The Birth of Stellar Interferometry

With only modest exaggeration, Andrew Robinson's biography of Thomas Young (1773–1829) is entitled The Last Man Who Knew Everything (Robinson 2006). Young, who hailed from a small village in southwest England, was trained as a physician in Edinburgh and Göttingen, but his intellectual and experimental attention was drawn to a variety of topics—including investigations into vision, music, language, Egyptology, and even life insurance—a diversity sufficient to tag him as a polymath. A portrait of him at age 49 appears in Figure 1.1. Fearful of damaging his professional reputation in medicine, Young published his earliest papers anonymously. Within a few years, though, he was widely noted for his brilliance and was openly and prolifically publishing in the Philosophical Transactions of the Royal Society of London. His lecture to the Society on 1803 November 24 on "Experiments and Calculations Relative to Physical Optics" (Young 1804) elegantly described work he began two years earlier regarding the colored fringes produced when sunlight admitted through a small aperture into a darkened room passes around the opposite edges of a paper card and onto a screen. The clincher in his deduction of interference in support of the wave theory of light of Christiaan Huygens (1629–1695) is that these fringes disappear if a second card blocks light from striking one or other edge of the occulting card before being allowed to combine with light from the other edge. I elaborate on this episode in the history of optics not only because of the fascination inherent in such a person as Young, but also because the simple and famous Young's double slit experiment laid out the beginnings of basic principles that would, after substantial theoretical buttressing by Augustin-Jean Fresnel (1788–1827), eventually enable interferometry's employment in stellar astronomy. For more about the basic principles and terminology of stellar interferometry, see Appendix B.

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The suggestion that interference fringes might be analyzed so as to reveal the diameters of stars is widely attributed to the French physicist Armand Hippolyte Louis Fizeau (1819–1896), shown in Figure 1.2 as he appeared later in life (Lawson 2000). In 1848, Fizeau had independently discovered the Doppler effect—sometimes referred to in France as the "Effet Doppler–Fizeau"—albeit six years after Christian Doppler's (1803–1853) postulation of this phenomenon. The following year Fizeau measured the speed of light to ±5% accuracy. He was clearly at his peak by 1850.

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Fizeau's connection to measuring star diameters is oddly buried in a report from a commission of the French Academy of Sciences charged with devising criteria for the award of the 1867 Prix Bordin in Mathematics (Fizeau 1868). Fizeau was appointed as the "rapporteur" (designated reporter) of the deliberations of this commission to the Academy. The other commissioners were Jean-Marie Duhamel (1797–1872), Claude Pouillet (1790–1868), Henri Victor Regnault (1810–1878), Joseph Louis François Bertrand (1822–1900), and either Alexandre Edmond Becquerel (1820–1891) or his father Antoine Cesar Becquerel (1788–1878). All were distinguished physicists except for Bertrand, primarily a mathematician who also did important work in thermodynamics.

The final of the topics desired by these luminaries to be treated by the prize winner was described in the following translation from the original specification statement. "For most of the phenomena of interference, such as the fringes of Young, those of Fresnel mirrors and those which are the result of the scintillation of stars according to Arago, there is a remarkable and necessary relationship between the size of the fringes and that of the light source, so that extremely tenuous fringes can only arise when the light source has angular dimensions almost insensitive; hence, to put it in passing, it is perhaps possible to hope that by relying on this principle and by forming interference fringes, for example, by means of two large widely spaced slits at large instruments to observe the stars, it will become possible to obtain some new data on the angular diameters of these stars. ¹ "

One naturally wonders how this particular prize criterion came to be. Was it purely the brainchild of Fizeau or was he merely reporting a goal set by another member? In the middle ground between these extremes, did Fizeau throw this out to the other committee members who participated actively in refining his idea to its final statement? Fizeau mentioned the scintillation theory of François Arago (1786–1853) in which the distorted image of a star arises from interference and cancellation of portions of the wavefront diverted by atmospheric irregularities rather than variations of refractive index of turbulent cells of air as would be correctly proposed later by others (see Rayleigh 1893; Danjon 1955). Arago had been an important figure in advancing interference phenomena in astronomy, and so it was natural that he would be cited by Fizeau.

