The Weight of the Air

[Part of a series: The Age of Steam]

The miners of Renaissance Europe, digging ever deeper into the earth in the search of ore, invariably found another, less welcome substance – water. Everywhere they dug, it found them, seeping into tunnels and shafts. If it could not be removed at least as quickly as it entered, it would flood the mine and make it useless. The deeper the mine, the more of a problem water presented, and by the later part of the middle ages, some miners were delving very deep indeed. Over the centuries, miners had devised numerous contrivances to remove this nuisance, from simple bucket brigades to complex lifting machinery, many of them documented in Agricola’s De re metallica of 1556, a treatise on the extraction of metals from the earth.

The history of the Rammelsberg mine in central Germany provides an exceptional example of the ingenuity and tenacity involved in keeping subterranean works clear of flooding.  Entrepreneurial Saxons cut an open pit mine to extract copper from the surface of the mountain of Rammelsberg in the tenth century, but in the years to follow miners dug ever deeper into the interior in pursuit of ore. Eventually, in the twelfth century, they were forced to dig a downward-sloping drainage tunnel (or adit) over half a mile long, between the mine out the side of the mountain, a project that took thirty years. Workers were employed to carry water by bucket up to the adit’s mouth from the parts of the mine that continued below it. This method could be sustained only so long, however, and the mine was abandoned until the fourteenth century, when new mine owners built a mechanical water-lifting system, powered by humans on a treadmill. In the following century a second, deeper adit was dug – this time it took nearly a century due to the greater distance – and sluiceways were built to supply water-powered drainage machinery within the mine itself. By this time the miners had dug almost a thousand feet below the surface.[1]

A system of drainage adits such as at Rammelsberg was only feasible on high ground, where it was possible to tunnel out from inside the mine to a drainage point on lower ground. Mines not situated on hills or mountains would necessarily depend more heavily on mechanisms to lift water, although few other mines of the period went as deep as Rammelsberg – 75 to 80 feet was more typical in Germany.[2]

The Suction Pump

One technique for lifting water from a mine bears particularly on the story of the steam engine – the suction pump. The piston-driven “force” pump was known from antiquity, and is described in two of the great classical engineering treatises, Vitruvius’ De architectura and Heron’s Pneumatica. The pistons of this pump drove water up through a central shaft on the downstroke, while a flap valve prevented the pumped-out water from re-entering the cylinder as it refilled with water on the upstroke. This machine, however, was not very suitable for mining work, since the machinery would have to rest in the sump inside the mine itself, where it was difficult to supply it with power. Moreover, the discharge pipe had to be very strong to withstand the force required to drive water up by many feet, a strength generally beyond the reach of Renaissance metallurgy.

A suction pump for draining a mine, as illustrated in De re metallica.

The suction pump first appeared in European literature in the unpublished notebooks of Italian engineer Mariano di Jacopo, known as Taccola (“crow”), in the middle of the fifteenth century. Whether it constituted part of a continuous tradition dating back to antiquity, a borrowing from the Muslim world (a kind of suction pump was described by Ismail al-Jazari, an engineer in the Abbasid caliphate, in 1206), or a novel invention by Taccola or a contemporary, is unknown. In any case, it differed from the force pump in that, rather than pushing water up, it pulled it, drawing the water up with a piston to an outlet pipe above ground. One or more valves in the piston itself allowed water to flow above it as it was pushed back into the sump with each downstroke. Since its machinery sat above ground, not in the sump itself, a suction pump could easily be harnessed to a power source – in addition to the more humane water mill, one of Agricola’s illustrations shows a man driving machinery with his legs in a kind of giant hamster wheel. Moreover, the pipe through which the pump drew the water did not need to withstand high pressures – a bored out wooden log sufficed.

A compound suction pump in three stages from De re metallica.

But the suction pump suffered from one puzzling, and vexing, limitation – no matter how one contrived to improve it, it could not lift water more than about thirty feet. To work around this, miners could create multiple pump stages, with one pump lifting water up to the sump of another, higher pump; of which Agricola also provides an example. But this was a complicated and expensive arrangement.

The Resistance of the Vacuum

To explain why a pump could not draw water more than thirty feet was therefore a matter of great practical and philosophical interest. Galileo addressed the problem in his Two New Sciences of 1638, as voiced by his character Sagredo:

This pump worked perfectly so long as the water in the cistern stood above a certain level; but below this level the pump failed to work.  When I first noticed this phenomenon I thought the machine was out of order; but the workman whom I called in to repair it told me the defect was not in the pump but in the water which had fallen too low to be raised through such a height; and he added that it was not possible, either by a pump or by any other machine working on the principle of attraction, to lift water a hair’s breadth above eighteen cubits; whether the pump be large or small this is the extreme limit of the lift [A typical cubit was roughly one-and-a-half feet, so eighteen cubits makes twenty-seven feet].[3] 

