Inventing Temperature Read online

  On top of all of those practical problems, there were tricks played by the phenomenon of supercooling. Mercury, like water, was capable of remaining fluid even when it had cooled below its "normal" freezing point. I have quoted Cavendish earlier as saying, "while any of the quicksilver in the cylinder remains fluid, it is impossible that it should sink sensibly below it [the freezing point]." He had to admit the falsity of that statement, in order to explain some "remarkable appearances" in Hutchins's experiments. Cavendish concluded that in some of the experiments the mercury must have been supercooled, remaining liquid below its freezing point. Supercooling created enough confusion when it was detected in water, but one can only imagine the bewilderment caused by the supercooling of mercury, since the "normal freezing point" itself was so disputed in that case. It is also easy to see how supercooling would have wreaked havoc with Cavendish's apparatus. Fortunately, the contemporary understanding of supercooling was just sufficient to

  15. See Jungnickel and McCormmach 1999, 398-399; Bergman 1783, 71, 83.

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  enable Cavendish to make sense of the most salient anomalies in Hutchins's results. Supercooling in mercury was still a hypothesis, but in fact Cavendish's analysis of Hutchins's results served to confirm the occurrence of supercooling, as well as the value of the freezing point. (This would make a good illustration of what Carl Hempel (1965, 371-374) called a "self-evidencing" explanation.)

  In two cases (Hutchins's second and third experiments), the mercury thermometer indicated −43°F while the mercury in the outer cylinder remained fluid; then when the outside mercury started to freeze, the thermometer suddenly went up to −40°F. This was interpreted by Cavendish (1783, 315-316) as the typical "shooting" behavior at the breakdown of supercooling, in which just so much of the supercooled liquid suddenly freezes that the released latent heat brings the whole to the normal freezing temperature (see "The Case of the Freezing Point" in chapter 1 for further information about supercooling and shooting). If so, this observation did provide another piece of evidence that the normal freezing point was indeed −40°F. More challenging was the behavior observed in four other cases (fourth to seventh experiments): each time the thermometer "sank a great deal below the freezing point without ever becoming stationary at −40°" (Cavendish 1783, 317). Not only that but the details recorded by Hutchins showed that there were various other stationary points, some sudden falls, and temperatures down to below −400°F. In Cavendish's view (1783, 318), all of this meant "that the quicksilver in the [outer] cylinder was quickly cooled so much below the freezing point as to make that in the inclosed thermometer freeze, though it did not freeze itself. If so, it accounts for the appearances perfectly well." Guthrie (1785, 5-6), using a similar apparatus by Black's suggestion, reported a similar puzzling observation, in which mercury was still fluid but the thermometer inserted into it indicated −150° Réaumur (−187.5°C, or −305.5°F). He thanked Blagden for providing an explanation of this fact by reference to supercooling (cf. Blagden 1783, 355-359).

  There was one remaining reason to be skeptical about the Hutchins-Cavendish value of the freezing point, which was curiously not discussed in any detail in either of their articles, or in Black's communication. The design of the Cavendish-Black apparatus focused on cajoling the mercury in the thermometer just near to the freezing point but not below it, thus avoiding the false readings caused by the significant contraction of mercury that occurs in the process of freezing. However, the design simply assumed that the contraction of mercury would continue regularly until it reached the freezing point. What was the argument for that assumption? Cavendish should have been wary of De Luc's earlier defense of mercurial regularity, since that was geared to defending the now-ludicrous freezing point of −568°F. Guthrie (1785, 5) thought that the assurance was only given by alcohol thermometers, which Hutchins had used alongside the mercury thermometers. I think Guthrie was correct to be suspicious of the mercury thermometer, but what were the grounds of his confidence that alcohol maintained a regular contraction right through the freezing point of mercury? He did not say.

