• 1 Agnes Clerke (1887) A Popular History of Astronomy During the Nineteenth Century, 2^nd éd (Londres: (...)

1Conspiracies, cash and controversy dominate Agnes Clerke’s historical accounts of methods to establish the distance from the sun to the earth, or, equivalently the solar parallax, in a wonderful chapter of her Popular History of Astronomy published in 18871. The conspiracies were those of errors that had been disguised by concordant proofs. Clerke described several occasions on which scientists had obtained similar results from different methods, briefly raising the hope that lasting agreement could be obtained. Challenged by the next set of numbers, in retrospect such moments of agreement usually looked highly suspicious. The cash flowed in extraordinary amounts from numerous national governments, totalling a quarter of a million dollars for the 1874 expeditions; and the controversies were all too common and surprisingly persistent. Diversity of judgement was the rule rather than an exception. Of course the main characters in Clerke’s history were the two transits of Venus that occurred in the nineteenth century, accompanied by the extraordinary expeditions mounted to observe them and dogged (but not dominated) by the black spot. But the main reason her chapter managed to finish with a happy ending was the result of an entry from another quarter. At the last moment velocity of light measurements had enabled physicists to time light’s wings and thereby solve the solar parallax problem, at least provisionally. That will be my subject today, but first I want to give an overview of the field of alternatives, before turning to the interrelated transit and velocity of light campaigns that were conducted in the United States.

• 2 The Astronomer Royal [George Bidell Airy] (1857) “On the Means, which will be available for correct (...)

2Even as they headed off with the most modem tools to observe the transits of 1874 and 1881, nineteenth-century scientists interpreted their work as but the next step in a long heritage. Astronomy’s “noblest problem”, to use Airy’s description2, had not won its reputation by being easy to solve, and its history had taught important lessons. Firstly, the transits of Venus were always just one of many ways of deriving a value for the solar parallax, only likely to be more accurate because Venus comes so close to the earth. Second, as well as requiring the comparison of observations across space in a single determination, determining the parallax often called for the comparison of observations across time. Third, the specific value obtained was important because it related different facets of both the theory of the planets and the alternative methods of observation available. Any synthetic evaluation had to engage in the difficult task of comparing widely different methods across broad timescales, raising tensions between completeness of treatment that would incorporate all relevant measures, and a reliance on particularly valued procedures.

• 3 William Harkness (1881) “On the Relative Accuracy of Different Methods of Determining the Solar Par (...)

3The opening pages of a paper given in 1881 by William Harkness of the Naval Observatory “On the Relative Accuracy of Different Methods of Determining the Solar Parallax”, can give a quick idea of the order of complexity involved3. As we will see later, Harkness wanted to convince his audience that the photographic method the U.S. employed in 1874 was one of the most accurate known. To compare different methods Harkness needed 34 different symbols for the constants and variables entering different algebraic formulae. In addition he drew his sources from the proceedings and observations of eleven different journals or observatories. Nevertheless, Harkness was able to classify every known method as belonging to one of three classes, according to whether they used what he described as trigonometric, gravitational, or photo-tachymetrical methods. In her narrative trawl, Clerke describes seven different primary objects of observation or kinds of experiments that were key to different determinations. Amongst them, observations of the opposition of Mars, transits of Venus, and transits of minor planets would all fit in Harknesses trigonometrical category. Her fourth object, data on the moon’s orbit, was the primary but by no means only method of using gravitational values obtained from the theory of planetary motion to derive a parallax. Finally, observations of eclipses of Jupiter’s satellites (leading to the light equation), terrestrial measures of the velocity of light, and aberration experiments provided different components of what Harkness described as the photo-tachymetrical method. They were related by two equations featuring, in all, seven constants:

• 4 Clerke A Popular History, p. 285.
• 5 Ibid., pp. 279-281, 285. Note that the cupola image of the transit of Venus in the Salle du Conseil (...)
• 6 For example, Simon Newcomb writes of his investigation of Father Hell’s manuscripts in Vienna: “Amo (...)

