Understanding Air as Distinct from Liquids and Solids in the Wake of Torricelli
Attempts to get a theoretical handle on the distinctive features of liquids and air moved forward significantly in the wake of Torricelli’s experiment in 1644 involving what later became recognized as the mercury barometer. Torricelli’s experiment, and, just as important, his theoretical reflections on it, were discussed in an interchange of letters between himself, in Florence, and Ricci, in Rome. Ricci sent extracts of these letters to Marin Mersenne and their contents became widely known and discussed, especially in France. These, and ensuing, discussions, especially amongst the Mersenne group in Paris and involving Blaise Pascal, were to set the scene for Pascal’s moves towards significant advances in the theorization of liquids.
Torricelli, in a letter of June 11, 1644, put his experiment in the context of the assumption that we ‘live submerged at the bottom of an ocean of the element air, which by unquestioned experiments is known to have weight’. The mercury in the tube is held up because ‘on the surface of the liquid which is in the basin, there gravitates a mass of air fifty miles high’. If mercury were to be replaced by water, then the water will rise ‘as much further than the quicksilver rises as quicksilver is heavier than water’. He elaborated on his explanation in a letter of June 28 in response to objections from Ricci in a letter of June 18.
One of Ricci’s objections involved placing a metal cap over the surface of the dish of mercury in which the barometer tube was held. He surmised that the mercury level would not fall following such an intervention, thus posing a challenge to Torricelli’s theory. In part of his response, Torricelli assumed that the metal cap be placed in such a way as to leave a layer of air between it and the mercury. He argued that this layer of air, which on his hypothesis was compressed by the weight of air above it, would remain compressed after the placement of the metal cap. It would therefore continue to press on the mercury as before and the mercury level in the barometer should remain unchanged. Torricelli developed his argument by drawing an analogy between the air he presumed to weigh down on the mercury and a cylinder of wool pressing on the base of its container by virtue of its weight. He invited Ricci to imagine that a sheet of iron be inserted part way up the wool so as to isolate the bottom portion from the top portion. Torricelli insisted that, since the bottom portion of wool would remain compressed, it would press down on the base as before. ‘Try it yourself’, wrote Torricelli, ‘for I shall not continue to bore you’.
A second objection put forward by Ricci directly introduced the issue of the direction of hydrostatic forces. Ricci observed that Torricelli’s explanation of the barometer assumed that the atmosphere presses down on the mercury in the dish. However, the resistance a syringe offers to the movement of a plunger is independent of the direction in which the syringe points, so, wrote Ricci, ‘it is still not evident that one can easily imagine how the weight of the air [which acts downwards] has anything to do with the effect’. Torricelli invoked two empirical effects by way of a response. One involved the observation that wine will spurt out in all directions from holes deep in the side of a barrel, showing that ‘although by nature liquids gravitate downwards, they press and spout in every direction, even upwards, as long as they find places to reach, - that is, places which resist with less force than their own’. The second involved the observation that if a pitcher filled with air is immersed mouth-downwards in water and then a hole is made in its base to allow the air to escape, then the water moves up into the pitcher, in spite of its natural tendency to fall. Note that, here, Torricelli answers Ricci’s objection, which involved the isotropy of forces in air, by examples involving isotropy in liquids! A notable feature of the developments in the decade separating Torricelli’s experiment and Pascal’s composition of his Treatise on the Equilibrium of Liquids is the extent to which the discussion moves freely between liquids, solids and gases exploiting various analogies between them.
Torricelli’s theoretical reflections and arguments were highly suggestive and fed productively into subsequent developments. But they are not all of a piece. The ‘ocean of air’ analogy with which Torricelli begins has an appeal if air is likened to a liquid, as is directly suggested by use of the term ‘ocean’. It was well known that columns of liquid in contact via their bases will be in equilibrium if their heights are proportional to their densities, the diameters of the columns being irrelevant. The barometer can be understood in these terms if the (very high) column of air resting on the mercury in the dish is likened to a column of a very rare liquid. Insofar as hydrostatic equilibrium can be comprehended in terms of balancing weights, so can Torricelli’s experiment via the ‘ocean of air’ metaphor.
Other strands in Torricelli’s reflections take him beyond an emphasis on weight. When he likened the atmosphere to a compressed pile of wool, air was likened to an elastic solid rather than a liquid. When a layer of air immediately above the mercury in the dish is cut off from the air above it, it continues to press on the mercury just as a compressed elastic solid would. The weight of air drops out of the picture and the forces engendered by its compression take its place. It is the compressed air pressing against the mercury in the dish that supports the column of mercury in the inverted tube. It may well have been the case that that air became compressed by the action of the weight of atmospheric air pressing on it from above, but the same effect would arise should the air be compressed in some other way.
