Feb 2015, 07:12

23rd Feb 2015, 10:05
A few rare minutes, occurring at a rate of about eight per decade, actually contain 61....'

And synchronising the computers at the control centre, the many tracking stations, the external facilities - and yes, the many orbiting spacecraft - in adding the extra second, when I was at work, was a nightmare.

The only time you'd see a digital clock readout display 55...56...57...58...59...60...01...02...03

(followed quite often by the ringing of alarms and people being called in from New Year's Eve parties to fix the problem).

23rd Feb 2015, 23:05
Galvanic corrosion have showed to stress constructions made before scientists realised the chemestry, and that's not that long ago!
The major monument of my hometown is only(?) 150 year old and showed accidentially to suffer hard of galvanic corrosion between the bronze pieces of wich the statue is made and the iron bolts used to span the pieces together :-o

Loose rivets
23rd Feb 2015, 23:45
Um . . . that's the one. :ok:

I guess there were several reasons such an item could have been on the cusp of disaster. * Seems hard to believe in a house that had a swimming pool and bowling ally in the basement.

I went back the next day for the extended walk-round it was so stunning.

DC electrics took up one main room with one wall made of Ebonite and covered in brass switch gear. Batteries were next door but too dodgy to go in.

AC was made down in the village. Far too risky, these curly amps, to have near the house.

One man, 1$ a day. 2$, if you'd got a donkey.

What got me was that our man died of appendicitis 14 years later in a NY hospital. All that, and you go and die. So darned annoying.

*Electrolysis is still a problem. In the little house I'm staying in I see iron nails rotting where they're holding copper GAS PIPE to an external wall. What'er they thinking?

24th Feb 2015, 09:53
You mean there's Foucault there?

Must be. Might explain the Eco. (See what I did there?)

24th Feb 2015, 12:36
Thinking about the original question at the start of tis topic - anyone who doesn't understand how counting rythm works has neither played in a band nor done military service...

... Left. Left. Left, Right, Left!

Even the bloody Romans could achieve perfect timing. :rolleyes:

24th Feb 2015, 13:11
Remember reading and interview with an F1 driver (Jackie Stewart?) years ago. He claimed that he could tell his lap time within a couple of tenths of a second. Of course, that may have been because he knew roughly what his time would be, and knew if he had done a fast or slow lap.

It's amazing what we can train our brains to do with awesome accuracy.

Talking of Racing Drivers of that era, I remember a Graham Hill story which illustrates the same. In an early attempt at in-car video (would have been wet film in them days) he commentated a lap at Brands Hatch whilst driving it.

When the film was processed, it turned out that the audio channel (or whatever) hadn't recorded, so no commentary! By the time that was discovered, Hill was at the other end of the country, or even out of it.

To solve the problem, apparently he asked what the lap time had been, and proceeded to record a perfectly matching commentary - gear changes, braking, corners etc - without seeing the film!


tony draper
24th Feb 2015, 13:42
They probably said that in Roman though Mr Blacksheep. :)
Sinistro. Sinistro. Sinistro, Dextro, Sinistro!

24th Feb 2015, 14:09
Sinistro. Sinistro. Sinistro, Dextro, Sinistro

That's Left. Left. Left. Right. Left. going backwards, is it?

24th Feb 2015, 15:48
Galileo's pendulum. Is that a euphemism?

23rd Jun 2016, 15:23
Thought Mr D might be interested in this update on the Antikythera Device. Link to the main paper is in the article.

My question is how such a highly developed level of technology could be totally lost, not even mentioned in writing let alone in surviving tomb items, such that it took nearly 2000 years to be reinvented.....

Secrets of the Antikythera Mechanism - The Atlantic (http://www.theatlantic.com/technology/archive/2016/06/antikythera-mechanism-whoa/487832/)