Astronomia Nova Research Articles

Darwin’s legacy

The year 2009 has been a year of numerous commemorations of both scientific and non-scientific achievements that contributed to the advancement of human kind. Protestants celebrated the 500th anniversary of the birth of Calvin; literary critics celebrated the 200th anniversary of the poet Edgar Allan Poe; and the musical genius Felix Mendelssohn-Bartholdy was also born 200 years ago. 2009 further marked the bicentennial of the birth of Louis Braille, the inventor of Braille; and Abraham Lincoln, the 16th president of the United States, who founded the National Academy of Sciences. Pierre Curie, famous for his work on radioactivity that he conducted together with his wife Marie Curie, was born 150 ago; as was John Dewey, a philosopher and psychologist who is recognized as one of the founding fathers of both pragmatism as well as functional psychology. UNESCO and the International Astronomical Union dubbed 2009 the International Year of Astronomy (IYA2009, http://www.astronomy2009.org/). By doing so, astronomers celebrated the 400th anniversary of Galileo Galilei’s telescopic observations as well as the publication of Johannes Kepler’s Astronomia nova wherein he formulated the first two laws of planetary motion. 2009 also marked the last of a 3-year-long celebration of Planet Earth http://www.yearofplanetearth.org/, another UNESCO-governed initiative. However, for evolutionary biologists and philosophers of science, 2009 will be largely remembered for its worldwide commemorations of the 200th anniversary of the birth of Charles Darwin, and the 150th anniversary of the publication of his magnum opus On the origin of species by means of natural selection. In order to pay tribute to Darwin’s major contribution to the advancement of evolutionary science, the International Union of Biological Sciences and the International Union of History and Philosophy of Science have called the year 2009 the Darwin Year http://darwin-year-2009.org/index.html. Given that so many scientific discoveries were commemorated, COPUS, the Coalition on the Public Understanding on Science, called out 2009 as the Year of Science http://www.yearofscience2009.org/home/, in the hope to pay equal tribute to both the field of biology as well as astronomy. 2009 was indeed a year of biology. Somewhat overshadowed by the big Darwin celebrations, smaller-scaled events were held to commemorate the 200th anniversary of the publication of Lamarck’s Philosophie Zoologique; and the 150th anniversary of the death of Alexander von Humboldt, the father of biogeography. In 1910, Constantin Mereschkowsky wrote his article on symbiogenesis entitled ‘The Theory of Two Plasmas as the Basis of Symbiogenesis, a New Study for the Origins of Organisms’. The N. Gontier Fund for Science and Technology, Portugal (FCT), Centre for Philosophy of Science, Universidade de Lisboa, Lisbon, Portugal

Galileo, Kepler share IYA anniversary

Here’s a little postscript to the International Year of Astronomy 2009. Although it celebrated the 400th anniversary of the telescopic discoveries of Galileo, the IYA was the quadricentennial of another monumental event in the history of astronomy and physics—the publication of Johannes Kepler’s Astronomia Nova. In that work Kepler stated his first two laws of planetary motion: the ellipticity of planetary orbits, which finally broke the circular mindset of his predecessors, and the sweeping of equal areas in equal times (conservation of angular momentum). Surely his text deserves celebration as well, for it led directly to Newton’s law of universal gravitation later in that century.© 2010 American Institute of Physics.

Marking the 400th Anniversary of Kepler's Astronomia nova

AbstractSpecial Session 9 of the XXVII General Assembly (11–14 August 2009, Rio de Janeiro) was devoted to the topic “Marking the 400th Anniversary of Kepler's Astronomia nova”. During the two-and-a-half day meeting (spread over four days), there were nine invited and three contributed talks, a round-table discussion on the future of Kepler studies and an open session to propose the setting up of a Johannes Kepler Working Group under the aegis of the IAU.

Kepler's Optical Part of Astronomy (1604): Introducing the Ecliptic Instrument

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova , Johannes Kepler (1571–1630) developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated (Ad Vitellionem Paralipomena, quibus astronomiae pars optica traditvr , 1604), was to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer.

