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In a land similar to the Roman Empire, slaves are used to drive machinery. Mostly this is a matter of getting them to pull carts or wind handles.

The Emperor wants a clock that is accurate to the minute, powered by slaves.

With the technology of Ancient Rome and unlimited slave-power, how can such a clock be accurately regulated?

Let us suppose that the clock has a face similar to a modern-day analog clock.


Notes

The clock cannot be regulated by referring to another clock. It must be self-regulating.

Water power, sand-timers, wound-springs etc. are not to be used directly to power the clock - just slave manual power. However an (unpowered?) mechanism will be need to regulate the machine.

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    $\begingroup$ The Romans had clocks. Water clocks, sand clocks, weight driven clocks, burning clocks. The power required by a clock movement is trivial -- you don't need a slave, you need a small mouse. What they didn't have was enough knowledge of physics to make an accurate clock. They did not know about isochronous oscillations. The question is about the wrong problem. $\endgroup$
    – AlexP
    Commented Jan 3, 2019 at 15:42
  • $\begingroup$ The reason the Emperor want his clock to be slave-powered is to display his wealth. It is a big clock to be displayed somewhere prominent. The more impressive the mechanism, the better. $\endgroup$ Commented Jan 3, 2019 at 15:46
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    $\begingroup$ If it was actually considered a clock and usable on cloudy days, I'd add an answer about training the slaves to stand in a Gnomon pattern (think cheerleaders) and make a sundial $\endgroup$ Commented Jan 3, 2019 at 16:07
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    $\begingroup$ Dear downvoters: the question isn't about Rome per se, it's about a Rome-like (Romanesque!) fictional world. It does not matter what the real Romans knew or didn't know. The only issue here, for us, is how to get these other Romans to make their slave clock run regular. $\endgroup$
    – elemtilas
    Commented Jan 3, 2019 at 18:10
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    $\begingroup$ If its just a show of wealth, why not have a real clock somewhere, and then just have the slaves move the hands of a giant 500m display clock, to match the time on the smaller real clock. Accurate time, and needless show of wealth and power achieved. $\endgroup$ Commented Jan 3, 2019 at 18:31

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One possibility would be this set-up, all components being available to your parallel world Roman Imperials:

Component I: is the temporal regulation mechanism. Deep within the works of the Horologon, is a water cistern that is kept full from municipal water supplies (the Aqueduct). Pipes bring water down to a valve that is set by the engineers to flow at a certain rate. The water itself is brought up into a marble statue of a water nymph and is ejected from her left nipple at a constant rate. The water so ejected squirts onto a small water wheel which thus rotates at a constant rate. Two of the water wheel's buckets have projections that strike a small brass chime held by a bronze satyr at the wheel's base.

Component II: is the slave regulating mechanism. This component consists of a slave, two wooden mallets and two bronze nakers (a kind of drum). The slave, taking his cues from the satyr's chime, beats out a lively rhythm on the nakers which will regulate the slaves that actually operate the horologon itself. The rhythms vary by the hour, and close attention paid by passersby will immediately tell them, just by listening, what the hour is, even if they don't look up at the horologon's clever display.

Component III: are the slave tableaus. This is all part of the magic of Romanesque time keeping: the day being divided into fifteen hours of the clock, based on the calculated number of chime beats on Midsummer's day, there are therefore fifteen tableaux visible on the horologon's portico. The figures in each tableau are dressed in characteristic fashion of a particular region of the Empire and the slaves in each tableau dance in a fashion characteristic of that region. Other slaves, the tempora magistri, or "conductors", beat time along with the nakers by tapping their feet and striking the floor of the portico with their batons. Baton strikes are carefully counted and choreographed with the rhythms of the nakers to occur every half minute, first one strike then a double-strike. Every minute, or every double-strike of the conductors' baton therefore denotes one minute. At this moment, the tableau advances slightly around the portico.

Component IIIJ: is the horologon's display. Resting upon a great toothed rondel of hard wood at the centre of the tableau is a similarly toothed rondel from which radiates fifteen long spars with red legionary shields at the end of each, upon which are painted large numbers: J, IJ, IIJ, IIIJ, etc. up to XV.

Component V: is the housing. Naturally, the Emperor wishes to help the people of the Eternal City tell time, else why build a public horologon at all? But more importantly, he wishes to make a grand and opulent public display of the whole matter. Sure, any Marcus Aurelius in the street can look up at the Sun and say, oh, it's a little after noon. But the Emperor wants to make sure that not only his own subjects, but also traders from distant lands and embassies from rival empires and visiting dignitaries alike are awed by the cunning engineering and obviously vast wealth of the Empire. To do this, the entire horologon is housed within a marble temple like building, perhaps on the end of one of the basilicas. The beauty of its painted statuary and mythological stonework is a feast for the eyes; and all eyes will be drawn to the huge arched skene, the stage where the tableaux play out.

