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Solution to the long-standing puzzle of Huygens’ “anomalous suspension”

Abstract

In 1662 Christiaan Huygens carried out the famous Torricelli experiment to test the existence of atmospheric pressure by inserting the apparatus in the glass receiver of a vacuum pump, and evacuating the air inside it. He reported that when the air was exhausted, a column of water remained suspended in a 4-foot tube. This unexpected result was in stark contrast with earlier experiments of Boyle and Hooke that apparently had confirmed Torricelli’s explanation that such a water column was supported by outside air pressure, and would fall when the air was removed. Huygen’s “anomalous suspension” led to the continuation of controversies in the seventeenth century about the nature of the vacuum that these experiments were expected to resolve. Surprisingly, the origin of Huygens’ unexpected result has remained a puzzle up to the present time. In this paper, I discuss the dynamics of such a column of water under the experimental conditions reported by Boyle and by Huygens, that turned out to be different, and present the results of a replication of their experiments with a modern vacuum pump. Contrary to the conventional explanations of these experiments, I demonstrate that in the Boyle–Hooke version of this experiment, the water column descends initially because it is forced down by the gas pressure due to air dissolved in the water which is released inside the Torricelli tube after the external pressure is sufficiently decreased. Huygens, however, first removed this trapped air before he carried out his experiment. In the absence of this internal gas pressure, the early rudimentary vacuum pumps were inadequate to decrease the air pressure sufficiently inside the receiver to demonstrate the descent of a Torricelli column of airless water 4-foot in height or less.

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Notes

  1. Reprinted in vol. 1 of Hunter and Davis (1999a). Huygens’ (1932a) notes on his experiments appear in vol. 17. Historical accounts of these experiments can be found in Stroud (1981a), van Helden (1991), Shapin and Schaffer (1985a) and Vermij (2004a).

  2. Letter of Robert Boyle to Charles Boyle, son of Boyle’s brother Richard.

  3. For example, Thomas Hobbes declared “Why such apparatus and the expense of machines [such as an air pump] of difficult manufacture, just so you could get as far as Hobbes has already progressed? Why did you not begin from where he left off? Why did you not use the principles that he established?”. T. Hobbes, Dialogus physicus 1661. Translated and reprinted in Shapin and Schaffer (1985b).

  4. In his book, Harvard Case Histories in Experimental Sciences (Harvard Univ 1957), J. B. Conant devotes the first 60 pages to “Robert Boyle’s experiments in Pneumatics.” In this account, however, there is not a single mention of Huygens the puzzling “anomalous suspension,” thus giving a somewhat lopsided history of the experimental discovery of the physical properties of air.

  5. One cubit \(=\) .46 m.

  6. An ell was a unit used by tailors for the distance between the elbow and the wrist. This unit varied between 27 and 45 in. depending apparently on the typical arm length of people of different nationalities.

  7. Huygens’ Ouvres XIV 481–497.

  8. Quoted in Shapin and Schaffer (1985d, p. 252).

  9. Huygens also reported that “I saw my experiment of purged water in the void in a pipe of 7-feet in height, where the water stayed up without falling, succeeded 2 or 3 times, in the presence of Lord Brouncker, Mr. Boyle and of many other persons” (quoted in Shapin and Schaffer 1985d, p. 252). Such a higher column of water, however, exceeded the height of his receiver and required that an apperture be made on top of it. After the 7-foot tube was inserted in the receiver, it had to be properly sealed with wax, but this change is likely to have decreased further the efficiency of the air pump. Claims were also made for anomalous suspension of mercury, e.g., Boyle and Brouncker reported that well-purged mercury would stand at a height of 52 in. without using an air-pump (Shapin and Schaffer 1985d, p. 254).

  10. In 1662, Boyle published the results of this experiment, as well as arguments against Hobbes and Linus, as an Appendix to the second edition of his book (Boyle 1660, see footnote 1). In 1665, Hooke also published similar results in his book Micrographia, reprinted in Gunther (1938).

  11. Hooke first conjectured the \(\textit{PV}=\) constant relation by the observation that during each cycle of his pump, the air density in the receiver decreased by a factor \(V/(V+V')\), where \(V\) is the volume of the receiver and \(V'\) is the volume of the pump and that, likewise, the height of his Torricellian column (with mercury) decreased approximately by the same factor. Boyle also credited this conjecture to Richard Towneley and to Lord Brouncker. See footnote 4, p. 54.

  12. Huygens’ Ouvres XIV 431–442.

  13. Leviathan, p. 241, footnote 24.

  14. Leviathan, p. 344.

References

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Acknowledgments

I would like to thank John Heilbron for a stimulating exchange on the puzzle of anomalous suspension, and Fred Kuttner for his assistance in replicating the air pump experiments presented here.

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Correspondence to Michael Nauenberg.

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Communicated by: Jed Buchwald.

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Nauenberg, M. Solution to the long-standing puzzle of Huygens’ “anomalous suspension”. Arch. Hist. Exact Sci. 69, 327–341 (2015). https://doi.org/10.1007/s00407-015-0152-1

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Keywords

  • Mercury
  • Water Column
  • Huygens
  • Vacuum Pump
  • Glass Wall