As all the commission members lived in Paris or its suburbs, it seems likely they did meet together to carry out their work for the French Academy. Regrettably, there was no fly on the wall of their committee room. In any event, there appears to have been no Prix Bordin awarded that cycle for someone's success in satisfying the commission's challenge.

As for the issue of Fizeau's ownership of the concept of measuring stellar diameters interferometrically, the matter was settled by Paris Observatory astronomer James Lequeux and described in his 2014 book Hippolyte Fizeau, Physicien de la lumière (Lequeux 2014a). Lequeux discovered Firzeau's original working notes that had been donated by his family to the Museum of Urban and Social History of Suresnes, France and to the archives of the French Academy of Sciences. These document clearly show that since 1851 June 22—smack in the middle of his most productive years—Fizeau had realized that the apparent diameter of a star could be measured by interferometry (Lequeux 2014b). But, he would leave that task to others. What better way to encourage someone to action, when the opportunity arose, than baiting a cash prize with stellar interferometry?

Five years would pass before Édouard Stephan (1837–1923), director of the Marseille Observatory, reported his successful observation of fringes from a stellar interferometer he devised for the Marseille 80 cm Foucault Reflector telescope (Figure 1.4). The account that appeared in the weekly bulletin for 1873 April 27 of the Scientific Association of France was labeled as "from a letter from M. Stephan, addressed to M. Fizeau" (Stephan 1873). Stephan, shown in Figure 1.3, began by reiterating Fizeau's 1868 awards document, quoting the passage translated above, and noting that no one to his knowledge had yet taken up Fizeau's commission's task of turning a telescope into an interferometer—until now, that is. Stephan went on to report that he had succeeded in obtaining fringes on the bright star Sirius after installing a mask with double slits separated by 15 cm over the 80 cm objective mirror of the Marseille telescope. The following night, he again attempted to see fringes but this time used a mask with slits separated by 50 cm. No fringes were to be seen, regardless of the magnification used at the telescope's eyepiece whereas bright stars in nearby Orion, which were a little higher in the sky than Sirius, did show fringes. Succeeding nights were troubled by a "poor state of the sky," but Stephan was anxious to report his observations and went out on a limb by saying that while he was "very far from presenting this result as definitive; but, by the way the fringes persist, regardless of the waviness of the images, I bow very strongly to think that the disappearance of the fringes of Sirius is not just an atmospheric influence." Stephan also published a similar report in the more formal Comptes Rendus of the French Academy of Sciences ending with the statement (translated from the original French) "I very much incline to think that the disappearance of the fringes of Sirius does not depend solely on an atmospheric influence. I have the firm hope that later experiments will show, with evidence, that the diameter of this star is not insensitive, and will make it possible to obtain some rough estimate" (Stephan 1874a).

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This hope that the fringe behavior was representative of the diameter of Sirius rather than the result of instrumental or atmospheric effects was something that Stephan intended to explore with additional observations of stars. It also required a mathematically-based analysis of the observing parameters and the geometrical configuration of his aperture mask, which employed large openings required to admit starlight sufficient in brightness to see fringes.

With this work completed sometime during late 1873 to early 1874, Stephan returned to the Comptes Rendus to summarize his efforts and conclusions (Stephan 1874b). The paper's title—"On the Extreme Smallness of the Apparent Diameters of the Fixed Stars"—is a tipoff that Sirius had, in reality, not been resolved. Stephan's very thorough geometrical and optical analysis of the problem showed that his large apertures had little effect and, more importantly, that the fringe behavior was indicative of angular diameters well below the threshold of resolution with the 80 cm Foucault telescope at Marseilles. The case was thus closed, and Stephan blamed the disappearing fringes of Sirius on atmospheric conditions. He never returned to the problem of measuring stellar diameters.

