Inventing Temperature Page 11
The freezing-point story conforms very well to the general account of standards and their validation and improvement given in "The Validation of Standards" and The Iterative Improvement of Standards." The freezing point was part of the basis on which the dominant form of the numerical thermometer was constructed, respecting and improving upon the thermoscopic standard; most of what I said in that connection about the boiling point applies to the freezing point as well. Likewise, the strategies for the plausible denial of variability discussed in "The Defense of Fixity" also apply quite well to the freezing point. In the freezing-point case, too, causes of variation were eliminated when possible, and small inexplicable variations were ignored. But corrections did not play a big role for the freezing point, since there did not happen to be significant causes of variation that were amenable to corrections.
This episode also reinforces the discussion of serendipity and robustness in "The Defense of Fixity." The robustness of the freezing point was due to the same kind of serendipity that made the boiling/steam point robust. In both cases there was a lack of clear theoretical understanding or at least a lack of theoretical consensus.
64. Gernez actually employed an iterative method in that proposal.
65. This experiment was attributed to Carnelly; see Aitken 1880-81, 339.
66. See De Luc 1772, 1:344, §436; and 1:349, §438.
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However, pragmatic measures for ensuring fixity were in place long before there was any good theoretical understanding about why they were effective. In fact, they often happened to be in place even before there was a recognition of the problems that they were solving! In the case of the freezing point, it was very easy to disturb the container and break supercooling, if one did not take particular care to maintain tranquility. Black (1775, 127-128) thought that even the imperceptible agitation caused by air molecules spontaneously entering into the water would be sufficient for that effect.67 Especially if one was taking thermometers in and out of the water to take temperature readings, that would have caused mechanical disturbances and also introduced a convenient solid surface on which ice crystals could start to form. If the experiments were done outdoors on a cold day, which they tended to be in the days before refrigeration, "frozen particles, which in frosty weather are almost always floating about in the air," would have dropped into the water and initiated ice-formation in any supercooled water.68 But the early experimenters would not have seen any particular reason to cover the vessel containing the water. In short, supercooling is a state of unstable equilibrium, and careless handling of various kinds will tend to break that equilibrium and induce shooting. Therefore, as in the boiling-point story, the theme of the freezing-point story is not the preservation of fixity by random chance, but its protection through a serendipitous meeting of the epistemic need for fixity and the natural human tendency for carelessness.
67. This was offered as a novel explanation of the puzzling observation that water that had previously been boiled seemed to freeze more easily. Since air would be expelled from the water in boiling, and it would re-enter the water after the boiling ceased, Black reckoned that the molecular agitation involved in that process would be sufficient to prevent supercooling. Therefore the once-boiled water would seem to freeze more readily than ordinary water, which was more liable to supercooling. Blagden (1788, 126-128), however, maintained that boiled water was more susceptible to supercooling, not less; he thought that the purging of air caused by the boiling was responsible for this effect (cf. De Luc's supercooling experiment with airless water, mentioned earlier).
68. This was a quite popular idea, expressed for example by Blagden (1788, 135), quoted here.
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2. Spirit, Air, and Quicksilver
Narrative: The Search for the "Real" Scale of Temperature
Abstract: The establishment of the fixed points of thermometry allowed the creation of numerical thermometers by finding a procedure for assigning numbers to the degrees of heat between fixed point and beyond them. This chapter discusses efforts to establish the numerical scale. This problem involved a deep philosophical challenge, which was overcome after more than a century of debates and experiments.
Keywords: thermometers, fixed point, numerical scale
Hasok Chang
The thermometer, as it is at present construed, cannot be applied to point out the exact proportion of heat. … It is indeed generally thought that equal divisions of its scale represent equal tensions of caloric; but this opinion is not founded on any well decided fact.
Joseph-Louis Gay-Lussac, "Enquiries Concerning the Dilatation of the Gases and Vapors," 1802
In chapter 1, I discussed the struggles involved in the task of establishing the fixed points of thermometry and the factors that enabled the considerable success that was eventually reached. Once the fixed points were reasonably established, numerical thermometers could be created by finding a procedure for assigning numbers to the degrees of heat between the fixed points and beyond them. This may seem like a trivial problem, but in fact it harbored a deep philosophical challenge, which was overcome only after more than a century of debates and experiments.