  At temperatures near the freezing point of mercury, both the alcohol and the mercury thermometers were on shaky ground. On the one hand, it was a widely accepted view that the thermal expansion of alcohol was generally not linear, as I have discussed in "De Luc and the Method of Mixtures" in chapter 2, and

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  Cavendish specifically declined to rely on alcohol thermometers.16 On the other hand, it was difficult not to be wary of the readings of the mercury thermometer near its own freezing point. Even De Luc, the best advocate of the mercury thermometer, had expressed a general view that liquids near their freezing points are not likely to expand linearly (see the end of "De Luc and the Method of Mixtures"). If this was a battle of plausibilities between mercury and alcohol, the result could only be a draw. Hutchins's observations in fact made it clear that there was a discrepancy of about 10°F between the readings of his alcohol and mercury thermometers at the very low temperatures; Cavendish's estimate (1783, 321) was that the freezing point of mercury was between −28.5° and −30°F by the alcohol thermometer.17

  Cavendish stuck to the mercury thermometer, with characteristic ingenuity. When he commissioned some further experiments in Hudson's Bay, this time carried out by John McNab at Henley House, Cavendish was forced to use alcohol thermometers, since the object was to produce and investigate temperatures clearly lower than the freezing point of mercury by means of more effective freezing mixtures. Still, Cavendish calibrated his alcohol thermometers against the standard of the mercury thermometer. Here is how: Mr. McNab in his experiments sometimes used one thermometer and sometimes another; but … I have reduced all the observations to the same standard; namely, in degrees of cold less than that of freezing mercury I have set down that degree which would have been shown by the mercurial thermometer in the same circumstances; but as that could not have been done in greater degrees of cold, as the mercurial thermometer then becomes of no use, I found how much lower the mercurial thermometer stood at its freezing point, than each of the spirit thermometers, and increased the cold shown by the latter by that difference. (Cavendish 1786, 247)

  This way the Cavendish-McNab team measured temperatures reaching down to −78.5°F (−61.4°C), which was produced by mixing some oil of vitriol (sulphuric acid, H 2 SO 4 ) with snow (Cavendish 1786, 266).

  Despite Cavendish's cares and confidence, it seems that temperature measurement at and below the freezing point of mercury remained an area of uncertainty for some time. When Blagden and Richard Kirwan made a suggestion that the freezing point of mercury should be used as the zero point of thermometry, the 3d edition of the Encyclopaedia Britannica in 1797 rejected the idea saying that the

  16. See Cavendish 1783, 307, where he said: "If the degree of cold at which mercury freezes had been known, a spirit thermometer would have answered better; but that was the point to be determined." I think what Cavendish meant was that knowing that point would have provided a calibration point from which his could extrapolate with some credibility the pattern of alcohol's contraction to lower temperatures, as he did do after the freezing point of mercury was stabilized.

  17. More details can be seen in Hutchins's comparison of the readings of different thermometers (1783, *308ff.); the thermometers are described on p. *307. This, then, throws suspicion on Guthrie's observation (1785, 11, etc.) that mercury was frozen at −32° Réaumur (−40°F) by the alcohol thermometer. That would make sense only if his alcohol thermometer was calibrated by comparison with the mercury thermometer, in a procedure explained by Cavendish later.

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  freezing point of mercury was "not a point well known."18 In 1808 John Dalton actually constructed a new thermometric scale that took the freezing of mercury as the zero point but, as we saw in "Caloric Theories against the Method of Mixtures" in chapter 2, he disputed the belief that mercury expanded nearly uniformly according to real t
emperature. Instead, Dalton's temperature scale was based on his own theoretical belief that the expansion of any pure liquid was as the square of the temperature reckoned from the point of greatest density (usually the freezing point, but not for water). Following this law, and fixing the freezing and boiling points of water at 32°F and 212°F, Dalton estimated the freezing point of mercury as −175°F (1808, 8, *13-14). There is no evidence that Dalton's thermometric scale came into any general use, but there were no arguments forthcoming to prove him wrong either. Both the mercury thermometer and the alcohol thermometer remained unjustified, and empirical progress in the realm of frozen mercury was difficult because such low temperatures were only rarely produced and even more rarely maintained steadily, until many decades later.

