There is also a klepsydra, a large earthenware pot with a spout at the bottom; it was filled with water when a citizen starting talking, and when it was empty he stopped. There is a collection of 'ostracism' potsherds, with names scribbled on them 2,500 years ago. Anyone with more than 600 of these cast against him was sent into exile for 10 years. Some of the names, like Nikias and Themistocles, are famous. The archaeologists found 190 anti-Themistocles sherds in one place, but analysis showed - suggestively - that they were written by only 14 different people.
Athenian democracy, it turns out, was unbelievably complicated. Even to explain the operation of the kleroterion, a machine for selecting juries, would take pages. Briefly, members of each of the 10 'tribes' (artificial divisions of the citizens, composed of equal numbers from city, coast and hinterland) stuck their bronze identity tags into one of the vertical slit- columns. Then black and white balls were fed into the tube, and a handle was turned to randomise them. If a black ball fell out, the top horizontal row of names was disqualified; if a white one, the top row (one from each tribe) was assigned to an enormous Athenian jury, never less than 201 men. This was only the start. More lot-selections with marked acorns in a basket, determined which court each juror would attend, and another process chose the magistrates, and yet more selected court officials, timekeepers and jury paymasters.
It all took a great deal of time. But the Athenians thought, in the most positive sense, that they had nothing better to do. As the historian Mogens Hansen writes in his book The Athenian Democracy, these mechanisms 'illustrate better than anything else the fascination of the Athenians for ingenious devices; more than 2,000 citizens, on some 200 days every year, spent at least an hour of their time playing this game . . .' And this was before they had even got down to hearings, and it was only one corner of the whole democratic process with the Assembly (all citizens, meeting every 10 days) and the Council (500 men, meeting daily).
Athens was not perfect. Only the Victorians, perhaps, thought that it was. Its astonishing institutions were more a way of using the collective to limit the individual than an empowering of the individual against the collective. Second, Athenian democracy was an imperial ideology; cities conquered by Athens had the system forced upon them. More dubious still, Athens belonged to the new Greek form of society which banned women from decision- making and public leadership of any kind. The world around Greece, in which women were often rulers and sometimes soldiers, found this quite bizarre.
But Athenians identified with their democracy. In battle, they died for this system, for the potsherds and the kleroterion and the right to speak while the water flowed, rather than for the 'nation' of Attica. Pericles said: 'We are a pattern to others, rather than imitators.'
When I had seen the exhibition, I went back to a conference which was also about democracy. Czechs and Slovaks had come to Edinburgh to discuss their own separation just a year ago, and to assess the new nation-state of Slovakia. So far, it would be hard for the Slovaks to feel like 'a pattern to others'. Indeed, Slovakia has been seized on by defenders of the status quo in the British constitutional debate and used as an awful warning to Scotland and Wales. Independent Slovakia is now regularly presented as a semi-fascist mire of primitive nationalism, its economy collapsing into rust and unemployment, its citizens bitterly regretting the mistake of thinking that they could go it alone without the Czechs.
Some of this has an element of truth. Slovak politics is a mess. As I write, the ruling party has just collected 470,000 signatures in order to demand a referendum in order to have a mid-term election in order to see if Vladimir Meciar, the prime minister, can regain his parliamentary majority. All the main parties have split in the last year, some twice. The economy, unreformed and burdened by useless arms industries, is floundering. Meciar himself, a man compared by his critics to a small, flesh- eating dinosaur, remarked the other day that 'the socially non- adaptable' (ie Slovak gypsies) should have their birth-rate reduced. Those around him have been heard to blame Jews and Hungarians for their problems, or to refer to the Czechs as 'the exit of Europe's digestive tract', or to explain economic failure by a 'world conspiracy against Slovakia'.
It is also true that nobody really asked the Slovaks what they wanted. Denied a referendum on independence, they would have preferred a looser, 'confederal' relationship with the Czechs. But that was not on offer. Two years of constitutional wrangling persuaded the Czech negotiators that a revised federation would not work. And Vaclav Klaus, the Czech prime minister, grew convinced that to keep Slovakia would cripple his ambition to build a Thatcherite free-market economy; the Slovaks were still too hooked on state subsidy and central planning. The real story of the 'velvet divorce' was that the Czechs lost patience, and pushed the Slovak negotiators into a choice between independence or nothing.
This is a long way from Athens. But the new republic is not as bad as Mr Meciar's rhetoric makes it seem. As a convert to nationalism, he came to power only because Czech intransigence had discredited better leaders who wanted something short of independence; in that sense, he is Slovakia's ugly leaving present from the Czechs. But there is a steadier, more liberal Slovakia waiting for him to move over.
And it is worth remembering that the Czechs themselves did not exactly choose independence. Most wanted Home Rule within the Habsburg Empire. But then the Empire collapsed in 1918, and there was nowhere else to go. The father and first President of Czechoslovakia, Thomas Masaryk, soothed their alarm: 'Don't be afraid, and don't steal]' Within a few years, Czechoslovakia seemed as natural to its people as breathing. So it will be with Slovakia. In Edinburgh, a Slovak woman commented: 'This is an unwanted child, but since it is here, we must adopt it]' Slovaks who did not want independence are usually shocked at suggestions that they should give it up again.
And the truth is that surprisingly many nation-states were unplanned births, or even babies found one morning on the doorstep. They get adopted and then, with a little practice, loved by their proud citizens. And when they have been to school, some of them even grow into democracies.