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Then there's a fountain that operates when the sun's rays fall on it, and a steam boiler that makes a mechanical blackbird sing or blows a horn. Yet another device, often referred to as the world's first steam engine, boils water in a cauldron and uses the steam to turn a metal globe about a horizontal axis. The steam emerges from a series of bent pipes around the sphere's `equator', at right angles to the axis.

In design, these machines weren't toys, but as far as their applications went, they might as well have been. Only the door-opener comes close to doing anything we would consider practical, although the priests probably found the ability to produce miracles on demand to be quite profitable, and that's practical enough for most businessmen today.

Looking back from the twenty-first century, it seems astonishing that it took steam engine time so long to gain proper momentum, with all these examples of steam power on public display all over the ancient world. Especially since there was plenty of demand for mechanical power, for the same reasons that finally gave birth to steam engine technology in the eighteenth century - pumping water, lifting heavy weights, mining, and transport. So we learn that it takes more than the mere ability to make steam engines, even in conjunction with a clear need for something of that kind, to kick-start steam engine time.

And so the steam engine bumbled along, never disappearing entirely, but never making any kind of breakthrough. In 1120 the church at Rheims had what looks suspiciously like a steam-powered organ. In 1571 Matthesius described a steam engine in a sermon. In 1519 the French academic Jacob Besson wrote about the production of steam and its mechanical uses. In 1543 the Spaniard Balso de Garay is reputed to have suggested the use of steam to power a ship. Leonardo da Vinci described a steam-gun that could throw a heavy metal ball. In 1606 Florence Rivault, gentleman of the bedchamber to Henry IV, discovered that a metal bombshell would explode if it was filled with water and heated. In 1615, Salomon de Caius, an engineer under Louis XIII, wrote about a machine that used steam to raise water. In 1629 ... but you get the idea. It went on like that, with person after person reinventing the steam engine, until 1663.

In that year Edward Somerset, Marquis of Worcester, not only invented a steam-powered machine for raising water: he got it built, and installed, two years later, at Vauxhall - now part of London, but then just outside it. This was probably the first genuine application of steam power to a serious practical problem. No drawing of the machine exists, but its general form has been inferred from grooves, still surviving, in the walls of Raglan Castle, where it was installed. Worcester planned to form a company to exploit his machine, but failed to raise the cash. His widow in her turn made the same attempt, with the same lack of success. So that's another necessary ingredient for steam engine time: money.

In some ways, Worcester was the true creator of the steam engine, but he gets little credit, because he was just a tiny bit ahead of the wave. He does mark a moment at which the whole game changed, however: from this point on, people didn't just invent steam engines - they used them. By 1683, Sir Samuel Morland was building steampowered pumps for Louis XIV, and his book of that year reveals a deep familiarity with the properties of steam and the associated mechanisms. The idea of the steam engine had now arrived, along with a few of the things themselves, earning their living by performing useful tasks. But it still wasn't steam engine time.

Now, however, the momentum began to grow rapidly, and what gave it a really big push was mining. Mines, for coal or minerals, had been around for millennia, but by the start of the eighteenth century they were becoming so big, and so deep, that they ran into what quickly became the miner's greatest enemy: water.

The deeper you try to dig mines, the more likely they are to become flooded, because they are more likely to run into underlying reservoirs of water, or cracks that lead to such reservoirs, or just cracks down which water from above can flow. Traditional methods of removing water were no longer successful, and something radically different was needed. The steam engine filled the gap neatly. Two people, above all, made it possible to build suitable machinery: Dennis Papin and Thomas Savery.

Papin trained in mathematics under the Jesuits at Blois, and in medicine in Paris, where he settled in 1672. He joined the laboratory of Robert Boyle, who would nowadays be called an experimental physicist. Boyle was working on pneumatics, the behaviour of gases -'Boyle's law', relating the pressure and volume of a gas at constant temperature, continues to be taught to this day. Papin invented the double air pump and the air gun, and then he invented the Digester. This is best described as a pressure-cooker, which is a saucepan with thick walls and a thick lid, held on securely so that water inside boils to form high-pressure steam. Food contained in the pan cooks very quickly.

The cookery aspect doesn't affect our story, but one bit of technology does. To avoid explosions, Papin added a safety valve, a feature replicated in the sixties domestic version, and an important invention because early involvement with steam engines was dangerous at the best of times. The idea probably originated earlier, but Papin gets the credit for using it to control steam pressure. In 1687 he moved to the University of Marburg, where he invented the first mechanical steam engine and the first piston engine. Throughout his career, he carried out innumerable experiments with steam-related apparatus, and introduced many significant pieces of gadgetry.

Steam engine time was hotting up. Savery, who also trained in mathematics, brought it to the boil. In 1698 he patented the first steam-powered pump that was actually used to clear mines of unwanted water - in this case, the deep mines of Cornwall. He sent a working model to the Royal Society, and later showed a model `fire engine', as the machines were then confusingly called, to William III. The King granted him a patent: A grant to Thomas Savery of the sole exercise of a new invention by him invented, for raising of water, and occasioning motion to all sorts of mill works, by the important force of fire, which will be of great use in draining mines, serving towns with water, and for the working of all sorts of mills, when they have not the benefit of water nor constant winds; to hold for 14 years; with usual clauses.

Steam engine time was close at hand. What clinched it was that Savery was a born businessman. He didn't wait for the world to beat a path to his door: he advertised. He gave lectures at the Royal Society, some of which were published in its journals. He circulated a prospectus among mine-owners and managers. And the selling point, naturally, was profit. If you can open up deeper levels of your mine, you can extract more minerals and make more money out of the same mine and the same bit of land.

Two more major steps were needed before what Thurston calls the `modern' steam engine - that of 125 years ago - became firmly established. The first was to move from specialised, single-purpose machines, to multi-purpose ones. The second was to improve the engine's efficiency.

The move to multi-purpose steam engines was made by Thomas Newcomen, a blacksmith by trade, who introduced a radical new kind of engine, the `atmospheric steam engine'. Previous engines had effectively combined a steam-driven piston and a pump in the same apparatus. Newcomen separated the components, and threw in a separate boiler and a condenser to boot. The piston moves up and down like a `nodding donkey', driving a rod, which can be attached to ... anything you like. Another engineer who must be mentioned here was John Smeaton, who scaled Newcomen's design up to much larger size.