  The most significant advance in the measurement of low temperatures in the first half of the nineteenth century arrived unceremoniously in 1837 and became an unassuming part of general knowledge. The author of this underappreciated work was Claude-Servais-Mathias Pouillet (1790-1868), who was soon to succeed Pierre Dulong in the chair of physics at the Faculty of Sciences in Paris at Dulong's death in 1838. Pouillet held that position until 1852, when he was dismissed for refusing to swear an oath of allegiance to the imperial government of Napoleon III. By the time Pouillet did his low-temperature work he had already taught physics in Paris for two decades (at the École Normale and then at the Faculty of Sciences), and he was also well known as a textbook writer. His early research was in optics under the direction of Biot, and he went on to do important experimental works in electricity and heat. Until Regnault, he was probably the most reliable experimenter on the expansion and compressibility of gases.19

  The main ingredients of Pouillet's work are quite simple, in retrospect. A. Thilorier had just recently manufactured dry ice (frozen CO 2 ) and described a paste made by mixing it with sulphuric ether. Thilorier's paste could effect higher degrees of cooling than any freezing mixtures. Pouillet seized this new material as a vehicle to take him further into the low-temperature domain. First of all he wanted to determine the temperature of the cooling paste and concluded that it was −78.8°C.20 For that purpose he used air thermometers. There is no surprise in Pouillet's use of the air thermometers, since he had worked with them previously and had voiced a clear advocacy of gas thermometers in his 1827 textbook, citing the arguments by

  18. See Blagden 1783, 397, and also Encyclopaedia Britannica, 3d ed. (1797), 18:496.

  19. See René Taton's entry on Pouillet in the Dictionary of Scientific Biography, 11:110-111.

  20. Pouillet 1837, 515, 519. This value is very close to the modern value of the sublimation point of carbon dioxide, which is −78.48°C or −109.26°F.

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  Dulong and Petit, and Laplace.21 The more interesting question is why apparently no one had used the air thermometer in the investigation of temperatures near the freezing of mercury, when the advantage would have been obvious that air at these temperatures was not anywhere near liquefying, or changing its state in any other drastic manner. I do not have a convincing answer to that historical question, but the primary reasons may have been practical, particularly that most air thermometers were relatively large in size, and to surround one with a sufficient amount of freezing mercury or other substances to be observed would have required an impractical amount of high-quality cooling material. Pouillet was probably the first person to have sufficient cooling material for the size of the air thermometer available, thanks to Thilorier's paste and his own work on the improvement of air thermometers.

  The extension of the air thermometer into the domain of the very cold gave Pouillet important advantages over previous investigators. Pouillet's confidence in the correctness of the air thermometer was probably unfounded (as we have seen in "The Calorist Mirage of Gaseous Linearity" in chapter 2), but at least the air thermometer provided an independent means of testing out the indications of the mercury and alcohol thermometers. Pouillet now set out to confirm the freezing point of mercury. He conceded that it was difficult to use the air thermometer for this experiment. He did not specify the difficulties, but I imagine that the experiment would have required a good deal of mercury for the immersion of the air thermometer, and it would have been quite tricky to cool so much mercury down to such a low temperature slowly enough while keeping the temperature uniform throughout the mass. A direct application of Thilorier's mixture would have produced an overly quick and uneven cooling. Whatever the difficulties were, they must have been severe enough because Pouillet took a laborious detour. This involved the use of a thermocouple, which measures temperature by measuring the electric current induced across the junction of two different metals when heat is applied to it. Pouillet (1837, 516) took a bismuth-copper thermocouple and checked its linearity against the air thermometer in a range of everyday temperatures (17.6°C to 77°C). Then he extended the thermocouple scale by simple extrapolation and was delighted by the "remarkable fact" that it measured the temperature of Thilorier's paste at −78.75°C, within about 0.1° of the air-thermometer readings of that particular point. This close agreement gave Pouillet confidence that the bismuth-copper thermocouple indicated very low temperatures correctly.