The Problem of Nomic Measurement
The main subject of this chapter is intimated in a curious passage in Elementa Chemiae, the enormously influential textbook of chemistry first published in 1732 by the renowned Dutch physician Herman Boerhaave (1668-1738):
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Table 2.1. The discrepancies between thermometers filled with different liquids Mercury
Alcohol
Water
0 (°C)
25
22
5
50
44
26
75
70
57
100
100
100
Source: The data are from Lamé 1836, 1:208.
I desired that industrious and incomparable Artist, Daniel Gabriel Fahrenheit, to make me a couple of Thermometers, one with the densest of all Fluids, Mercury, the other with the rarest, Alcohol, which should be so nicely adjusted, that the ascents of the included liquor in the same degree of Heat, should be always exactly equal in both. (Boerhaave [1732] 1735, 87)
The goods were delivered, but Boerhaave found that the two thermometers did not quite agree with each other. Fahrenheit was at a loss for an explanation, since he had graduated the two thermometers in exactly the same way using the same fixed points and the same procedures. In the end he attributed the problem to the fact that he had not made the instruments with the same types of glass. Apparently "the various sorts of Glass made in Bohemia, England, and Holland, were not expanded in the same manner by the same degree of Heat." Boerhaave accepted this explanation and went away feeling quite enlightened.1
The same situation was seen in a different light by another celebrated maker of thermometers, the French aristocrat R. A. F. de Réaumur (1683-1757), "the most prestigious member of the Académie des Sciences in the first half of the eighteenth century," a polymath known for his works in areas ranging widely from metallurgy to heredity.2 Roughly at the same time as Boerhaave, Réaumur had noticed that mercury and alcohol thermometers did not read the same throughout their common range (1739, 462). He attributed the discrepancy to the fact that the expansions of those liquids followed different patterns. Réaumur's observation and explanation soon became accepted. It is not a subtle effect, as table 2.1 shows.
There are various attitudes one can take about this problem. A thoroughgoing operationalist, such as Percy Bridgman, would say that each type of instrument defines a separate concept, so there is no reason for us to expect or insist that they should agree.3 A simple-minded conventionalist would say that we can just choose one instrument and make the others incorrect by definition. As Réaumur put it, one
1. The lesson that Boerhaave drew from this incident was caution against rash assumptions in empirical science: "How infinitely careful
therefore ought we to be in our searches after natural knowledge, if we would come at the truth? How frequently shall we fall into mistakes, if we are over hasty in laying down general rules?"
2. See J. B. Gough's entry on Réaumur in the Dictionary of Scientific Biography, 11:334.
3. See Bridgman 1927, esp. 3-9. Bridgman's views will be discussed in much more detail in "Travel Advisory from Percy Bridgman" and "Beyond Bridgman" in chapter 3.
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will calibrate an alcohol thermometer on the standard of a mercury thermometer "when one wishes the alcohol thermometer to speak the language of the mercury thermometer" and vice versa (1739, 462). A more sophisticated conventionalist like Henri Poincaré would say that we ought to choose the temperature standard that makes the laws of thermal phenomena as simple as possible.
Very few scientists making or using thermometers took any of those philosophical positions. Instead, most were realists in the sense that they believed in the existence of an objective property called temperature and persisted in wanting to know how to measure its true values. If various thermometers disagreed in their readings, at most one of them could be right. The question, then, was which one of these thermometers gave the "real temperature" or the "real degree of heat," or most nearly so. This is a more profound and difficult question than it might seem at first glance.
Let us examine the situation more carefully. As discussed in "Blood, Butter, and Deep Cellars" in chapter 1, by the middle of the eighteenth century the accepted method of graduating thermometers was what we now call the "two-point method." For instance, the centigrade scale takes the freezing and boiling points of water as the fixed points. We mark the height of the thermometric fluid at freezing 0°, and the height at boiling 100°; then we divide up the interval equally, so it reads 50° halfway up and so on. The procedure operates on the assumption that the fluid expands uniformly (or, linearly) with temperature, so that equal increments of temperature results in equal increments of volume. To test this assumption, we need to make an experimental plot of volume vs. temperature. But there is a problem here, because we cannot have the temperature readings until we have a reliable thermometer, which is the very thing we are trying to create. If we used the mercury thermometer here, we might trivially get the result that the expansion of mercury is uniform. And if we wanted to use another kind of thermometer for the test, how would we go about establishing the accuracy of that thermometer?
This problem, which I have called the "problem of nomic measurement," is not unique to thermometry.4 Whenever we have a method of measurement that rests on an empirical law, we have the same kind of problem in testing and justifying that law. To put it more precisely and abstractly: 1.
We want to measure quantity X.
2.