Lequeux's discovery of Fizeau's papers at Suresnes included a fascinating personal letter from Stephan to Fizeau dated 1874 February 1. Stephan set out to describe his efforts with an apologetic preamble stating that he had not stopped worrying about the problem since they were last together, indicating that the two had personally discussed the observing program. Stephan had by then observed most stars down to third magnitude and some a magnitude fainter. He had also adopted a modified mask laid directly on the mirror rather than mounted to the top of the tube to avoid path-length differences arising from flexure of the telescope's wooden tube, which might explain his earlier false positive. He reported anxiously awaiting the seasonal return of Sirius to the sky and then his great disappointment in seeing Sirius' fringes behave as they did for the other stars implying that it was far from resolved. He deduced, correctly of course, that all stars are much smaller in angular size than might have been thought. Stellar parallax data were in hand by 1874, and the distance to Sirius was known with reasonable accuracy. It does not appear that he had estimated Sirius' diameter from its distance and adopting the size of the Sun as an approximation that would have shown him the unlikelihood of its resolution with this modest aperture.

Of course, no one then had much of a notion as to the physical diameters of stars other than by analogy to the Sun—that was necessarily a few decades away pending the development of the theory of stellar evolution and its anticipation of giant and supergiant stars. Perhaps Sirius was the largest star because it was the brightest and relatively nearby. With the maximum aperture spacing on the refractor's mask of 65 cm used in the second round of observations, the angular diameter that would have corresponded with fringes that just washed out at that spacing would be 160 milliarcseconds (mas). The actual angular diameter of Sirius was first determined more than three-quarters of a century after Stephan's attempts to be 7.1 ± 0.6 mas, by Robert Hanbury Brown and Richard Twiss (Hanbury Brown & Twiss 1956, 1958) using the University of Sydney's Intensity Interferometer at Narrabri, New South Wales, Australia. This value is more than 20 times too small to have been resolved by the Marseilles reflector acting as an interferometer. So, Stephan was indeed carried away by his original optimism as to the cause of Sirius' fringe disappearance at the wider slit spacings.

Stellar interferometry at optical wavelengths entered a hiatus at this point but would re-emerge in fits and starts in the coming century and a half. We can mark the brief period from 1868 to 1874 as the birth of the field. The problem was that there was no straightforward way to obtain the resolution that Stephan reckoned would be necessary to measure stellar angular diameters. They required sampling two apertures far wider than permitted by simply masking any existing telescope. Thus, Stephan set star diameters and interferometry aside and continued his work at Meudon on "nebulae," virtually all of which were distant galaxies.

However, Fizeau had already envisioned the means to achieve an extended baseline by 1851. In his Suresnes notes, there is a rough sketch of mirrors on a beam mounted perpendicular to the optical axis of a refracting telescope (Lequeux 2014b, p. 5). This exact configuration would be fulfilled 70 years later at the Mount Wilson 100 inch telescope, although there is no indication that its implementers were aware of Fizeau's originality in their concept. In the meantime, interferometry went to sleep for more than 15 years until it reawakened in America in the hands of Albert Michelson.

Albert Abraham Michelson (1852–1931), (Figure 1.5), is justly celebrated for his experimental determinations of an accurate value of the speed of light—a quest he began in earnest as early as 1878 when he was a young naval officer and instructor of physics at Annapolis. His experimental apparatus derived from the rotating-mirror method used by the French physicist Leon Foucault (1819–1868) in 1850 who had adopted the approach originally suggested by the intellectually relentless Fizeau. This French connection points back to Michelson's odd lack of citation of Fizeau's precedence in stellar interferometry. In his first scientific paper (Michelson 1878)—essentially an abstract—the future Nobel laureate described how his approach "dispenses with Foucault's concave reflector, and permits to use of any distance." This important modification allows for a potentially very long lever arm of sorts to improve measurement precision, which was a goal inherent in Michelson's focus on this problem for decades. Foucault is not cited here other than by name, and Fizeau is not mentioned at all. A few years later, Michelson detailed his experiments while in the Navy in a beautifully-illustrated, fifty-four page paper published by the U.S. Naval Observatory (Michelson 1882). Again, Foucault's work was referred to without its ties to Fizeau.

