3-36. George William Myers

George William Myers (1864–1931) was born in Champaign County, Illinois. He studied engineering at the University of Illinois. Like many other American students in the exact sciences at the time, he went to Germany to obtain a Ph.D. In 1896, he defended a thesis in theoretical astronomy at the University of Munich under Hugo von Seeliger’s direction, on the source of the variability in the $\beta$ Lyræ binary star system.

From 1888 to 1900, Myers held several positions in succession at the University of Illinois, from instructor of mathematics to assistant, associate, and full professor of mathematics and astronomy. Upon completion of his thesis in Munich, he directed the new observatory in Urbana. In 1900, Myers became head of astronomy and mathematics at the Chicago Institute, an institution for educating future schoolteachers founded by Francis Wayland Parker (1837–1902), a pioneer of the progressive school movement in the United States. In 1901, the Chicago Institute became the School of Education of the University of Chicago (Dewey 1902), where Myers was named professor of mathematics education and astronomy, a position he held until his retirement in 1929.

Myers was a member of the astronomical societies of Germany, France, Belgium, Mexico and South America, and belonged to the American Academy for the Advancement of Science, and the American Mathematical Society. An author of high-school mathematics texts, and translator of a German text on experimental physics, Myers contributed to theoretical astronomy, which is the subject of his letter to Poincaré in 1901 (§ 3-36-1).

Myers’ interest in $\beta$ Lyrae stemmed from his doctoral thesis. His thesis advisor, and director of the Munich Observatory, Hugo von Seeliger, suggested that he work out a model assuming two spheroidal objects in Keplerian motion. Several astronomers had produced light-curves for $beta$ Lyrae by then; Myers used one with 1500 measurements taken over a span of nineteen years in Bonn by F. W. Argelander, and published in 1859.

Seeliger’s own doctoral thesis (Leipzig, 1872) outlined a method for finding the orbital elements of visual double stars, and several other astronomers had proposed analytical or graphical methods by the 1890s. In 1889, Harting, another doctoral student of Seeliger’s had already reconstructed the orbital elements of Algol ($\beta$ Persei) from its light-curve.

The idea for Myers was to tune the parameters of his model to obtain a close representation of Argelander’s light-curve. The nature of the light-curve, with a period of about 12.91 days, two roughly-equal maxima and two unequal minima, were such that Myers assumed two orbiting stars of unequal mass and luminosity, with a small orbital eccentricity. While he obtained a close fit, the parameter selection was unconstrained, with the result that the model was not fully compelling from a physical standpoint. Among the parameters was the form of the orbiting stars, which Myers assumed at first to be spherical. To obtain a better fit with the light-curve, he revised his original assumption of form to that of two ellipsoids of revolution. As a result, the distance of their centers Myers found to be only about 2.4 times the semi-major axis of the larger ellipsoid. The separation of the two bodies was then very small indeed.

Remarkably, Myers concluded his thesis with the observation that $\beta$ Lyrae may not be a binary system at all. Instead, the light-curve may be produced by a single spinning body – a body whose form, he wrote, had been studied mathematically by Poincaré and Darwin. In the related article in English Myers published later in the Astrophysical Journal, he was more precise:

It appears then that the $\beta$ Lyrae furnishes us a concrete illustration of the actual existence in space of a Poincaré figure of equilibrium. (Myers, 1898, 19)

Myers here goes well beyond what his calculations showed, since he considered only rotational figures of equilibrium, to the neglect of Jacobian and piriform figures.

What did Myers’s know of the work of Poincaré and Darwin on equilibrium figures of rotation? His publications assume the reader’s familiarity with their contributions, and in fact, these were well-known to Munich’s young mathematical astronomers. Along with Myers, Karl Schwarzschild defended his doctoral thesis in Munich under Von Seeliger’s direction in 1896, on the topic of Poincaré’s theory of rotating fluid masses (Schwarzschild, 1898). Much like Myers, Schwarzschild expressed his readiness to tread where Poincaré would not:

Mr. Poincaré considers it too bold to want to infer from this history of a constantly-homogenous mass the reform of Laplace’s inhomogeneous nebula. However, if one were to imagine not a gaseous mass, but a liquid one which, even with vanishing surface pressure, always has finite density, [..] then one may conclude that such a liquid mass undergoing increasing contraction will lose its rotational form, and eventually will split.

Clearly, Schwarzschild felt that Laplace’s nebular hypothesis did not rule out Poincaré’s fission theory, the two approaches being based on formally incompatible assumptions.

