Inventing Temperature Read online

  The general notion of comparability was not Regnault's invention. It was in fact almost an item of common sense for a long time in thermometry, widely considered a basic requirement for reliability. The term is easier to understand if we go back to its origin, namely when thermometers were so notoriously unstandardized that the readings of different thermometers could not be meaningfully compared with each other. The early difficulty may be illustrated by an exception that proves the rule. In 1714 Fahrenheit astonished Christian Freiherr von Wolff, then professor of mathematics and physics at the University of Halle and later its chancellor, by presenting him with two spirit thermometers that agreed perfectly with each other (a feat he could not manage for Boerhaave when different liquids were involved, as we saw in "The Problem of Nomic Measurement").49 Comparability was almost a battle cry as the early pioneers of thermometry called for standardization.

  Regnault transformed this old notion of comparability into a powerful tool for testing the goodness of each given type of thermometer. The novelty introduced by Regnault was a higher degree of skepticism: in earlier times, once a rigorous method of graduating thermometers was settled on, people tended to assume that all instruments produced by that method would be exactly comparable to each other. For Regnault (1847, 165), this was much too hasty. Methods of standard graduation generally only involved making different thermometers agree with each other at a small number of points on the scale. This gave no guarantee that the thermometers would agree with each other at all other points. The agreement at other points was a hypothesis open to empirical tests, even for thermometers employing the same fluid as long as they differed in any other ways.

  48. Regnault did assume heat conservation in some other experiments (especially for calorimetry).

  49. On Fahrenheit's interaction with Wolff, see Bolton 1900, 65-66, and also Van der Star 1983, 5.

  end p.77

  Figure 2.1. De Luc's comparison of spirit thermometers. The data and explanations are from De Luc 1772, 1:326, §426.

  In the next section we shall see in good detail how fruitful Regnault's use of comparability was. One final note before passing on to that discussion: this innovation in the use of comparability must be credited at least partly to De Luc, although he did not use it nearly as systematically as Regnault did. De Luc was already accustomed to thinking about comparability through his famous work in barometry, and there is also some indication that he regarded comparability as a requirement for measurements in general.50 In thermometry he used the comparability criterion in order to give an additional argument against the spirit thermometer. De Luc's results, some of which are represented in Figure 2.1, showed that the spirit thermometer was not a comparable instrument, since spirit expanded according to different laws depending on its concentration.51 But why was it not possible to avoid this difficulty by simply specifying a standard concentration of the

  50. See the discussion of barometry in De Luc 1772, vol. 1, part 2, ch. 1, and his attempts to bring comparability into areometry in De Luc 1779, 93ff.

  51. The assumption in De Luc's attack on the spirit thermometer was that mercury thermometers, in contrast, were comparable amongst each other. Since mercury is a homogeneous liquid and does not mix well with anything else, De Luc thought its concentration was not likely to vary; he also believed that any impurities in mercury became readily noticeable by a diminution in its fluidity. For these points, see De Luc 1772, 1:325-326, 330, §426. The comparability of the mercury thermometer seems to have remained the going opinion for decades afterwards; see, for instance, Haüy [1803] 1807, 1:142-143 (and corresponding passages in subsequent editions), and Lamé 1836, 1:219.

  end p.78

  spirit to be used in thermometers? That would have created another fundamental difficulty, of having to measure the concentration accurately. This was not easy, as we can see in the extended essay on areometry (the measurement of the specific gravity of liquids), which De Luc (1779) published seven years later.52

  The Verdict: Air over Mercury

  What was the outcome of Regnault's comparability-based tests? Since the spirit thermometer had been discredited beyond rescue (in terms of comparability and in other ways, too), Regnault's main concern was to decide between the air thermometer and the mercury thermometer. This particular issue had also assumed a greater practical urgency in the meantime, thanks to Dulong and Petit's work in regions of higher temperatures that revealed a mercury-air discrepancy reaching up to 10° on the centigrade scale (see "Regnault and Post-Laplacian Empiricism" for further details about this work). Clearly it would not do to use the mercury thermometer and the air thermometer interchangeably for serious scientific work, and a choice had to be made.

  With regard to comparability, it was mercury that betrayed clearer signs of trouble. In the course of his work on the comparison between the readings of the air thermometer and the mercury thermometer, first published in 1842, Regnault (1842c, 100-103) confirmed that there was no such thing as "the" mercury thermometer. Mercury thermometers made with different types of glass differed from each other even if they were calibrated to read the same at the fixed points. The divergence was noticeable particularly at temperatures above 100° centigrade. Worse yet, as Regnault (1847, 165) added in his later and more extensive report, samples of the same type of glass that had undergone different thermal treatments did not follow the same law of expansion. Regnault (1847, 205-239) laid to waste the assumed comparability of the mercury thermometer in his painstaking series of experiments on eleven different mercury thermometers made with four different types of glass. As the data in table 2.4 show, there were significant differences, exceeding 5°C in the worst cases. It was as if Fahrenheit's ghost had revisited the scene with a grin: he was correct after all, that the types of glass used made a substantial difference! A further irony is that De Luc's technique originally intended for his advocacy of mercury was now being used to discredit mercury.