4Then there are fine distinctions to reckon with, within these different kinds of observations. In regard to the opposition of Mars, Clerke distinguishes two different methods. The first was simultaneous observations from different places in the normal manner of parallactic determinations. The second was diurnal observations by the same observer like those Gill made on Ascension Island in 1877. This method gained its strength from unity of performance: the same man made all observations, providing an instance of the many cases in which one man can do the work of two, better than two can do the work of one4. In the case of transits of Venus four different methods of observation were in play. Halley and Delisle’s “older” methods of visual observations differed on whether the duration or moment of transit is important, while the modem methods were distinguished by their use of different instruments: the camera and heliometer. Unlike the old contact methods, the new methods by projection measured the position of the centre of Venus relative to the centre of the Sun5. The distinction between old and modem was by no means confined to instruments: the theoretical redetermination of earlier results could also subject them to “modern” methods of analysis6.

• 7 A. Cornu (1898) “Notice sur l’œuvre scientifique de H. Fizeau”, Annuaire du Bureau des Longitudes, (...)

5While the field of alternatives was extremely wide, late nineteenth-century discussions often drew a primary contrast between two methods in particular, transit observations and velocity-of-light experiments. Perhaps this is because they seemed to pose most strongly a contrast between measures focused on rare astronomical events on the one hand, and fantastically difficult terrestrial experiments on the other hand. In some treatments this was also importantly a contrast between the two different disciplines of astronomy and physics. Commenting on Hippolyte Fizeau’s early experiments from 1849, the French physicist Alfred Cornu celebrated the reversal that precise determinations of the terrestrial velocity of light had affected. For the first time physics had provided astronomy with the constant that determined the absolute unit of length for the measure of celestial space7.

• 8 For a very helpful account of the relations between the two men and the transit expeditions see Ste (...)
• 9 William Harkness (1891) “The Solar Parallax and its Related Constants”, in Washington Observations (...)

7Without doubt Simon Newcomb was principally responsible for setting expeditions to observe the transits of Venus onto the agenda of the U.S. Congress, and probably played the most important role in shaping public opinion of the transits in his country. Newcomb provided the public face of the transits. His junior colleague at the Naval Observatory and successor as Director of the Nautical Almanac, William Harkness played the most integral role in the actual observations and their reduction8. But the two men differed in their fundamental orientation. While Harkness became a determined advocate of the accuracy of transit photographs, Newcomb was the most important proponent of velocity-of-light measures. Despite his influence on the perception of the transit expeditions, Newcomb gave them much less weight than velocity-of-light measures. Both Harkness and Newcomb published monographs on astronomical constants, but Newcomb’s 1895 work on The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy was adopted internationally from 1900, together with its value for the solar parallax9. The conflict between Newcomb and Harkness was one that reflected different ways of resolving diversity of judgement. It will show a rhetoric of embarrassment running through the treatment of the solar parallax over a thirty year period. The rhetoric was both public and private, and it is important to note that it touched both transits and velocities.

• 10 For accounts of Newcomb’s early astronomical work see Norberg’s studies. Moyer describes Newcomb’s (...)

8After employment as an astronomical computer in the Nautical Almanac Office, Simon Newcomb became a member of the Naval Observatory in 1861. Finding that different observers used different methods of reducing their observations led Newcomb to a focus on methods and procedures that he was to carry throughout his scientific career. He thought that any use of concepts required a clear description of protocols, a point that was as important for experimental work and calculations as it was for methods of observation and data reduction in astronomy. The point also came up again and again in his discussions of social and economical fields, where from the late 1870s he became a well-known spokesman and probably America’s best-known scientist10.

• 11 William Tobin (2002) Léon Foucault. Le miroir et le pendule, French adapt. James Lequeux (Paris : E (...)
• 12 Simon Newcomb (1882) “Measures of the Velocity of Light Made Under Direction of the Secretary to th (...)