Within the structure of Aristotelian physics that prevailed in Europe during this time period, the proper explanation for the phenomenon lay in the horror vacui, nature’s inherent resistance to the creation of a vacuum. The natural world of Aristotle was a kingdom of ends, one where matter had purpose and intent. The universe as he imagined it consisted of a series of nested spheres – earth innermost, then water, air, fire, and finally the eternal quintessence of the heavens. Every form of matter craved to reach its natural place, and so a dropped stone descends to the earth, just as flames reach up toward the sky. Aristotle’s philosophy conflicted with Christian orthodoxy in many ways – he argued that the universe was eternal and uncreated, and his deterministic cosmology allowed no room for divine will. Nonetheless, an assimilated settlement had occurred within the universities of western Europe by the thirteenth century, taming Aristotelian insights within a framework of Christian theology, and this settlement remained fundamental to the standard scholarly curriculum in Galileo’s time.[4]

According to Aristotle, the world was full of substance and a vacuum could not logically exist. The active nature of matter, contriving to prevent the formation of an impossibility, thus could explain why a suction pump can draw up water, since the alternative would be the creation of a vacuum between the piston and the liquid. Even ancient philosophers who believed that a vacuum could exist, such as Heron of Alexandria, resorted to a similar explanation, though they ascribed a power of attraction to the vacuum itself, which had a kind of death wish, a will to self-destruction. Heron accounted for the fact that a cup will stick to ones lips after sucking the air out of it because “the vacuum [draws] the flesh towards it that the exhausted space may be filled.”[5] Galileo refers to a similar concept in the explanation of the phenomenon given by his alter-ego, Salviati: “…on weighing the water contained in a tube eighteen cubits long, no matter what the diameter, we shall obtain the value of the resistance of the vacuum in a cylinder of any solid material having a bore of this same diameter.”[6] Indeed, Galileo likely found inspiration in Heron for his ideas about the vacuum and its role in nature.

The first to record an alternative explanation of the suction pump was the Dutch natural philosopher Isaac Beeckman, an early mentor of Descartes. He recorded in his journal in the early 1610s that “the air… presses upon things and compresses them according to the superincumbent air.” The supposed power of the vacuum is actually the force of the surrounding air; matter “rush[es] towards an empty space with great force, on account of the immense depth of the superincumbent air, and in this way the weight [of the air] arises.”[7] Beeckman seems to have arrived at the idea by analogy to the pressure felt by divers felt when they dive deeper into water.

The notion that the air could have weight contradicted the Aristotelian cosmology – air in the sky is already in its natural place, and so would have no reason to press downward. But a new mechanistic philosophy was on the rise, which would refuse to resort to purposes and desires as an explanation for the workings of nature. Increasingly dissatisfied with the natural philosophy taught at the university, its adherents revived other ancient authorities to challenge Aristotle, including Heron, but also atomists such as Democritus and Lucretius. They would also insist on a world without purpose, with a physical impetus required to explain motion – the natural world, they believed, should be explainable within the same causal framework as the machinery that increasingly filled the European landscape of the seventeenth century – mining machinery, watermills, windmills, and town clocks.[8] As Beeckman wrote in a 1629 letter to the mathematician Mersenne, “… I admit nothing in philosophy, unless it is represented to the imagination as being material.”[9]

More significant than their metaphysical commitments, however, was the innovation in the philosophical practice of the new mechanists over that of the ancient atomists. Rather than simply devising explanations for existing phenomena, they determined to resolve their disputes through the creation of new phenomena, devising empirical tests to sort out the true from the false.[10] By 1640, a cluster of Italian philosophers, though they looked up to Galileo as a pioneer, had come to disagree with him about the vacuum. They had arrived at the view, like Beeckman, that the weight of the air, not the pull of the vacuum, explained the drawing of water by a suction pump or a siphon.[11] So, in accordance with the new philosophy, they began to work out ways to demonstrate that their view was correct, and that the idea of “the resistance of the vacuum” untenable. Foremost among them was Evangelista Torricelli.

The Torricellian Void

Torricelli, though over forty years younger than Galileo, was one of his few close disciples. He replaced his master as court mathematician to Ferdinando II de’ Medici after Galileo’s death in 1642. Sometime not long thereafter, he conceived of an idea for a new experiment to simultaneously prove the Aristotelians wrong about the possibility of a vacuum, and to prove his late master wrong about the force that draws water up a pump or siphon. His key innovation was to substitute a column of mercury for that of water. Because mercury rose only about thirty inches, rather than thirty feet, under normal air pressure, this reduced the apparatus needed to study the vacuum to a scale that could be placed on a laboratory table – or even carried about. It also became possible at this scale to make the tube containing the fluid entirely out of glass, so it was possible to directly observe what was happening during the experiment.

It is likely that Torricelli did not actually carry out the study himself, but delegated the work to his young pupil Vincenzo Viviani. Whoever it was, they first filled glass tube (closed at one end) with mercury, then inverted it into a basin filled with the same metal. The mercury descended until it rested about thirty inches above the level of the basin, leaving a (presumably vacuous) space at the top of the glass.

Torricelli’s experiment, with two separate mercury-filled tubes. The righthand tube, with a bulbous end, was intended to show that the force of the vacuum did not hold up the mercury.