Pondering Astronomy in 2009

This week in Paris, An opening ceremony held by the United Nations Educational, Scientific and Cultural Organization and the International Astronomical Union proclaims 2009 as the International Year of Astronomy. The year marks the 400th anniversary of Galileo's first observations with his telescope, when he detected the moons of Jupiter; and of Kepler's great book Astronomia Nova , which showed that the planets move in elliptical orbits.

Kepler, Galileo and the birth of modern astronomy

AbstractThe International Year of Astronomy marks the 400th anniversary of Kepler's Astronomia nova and the first use of the telescope for astronomy, most notably leading to Galileo's Sidereus nuncius (1610). Kepler's book for the first time argued strongly for a physical basis to astronomical explanations. Galileo's work showed that a coherent understanding was more important for scientific progress than specific proofs. The efforts of both astronomers undermined the traditional geocentric cosmology and essentially brought about the birth of modern astronomy.

Kepler's Move from Orbs to Orbits: Documenting a Revolutionary Scientific Concept

This study of the concept of orbit is intended to throw light on the nature of revolutionary concepts in science. We observe that Kepler transformed theoretical astronomy that was understood in terms of orbs [Latin:orbes](spherical shells to which the planets were attached) and models (called hypotheses at the time), by introducing a single term, orbit [Latin:orbita], that is, the path of a planet in space resulting from the action of physical causes expressed in laws of nature. To demonstrate the claim that orbit is a revolutionary concept we pursue three lines of argument. First we trace the origin of the term;second, we document its development and specify the meaning of the novel term as it was introduced into astronomy by Kepler in his Astronomia nova (1609). Finally, in order to establish in what sense the concept is revolutionary, we pay attention to the enduring impact that the concept has had on the relevant sciences, in this case astronomy and indeed physics. We claim that orbit is an instance o...

Publish or Perish: Legal Contingencies and the Publication of Kepler's Astronomia nova

The ArgumentThe publication of Johannes Kepler's brilliant and revolutionary Astronomia nova (1609) has hitherto been viewed as somehow inevitable. This paper argues that, on the contrary, the book's very existence and a measure of its unusual form and content are in fact highly contingent, and derive from a legal dispute between Kepler and Tycho's heirs over the right to capitalize on his astronomical legacy. On Tycho's death, Kepler rather accidentally found himself in charge of Tycho's posthumous astronomical publications, especially the highly prestigious Rudol phine Tables. Tycho's legal heirs, not having been paid by the emperor for Tycho's astronomical assets and feigning Kepler's unworthiness as his successor, wrested this mandate back. Ordered in turn to justify his employment, Kepler contrived the Astronomia nova as an interim announcement of the fruits of his astronomical research. In an effort to block Kepler's continuing exploitation of Tycho's observations, the heirs obtained the legal right to censor his publications, which severely threatened his philosophical freedom. The threat of editorial interference was responsible in part for Astronomia nova's unusual narrative form.

Zu Kepplers Conchoid-Konstruktion

The physical models introduced by Johannes Keppler into astronomy were not only much more accurate than their predecessors, they were innovative theoretically to such an extent that they stand quite alone. The conchoid construction he presented in his ”Astronomia Nova” (1609) seems to have almost escaped notice in the literature. A misguided and sometimes unwitting interpretation of Keppler’s physical astronomy as a precursor to Newton’s celestial mechanics has impeded any fair analysis of it. Keppler’s physics is a physics of phases and frequencies, as Newton’s is a physics of accelerations. The purpose of this paper is to outline the impact of Keppler’s conchoid construction. His dynamical approach which is a profoundly original filter bank construction has found recently an unexpected revelation in magnetic resonance tomography.

