Inventing Temperature Read online

  Now, this immediate problem of simple prejudice could be solved by sufficient experience, or even be prevented by a healthy does of open-mindedness or theoretical daring. For instance, William Cleghorn of Edinburgh, who developed an early version of the caloric theory, reckoned that "it is not improbable, that by a very great diminution of its heat air itself might become solid," long before any such thing was physically realized.8 However, Gmelin's predicament also indicated a more profound and difficult question. If we admit, with Blagden, that the mercury thermometer must malfunction as it approaches the freezing point of mercury, what do we propose to use instead for the measurement of such low temperatures? More generally, if we admit that the behavior of matter in new domains may not conform

  5. See Urness 1967, 161-168, for a biographical sketch of Pallas.

  6. Voyages 1791, 2:237-242.

  7. Bentham 1843, 7:95; I thank Dr. Jonathan Harris for this reference.

  8. This conjecture, he said, was "confirmed by the analogy of other vapours"; see Encyclopaedia Britannica, 2d ed., vol. 5 (1780), 3542.

  end p.106

  to what we know from more familiar domains, we are also forced to admit that our familiar and trusted observational instruments may cease to function in those new domains. If the observational instruments cannot be trusted, how do we engage in empirical investigations of phenomena in the new domains? We have seen in chapter 2 that the mercury thermometer was the best temperature standard in the eighteenth century. When the best available standard fails, how do we create a new standard, and on what basis do we certify the new standard?

  Can Mercury Tell Us Its Own Freezing Point?

  The immediate difficulty, after it was admitted that mercury was indeed capable of freezing, was to determine its freezing temperature. Braun admitted that the point seemed to be "at too great a latitude to be exactly determined." His reported that 469° Delisle (−212.7°C) was the warmest at which he observed any congelation of mercury, but the "mean term of the congealation [sic] of mercury" was estimated at 650° Delisle (−333.3°C). These were numbers obtained from the readings of the mercury thermometer. Braun also had thermometers made with "highly rectified spirit of wine" (concentrated ethyl alcohol). He reported that he was unable to freeze the alcohol, and that the alcohol thermometers only indicated 300° Delisle (−100°C) at the degrees of cold that froze mercury. All three alcohol thermometers he employed agreed well with each other and also agreed with mercury thermometers at lesser degrees of cold.9 Later Pallas reported from Siberia that his frozen mercury was observed to melt at 215° Delisle (−43.3°C).10 So there was a broad range, spanning nearly 300°C, in which the true freezing point of mercury lay hidden, if one took Braun and Pallas as the best and equally trustworthy authorities on this point. Matthew Guthrie (1732-1807), Scottish physician then working for the army in St. Petersburg, commented in 1785 that nothing at all was certain about the freezing of mercury, except that it was possible. Guthrie (1785, 1-4, 15) concluded from his own experiments, employing an alcohol thermometer, that "the true point of congelation of the purest mercury" was −32° Réaumur (−40°C), and noted the good agreement of that value with Pallas's.

  A good sense of the early uncertainties on this matter can be gained from Jean-André De Luc's defense of Braun. In "De Luc and the Method of Mixtures" in chapter 2, we saw that De Luc made a strong argument for mercury as the thermometric fluid of choice, in his 1772 treatise Inquiries on the Modifications of the Atmosphere. In the same text he argued that Braun's experiments presented no reason to doubt that the contraction of mercury by cold was quite regular down to its freezing point. Shortly after the announcement of Braun's results, an objection

  9. These estimates are cited in Watson 1761, 167-171.

  10. Voyages 1791, 2:241. There is a slight puzzle there, since Pallas also seems to have said that this number (215° Delisle) corresponded to 29 degrees below the freezing point (of water) on the Réaumur scale. With the Réaumur scale as commonly understood in the late eighteenth century (De Luc's design), −29°R would have been −36.25°C. But it is not clear how exactly Pallas's "Réaumur" scale was graduated, so it is safer to go with the number cited on the Delisle scale.