Component VJ: is the general orchestration of the horologon. All well and good, but how does one actually tell time? Quite simply, if one is sufficiently literate, one can simply read the numbers on the dial. As the big XIJ moves across the stage, you know it's twelve o'clock. If you're clever and you notice the evenly spaced markings along the base of the stage, you'll see that each time the conductor double-strikes his baton, the cartouche moves from one marking to the next. And, again, if you're literate, you'll notice that these markings are labelled: prima, secunda, tertia, etc. The big numbers indicate hours of the clock, the small numbers indicate minutes.

But the wise observer will note the horologon does much more than count minutes and hours. Indeed, the wise Emperor has devised the tableaux in such a way that each set of costumes and each set of dances is constantly changed over the course of time. Every day, the timed syllable chanting of the slaves, with its calculated number of syllables per line & strophe, corresponding to the passage of minutes, changes -- one day, hymns to the Moon or the Stars or to Istar or Ares; every two weeks, the dances change slightly and every month the costumes change as well. Every three months, the over-arching theme changes. Thus, the observant student of the imperial horologon can tell you what day, what hour and minute and in what fortnight and season you are currently in, all by observing and listening to what the horlogon of Emperor Minimus is telling!

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  • $\begingroup$ This is how the Remans in my own world went about it, anyway! $\endgroup$
    – elemtilas
    Commented Jan 3, 2019 at 19:23
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    $\begingroup$ When you remove the gilded lilly, what's left of this answer is remarkably simple and, IMHO, the best answser. The slaves keep a cistern filled with water. The sistern can be made of a central, deep column and a larger, wider bowl at the top so the pressure remains reasonably constant while the water level shifts up and down with human error. The result is a constant and predictable flow of water that can be used to drive gearing of any complexity known to the Romans and easily calibrated to any desired timekeeping condition. Boom, baby. Well done Elemtilas. $\endgroup$
    – JBH
    Commented Jan 3, 2019 at 20:40
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    $\begingroup$ Thank you much, @JBH! I, of course, appreciate the gilded lily aspect of this answer. The "clock" proper is simply constant water flow and a chime to help the human mind keep track of the time factor with respect to water flow. But, hey, this is Rome! And wealthy Romans thrive on opulent displays of wealth and power! Plus, I needed something for all the slaves to occupy their time. $\endgroup$
    – elemtilas
    Commented Jan 3, 2019 at 21:04
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    $\begingroup$ @Eth, that doesn't make any sense. Water pressure is simply the amount of water above a point. If a big box or bowl existed above the column, any water not directly over the column wouldn't contribute to water pressure at the base of the column. By maximizing surface area vs. column volume, you avoid the need for the water delivery precision - which is the point. Without a spring to create a primitive pressure regulator it's the best accuracy-vs-complexity trade-off. $\endgroup$
    – JBH
    Commented Jan 4, 2019 at 15:00
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    $\begingroup$ If your cistern has a overflow at the top you can precisely maintain the water column height, and therefore pressure without any complex regulators. $\endgroup$ Commented Jan 4, 2019 at 15:17
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With a pendulum

The quirk being that neither the pendulum nor the need for accurate time keeping had been invented in the period you're asking for, but gearing was already in use, the basic physics of a pendulum regulator could follow well enough.

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  • $\begingroup$ I'm not sure how they make the pendulum swing regularly. Surely a slave would have to push it. That is subject to error. Do you have a reference that indicates how the Romans were using gearing - that sounds interesting. $\endgroup$ Commented Jan 3, 2019 at 15:31
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    $\begingroup$ @chaslyfromUK, the source you're looking for for gears is the Antikythera mechanism this could be the work of a lone raving genius, but it shows the principle of gears was known in the period. $\endgroup$
    – Separatrix
    Commented Jan 3, 2019 at 15:40
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    $\begingroup$ @chaslyfromUK: In 1602 Galileo discovered that the period of oscillation of a pendulum is almost independent of the amplitude of the oscillations, as long as the oscillations are small. You don't need to do anything for the pendulum to swing regularly -- it does that all by itself. The small power input is needed to compensate for energy loss due to friction in the mechanism. A large grandfather clock uses about 0.1 milliwatts of power. A huge tower clock uses about 100 milliwatts for the clock movement. $\endgroup$
    – AlexP
    Commented Jan 3, 2019 at 16:03
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    $\begingroup$ Two pendulums (pendula?). When one needs to be pushed, it is later synchronized to the other. When the other needs to be pushed, the process is repeated. $\endgroup$ Commented Jan 3, 2019 at 23:43
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    $\begingroup$ @Separatrix - I get you - of course the fictional emperor who wanted the accurate clock could have had his greatest philosophers research the idea and it would not be beyond the bounds of possibility that they could discover a pendulum ahead of (real-life) time... $\endgroup$
    – komodosp
    Commented Jan 4, 2019 at 9:50
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  • Have the slaves build a large wheel, with an even number of carts evenly spread around it and a clear mark on it.

  • Have the wheel installed with an horizontal axis, free of spinning.

  • Have the slaves cut a number of stones, all from the same mine, all with the same shape and weight.