  It may be objected here that the failure of comparability due to the behavior of glass was merely a practical difficulty, having nothing to do with the thermal expansion of mercury itself. Would it not be easy enough to specify a certain type of glass as the standard glass for making mercury thermometers? But the thermal behavior of glass was complex and not understood very well. Achieving comparability in the standard mercury thermometer would have required the specification

  52. See also De Luc 1772, 1:327-328, §426. There is an indication that Fahrenheit, who was an earlier pioneer of areometry, had kept a standard sample of spirit to use as the standard for all his spirit thermometers. It seems that he was aware of the variation in the patterns of expansion, but only as a minor annoyance. See Fahrenheit's letter of 17 April 1729 to Boerhaave, in Van der Star 1983, 161, 163.

  end p.79

  Table 2.4. Regnault's comparison of mercury thermometers made with different types of glass Air thermometer

  Mercury with "Choisy-le-Roi" crystal

  Mercury with ordinary glass (thermometer No. 5)a

  Mercury with green glass (thermometer No. 10)

  Mercury with Swedish glass (thermometer No. 11)

  100 (°C)

  100.00

  100.00

  100.00

  100.00

  150

  150.40

  149.80

  150.30

  150.15

  200

  201.25

  199.70

  200.80

  200.50

  250

  253.00

  250.05

  251.85

  251.44

  300

  305.72

  301.08

  −

  −

  350

  360.50

  354.00

  −

  −

  Source: Adapted from Regnault 1847, 239.

  a Note that the pattern of expansion of ordinary glass happens to match that of mercury quite well up to nearly 300° C, so that the readings of th
e air thermometer agrees quite well with the readings of the mercury-in-ordinary-glass thermometer.

  of the exact chemical composition of the glass, the process of its manufacture (down to the exact manner of blowing the thermometer bulb), and also the conditions of usage. Controlling such specifications to meet the degree of precision wanted by Regnault would have required not only totally impractical procedures but also theoretical and empirical knowledge beyond anyone's grasp at that time. The uncertainties involved would have been enough to defeat the purpose of increased precision. (This is similar to the situation with the failure of comparability in the spirit thermometer due to variations in the concentration of spirit.) In addition, the familiar vicious circularity would also have plagued any attempt to make empirical determinations of the behavior of glass as a function of temperature, since this would have required an already trusted thermometer.

  When he announced the mercury thermometer to be lacking in comparability in 1842, Regnault was nearly prepared to endorse the use of the air thermometer as the only comparable type. As the thermal expansion of air was so great (roughly 160 times that of glass), the variations in the expansion of the glass envelope could be made negligible (Regnault 1842c, 103). Still, he was not entirely comfortable. Refusing to grant any special status to gases, Regnault (1847, 167) demanded that the air thermometer, and gas thermometers in general, should be subjected to a rigorous empirical test for comparability like all other thermometers. He had good reason to hesitate. His own work had shown that the average coefficient of expansion was variable according to the density even for a given type of gas. Perhaps the form of the expansion law also varied, as in the case of alcohol with different concentrations? The variation in the coefficient was an annoyance, but there was no conceptual problem in graduating each thermometer individually so that it gave 100° at the boiling point of water. On the other hand, variations in the form of the law would have been a more serious matter, resulting in a failure of comparability. Regnault (1847, 172) considered it "absolutely essential" to submit this question to an experimental investigation.

  To that end Regnault built constant-volume thermometers filled with gases of various densities, starting with atmospheric air. He rejected air thermometers at

  end p.80

  Table 2.5. Regnault's comparison of air thermometers filled with different densities of air Air thermometer A

  Air thermometer A′

  Temperature difference (A−A′)

  Pressure (mmHg)

  Temperature reading (°C)

  Pressure (mmHg)

  Temperature reading (°C)

  762.75

  583.07

  1027.01

  95.57

  782.21

  95.57

  0.00

  1192.91

  155.99

  911.78

  155.82

  +0.17

  1346.99

  212.25

  1030.48

  212.27

  −0.02

  1421.77

  239.17

  1086.76

  239.21

  −0.04

  1534.17

  281.07

  1173.28

  280.85

  +0.22

  1696.86

  339.68

  1296.72

  339.39

  +0.29

  Source: Adapted from Regnault 1847, 181.