  end p.107

  had been published in the Paris Journal des Savants. At bottom the author, by the name of Anac, was simply incredulous that temperatures like 650° Delisle (−333°C, or −568°F) could have been reached by the quite ordinary cooling methods used by Braun. But De Luc chided Anac for presuming to judge observations about a new domain of phenomena on the basis of what he knew about more familiar cases. Anac also maintained that Braun's temperatures could not be real because they were even lower than absolute zero, which was estimated at 521 and 3/7 degrees Delisle (−247.6°C). Here he was citing the number originating from the work of Guillaume Amontons, obtained by extrapolating the observed temperature-pressure relation of air to the point of vanishing pressure (see "William Thomson's Move to the Abstract" in chapter 4 for more on "Amontons temperature"). De Luc scoffed at this estimate and the very concept of absolute zero, pointing out the shakiness of both the assumption that the observed linear temperature-pressure relation would continue down to zero and the theoretical presumption that temperature was so essentially connected to air pressure (De Luc 1772, 1:256-263, §416).

  De Luc also argued that the apparent discrepancy in Braun's own numbers could be reconciled. This argument pointed up a serious question about the apparently sensible practice of using an alcohol thermometer to take temperatures where mercury freezes or presumably begins to behave anomalously near its freezing point. We have seen in "De Luc and the Method of Mixtures" in chapter 2 that De Luc used the method of mixtures to argue that the readings of the standard alcohol thermometer were inaccurate, nearly 8°C below the "real" temperature at the midpoint between the boiling point and the freezing point. De Luc had also demonstrated a serious discrepancy between the readings of the alcohol and the mercury thermometers; the mercury-alcohol discrepancy is real regardless of the cogency of the method of mixtures.

  De Luc's data indicated that alcohol had a more "accelerated" expansion than mercury at higher temperatures. If the same pattern continued down to lower temperatures, alcohol would contract considerably less than would be expected from assuming linearity, which means that the linearly graduated alcohol thermometer would show readings that are not as low as the real temperature, or not as low as the readings of a mercury thermometer in any case. De Luc estimated that 300.5° Delisle (−80.75° on De Luc's own scale) on the alcohol thermometer would actually be the same degree of heat as 628° Delisle (−255° De Luc) on the mercury thermometer (see fig. 3.1). That made sense of Braun's puzzling result mentioned earlier, which gave the freezing point of mercury as 650° Delisle on the mercury thermometer and 300° Delisle on the alcohol thermometer. Hence, De Luc argued, there was no mystery there, and no particular reason to distrust the mercury thermometer near its freezing point. A more serious concern was about the accuracy of the alcohol thermometer, which seemed to be at least about 300° Delisle (or 200°C) off the mark near the freezing point of mercury.11

  11. For this interpretation, see De Luc 1772, 1:255-256, §416. De Luc's extrapolation also gave the result that the condensation of alcohol would stop altogether at 300.5° Delisle (−80.75° De Luc).

  end p.108

  Figure 3.1. De Luc's comparison of mercury and alcohol thermometers, and an extrapolation of the results. The same data have been used here as in series 1 in fig. 2.1 in chapter 2. The curve shown here is the best quadratic fit I can make on the basis of De Luc's data and extrapolation.

  De Luc's arguments clearly reveal two obstacles in the inquiry concerning the freezing of mercury. First, there were no temperature standards known to be reliable in such extreme degrees of cold. While De Luc shattered the false sense of security that some people might have derived from the alcohol thermometer, he himself could not offer any alternative standard that was more reliable. De Luc only m
ade a wishful and ill-supported conjecture that mercury probably continued its reasonably regular contraction right down to its freezing point. Second, we may note that De Luc's arguments were speculative, even as he chided Anac for his groundless assumptions about the absolute zero. It was difficult for De Luc to avoid speculation, since in the relatively mild climate of Geneva he could not perform his own experiments to clear up the uncertainties that arose in his discussion. At that time, even with the best freezing mixtures, it was impossible to attain low enough temperature unless one started out at very cold natural temperatures found in such places as St. Petersburg.