9Newcomb’s involvement with solar parallax began with observations of Mars at its 1862 opposition, but he also took note of the publication of Foucault’s determination of the velocity of light using a revolving mirror and a light path of approximately 66 feet in the same year. This experiment was prompted by Urbain Le Verrier, the director of the Paris Observatory, and it built on a French tradition that used experiments on the velocity of light to test wave and particle theories of light, and investigate the nature of the ether11. Two motivations almost always accompanied experiments on velocity of light: astronomical measures, and ethereal investigations. Foucault’s value differed from previous astronomical determinations by only 1,234 miles per second, indicating a potential concordance between terrestrial and astronomical measures. In 1867 Newcomb published a paper investigating “The Distance of the Sun”. There he reduced the 1862 measurements of Mars but wrote also of the importance of repeating Foucault’s experiments on a much larger scale, with a distance of three to four kilometres12.

• 13 Newcomb (1903) The Reminiscences of an Astronomer, pp. 165-166.

11First, the telescope lens was constructed with the photographic spectrum rather than the visual spectrum in mind. Second, the photographic telescope was mounted in the meridian, its direction tested by having the transit instrument mounted in front of it. Third, a plumb line with a very fine silver wire thread was to be suspended in front of the photographic plate. This was so that the direction of the north-south line on the plate could be calculated with the greatest exactness, and the position angle could be measured with the same precision that any other measure could be made. Finally, the distance between the photographic plate and the object glass of the telescope was measured with a long iron rod, which was kept in position above the line of sight of the telescope itself. This made it possible to determine to what angle a given measure on the plate would correspond13. While the difference between old and new methods has sometimes been described as one between geometrical and photographic astronomy, that was decidedly not the case in the American campaign. The distinction between the wet bromide plates used in 1874 and the dry collodion emulsion plates used in 1882 was also less important than the fact that the photograph simply required different protocols to be incorporated within a geometrical regime than an observer.

• 14 William Harkness (1888) “On the Value of the Solar Parallax Deducible from the American Photographs (...)

14Everything was more hurried in preparations for the 1882 transits. Four months before the transit Congress appropriated $10,000 for improving the instruments and $75,000 for the expeditions. Better weather meant that the 1882 observations yielded 1380 measurable photographs. Six years later, in 1888 Harkness was able to report a result, improved the following year14. That, very briefly, is the story of the U.S. photographs, achieving a result but doing so late and without publishing a forma! account of the observations as a whole. Parallel to this runs the story of U.S. measures of the velocity of light, in which Newcomb was again the principal moving figure, though Albert Michelson became the poster boy of the measuring campaign.

• 15 Newcomb offers a brief history of velocity of light measurements and his involvement in Newcomb (18 (...)
• 16 See Newcomb to Com. R.W. Thompson, Secretary of the Navy, 12 December 1878; and Simon Newcomb, “On (...)

15Newcomb’s first concrete plans for velocity of light measures began in 1876 and briefly involved Thomas Edison15. Looking for funding Newcomb went from the secretary of the Navy to the National Academy of Sciences and then back to the Navy for appropriations from Congress. He wanted $7,000 and offered four arguments. The first was to point out the imperfection of present astronomical tables. These depended on the distance of the sun and were so bad that correction of astronomical data was a considerable part of the labour of calculation even in running boundary lines. The second was a contrast with costly and time-consuming transit campaigns, which led Newcomb to promise that if he was fast enough another overseas campaign would not be necessary in 1882. The third was the present difference of 1% between the best available velocity-of-light measures, which needed to be closed down. And the final cherry was the possibility of delivering information on “the luminiferous ether and the relation between light, electricity and other visible forces16.”

• 17 On Michelson see especially Stanley Goldberg and Roger H. Stuewer, eds. (1988) The Michelson Era in (...)
• 18 A. A. Michelson (1879) “Experimental Determination of the Velocity of Light”, US. Nautical Almanac (...)
• 19 See Michelson to Newcomb, 18 December 1878, in Ibid. p. 116; Reingold (1964) Science in Nineteenth- (...)

