Kapteyn, Jacobus Cornelius
Kapteyn, Jacobus Cornelius
(b. Barneveld, Netherlands, 19 January 1851; d. Amsterdam, Netherlands, 18 June 1922)
Kapteyn was the ninth of fifteen children of G. J. Kapteyn and E. C. Koomans, who conducted a boarding school for boys in Barneveld. Many of these children were extraodinarily gifted in science. As a boy Kapteyn showed outstanding intellectual ability and curiosity. At the age of sixteen he passed the entrance examination for the University of Utrecht, which, however, his parents judged him too young to enter until the following year. He studied mathematics and physics and obtained the doctor’s degree with a thesis on the vibration of a membrane. Kapteyn was interested in many branches of science, and it was mostly through his accepting (1875) a position as observator at the Leiden observatory that he began his career in astronomy. In 1878, at the age of twerntyseven, he was elected to the newly instituted chair of astronomy and thoerectical mechanics at the University of Groningen, which he held until his retirement in 1921 at the age of seventy.
Kapteyn’s major contributions are in the field of stellar astronomy, particularly in research on the space distribution and motions of the stars. At the time of these studies, the problem of the space distribution of the stars was still tantamount to the problem of the structure of the universe. Kapteyn’s work presents the first major step in this field after the great works of William and John Herschel. It culminated in the views presented in the article “First Attempt at a Theory of the Arrangement and Motion of the Sidereal System,” published in the May 1922 issue of the Astrophysical Journal, shortly before Kapteyn’s death. Seeking to resolve the structure and kinematic properties of the stellar system, Kapteyn devoted his efforts both to the problem of the methods to be developed and their mathematical aspects, and to that of obtaining proper observational data. For the latter purpose he established and participated in extensive international observational projects of many kinds. These have served astronomical research in fields remorte from Kapteyn’s own. Thus Kapteyn deeply influenced astronomy not only by his analyses of (sometimes rather meager) observational material available at his time but also by providing the frame-work for future observational programs and more detailed analyses.
Kapteyn possessed the ability to conduct several large-scale undertakings at once, and to handle with great care and ability the more detailed matters essential to their successful completion. He thereby made significant contributions to several special fields of astronomy. This article will concentrate first on his major contributions.
Kapteyn’ first major achievement was the compilation, togaether with David Gill, of the Cape Photographic Durchmusterung, a catalogue of stars in the southern hemisphere. Their approach to this project was quite untraditional according to astro-nomical practice of that time. Since the University of Groningen, in spite of Kapteyn’s requests, could not provide him with a telescope, he looked for other ways to contribute to the observational work. In 1885 he contacted Gill, then director of the Royal Observatory in Cape Town, South Africa, to offer to measure the photographic plates, covering the whole southern sky, which Gill had taken at the Cape with a Dallmeyer objective. These would be measurements of the position and apparent brightness of the stars, down to magnitudes comparable with those of the Bonner Durchmusterung (Bonn, 1859–1862), and thus would supplement, by photographic means, what had been accomplished by Argelander, by visual means, for the northern sky.
The extremely laborious work was finished after thirteen years of excellent collaboration. For the measurement of the plates, done from 1886 to 1896, Kapteyn devised an unconventional method. Instead of measuring x and y coordinates, he used a theodolite, observing the plate from a distance equal to the focal length of the telescope that had produced the plates. He thus obtained equatorial coordinates directly; the catalogue gives the right ascensions to 0s.1 and the declinations to 0´.1. Approximate apparent (photo-graphic) magnitudes were also given. The catalogue was published as volumes III, IV, and V of the Annals of the Royal Observatory, Cape Town (1896– 1900) and lists the positions of 454, 875 stars, between the South Pole and declination — 18°, down to the tenth magnitude. An invaluable reference work on the southern sky. it is remarkably free of errors because of the painstaking care with which Kapteyn himself participated in much of the routine work. Assistance in the routine included labor by certain convicts of the state prison at Groningen, who were put at Kapteyn’s disposal by the prison authorities. The measurements were all carried out in two small rooms of the physiological laboratory of the University of Groningen. Thus started Kapteyn’s “astronomical laboratory,” a kind of institute unique at that time, which soon would become world famous and recognized a much-needed complement to institutes equipped with telescopes. After being housed in various other “guest” institutes, the “laboratory” in 1913 acquired the whole of the building of the original physiological laboratory.