  A development to overcome these obstacles occurred shortly after De Luc's work, with a little help from British imperialism.12 The Royal Society's desire to arrange new experiments on the freezing of mercury found its fulfillment in the

  12. For a concise yet fully informative account of this development, see Jungnickel and McCormmach 1999, 393-400.

  end p.109

  person of Thomas Hutchins (?-1790), the governor of Fort Albany, in present-day Ontario.13 Hutchins had been in North America in the employ of the Hudson's Bay Company since 1766, where he also began to build a reputation as a naturalist in collaboration with Andrew Graham. In 1773, while back in England on leave, he entered into agreement with the Royal Society to make some observations on the dipping needle and the congelation of mercury. Hutchins first made successful experiments in 1775 to freeze mercury (in the relative tranquility of Hudson's Bay, even as Britain started to wage war with the colonial revolutionaries down south). However, like Braun earlier, Hutchins was not able to determine the freezing point with any confidence.

  Hearing about Hutchins's experiments, Joseph Black stepped in to pass on some sage advice, via Graham, in a letter of 1779 (reproduced in Hutchins 1783, *305-*306). Black started with a negative assessment: "I have always thought it evident, from Professor Braun's experiments, that this degree of cold [necessary to freeze mercury] cannot be discovered conveniently by congealing the mercury of the thermometer itself." However, he suggested that the mercury thermometer could still be used to determine the freezing point of mercury, as follows. Insert a mercury thermometer into the middle of a wider cylinder filled with mercury, and cool the cylinder gradually from the outside. That way, the mercury outside the thermometer would begin to freeze before the mercury inside the thermometer. As soon as the mercury outside starts to assume the consistency of an amalgam, the reading on the thermometer should be noted. Black predicted confidently: "I have no doubt, that in every experiment, thus made, with the same mercury, the instrument will always point to the same degree."

  Directing Hutchins's experiments from London on behalf of the Royal Society was Henry Cavendish. It was a happy enough coincidence that Cavendish, independently of Black, came up with almost precisely the same clever design for Hutchins. Perhaps it was not so much of a coincidence, if we consider that the design hinged crucially on Black's ideas about latent heat, which Cavendish also shared. Since freezing requires a great deal of heat to be taken away from the liquid even after its temperature reaches its freezing point (as explained in "The Case of the Freezing Point" in chapter 1), Black and Cavendish were confident that the larger cylinder full of mercury would take a good amount of time to freeze, and that its temperature would be nearly uniform and constant during that time. Cavendish (1783, 305) had in fact observed a similar pattern of behavior when molten lead and tin cooled and solidified. In short, keeping the thermometer in the middle portion, which would be the last to receive the full effect of the cooling, ensured that the mercury in the thermometer would not itself freeze yet approach the freezing point very closely. Cavendish explained the design of his apparatus as follows:

  13. The following information about Hutchins is from Glyndwr Williams's entry on him in the Dictionary of Canadian Biography, 4:377-378. I believe he is a different person from a contemporary of the same name, who was geographer to the United States.

  end p.110

  If this cylinder is immersed in a freezing mixture till great part of the quicksilver in it is frozen, it is evident, that the degree shewn at that time by the inclosed thermometer is the precise point at which mercury freezes; for as in this case the ball of the thermometer must be surrounded for some time with quicksilver, part of which is actually frozen, it seems impossible, that the thermometer should be sensibly above that point; and while any of the quicksilver in the cylinder remains fluid, it is impossible that it should sink sensibly below it. (Cavendish 1783, 303-304)