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During many years of mentoring graduate astronomy students, I was frequently struck by their lack of historical interest in digging back in time to the progenitor of their subfield or technique. They would merely cite the most recent work before them as sufficient with no concern for crediting the person who had the first spark of brilliance that enabled their particular dissertation topic. While doing my best to dispel them of this inclination, I would ask how they would feel if their own great ideas appeared to be assigned to a successor. Perhaps Michelson, who was only 26 in 1878, had this same disregard for the achievements of his scientific ancestors. Others have pondered Michelson's failure to acknowledge Fizeau, (see DeVorkin 1975; Lawson 2000, p. 326), but it is what it is.

In Michelson's 1903 book Light Waves and Their Uses, Fizeau's name appears in four places, none of which pertain to astronomical applications, a topic addressed in the 20 pages of the book's final lecture on "Applications of Interference methods to Astronomy." That chapter is largely descriptive of the theory and applications at an introductory level with the exception of a description of Michelson's work in the summer of 1891 measuring the diameters of the Galilean satellites of Jupiter with the Lick Observatory's 12 inch refractor.

In her biography of her father (Livingston 1973), Dorothy Michelson Livingston describes how Michelson's interest turned in 1890 toward astronomical applications of the interferometer, stating that he "discovered that the interferometer could be adapted so as to measure the diameters of very small and distant sources of light such as planetoids and satellites." After setting up an artificial double star in his laboratory at Clark University, where he had been appointed to its inaugural faculty as professor of physics, Michelson was inspired to make actual measurements of astronomical sources, settling on Jupiter's four bright Galilean satellites. During this time frame, he also fully developed the relevant theory to support his goal of obtaining data at a telescope. He published that theory in a mathematically detailed presentation in the Philosophical Magazine for 1890 July (Michelson 1890). It is in this paper where he first published his famous definition of fringe visibility V in the form of:

$$\begin{eqnarray*}&&V=\left({I}_{\max }-{I}_{\min }\right)/\left({I}_{\max }+{I}_{\min }\right),\end{eqnarray*}$$

where I_max and I_min are the maximum and minimum brightnesses of a fringe. Visibility is essentially a measure of fringe contrast and ranges from 0 to 1. He goes on to show that V is related to the wavelength at which the observation is made, the linear separation (or baseline) between the wavefront sampling mirrors or telescopes in an interferometer, and the angular diameter of the source. Visibility remains the basic observable of astronomical interferometers (see Appendix B.2.3). Michelson being Michelson, he closed out this thorough presentation with an equally complete discussion of the experimental apparatus he had developed.

Enthusiastic from his theoretical exploration of making practical astronomical measurements, Michelson contacted Harvard College Observatory Director Edward C. Pickering (1846–1919) that same summer seeking access to HCO's 15 inch refractor in order to observe the bright Jovian moons. Receiving a positive response, Michelson quickly set out for Cambridge where through a combination of delays, bad weather, and poor "seeing" (the motion and blurring of astronomical images by atmospheric turbulence; see Appendix B.6)—a triple threat familiar to most astronomers—he was unable to obtain measurements of the diameters of these ostensibly low-hanging fruit. That stay at Harvard, at least gave Michelson the opportunity to spend some time with George Ellery Hale (1868–1938)—Mount Wilson Observatory's future founder—who was there working with Pickering. Michelson and Hale had first met at the 1888 meeting of the American Association for the Advancement of Science in Cleveland (Livingston 1973, p. 140).