Structure of the Stellar System. The principal unknowns which Kapteyn tried to solve were the function D (r), that is, the space density of stars as a function of the distance r from the sun; and the function φ(M), or the distribution of the stars according to brightness per unit volume. In a series of investigations by Kapteyn and his collaborators, extending over several decades, these functions became defined in more and more detail. Thus, the function D (r), initially determined only for stars generally without regard to their spectral type or galactic latitude or longitude, could later be determined separately for different types of stars, and φ(M) could be distinguished more and more according to both distance from the galactic plane and spectral type.
Kapteyn’s approach to these problems was basically different from that of contemporaries such as Hugo von Seeliger and Karl Schwarzschild. The latter proposed certain analytical expressions for the aforementioned functions, as well as for the distribution of observed quantities, and then tried to solve for the parameters involved by means of integral equations. Kapteyn, on the other hand, preferred the purely numerical approach, allowing full freedom for the form of the solution.
In principle the procedure applied was the following. Statistics could be obtained on the numbers of stars of given apparent brightness N (m) and, to some extent, on these numbers subdivided according to the size of the proper motion, µ, of the stars, N (m,µ). The proper motion was introduced as an auxiliary quantity because, like m, it is a measure of distance; hence, if the velocity distribution of the stars is independent of r, then knowledge of μ should help in unraveling the distance distribution. Moreover, largely through his own efforts, Kapteyn obtained for stars of a given apparent magnitude the mean value of the trignometric parallax <π(m)> and, to some extent, this mean subdivided according to the stars’s proper motions, < π(m, μ) >. It one assumes that all stars have the same intrinsic brightness—a very special case of φ(M)—and that the space density is uniform (that is, D (r) is constant), then a certain, predictable form of the statistics N (m) results. The actually observed shape of N (m) is different, and the problem is to find by proper adjustments the true D (r) and φ(M). For these adjustments the values <π(m)> and (more refined) <π(m, μ)> appeared the most adequate quantities.
For a detailed account of Kapteyn’s procedure, we refer to the literature cited below, especially to the relevant chapters in the books by von der Pahlen and by de Sitter. In a long series of papers, mostly in Publications. Astronomical Laboratory at Groningen (referred to below as Gron. Publ)., Kapteyn and his co-workers gave ever more complete tables for the quantities and the resulting solutions. Data on <π(m)> published in Astronomische Nachrichten, no. 3487 (1898); on <(m,μ)> in Gron. Publ., no. 8 (1901); and on N (m) and N (m,μ) in Gron. Publ., no.11 (1902), were analyzed for a provisional solution of D (r) and φ(M) in Gron. Publ., no. 11 (1902). The final, more precise and detailed solutions were published by Kapteyn and van Rhijn in 1920 in Contributions from the Mount Wilson Solar Observatory, no. 188 (also in Astrophysical Journal, 52 ) and, after Kapteyn’s death, by van Rhiji in Gron. Publ., no. 38 (1925). These were based on the improved data for
N (m), in Gron. Publ., no. 18 (1908) and no. 27 (1917);
N (m, μ), ibid., no. 30 (1920) and no. 36 (1925);
<π(m)>, ibid., no. 29 (1918); see also no. 45 (1932); and for
<(m, μ)>, ibid., no. 8 (1901), Contributions from Mount Wilson Solar Observatory, no. 188, and Gron. Publ., no. 34 (1923).
Some of the results of these investigations have been of lasting value and some have been superseded. As to those for D(r), we should distinguish between the change of densities with distance in the direction of the galactic plane (or at adjacent, low, galactic latitudes) and in the directions away from the plane. Whereas the latter results have proved to be essentially correct, the former are now known to be spurious. Kapteyn and van Rhijn found that at low galactic latitudes the star density in all directions diminishes with increasing distance from the sun. Thus, at 600 parsecs (2,000 light-years) it was found to be about 60 percent of that near the sun, at 1,600 parsecs about 20 percent, and at 4,000 parsecs only 5 percent. This apparent decrease, which gave rise to interpretation in terms of a more or less isolated, flattened, and spheriodial local stellar system (the “Kapteyn system”), is due to the fact that Kapteyn assumed starlight to pass through space without being dimmed on its way to the earth.
Actually, as is now known, interstellar absorption by small grains does cause a dimming effect, hence in the numerical solutions the stars appear too distant. This results in an apparent decrease of the derived star density with distance. Kapteyn was fully aware of the interstellar absorption as a possible cause of inaccuracies in his results, and therefore he made several attempts to detect its existence. He correctly assumed that interstellar absorption should be accompanied by reddening of the starlight, the expected absorption in the blue being stronger that in the yellow and the red. But investigations of this reddening did not lead to positive results, and accordingly absorption could not be taken into account. (It was only in 1930 that Trüpler could prove its existence.)