Kepler's Physical Astronomy , and: The Music of the Heavens: Kepler's Harmonic Astronomy (review)

Reviews 243 Stephenson, Bruce, Kepler's Physical Astronomy, Princeton, Princeton University Press, rpt. 1994; paper; viii, 216, 50 figures; R.R.P. US$16.95, £12.95. Stephenson, Bruce, The Music of the Heavens: Kepler's Harmonic Astronomy, Princeton, Princeton University Press, 1994; cloth; pp. xii, 260; R.R.P. US$42.50, £30.00. A m o n g the major figures of the Scientific Revolution, no one was as prolix or complex as Johannes Kepler. Much of his voluminous writing has remained obscure because of the great difficulty modern scholars encounter in respect to both his language and his thought. It is the good fortune of historians of science that Bruce Stephenson now can serve as an expert guide through some of the densest parts of Kepler's cosmology and astronomy. Stephenson wrote Kepler's Physical Astronomy as his doctoral dissertation andfirstpublished it in 1987. Its successful reception led to this paperback edition. There seem to be no changes made, certainly none of any substance, in the new printing. The starting point of the book is the view that Kepler was the 'last great practitioner of the science of ancient astronomy' (p. 1). As such he served both as its culmination and its .termination. Kepler's work was the crowning achievement of ancient astronomy, among whose practitioners the author includes several of Kepler's recent predecessors such as Regimontanus and Copernicus himself. That discipline used geometrical models to predict the motion of the heavenly bodies w e now call the solar system, and Kepler was very much within that tradition when he formulated the laws of planetary motion, the achievement for which he gained permanent fame. Yet he also acted to undermine ancient astronomy by being thefirstto see astronomy as being part of physics, which required a physical explanation for the motion of the planets. Stephensonfirstexamines Kepler's Mysterium Cosmographicum (1596), which he finds to be still in the geometrical traditional of ancient astronomy, despite its advocacy of the heliocentric theory. Stephenson sees Copernicus, for all of his importance in the Scientific Revolution, as belonging to that tradition, because his support of a sun-centred universe was based on geometry, not physics. The author devotes most of his book, in an overlylong chapter of 116 pages, to Kepler's Astronomia Nova (1609). Stephenson argues that the astronomer broke new ground in it, not so much for its presentation of hisfirsttwo laws of planetary motion, the work's usual cause for mention in history of science textbooks, but for the attempt to fashion a 244 Reviews physical theory for the planets. Stephenson persuasively argues that Kepler was far more systematic and organised in Astronomia Nova than previous historians of science have seen him, such as Arthur Koestler, who used the term 'sleepwalking' to describe Kepler's mode of thought. Stephenson painstakingly follows the order of the book to lay out Kepler's goals: 'to demonstrate that the models used by all the astronomers were wrong, and that they could not be salvaged in any reasonable manner'; second, 'to develop his new astronomy, and show it to be accurate to the limits of the Tychonic observations';finally,'to argue that... his theories were much more likely to represent what was actually taking place in the heavens' (p. 22). The 'conquest of Mars', successfully fitting into his theory the motions of Mars, which had caused so much trouble for ancient astronomy, allowed Kepler to claim success. Stephenson turns more briefly to Kepler's Epitome Astronomiae Copernicanae (1621), in which Kepler argued more explicitly for a 'dynamic physical astronomy centred on the sun' (p. 139). The physical force that produced the motion of the earth and the other planets around the sun was a type of planetaryfilament,similar to but not identical with magnetism. In this way Kepler anticipated Newton's law of universal gravitation in sensing that both mass and distance were factors in the strength of that force. In his first book Stephenson largely avoided any discussion of the more esoteric aspects of Kepler's work, which make him so difficult for m o d e m scholars to understand. In The Music of the Heavens, Stephenson tackles Kepler at...

Distance and velocity in Kepler's astronomy

Summary We will examine Kepler's use of a relation between velocity and distance from a centre of circular motion. This relation plays an essential role, through a derivation in chapter 40 of the Astronomia Nova, in the presentation of the Area Law of planetary motion. Kepler transcends ancient and contemporary applications of the distance-velocity relation by connecting it with his metaphysical commitment to the causal role of the Sun. His second main innovation is to replace the astronomical models of his predecessors with an account that derives trajectories from physical principles. In this paper we restrict our attention primarily to the first 40 chapters of Kepler's Astronomia Nova. Hence, we do not discuss Kepler's discovery of elliptical planetary orbits.