The preceding observations were implicit in Torricelli’s talk of the compression of low-lying air but not made explicit to the extent that I have done. We have seen that Torricelli compared compressed air to compressed solids such as wool to help make his position intelligible. However, too close an analogy between compressed air and compressed solids suffer from the limitation that the effects of compression in air is isotropic in a way that they are not in the case of solids. When Ricci, in effect, pointed to the isotropy of the forces engendered by the expansion or compression of air, pointing out that the effects of shifting the plunger in a syringe do not depend on its orientation, Torricelli, in his reply, dropped the analogy with compressed wool and invoked examples involving isotropy in liquids, as we have seen.
Freeing the question of the forces exerted by air as a result of its compression from considerations of its weight was facilitated by experiments that built on Torricelli’s and which exploited the space above the mercury in a barometer. One of them, versions of which were conducted independently by Etienne Noel and Gilles Personne De Roberval in 1647, involved introducing equal volumes of water and air into that space, with dramatically different results. The introduction of the air resulted in a much greater reduction in the height of mercury in the tube than that caused by the introduction of an equal volume of water, in spite of the fact that the water weighed around a thousand times more than the air did. Roberval’s discussion of the experiment led him, not only to free considerations of the force arising from the compression of air from weight considerations, but also to distinguish the character of those forces from those arising from the compression of solids. Indeed, Roberval in effect manages to capture with considerable precision key ways in which air, as such, differs from liquids and solids, the key one being the its propensity to fill any space available to it and to exert a force on a surface that stands in the way of it doing so, whatever its orientation.
What is conveyed by Roberval’s text is that it is a natural property of air, that is, a property it possesses by virtue of being air, to expand spontaneously into any space available to it. When a volume of condensed air from the atmosphere was introduced into the space above the mercury ‘it spontaneously and of itself became rarefied in the tube’ and again, ‘as a matter of fact, if besides mercury or water, there be admitted into any part of the tube some of our compressed and condensed air, as we have stated above, this air obtains its freedom and all its parts recoil and become rarified and drive out the mercury or water, which for that reason will be depressed below the aforesaid height, either more or less, according to the air itself possesses greater or lesser power of rarefaction’. Air has a ‘power of rarefaction’ not possessed by liquids or solids.
The detachment of the force exerted by condensed air from weight considerations was taken a step further by Roberval’s insertion of a carp’s bladder, freed of most of its air and tied at the neck, into the space at the top of the barometer. The force of expansion exhibited by air was illustrated in a visually compelling way when the bladder was seen to expand markedly.
As well as supporting the view that air exerts an expansive force that is greater or less depending in its degree of compression, this experiment gives a visual display of the isotropy of the expansive force, the near spherical shape of the bladder arising from the fact that it is ‘pressed by force on all sides’. This remark of Roberval’s reinforces the point he had already made in the context of the introduction of a small volume of air into the Torricellian space, where he had stressed that the introduced air presses ‘in all directions on the adjacent bodies’, driving the mercury downwards because it is only it, rather than the containing glass, that can give way.
The point that air possesses a power of expansion which distinguishes it from liquids and which is implicated in the new experiments we have described above, as well as in the new understanding of the phenomenon of atmospheric pressure, was expressed very forcefully by J. Pecquet. As C. Webster has noted, Pecquet was an anatomist who became interested in the new experiments on air and, in 1651, included his own account and interpretation of them in a book on anatomy. Pecquet introduced the term ‘elater’ to single out the propensity of air to exert a force arising from its degree of compression, and insisted that it was this feature of air that distinguished it from liquids. ‘So’, wrote Pecquet in the context of the experiment that compared the effects of introducing water and air into the barometer tube, ‘it is evident that the adjacent mercury was not forced down as much by weight as by the strongest elater; and it is thus that the Terraquaceous Globe is compressed by air’. Here Pecquet explicitly distinguishes the weight and elator of air.
-  Spiers and Spiers, op.cit., p. 164.
-  Ibid., p. 165.
-  Ibid.
-  Ibid., p. 169.
-  Ibid., p. 167.
-  Ibid., p. 169. Note that already Torricelli talks of the pressing and spouting in all directions asresulting from a propensity that liquids possess of ‘their own’, and which is distinct from theirnatural tendency to gravitate downwards.
-  The quotations are from the English translations of Roberval’s letters in C. Webster, “TheDiscovery of Boyle’s Law and the Concept of the Elasticity of Air in the Seventeenth Century” in:Archive for the History of Exact Sciences 2, 1965, pp. 497 and 499. This reference gave me aninvaluable starting point for the material discussed in this section.
-  See ibid., p. 496.
-  Ibid., p. 497.
-  Ibid., p. 498.
-  See Webster, op. cit., pp. 451-454.
-  Ibid., p. 499.