So much for proving the reality of the vacuum. What of the force of the vacuum? Could that not explain why mercury remained suspended in the glass? Torricelli sought to dismiss this objection by using a second tube, this one with a bulbous end. If the force of the vacuum accounted for the position of the mercury, it should be all the stronger in this case, since the vacuum would be wider. Yet the mercury came to rest at exactly the same place as in the normal tube. Torricelli felt he had made his point. In a now-famous letter of 1644 describing the results of the experiment, he wrote that “[w]e live submerged at the bottom of an ocean of elementary air, which is known by incontestable experiments to have weight…”[12]  Once again we see the prominence of the analogy to the pressure of water at depth in prompting thinking about the weight of the air.

Despite his private sense of triumph, Torricelli published nothing about his experiments. The climate was not propitious for pursuing this line of inquiry in Italy. The papacy loomed nearby, and indeed ruled a central strip of the peninsula; the principles of natural philosophy remained deeply entangled with orthodox Catholic theology; and only a decade had passed since the conviction of Galileo of heresy for asserting the heliocentricity of the universe. Like-minded philosophers throughout Europe instead learned of the mercury experiment via the French mathematician Marin Mersenne, a central hub in the letter-writing communication network of European intellectuals.

A wave of experimentation with vacuums and air pressure ensued in the following decades.[13] In 1650, Otto von Guericke, burgomeister of Magedeburg, developed an air pump modeled on firefighting water pumps, which he used to pump the air out of a copper vessel. The air pump was refined by Robert Hooke in England about a decade later, using a glass receiver so that visible experiments could be performed within the evacuated space. The most important follow-on experiment for the development of the steam engine, however, took place in France in 1648. Once again, it was not performed by the man by whose name it is remembered – Blaise Pascal. It was instead Pascal’s brother-in-law, Florin Périer, who led an expedition to the summit of the Puy de Dôme, some 3,500 feet above the town of Clermont. Armed with Torricellian barometers, they watched the mercury fall as their steps ascended, from 711 millimeters at the base to 627 at the top. This experiment provided more definite evidence that the weight of the air lifted the mercury in Torricelli’s column, and that different levels of rarefaction of that air produced different amounts of force.[14]

Some of the most astute of the new empiricists – among them Christian Huygens and Gottfried Leibniz – realized that this newly discovered force of the air could be used to reverse the suction pump, by turning suction into physical work, rather than the other way around. A change in air pressure within the cylinder of a pump would move the piston – down if the pressure decreased and up if it increased, overpowering the pressure of the atmosphere. This was the first concrete step on the path to the steam engine. But rather than turning to steam to alter the level of pressure, they turned at first to gunpowder.

[1] Robert Raymond, Out of the Fiery Furnace: The Impact of Metals on the History of Mankind (1986), 99.

[2] Sheldon Shapiro, “The Origin of the Suction Pump,” Technology and Culture 5, 4 (Autumn, 1964), 573.

[3] Galileo Galilei, Dialogues Concerning Two New Sciences (New York: Macmillan Company, 1914),16.

[4] David C. Lindberg, The Beginnings of Western Science (Chicago: University of Chicago Press, 1992), 234-244.

[5] Bennett Woodcroft, ed., The Pneumatics of Heron of Alexandria (London: Charles Whittingham, 1851), 3.

[6] Galileo, 17. Galileo also believed that tiny vacua between the particles of matter could account for the attractive force that held matter together.

[7] Quoted in W. E. Knowles Middleton, “The Place of Torricelli in the History of the Barometer,” Isis 54, 1 (March 1963), 12.

[8] Steven Shapin, The Scientific Revolution (Chicago: University of Chicago, 1996), 30-33; Marie Boas, “The Establishment of the Mechanical Philosophy,” Osiris 10 (1952): 412-541.

[9] Quoted in Middleton, 13.

[10] What Michael Strevens calls the “iron rule of explanation.” Strevens, The Knowledge Machine: How Irrationality Created Modern Science (New York: Liveright, 2020).

[11] In 1630, Giambattista Baliani wrote to Galileo proposing the weight of the air as the explanation for the action of a siphon. Galileo himself had argued in Two New Sciences that air has weight, basing his argument in an experiment described by Aristotle himself, who was not entirely self-consistent in this matter. But he did not make a connection between the weight of an individual portion of air and the idea of an all-pervading air pressure. Galileo, Dialogues Concerning Two New Sciences, 77-78.

[12] Quoted in Middleton, 20.

[13] A detailed account of the seventeenth-century reception of Torricelli’s work can be found in W.E. Knowles Middleton, The History of the Barometer (Baltimore: Johns Hopkins Press, 1964), 33-82. He quotes a 1663 letter from Christopher Wren: “It is not every yeare, will produce such a Master-Expt as the Torricellian, and so fruitful as it is of New Expts, and therefore the [Royal] Society hath deservedly spent much time upon it, and its offspring…”, 55.

[14] An even more compelling experiment came a decade later, when Robert Boyle used Hooke’s pump to empty a chamber containing a mercury barometer, and watched the mercury gradually fall as he removed the air.

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