Kepler' ‘Distance Law’ - Myth not Reality

I have carried out a selective reworking of Chapter 32 of Kepler's Astronomia Nova - which was the source of all his physical ideas - and have established that no foundation exists either there, or subsequently, for what is nowadays known as ‘Kepler's distance law‘. By contrast, I show that his innovative approach led him to consider the component of velocity which is precisely perpendicular to the Sun-planet line, and so to formulate motion taking place instantaneously in a circle round the Sun; this is exactly equivalent to the area law according to modern standards. Moreover, no other interpretation would have been compatible with Kepler's Aristotelian principles.

Kepler's Road to Damascus

Summary In Astronomia Nova Kepler established the two laws that govern the motion of an individual planet. I show here that his achievement depended on the Euclidean - geometrical - method he invented to determine a typical point of each of the three curves he successively proposed (corresponding respectively to the three stages of his progress). At the final stage, Kepler's first flash of enlightenment was sparked by his discovery of a general construction-rule for the (medial-grade) curve he required; the second, by his realization that this rule would produce a perfect ellipse, described in accordance with the (Keplerian-style) area law. This exact curve-time correlation is notable for attaining, by modern standards, the status of an orbit.

Grading the Eggs (Kepler's Sizing-Procedure for the Planetary Orbit)

Summary Kepler's investigation of Mars in Astronomia Nova progressed through three distinct stages, each associated with an ‘ovoid’ curve of a particular grade (the egg-metaphor was originated by Kepler himself). The geometrical separation of the first two proposed ovoids is greatest for their quadrant-positions, so that is where Kepler assessed them. Via a previously-unnoticed diagram, I exhibit the simple Euclidean construction he used to determine the optimum position of the Earth acting as a mobile observing-platform. Then I extend Kepler's method to verify that, for at least half its orbit, the Earth will provide a viewing-angle amply large enough to justify his conclusion that the observed quadrant-position lay ‘in the middle’. Hence - regardless of shape - the planetary orbit is identified as an ovoid of medial grade.

Bessel Functions and Kepler's Equation

2. KEPLER'S EQUATION. After years of work, Johannes Kepler announced three laws of planetary motion early in the seventeenth century. Kepler's three laws state that the planets move in elliptical orbits in a common plane with the sun at one focus, that for each planet the line connecting the sun with the planet sweeps out equal areas in equal times and that the ratio of the square of the period of revolution of each planet to the cube of the semimajor axis of its orbit is the same for all planets. Kepler stated the first two laws in 1609 in the Astronomia Nova and the third in 1619 in The Harmony of the World. As we know now, these laws are only approximations, but for the six planets known at the time and to the limits of observation then they were essentially exact. Kepler's Equation is a consequence of the first two laws only. Suppose a planet moves in the counterclockwise direction in an elliptical orbit with the sun at one focus which has eccentricity e, 0 < e < 1, has semimajor axis a, and is traveled once in time T. In the figure, A denotes perihelion, C center of the orbit, and S the position of the sun. If, having passed through A, the planet after elapsed time t is at position P, we wish to express the polar coordinates of P, (r, v), relative to S at time t. The quantity v = angle PSA is called the true anomaly of the planet at time t. The circle centered at C with radius a is called the eccentric circle. If we draw the line P perpendicular to radius CA and mark R, its intersection with CA, and Q, its intersection with the eccentric circle, the quantity E = angle QCA is called the eccentric anomaly of the planet at time t.

Kepler's hypothesis vicaria

Introduction In his Astronomia nova (1609) Kepler developed a new planetary hypothesis (Chapter 16), the hypothesis vicaria, as he himself later called it, which reproduced Tycho's and his own obser ations of the longitudes of Mars at opposition systematically all around the zodiac t within 2' (Chapter 18). In the history of astronom this has generally been considered to be one of man's most audacious c nfrontations with the apparent motion of the celestial bodies, achieving an nprecedented order of accuracy. The assumption has been made that Kepler's deviatio of 2' from observ tion, of the same order as Tycho's, is here fore to be attributed mainly to observational error.1 However, even a simple analysis reveals that Kepler's hypothesis vicaria sh uld show, o ly because of his value for the ecc ntricity, a systematic deviation of as much as ±4' from modern theory as a function of longitude.2 Kep1 E.g., Astr. nova, GW 3; XVIII, 174. 2 Whiteside (1974.1), 18, n. 16; Maeyama (1975), 774.