  constant pressure because they suffered from an inherent lowering of sensitivity at higher temperatures.53 (The design of these instruments will be discussed further in "The Achievement of Observability, by Stages.") Regnault's typical procedure was to set two such thermometers side by side in a bath of oil, to see how much they differed from each other at each point. Such pairs of temperature readings were taken at various points on the scale ranging from 0° to over 300° centigrade. The results of these tests provided a relief. The data in table 2.5, for instance, give a comparison of the readings of air thermometer A, whose "initial" pressure (that is, pressure at temperature 0°) was 762.75 mm of mercury, with the readings of A′, whose initial pressure was 583.07 mm. The divergence between these two thermometers was always less than 0.3° in the range from 0° to 340°, and always below 0.1% of the magnitudes of the measured values. Also attesting to the high comparability of these two thermometers was the fact that the discrepancy between their readings was not systematic, but varied randomly. The results from other similar tests, with initial pressures ranging from 438.13 mm to 1486.58 mm, were similarly encouraging.54 Regnault (1847, 185) declared: "One can therefore conclude with all certainty from the preceding experiments: the air thermometer is a perfectly comparable instrument even when it is filled with air at different densities."

  Regnault also attempted some other experiments to see if the comparability could be extended to the generalized gas thermometer. He found that comparability held well between air and hydrogen, and also between air and carbonic acid gas (carbon dioxide). As with air at different densities, it turned out that these gases had the same form of the law of expansion, though their coefficients of expansion were quite different from each other. However, as shown in table 2.6, there were some serious and systematic discrepancies between air and sulfuric acid gas.55 So, once again, Regnault exposed a place where the behavior of all gases was not identical

  53. See Regnault 1847, 168-171, for an explanation of this effect.

  54. See, for instance, tables in Regnault 1847, 181, 184.

  55. For the other inter-gas comparisons, see the tables on 186-187.

  end p.81

  Table 2.6. Regnault's comparison of thermometers of air and sulfuric acid gas Air thermometer A

  Sulfuric acid thermometer A′

  Temperature difference (A−A′)

  Pressure (mmHg)

  Temperature reading (°C)

  Pressure (mmHg)

  Temperature reading (°C)

  762.38

  588.70

  1032.07

  97.56

  804.21

  97.56

  0.00

  1141.54

  137.24

  890.70

  136.78

  +0.46

  1301.33

  195.42

  1016.87

  194.21

  +1.21

  1391.07

  228.16

  1088.08

  226.59

  +1.57

  1394.41

  229.38

  1089.98

  227.65

  +1.73

  1480.09

  260.84

  1157.88

  258.75

  +2.09

  1643.85

  320.68

  1286.93

  317.73

  +2.95

  Source: Adapted from the second series of data given in Regnault 1847, 188.

  and showed that the generalized gas thermometer would not be a comparable instrument. Regnault (1847, 259) was happy enough to assert: "[T]he air thermometer is the only measuring instrument that one could employ with confidence for the determination of elevated temperatures; it is the only one which we will employ in the future, when the temperatures exceed 100°."

  A couple of questions may be raised regarding this conclusion. First of all, why was air preferred to other kinds of gases? It is not that each of the other gas thermometers had been shown to lack comparability. Having found no explicit discussion of this issue in Regnault's writings, I can only speculate. The practical aspect may have been enough to decide the issue, namely that atmospheric air was the easiest and cheapest gas to acquire, preserve, and control. This may explain why Regnault chose not to produce results on the comparability of other gas thermometers with regard to density, and without such tests he would not have felt comfortable adopting those thermometers for use. It is interesting to note that Regnault was apparently not concerned by the fact that atmospheric air was a mixture of different gases. As long as it satisfied the comparability conditio
n and did not exhibit any overtly strange behavior, he saw no reason to make apologies for air or prefer pure gases to it. This was in line with his antitheoretical bias, which I will discuss further in "Regnault and Post-Laplacian Empiricism."

  The second question is whether Regnault thought he had good reason to believe the comparability of air thermometers to be sufficiently proven. Just as his own work had exposed the lack of comparability in the mercury thermometer with the variation in glass-type, was it not possible that there were other parameters of the air thermometer whose variation would destroy its comparability? Again, I can only speculate on what Regnault thought about this. I think that there were no other remaining variations that seemed particularly significant to him, and that he would have made the tests if any had occurred to him. On the other hand, there was no end of parameters to study and subject to doubt, so it is also possible that even Victor Regnault was pragmatically forced to stop somewhere in testing possible variations, against his own principles. In any case, as even Karl Popper would have

  end p.82

  recommended, the only thing one can do is to adopt and use, for the time being, whatever has not been falsified yet.

  Possibly because of these remaining questions, Regnault's final pronouncement in favor of air was muted. His 1842 article on the comparison of mercury and air thermometers had ended on a pessimistic note: Such simple laws accepted so far for the expansion of gases had led physicists to regard the air thermometer as a standard thermometer whose indications are really proportional to the increases in the quantities of heat. Since these laws are now recognized as inexact, the air thermometer falls back into the same class as all other thermometers, whose movement is a more or less complicated function of the increases in heat. We can see from this how far we still are from possessing the means of measuring absolute quantities of heat; in our present state of knowledge, there is little hope of finding by experiment simple laws in the phenomena which depend on these quantities. (Regnault 1842c, 103-104)