16By late 1878 Newcomb was referring to recent experiments of a similar kind at the Naval Academy to argue for the feasibility of obtaining an accurate result. Albert Michelson, an instructor in physics and chemistry at the Academy had devised a new arrangement that made the best of previous French attempts17. Cornu’s toothed wheel measurements suffered from the fact that the transition from darkness to light that indicated that the wheel was revolving rapidly enough was indistinct. Using a mirror obviated that difficulty, and Michelson found a way of achieving a path length much longer than Foucault’s 66 feet. His first trials were carried out using a lens from the 1874 transits to focus the ray of light, although he had a new lens with a longer focal length purpose-built for his final experiments, conducted in 1879. Michelson used a light path of approximately 2,000 feet, and came to a value of 299,944 ±51 km/s, 46 km/s lower than Cornu’s result18. He needed $2,000 to do it, but the fact that his first mirror had cost only $10 was as important rhetorically19.

• 20 Newcomb to Michelson 2 May 1881 and 23 June 1881 in Reingold (1964) Science in Nineteenth-century A (...)

17Having obtained a number kept Michelson one step ahead of Newcomb, who got an appropriation of $5,000 from Congress in 1879 and began trials in 1880, with Michelson detailed to the Nautical Almanac to aid in the performance of the experiment. Before Newcomb s experiments ended Michelson left for a study leave in Europe. When Newcomb’s observations were completed it became clear that his results would come in as much as 200 km/s lower than Michelson’s (and hence even further away from Cornu’s figure). The worried astronomer interrogated both his own procedures and Michelson’s, in order to track down the reason for discord. In May 1881 he wrote to Michelson “I have been much embarrassed at the result I am going to get for the velocity of light”. A month and a half later he admitted “if it turns out that there is no mistake in the Coast Survey distance the difference of results will be simply unaccountable”. But reporting to the National Academy in 1881 he highlighted problems with Michelson’s published measurement of distance: “his description of this process is not so explicit that a scientific jury could pronounce the measure absolutely free from the possibility of error”20.

• 21 J. Young and G. Forbes (1881) “Experimental determination of the velocity of white and coloured lig (...)
• 22 A. A. Michelson (1882) “Supplementary Measures of the Velocities of White and Colored Light in Air, (...)
• 23 Simon Newcomb, “Introductory Note,” (dated April 1885) to Michelson (1882) “Supplementary Measures” (...)
• 24 Taking the period from the beginning of Newcomb’s practical plans in 1876 to the formal publication (...)

18Distance measures were the key problem in the experimental protocols, and the Coast Survey proved unable to answer them, being itself subject to a deep controversy over standards that in part accounts for Michelson’s later interferometric concern with establishing light as a standard of length. But in the short term Newcomb’s inquiry first forced Michelson to revisit his 1879 result, modifying it downwards because he had measured the distance between the mirror and the lens incorrectly. Then Newcomb obtained funding from the Bache foundation to get Michelson to repeat his measures, which he undertook as he took up a new job at the Case School of Applied Science in Cleveland in 1882. Now Michelson also tested the velocity of red light and blue light (in addition to the sunlight tested previously). This was necessary because the British researchers George Forbes and James Young had published results exceeding those of both Michelson and Cornu. Michelson’s work countered their suggestion that the velocity of light might vary with colour21. Eventually Newcomb and Michelson published values rather closer to each other than they had achieved previously, in reports bound together in the same volume of the Naval Observatory Papers. Newcomb gave two figures, one using only results supposed to be nearly free from constant errors, of 299,860 (with a discordance of less than 10 km/s between the separate measures) and one including all determinations, of 299,810 ± 50 km/s. Michelson’s figure from his Cleveland trials was 299,853 ± 60 km/s and he corrected his Annapolis result to read 299,910 km/s22. It was crucial for Newcomb to make clear that Michelson’s repetition was an independent experiment, despite their collaborations and the fact that the funding came in part through Newcomb. Newcomb wrote in an introductory note to Michelson’s paper that “no instructions and suggestions had been sent to him except such as related to the investigation of possible sources of error in the application of his method23”. Velocity-of-light measures were subject to diversity and raised a rhetoric of embarrassment. The diversity and embarrassment could be managed though, in part by controlling methods and negotiating independence. There is another important feature of this story. While the whole process took about nine years from beginning to end, Newcomb and Michelson had been able to publish concordant results rather quickly24. Now to the way the story was reduced. We can describe this as a cooking class.