Michelson then turned to Lick Observatory and its director Edward S. Holden (1846–1914), a famously explosive individual (Osterbrock 1984), but with whom Michelson would have no difficulties. Holden took to the idea of measuring the Jovian moons as there was scant agreement among the existing micrometer measurements made by several observers skilled at observing closely separated "double stars" (gravitationally bound pairs of stars aka "binary stars") in varying seeing conditions. In 1891 August, Michelson mounted his variable slit mask device (Figure 1.6), on Lick's 12 inch refractor to obtain diameters for each satellite on four nights. The seeing on only one of those nights was judged as "good," the remaining three being "poor." In this effort, Michelson had observing assistance from William Wallace Campbell (1862–1939)—later president of the University of California.

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Michelson published his results in the 1891 October issue of the Publications of the Astronomical Society of the Pacific (Michelson 1891a) followed more or less verbatim in the 1891 December 17 issue of Nature (Michelson 1891b). The duplicate publishing was presumably due to his wanting to attract European attention to the work. In order to judge the quality of his results, Michelson compared them with micrometer measures made by Rudolf Engelmann (1841–1888) of Leipzig Observatory, Friedrich G. W. Struve (1793–1864) of Dorpat (later Tartu) Observatory in Estonia, George W. Hough (1836–1909) of Dearborn Observatory, and Lick Observatory's Sherburne W. Burnham (1838–1921). Burnham's micrometer measurements had been made at the Lick 36 inch telescope on Michelson's last night at the 12 inch. After he transformed all measurements to represent an angular diameter subtended at the Sun from Jupiter's mean distance, Michelson could then compare them.

A few years later, these same data would draw the attention of another famous astronomer. With the goal of determining the physical diameters of these satellites, Edward Emerson Barnard (1857–1923) published an analysis in 1895 of their angular diameter data going as far back as the 1693 eclipse timings of Giovanni Domenico Cassini (1625–1712) (Barnard 1895). Barnard settled upon using "later measures" starting with those from 1829 of F. G. W. Struve, a founder of double star astronomy. Barnard's sample, shown in Table 1.1, included Michelson's along with results from four additional observers.

Unavailable to Michelson and Barnard, of course, were the actual physical diameters of the moons based upon spacecraft measurements, which today give us an absolute level of intercomparison of the historical results. Inspection of the last column of Table 1.1 shows that Michelson more or less tied with F .G. W. Struve's 1829 visual micrometer observations made at Tartu. Struve used the "Great Dorpat Refractor," a 9 inch instrument built by Fraunhofer, that was smaller in aperture than the instrument Michelson used at Mount Hamilton. Comprising the second tier are Engelmann and Barnard whose residuals from the true diameters are very slightly systematic. The results of the other observers are substantially inferior and exhibit real systematic errors. Note that the large outlier is Pickering's photometric estimate, which apparently relied on a common albedo assumption about which these moons would a century later show many surprises.

What can we deduce from this? First, it has long been known that visual micrometry is a skill susceptible to systematic effects most likely related to an observer's ability to deal with astronomical seeing conditions. Some observers are simply better than others and have what has been dubbed the "double star eye," as elaborated upon in the next paragraph. Struve and Engelmann had that rare skill. A few of the others in the table apparently did not. On the other hand, measuring diameters of disks is not the same problem as measuring the separations between two unresolved disks as is the case with a double star. Interferometry, as practiced visually, then relied upon the disappearance of fringes at the first null in visibility at which point the angular diameter is given by the interferometer slit spacing B at which the visibility goes to 0 and the wavelength of the observation through the simple relation 1.22λ/B (V = 0). This disappearance is less susceptible to atmospheric disturbances than is the far more complex act of comparing an image with the separation of micrometer threads. Michelson was, of course, a remarkably skilled instrumentalist so that his apparatus was very well calibrated. See Appendix B.3.2 for more on micrometry and visual interferometry.