  Cavendish dispatched to Hudson's Bay the apparatus shown in figure 3.2, with detailed instructions. Hutchins carried out the experiments during the winter of 1781-1782 (just after the surrender of the British Army at Yorktown, Virginia): "The experiments were made in the open air, on the top of the Fort, with only a few deer-skins sewed together, placed to windward for a shelter: there was plenty of snow (eighteen inches deep) upon the works …" (Hutchins 1783, *320). Despite various technical difficulties and interpretive confusions, Hutchins managed to carry out the experiments to Cavendish's satisfaction, and he also performed some experiments of his own design. Hutchins concluded that the freezing point of mercury was −40°F (or −40°C; amusingly, this is exactly the point where the numbers on the Fahrenheit and the centigrade scales coincide). What gave Hutchins and Cavendish confidence about that number was that it was recorded in three different types of circumstances: while the mercury in the cylinder was freezing; while a ball of mercury frozen around the thermometer bulb was melting; and also when the thermometer was inserted into the liquid part of a frozen block of mercury that was melting (Cavendish 1783, 321-322).

  The Hutchins-Cavendish result on the freezing point of mercury was accepted very gladly by many scientists. It agreed well with Pallas's earlier estimate (−43°C), and exactly with Guthrie's measurements using alcohol thermometers. Blagden was delighted:14 The late experiments at Hudson's Bay have determined a point, on which philosophers not only were much divided in their opinion, but also entertained, in general, very erroneous sentiments. Though many obvious circumstances rendered it improbable, that the term of mercurial congelation should be 5[00] or 600 degrees below 0 of Fahrenheit's scale … yet scarcely any one ventured to imagine that it was short of 100°. Mr. Hutchins, however, has clearly proved, that even this number is far beyond the truth. … (Blagden 1783, 329)

  There was only one slight modification to the result, arising from Cavendish's re-examination of Hutchins's thermometers after they were brought back to London. Hutchins's thermometers were found to be slightly off when compared to the standard thermometers graduated according to the procedures laid out by Cavendish's Royal Society committee in 1777. Accordingly Cavendish (1783, 309 and 321) estimated that the true freezing point of mercury was 38 and 2/3 degrees below

  14. According to Jungnickel and McCormmach (1999, 294), Blagden assisted Cavendish in the analysis of Hutchins's data and also in Cavendish's own experiments to freeze mercury in London.

  end p.111

  Figure 3.2. Cavendish's apparatus for determining the freezing point of mercury, used by Hutchins (1783, tab. 7, facing p.*370). Courtesy of the British Library.

  end p.112

  zero, which he rounded up to −39°F. The Hutchins-Cavendish work certainly made a quick impression, as represented in the following small incident. When the Swedish chemist Torbern Bergman published his Outlines of Mineralogy in 1782, he had listed the freezing point of mercury as −654°F. William Withering, English physician and member of the Lunar Society of Birmingham, who translated the text into English, felt obliged to correct Bergman's table so that the "melting heat" of mercury read "−39 or −654 degrees Fahrenheit."15 However, as we will see in the next section, Hutchins's results were not all straightforward.

  Consolidating the Freezing Point of Mercury

  Cavendish and Blagden spent the winter of 1782-1783 going over Hutchins's results, and the outcome was an article by Cavendish (1783) in w
hich he made a largely successful effort to reach a clear and coherent interpretation of all of Hutchins's observations. From the vantage point of the twenty-first century, it is easy to underestimate the challenges involved in the eighteenth-century experimental work on the freezing of mercury. Most thermometers were unreliable and lacked agreement with each other. Freezing mixtures provided only temporary and variable sources of cold, making it difficult to freeze the mercury either slowly or in large quantities. The degree of cold attained depended crucially on the outside air temperature, over which one had no control. Reading the mercury thermometer near the freezing point of mercury was treacherous, because it was visually difficult to tell whether a thin column of mercury was frozen solid, or still liquid but stationary. Worse yet, frozen mercury would often stick to the inside of the thermometer stem, and then slide off when it got warmer, creating an inexplicable appearance of falling temperature. And the precious thermometers (brought over carefully on long bumpy journeys from St. Petersburg, London, etc. out to the wilderness) routinely broke in the middle of the experiments, because the extreme degree of cold made the glass brittle.