  The thermocouple was then applied to the freezing mercury and gave the temperature of −40.5°C (or −40.9°F), which was very close to the Cavendish-Hutchins result of −39°F obtained by the mercury thermometer. Now Pouillet constructed alcohol thermometers graduated between the freezing point and the temperature of Thilorier's paste. Note that this scale, assuming the expansion of

  21. Pouillet 1827-29, 1:259, 263; see "The Calorist Mirage of Gaseous Linearity" in chapter 2 for the content of the arguments that Pouillet cited.

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  alcohol to be linear in that sub-zero range, was not the same as the alcohol scale extrapolated linearly from warmer temperatures. Pouillet (1837, 517-519) made six different alcohol thermometers, and noted that they all gave readings within 0.5° of −40.5°C for the freezing point of mercury. He was pleased to note: "These differences are so small as to allow us to conclude that the alcohol thermometer is in perfect accord with the air thermometer from 0°C down to −80°C." What he had established was quite an impressive consistent ring of measurement methods: the expansion of air, the intensity of current in the bismuth-copper thermocouple, and the expansion of alcohol all seemed to be proportional to each other in the range between the freezing point of water and the temperature of Thilorier's paste; moreover, the expansion of mercury also seemed to conform to the same pattern down to the freezing point of mercury itself. Of course, we must admit that Pouillet's work was nowhere near complete, since he had only checked the agreement at one point around the middle of the relevant range, namely the freezing point of mercury, and also did not bring the air thermometer itself to that point. But if we consider how much the expansion of alcohol, air, and mercury differed from each other in higher temperatures,22 even the degree of consistency shown in Pouillet's results could not have been expected with any complacency. At last, a century after Gmelin's troubles in Siberia, there was reasonable assurance that the freezing point of mercury was somewhere near −40°C.

  Adventures of a Scientific Potter

  When we shift our attention to scientific work at the other end of the temperature scale, we find a rather different kind of history. The production of temperatures so low as to push established thermometers to their limits was a difficult task in itself. In contrast, extremely high temperatures were well known to humans both naturally and artificially for many centuries; by the eighteenth century they were routinely used for various practical purposes and needed to be regulated. Yet, the measurement of such high temperatures was open to the same kind of epistemic and practical difficulties as those that obstructed the measurement of extremely low temperatures. Therefore pyrometry, or the measurement of high temperatures, became an area of research occupying the attention of a wide range of investigators, from the merely "curious" gentle
men to the most hard-nosed industrialists.

  In 1797 the much-expanded third edition of the Encyclopaedia Britannica was pleased to note the recent progress in thermometry (18:499-500): "We are now therefore enabled to give a scale of heat from the highest degree of heat produced by an air furnace to the greatest degree of cold hitherto known." Britannica identified the latest development in pyrometry as the work of "the ingenious Mr Josiah Wedgwood, who is well known for his great improvement in the art of pottery." But

  22. See the discussion of De Luc's comparison of mercury and alcohol in "De Luc and the Method of Mixtures" and the discussion of Dulong and Petit's comparison of mercury and air in "Regnault and Post-Laplacian Empiricism" in chapter 2.

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  the high temperatures reported there are suspect: the melting point of cast iron is put down as 17,977°F, and the greatest heat of Wedgwood's small air-furnace as 21,877°F. Surely these are much too high? Scientists now believe that the surface of the sun has a temperature of about 10,000°F.23 Can we really believe that Wedgwood's furnace was 10,000 degrees hotter than the sun? A couple of questions arise immediately. What kind of thermometer was Wedgwood using to read temperatures so far beyond where mercury boils off and glass melts away? And how can one evaluate the reliability of a thermometer that claims to work in the range where all other thermometers fail? Wedgwood's thermometer was widely used and his numbers were cited in standard textbooks for some time, but over the course of the first few decades of the nineteenth century they became widely discredited.24 The rise and fall of the Wedgwood pyrometer is a fascinating story of a pioneering expedition into an entirely unmapped territory in the physics and technology of heat.