Michelson closed out his summary of the Galilean satellites by noting, without elaboration, that Engelmann's measures were "probably more reliable than the succeeding ones." Was that because they were in better agreement with his results? He also claimed that a 6 inch telescope equipped with adjustable slits was "fully equal to the largest telescopes now used without them." Of course, he was unaware of Struve's 1829 Dorpat measurements with a small refractor. Finally, he expressed hope that the Lick 36 inch telescope, which would afford higher resolution from wider slit spacings, would be suitably equipped for "definitive measurement of the satellites of Jupiter and Saturn and such of the asteroids as may come within the range of the instrument." Alas, no one rose to that challenge.

Michelson's interest in astronomical applications turned next to spectroscopy, and he would only come back to astrometric measurements by interferometry thirty years later in collaboration with George Ellery Hale, when a superb new telescope would allow slit spacings and resolutions far beyond what he had utilized in 1891. However, there was still more to come in the 19th century, including a set of high-quality double star measurements employing an innovative use of interferometry by one of the most brilliant astronomers of all time.

Nearly lost among his other monumental achievements are the results of a brief 1895 venture into interferometry by Karl Schwarzschild (1873–1916), seen in his prime in Figure 1.7. In 1895, he was a young graduate student working under Professor Hugo von Seeliger (1849–1924) in Munich. His dissertation was on the theory of rotating stars and had nothing to do with interferometric observations other than mentioning that one day interferometry would image the oblate spheroids of the most extreme of these spinning stars, a prospect likely unimaginable in the 1890s (see Suhendro 2008; Hertzsprung 1917).

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It seems that his foray into this field was at Seeliger's introduction to him of Michelson's work from a few years earlier. However, Schwarzschild chose to measure double stars rather than redo Jupiter's moons. And, rather than applying Michelson's method of measuring the disappearance of fringes at the first null in visibility, Schwarzschild's device acted more like a coarse, full-aperture diffraction grating. His mask, shown in Figure 1.8, employed a clever means of varying the slit spacing so that the angular separation of the low-frequency fringes it yields for each component of the double star could be adjusted to reproduce the angular separation on the sky of the components themselves. Rotation of the mask about the optical axis would align the projection of the fringes onto the vector separating the stellar components. While still involving the interference phenomenon, this is a far more direct way of getting at the angular separation of a double star than by attempting to match it to the separation of micrometer threads. We shall see that the instrument worked quite well for bright double stars on the 10 inch refractor of Munich University's observatory (Schwarzschild 1896).

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The mask was designed and fabricated with the assistance of "Herrn Mechaniker Sendtner," undoubtedly the observatory's instrument maker, whom Schwarzschild so kindly thanked in his publication. He was assisted in the observing itself by Walther A. Villiger (1872–1938), who would not be generally remembered for his contribution to this history, ² although his observations are separately attributed to him in the Washington Double Star (WDS) Catalog. ³ Schwarzschild and Villiger observed 13 star systems over 18 nights during May through 1895 August, accumulating a total of 46 measurements of bright binaries mostly discovered by F. G. W. Struve. The angular separations ranged from 0.86 to 4.25 arcsec.

To illustrate the quality of their data among the visual micrometry carried out in the same period by a number of international observers, I show in Figure 1.9 mean values of the interferometric measures by Schwarzschild and Villiger for the 59.9 year binary star system ξ Ursae Majoris—in reality at least a quadruple star system—surrounded by similarly calculated means for the contemporary micrometry. The mean residuals and their standard deviations in arcseconds from the orbit referred to in the figure caption in X and Y (i.e., right ascension and declination) for the micrometry are 0.018 ± 0.073 and 0.077 ± 0.147 compared with 0.007 ± 0.029 and 0.000 ± 0.050 for the interferometry. The latter clearly wins this competition. As with the results of Michelson, however, if we went through and selected only the "good" micrometrists, it is highly likely that their means would be comparable with those of the young Munich interferometrists.