On Kepler's awareness of the problem of experimental error

Summary This paper is an account of Kepler's explicit awareness of the problem of experimental error. As a study of the Astronomia nova shows, Kepler exploited his awareness of the occurrences of experimental errors to guide him to the right conclusion. Errors were thus employed, so to speak, perhaps for the first time, to bring about a major physical discovery: Kepler's laws of planetary motion. ‘Know then’, to use Kepler's own words, ‘that errors show us the way to truth.’ With a survey of Kepler's revolutionary contribution to optics, the paper demonstrates that Kepler's awareness of the problem of experimental error extended beyond discrepancies between calculations and observations to types of error which pertain to observations and instruments. It emerges that Kepler's belief in the unity of knowledge and physical realism, facilitated—indeed created—the right philosophical posture for comprehending the problem of error in an entirely novel way.

2.7. Continuities in Kepler scholarship: the European Kepler symposia in historiographical perspective

BETWEEN August and October 1971 many conferences in honor of Kepler were held across Europe? Several of these symposia (reviewed in this paper) took place in a number of cities where Kepler lived and worked and where many others have since labored to uncover the significance of his writings: in Weil der Stadt, Kepler's birthplace; in Linz, where he was district mathematician from 1612 to 1626; in Leningrad, where Kepler's manuscripts were brought in the eighteenth century by Catherine the Great; in London, at a meeting of the British Society for the History of Science held at the Warburg Institute; and in Zag~in, where Kepler spent the last two years of his life in great loneliness before his death in Regensburg. Special displays of Kepleriana could be seen not only at the various symposia, but also in Prague, where Kepler succeeded Tycho Brahe as Court Astronomer to the Emperor Rudolph II and where he composed his great Astronomiae pars opticae (1604) and the Astronomia Nova (1609); and in Tiibingen, the site of Kepler's university training, his work with Michael M/istlin and his adoption of the Copernican theory. A series of lectures on Kepler's life were given at Graz, location of the young astronomer's