• 25 Harkness (1881) “On the Relative Accuracy”, p. 392. Note that the differences between Harkness and (...)

19We have already seen that in 1881, while everything was still in flux, William Harkness offered a paper on the relative accuracy of different methods. Harkness entered the lists both to question the faith being expressed in the velocity of light method, and to argue for the value of photographic methods. His discussion showed how the rhetoric of embarrassment could be shifted. Harkness described the velocity-of-light measures as “photo-tachymetrical”, probably to emphasize that much more than velocity of light was involved. Harkness pointed out that the accuracy of the method as a whole relied upon determinations of either the light equation or the mean distance between the sun and the earth. However precise velocity-of-light measures were, the accuracy of the two other determinations did not come close to the degree of accuracy required to bring the parallax to within the target accuracy of 0.01"25.

• 26 Harkness (1881) “On the Relative Accuracy”, p. 392.
• 27 Ibid., p. 393.

20The method, therefore, was only as strong as its weakest links, and Harkness raised other spectres also, writing pointedly: “The photo-tachymetric method is embarrassed by serious theoretical difficulties”. These concerned ignorance of the relations between the optical constitution of interplanetary space, the lack of a rigorous proof that the constant of aberration gave the exact ratio of the velocity of light to the earth’s orbital velocity, and worries concerning the relations between group and wave velocity26. Harkness displayed the results for the solar parallax obtained after 1857 in a way that emphasized similarities in the accuracy of the different measures by showing the range between the highest and lowest values for different methods. This way, measures of the 1874 transit of Venus by the U.S. observers came out rather well. There was a difference of 0.09" between their limiting values, while the difference for the two different velocity-of-light methods was nearly double that at 0.17". In 1881 Harkness questioned the use of providing a definitive value for the solar parallax. He thought almost any value between 8.8 and 8.9" could be obtained by adopting suitable weights; and he wrote that “no matter what the result actually was, it would always be open to a suspicion of having been cooked in the weighting”27.

• 28 William Harkness (1894) "On the Magnitude of the Solar System”, Astronomy and Astrophysics 13, p. 6 (...)
• 29 Newcomb (1895) The Elements of the Four Inner Planets.
• 30 On Newcomb’s work, the conference and the controversy see Arthur L. Norberg (1983) “Simon Newcomb’s (...)
• 31 Simon Newcomb (1895) “On the Principal Fundamental Constants of Astronomy”, Astronomical Journal 14 (...)

21Harkness was not to shy away from the figures for too long, though it still took seven years before he was able to reduce all the results of the American transit of Venus expeditions of 1882. In 1888 and 89 he published them giving the value of 8.842" for the parallax with a probable error of ± 0.0118", corresponding to 92,455,000 miles with a probable error of 123,400 miles. In 1894 he got into the weighting game, offering a system of constants value of 8.809" with a probable error of 0.00567"28. His efforts were to be outweighed, however, by another author who proved himself ready to live with the suspicion of having cooked the results. In 1895 Newcomb came up with a system of constants value for the solar parallax of 8.800” with a probable error of 0.0038. In the course of doing so he roasted Harkness’s work, giving photographic measurements of the transit of Venus a weight of 2 and contact measurements a weight of 3, in comparison with determinations of the constant of aberration from Pulkowa which were given a weight of 4029. Newcomb’s value, embodied in a major book, was adopted above Harkness’s for international use at the Conférence internationale des étoiles fondamentales de 1896, held in Paris. It began coming into effect, with some controversy, from 190030. But in fact the embarrassment had never disappeared: when Newcomb summarized his work on astronomical constants he highlighted the difficulty his result for the solar parallax encountered in treating the theory of the planets, which he wrote over the last four months had caused more embarrassment and more trouble than any other questions growing out of the work31.