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Neither Schwarzschild nor Villiger would continue pursuing this technique. Schwarzschild, who was destined to take Einstein's General Relativity Theory to another level at the end of his mere 43 yr of life, finished his doctorate at Munich and left there for a position in Vienna. He was appointed director of the Astrophysical Observatory in Potsdam in 1909, from which post he volunteered for the German Army in 1914, serving as a junior artillery officer. Villiger remained in Munich for another decade before joining Zeiss as an engineer, wherein he developed the Mark II Zeiss planetarium projector. In 1906 and 1907, Villiger was the second author on three papers with his old Munich colleague. Schwarzschild's last paper, entitled About the Gravitational Field of a Sphere of Incompressible Liquid According to Einstein's Theory, appeared in 1916 March. Two months later, he died from an illness contracted while serving Germany on the Eastern Front in World War I, a tragic loss for science.

The last 19th century manifestation of interferometry in observational astronomy came from Maurice Hamy (1831–1936) at the Paris Observatory. Hamy was working in the Observatory's meridian circle department where positions on the sky of stars, minor planets, etc were measured with the greatest possible precision. In 1895, he wrote a paper (Hamy 1895) describing how "the use of M. Fizeau's fringes considerably simplifies the control of the trunnions of the meridian instrument." Notice that he cites Fizeau, while Michelson is nowhere mentioned in the paper. The following year, Hamy continued experimenting with an interferometer attached to the meridian circle, this time using it to measure displacements produced by heating the instrument in order to see how the thermal radiation of the human observer can result in displacement errors in the results. He found it to be a non-trivial effect—Michelson would have liked this (Hamy 1896). Nature also liked it and published a quarter-column note describing how Hamy found the effect to reduce as the square of the distance of the heat source from the instrument. The human influence arose because observers traditionally lie supine below the meridian telescope, heating it differentially from below. Hamy concluded that illumination using gas flames with chimneys is to be "studiously avoided" and that high conductivity metals such as copper are desirable to reduce the preferential heating of one side and not the other of the telescope tube. ⁴ Hamy was thus a careful observer who sought to reduce the influence of external factors on the quality of observational data prior to securing them.

Hamy next undertook interferometric observations of Jupiter's bright moons and published his results in 1899 (Hamy 1899). As the bright minor planet Vesta was then in the sky, Hamy threw that into the mix as well. This paper also includes a very detailed mathematical development of the interferometric technique, and this time he does cite Michelson as his new observations could be compared with the American's results. As described in the modern article by James Lequeux about The Coudé Equatorials put into service during 1884–1892 in France, Algeria, and Austria (Lequeux 2011). Hamy used the Great Equatorial Coudé telescope at Paris. On this 60 cm aperture instrument, Hamy installed an interferometric mask, whose specific design I have been unable to find. With it, he obtained values for the four satellite diameters, which compared with the now known physical diameters, show a mean residual in terms of fractional radius of −0.019 ± 0.076 compared with those for Michelson of 0.051 ± 0.063. Thus, both men achieved similar levels of accuracy in their measurements. Hamy's value for the diameter of Vesta was almost a third smaller than reality.

These results were more demonstrative of the new technique of interferometry than they were useful in shedding new light on these solar system bodies. They also more or less exhausted the accessible targets in regard to brightness and angular size. And so, interferometry again dozed off in the closing years of the 19th century.

One can summarize these activities as having developed the needed mathematical tools and observational techniques to explore the feasibility of interferometry as an observational methodology—with mixed results. Apparently, satellite diameters could be no better determined interferometrically than those measured by classical micrometers employed by the best observers. On the other hand, the double star measures of Schwarzschild were more promising. Astronomy is a small field wherein individuals can make a big difference. Had the right person come along in the 1880s and 1890s, double star interferometry might have supplanted the use of visual micrometry, a fate that speckle interferometry would ultimately deal to that last visual technique.