Kepler's Second Law of Planetary Motion

Previous articleNext article No AccessKepler's Second Law of Planetary MotionE. J. AitonE. J. Aiton Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Isis Volume 60, Number 1Spring, 1969 Publication of the History of Science Society Article DOIhttps://doi.org/10.1086/350450 Views: 64Total views on this site Citations: 23Citations are reported from Crossref Copyright 1969 History of Science Society, Inc.PDF download Crossref reports the following articles citing this article:Todd Timberlake, Paul Wallace Finding our Place in the Solar System, 37 (Mar 2019).https://doi.org/10.1017/9781316856208W Y Hsiang, H C Chang, H Yao, P S Lee Re-establishing Kepler’s first two laws for planets in a concise way through the non-stationary Earth, European Journal of Physics 36, no.44 (Apr 2015): 045006.https://doi.org/10.1088/0143-0807/36/4/045006Paolo Bussotti Kepler’s Influence on Leibniz’s Planetary Theory, (Jan 2015): 115–163.https://doi.org/10.1007/978-3-319-21236-4_6C Bracco, J-P Provost Had the planet Mars not existed: Kepler's equant model and its physical consequences, European Journal of Physics 30, no.55 (Jul 2009): 1085–1092.https://doi.org/10.1088/0143-0807/30/5/015Stefano Gattei “Why, and to What Extent, May a False Hypothesis Yield the Truth?”, (Jan 2009): 47–61.https://doi.org/10.1007/978-1-4020-9338-8_4James Casey Areal velocity and angular momentum for non-planar problems in particle mechanics, American Journal of Physics 75, no.88 (Jan 2007): 677.https://doi.org/10.1119/1.2735630William Donahue Astronomy, (Jul 2006): 562–595.https://doi.org/10.1017/CHOL9780521572446.025Davaadorjin Monhor, Shuzo Takemoto Understanding the concept of outlier and its relevance to the assessment of data quality: Probabilistic background theory, Earth, Planets and Space 57, no.1111 (Jun 2014): 1009–1018.https://doi.org/10.1186/BF03351881William H. Donahue Kepler's invention of the second planetary law, The British Journal for the History of Science 27, no.11 (Jan 2009): 89–102.https://doi.org/10.1017/S000708740003168XA. E. L. Davis Kepler's Resolution of Individual Planetary Motion, Centaurus 35, no.22 (Jul 1992): 97–102.https://doi.org/10.1111/j.1600-0498.1992.tb00871.xD. Bertoloni Meli Public claims, private worries: Newton's principia and Leibniz's theory of planetary motion, Studies in History and Philosophy of Science Part A 22, no.33 (Sep 1991): 415–449.https://doi.org/10.1016/0039-3681(91)90003-BFritz Krafft The New Celestial Physics of Johannes Kepler, (Jan 1991): 185–227.https://doi.org/10.1007/978-94-011-3342-5_9Andrew Lugg History, Discovery and Induction: Whewell on Kepler on the Orbit of Mars, (Jan 1989): 283–298.https://doi.org/10.1007/978-94-009-2327-0_14Giora Hon On Kepler's awareness of the problem of experimental error, Annals of Science 44, no.66 (Aug 2006): 545–591.https://doi.org/10.1080/00033798700200361Brian S. Baigrie Kepler's laws of planetary motion, before and after Newton's Principia: An essay on the transformation of scientific problems, Studies in History and Philosophy of Science Part A 18, no.22 (Jun 1987): 177–208.https://doi.org/10.1016/0039-3681(87)90017-3Bruce Stephenson Astronomia nova, (Jan 1987): 21–137.https://doi.org/10.1007/978-1-4613-8737-4_3Scott A. Kleiner AN ASPECT OF THE LOGIC OF DISCOVERY, The Southern Journal of Philosophy 21, no.44 (Dec 1983): 513–536.https://doi.org/10.1111/j.2041-6962.1983.tb01525.xI. Bernard Cohen The Principia, Universal Gravitation, and the “Newtonian Style”, in relation to the Newtonian Revolution in Science:, (Jan 1982): 21–108.https://doi.org/10.1007/978-94-009-7715-0_2C. H. Edwards Early Indivisibles and Infinitesimal Techniques, (Jan 1979): 98–121.https://doi.org/10.1007/978-1-4612-6230-5_4I.Bernard Cohen Newtonian astronomy, Vistas in Astronomy 20 (Jan 1976): 85–98.https://doi.org/10.1016/0083-6656(76)90016-7Eric J. Aiton How Kepler discovered the elliptical orbit, The Mathematical Gazette 59, no.410410 (Sep 2016): 250–260.https://doi.org/10.2307/3616881Owen Gingerich 6.1. Kepler's place in astronomy, Vistas in Astronomy 18 (Jan 1975): 261–278.https://doi.org/10.1016/0083-6656(75)90105-1E. Rybka, O. J. Gingerich, J. O. Fleckenstein, C. D. Hellman, Z. Horský, P. G. Kulikovsky, W. Petri, V. L. Tchenakal 41. History of Astronomy, Transactions of the International Astronomical Union 14, no.11 (Apr 2016): 481–489.https://doi.org/10.1017/S0251107X00024081

Johannes Kepler Gesammelte Werke

WITH the appearance of the second volume of the new edition of Kepler's works the first three volumes are now available, the third containing the “Astronomia Nova” having been issued first in order of date. It is curious that the three already exhibit the complex personality of Kepler in a violently contrasted way. In the first, the mystic element is predominant, and that is hard to reconcile with a truly scientific spirit. The second reveals the impatience of a sanguine temperament, which is not easily compatible with a philosophic outlook. The third, equally the product of those active years which followed the death of Tycho Brahe, reflects an assured serenity, when insight and resource never fail and every difficulty is met and overcome with untiring industry. No voluminous writer can be expected to produce a succession of masterpieces of the highest order, but in the inequality of his work it would be hard to find a parallel to Kepler. Johannes Kepler Gesammelte Werke Herausgegeben im Auftrag der Deutschen Forsch-ungsgemeinschaft und der Bayerischen Akademie der Wissenschaften. Unter der Leitung von Walther von Dyck und Max Caspar. Band 2: Astronomiae Pars Optica. Herausgegeben von Franz Hammer. Pp. 466. (Munchen: C. H. Beck, 1939.) 9 gold marks.