  • Have the slaves carry the stones to the top of the wheel, where they will put one stone in each cart reaching the top.

  • Have the slaves take away the stone from the cart when it reaches the bottom and carry the stone to the top.

  • Define every round trip of the mark on the wheel your base time unit.

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    $\begingroup$ That is interesting - I like it. How would you prevent slaves putting stones onto the wheel too soon or too late? $\endgroup$ Commented Jan 3, 2019 at 15:43
  • $\begingroup$ @chaslyfromUK, mechanical safety or slave supervisors equipped with whips $\endgroup$
    – L.Dutch
    Commented Jan 3, 2019 at 15:46
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    $\begingroup$ I read it as "an even number of cats" which makes a good answer even better. $\endgroup$
    – user535733
    Commented Jan 3, 2019 at 17:05
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    $\begingroup$ This machine works only against the friction in the wheel axis. After a day it will become faster or slower, depending on the wear. $\endgroup$
    – Karl
    Commented Jan 3, 2019 at 18:17
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    $\begingroup$ A neat idea but doesn't seem like it would be very accuracte. The moment you switch slaves, their speed, carrying capacity, etc would change, as would there performance at different energy levels (fresh/tired/hungry/sleep deprived). But the real problem is the absurd limitations of the question. $\endgroup$ Commented Jan 3, 2019 at 18:29
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With the mention of the analogue face, I'm going to assume they have a decent grasp of gearing. From there you need to control the speed that the slaves are rotating, for that you can use a simplified centrifuge governor.

 centrifuge governor

Attach an arrow to the flyweights and have them point to a sweetspot chart and you could maintain a somewhat accurate fixed rotation speed.

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    $\begingroup$ So, basically, replace flyballs d(sub-b) and h(sub-s) with equally weighted slaves... $\endgroup$
    – elemtilas
    Commented Jan 3, 2019 at 18:12
  • $\begingroup$ nah, rig it so if the slaves don't get the flyballs spinning fast enough, the flyballs his levers that cause whips to auto-lash the slaves pushing the main drive wheel. $\endgroup$ Commented Jan 3, 2019 at 18:26
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You build a release for polished, uniform stones on the top of a slope or fall, which is triggered by the stones hitting the ground.

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Have a giant isochronous curve (a curve that a falling object always takes the same time to traverse despite starting position, plug it into youtube to see toys based on them) with giant round rocks that roll back and forth in it, attached to an arm that pushes the clock.

Over time the rocks will lose momentum due to friction and a slave will need to push the rock back up to the top.

If there are a pair of curves, a well trained group of slaves can keep at least one ball rolling at all times. Naturally, when they release the rock, it's a dangerous business.

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How the Romans actually did it

A clepsydra is an ancient style of mechanical water clock used by the Greeks an Romans. It used a float and gear system to turn a clock face. Too keep it accurate, a slave would simply need to once a day empty the water from the float container, refill the water supply, and refill the float container until the time on the clepsydra matches the time on the sun dial. A sun dial is always going to be accurate during the day, and the mechanical mechanism of the clepsydra allows you to estimate the current time from the last syncing so you can continue to tell what time it is when the sun is down or obscured.

enter image description here

Water power, sand-timers, wound-springs etc. are not to be used directly to power the clock - just slave manual power. However an (unpowered?) mechanism will be need to regulate the machine.

Frame Challenge: Water, sand, springs, etc. are not really a source of power for a clock, they are how the clock regulates its power to keep it from going too fast or too slow. Without one of these, you have no clock.

For example, my daughter has a model Da Vinci clock that uses a weight to turn it. It works just fine if the weight is properly calibrated to the gearing, but if you add extra weight, it moves faster, less weight, it moves slower. So, using ancient technology, you need one of these "power sources" to regulate the time because direct human power will not be consistent enough. That said, when you use these things to regulate a clock the real power is actually coming from the person winding the spring, or moving the water or sand back up into the supply chamber. In a small clock, this could be a job that only takes a person a few moments out of thier day, but the bigger your clock, the more energy it will take to reset the regulating medium.

So if we go with a clepsydra (but on a large scale), you could imagine a giant clock tower that raises above the level of the town cisterns so that it can be high enough to be seen from all around. But because of its height, you cant just passively fill its water supply from an aqueduct, you will need slaves to carry buckets of water up the tower all day to fill the water supply to keep it running. So it is literally powered by the work of slaves even though it is a water clock.

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Simple: You have a mechanism that stores built-up energy from the slaves, and uses that energy to power the clock. We already have this in the form of old wind-up clocks that rely on a person being willing to regularly wind them to function.

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Given the Era concerned the Emperor simply declares that 'money is no object' i.e. the project is the Apollo moon mission of the the era concerned.

Slaves are simply tasked with implementing or assisting in the implementation/engineering of ever finer/more refined and accurate versions of both clocks. The exception being land holders in proportion to the (e.g. clocks cast/etched in metal) until such time as they refine meticulously precise versions of both types of clock by trial and error.

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