Quantity X is not directly observable, so we infer it from another quantity Y, which is directly observable. (See "The Validation of Standards" in the analysis part for a full discussion of the exact meaning of "observability.")
3.
For this inference we need a law that expresses X as a function of Y, as follows: X = f(Y).
4.
The form of this function f cannot be discovered or tested empirically, because that would involve knowing the values of both Y and X, and X is the unknown variable that we are trying to measure.
4. See Chang 1995a, esp. 153-154. The problem first came up in my study of energy measurements in quantum physics.
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This circularity is probably the most crippling form of the theory-ladenness of observation. (For further discussions of the problem of nomic measurement, see "Comparability and the Ontological Principle of Single Value" in the analysis part.)
Given this fundamental philosophical puzzle, it should not come as a surprise that there was a complex and protracted fight over the choice of the right thermometric fluid. A bewildering variety of substances had been suggested, according to this or that person's fancy: mercury, ether, alcohol, air, sulphuric acid, linseed oil, water, salt water, olive oil, petroleum, and more. Josiah Wedgwood even used lumps of clay, which actually contracted under high degrees of heat, as in his pottery kilns (see "Adventures of a Scientific Potter" in chapter 3). Just as wonderfully varied as the list of thermometric substances is the list of eminent scientists who concerned themselves seriously with this particular issue: Black, De Luc, Dalton, Laplace, Gay-Lussac, Dulong, Petit, Regnault, and Kelvin, just to mention some of the more familiar names.
Three of the known thermometric fluids became significant contenders for the claim of indicating true temperatures: (1) atmospheric air; (2) mercury, or quicksilver; and (3) ethyl alcohol, most often referred to as "the spirit of wine" or simply "spirit." The rest of the narrative of this chapter charts the history of their contention, ending with the establishment of the air thermometer as the best standard in the 1840s. Throughout the discussion there will be an emphasis on how various scientists who worked in this area attempted to tackle the basic epistemological problem, and these attempts will be analyzed further in broader philosophical and historical contexts in the second part of the chapter.
De Luc and the Method of Mixtures
Thermometry began with no firm principles regarding the choice of thermometric substances.5 The very early thermoscopes and thermometers of the seventeenth century used air. Those fickle instruments were easily replaced by "liquid-in-glass" thermometers, for which the preferred liquid for some time was spirit. Fahrenheit, working in Amsterdam, was responsible for establishing the use of mercury in the 1710s; small, neat and reliable, his mercury thermometers gained much currency in the rest of Europe partly through the physicians who had received their training in the Netherlands (under Boerhaave, for instance), where they became familiar with Fahrenheit's instruments.6 Réaumur preferred spirit, and due to his authority spirit thermometers retained quite a bit of popularity in France for some time. Elsewhere mercury came to be preferred by most people including Anders Celsius, who pioneered the centigrade scale.
Initially people tended to assume that whichever thermometric fluids they were using expanded uniformly with increasing temperature. The observations showing
5. For the early history that will not be treated in detail in this chapter, see Bolton 1900, Barnett 1956, and the early chapters of Middleton 1966.
6. For this account of the dissemination of the mercury thermometer by physicians, see Encyclopaedia Britannica, supplement to the 4th, 5th, and 6th editions (1824), 5:331.
end p.60
the disagreement between different types of thermometers made the need for justification clearer, but it seems that for some time the unreflective habit continued in the form of unsupported assertions that one or another fluid expanded uniformly and others did not. There was even a view that solids expanded more uniformly than liquids and gases, advanced by Thomas Young (1773-1829), the promulgator of the wave theory of light, as late as the beginning of the nineteenth century (Young 1807, 1:647). Jacques Barthélemi Micheli du Crest (1690-1766), Swiss military engineer who spent much of his life in political exile and prison, published an idiosyncratic argument in 1741 to the effect that spirit expanded more regularly than mercury.7 However, his contemporary George Martine (1702-1741), Scottish physician, stated a contrary opinion: "it would seem, from some experiments, that [spirit] does not condense very regularly" in strong colds; that seemed to go conveniently with Martine's advocacy of the mercury thermometer, which was mostly for practical reasons (Martine [1738] 1772, 26). The German physicist-metaphysician Johann Heinrich Lambert (1728-1777) also claimed that the expansion of spirit was irregular. He believed, as had the seventeenth-century French savant Guillaume Amontons (1663-1738), that air expanded uniformly and liquids did not. Neither Amontons nor Lambert, however, gave adequate arguments in support of that assumption.8