How did Poincaré feel about these interpretations of the pear figure? Judging from Poincaré’s review of André’s Traité, he found Myers’ suggestion to be quite plausible. Although Poincaré did not mention André or Myers by name, he surely was thinking of them when he wrote, around 1901, that

“[s]ome astronomers thought that [the piriform figure of equilibrium] could be true for certain double stars, and that double stars of the $\beta$ Lyrae type could feature transition forms analogous to those of which we have just spoken.

It’s clear from this remark that Poincaré was aware of Myers’ thesis by 1901 at the latest.

In fact, Poincaré had engaged with variable stars already in 1899, when he reviewed the first volume of Charles André’s Treatise on Astronomy (André, 1899) for the Bulletin astronomique. The review was an event of sorts in and of itself, at least for Poincaré, as it was the first of the two book reviews he published in his entire lifetime. What was it about André’s textbook that captured Poincaré’s attention? André (1842–1912), who was professor of astronomy at the University of Lyons and the founding director of the Lyons Observatory, took up in this textbook a topic he described as “a bit neglected” in France: observational astronomy (André, 1899, V). This was hardly a topic that Poincaré was much engaged with, although since taking up Tisserand’s chair in mathematical astronomy at the Sorbonne in 1896, and replacing him as the chief editor of the Bulletin, he was no stranger to the subject.

Myers’ letter to Poincaré was apparently prompted either by a passage in second volume of Charles André’s Traité d’astronomie stellaire (1900), or by Poincaré’s review of the volume; Myers mentioned only the former in his letter to Poincaré. André presented in detail for French readers Myers’ theory of $beta$ Lyrae, which Poincaré summarized as follows:

These photometric double stars are distributed in two classes: those of Algol, with discontinuous variation, and those of $\beta$ Lyrae, with continuous variation. …The variability of Algol-type stars may be attributed to eclipses, while that of $\beta$-Lyrae-type stars seems due to the considerable flattening of the two components which, during their rotation and orbital revolution, show to the observer’s eye now a slim section, now a considerable section. The Algol-type would be fully-constituted binary systems, the others would be binary systems in the process of formation.

Time-stamp: "18.11.2023 22:14"

Notes

• 1 See Myers (1896), or the summary in English (Myers 1898). In Myers’ time, $\beta$ Lyrae was understood to be a spectroscopic binary star, but it was later found to be a multiple-star system, the brightest component of which is a triple star system composed of an eclipsing binary and a single star (Abt and Levy, 1976).
• 2 On the astrophysical interpretation of the Poincaré pear and Poincaré-Darwin fission theory, including a summary of Myers’ thesis, see Walter (2023).
• 3 “Herr Poincare hält es für zu gewagt, aus dieser Geschichte einer stets homogen bleibenden Masse auf die Umgestaltung des von vornherein inhomogenen Laplace’schen Nebels schliessen zu wollen. Denkt man aber nicht an eine Gasmasse, sondern an eine Flüssigkeit, die auch bei verschwindendem Druck an der Oberfläche stets eine endliche Dichte behält, wie sie die Erde zu einer gewissen Epoche gewesen sein mag, so darf man folgern, dass auch eine solche Flüssigkeit bei zunehmender Kontraktion einmal die Rotationsform verlieren und sich schliesslich spalten wird.” Schwarzschild (1898, 296).
• 4 Poincaré was not alone in this judgment. Simon Newcomb (1902, 112) echoed Myers’ view of $\beta$ Lyræ and U Pegasi, and added a third example: $\zeta$ Herculis. Several astronomers took up the problem of calculating orbital elements from the light-curves of $\beta$ Lyræ, including Johann Stein, who wrote a historical review of such efforts (Stein, 1924).
• 5 Quelques astronomes ont pensé [que la figure piriforme] pourrait être vraie pour certaines étoiles doubles, et que des étoiles doubles du type de $\beta$ de la Lyre présenteraient des formes de transition analogues à celles dont nous venons de parler.” Poincaré (1921, 113)
• 6 See Poincaré (1899). The review is referenced in Lebon’s bibliography (Lebon, 1912, 107), but Poincaré’s subsequent review of the second volume of André’s Traité (Poincaré, 1901) is neglected.
• 7 “Ces étoiles doubles photométriques se répartissent en deux classes, celle d’Algol dont les variations sont discontinues et celle de $\beta$ Lyre dont les variations sont continues. [..] La variabilité des étoiles du type d’Algol paraît due à des éclipses, celle des étoiles du type $\beta$ de la Lyre à l’aplatissement considérable des deux composantes qui, pendant leur rotation et leur révolution orbitale, présenteraient à l’œil de l’observateur tantôt une section faible, tantôt une section considérable. Les premières seraient des systèmes binaires formés, les autres des systèmes binaires en voie de formation.” Poincaré (1901, 44)