Kapteyn’s results for high galactic latitudes were hardly affected by the dimming because the absorbing matter is concentrated close to the galactic plane. At 100 parsecs the star density appeared to be about 55 percent of that near the sun, at 250 parsecs 40 percent, at 600 parsecs 12 percent, and at 1,600 parsecs less than 2 percent. The sun was found to be close to the plane of symmetry. These results apply to the combined population of all spectral types. Results for the luminosity function φ(M) were essentially correct because they had been derived mostly from the nearest, unobscured stars. It was shown that the frequency of stars per unit volume increases from the most luminous objects (with intrinsic brightnesses about 1,000 times that of the sun) to those of about solar brightness, which are about 1,000 times more prevalent, and that the frequency subsequently tends to level off. The results included stars with a luminosity down to about half solar brightness.
Discovery of the Star Steams . Reference has been made to the use for the proper motion, μ, as well as the apparent magnitude, m, as an indicator of distance. In the early stages of his work, after having explored the use of the trigonometric parallaxes, Kapteyn emphasized the use of μ rather than of of m because of the large spread known to exist among the absolute magnitudes. As a prerequisite to the application of the method, an attempt was made to determine the distribution of the stars according to their peculiar velocities; that is, of the velocities with respect to the mean motion of the stars, the latter, in turn, being the reflex of the motion of the sun. A basic assumption was that the stellar motions have a random character, like those of the molecules of a gas, without preferred direction.
When tests of the method using μ as a distance indicator gave unsatisfactory results, Kapteyn found that the assumption of random motion was incorrect: preferred directions did exist. It appeared that the stars belong to two different, but intermingled, groups having different mean motions with respect to the sun.
This phenomenon, termed “the two star streams,” was announced by Kapteyn at the International Congress of Science at St. Louis in 1904 and before the British Association in Cape Town in 1905 (Report of the British Association for the Advancement of Science, Sec. A) and deeply impressed the astronomical world. It demonstrated that a certain order, rather than the hitherto assumed random motion, dominated stellar motions. During the subsequent decades, numerous investigations were devoted to the subject and alternative interpretations presented. Of these latter by far the most significant is that of K. Schwarzschild, who, in 1907, instead of assuming the existence of two intermingling populations, postulated an undivided population; however, he conceived this population to have an ellipsoidal distribution of peculiar velocities, with the largest peculiar velocity components in the direction of the largest axis of the velocity ellipsoid. This interpretation appeared to accord with the observational data equally well. The discovery of the two star streams—and especially the hypothesis of elliposidal distribution-was of fundamental importance for the theory of the dynamics of the stellar system.
The Plan of Selected Areas. During the early stages of Kapteyn’s investigations, the approximate position and apparent brightness were known for somewhat less than a million stars; proper motions were known with verying degrees of accuracy for several thousand, and trigonometric parallaxes for fewer than 100 stars. Kapteyn encouraged efforts of many observatories to procure more data on trigonometric parallaxes, radial velocities, spectra, and proper motions; wherever possible, he assisted in the measurements of plates by means of the facilities of his growing laboratory. A carefully planned undertaking appeared in order, however, particularly because from the fainter stars (there are about ten million down to the fourteenth magnitude) a selection had to be made.
In order to make sure that this selection would involves as much as possible the same stars for each observational program, Kapteyn devised a plan which was proposed to the international astronomical world in the booklet plan of Selected Areas (Groningen, 1906). His plan resulted from many letters and discussions with colleagues abroad (and was a study topic for an Astronomical Society of the Atlantic, created ad hoc aboard the ship on which Kapteyn and other astronomers made a voyage to South Africa for their meeting in 1905).
The Plan proposed to concentrate work on 206 stellar areas, uniformly demarcated over the sky and at declinations +90°, +75°, +60° . . . to —90°. Photographic and visual magnitudes were to be measured for all stars in these areas (±200,000); and, for more limited numbers, the quantities more difficult to measure, such as proper motion,. parallax, spectral type, and radial velocity. This observational material would provide a proper sampling of the stellar system for the purpose of revealing its main structural features. At the instigation of the astronomer E. C. Pickering, a supplementary program of forty-six areas was proposed, chosen where the Milky Way shows particularly striking features, such as excessive star density and dark or bright nebulae. Pickering’s program became known as the “Special Plan,” Methods for observing and for evaluation of the material and the prospects for analyses were extensively discussed in the booklet.
Astronomical institutes throughout the world responded most favorably to the proposal—not least because of the cooperative spirit Kapteyn and his laboratory had shown on many occasions when their help was solicited by others. Work on Kapteyn’s plan, and to a lesser degree on Pickering’s special plan, progressed during the first half of the twentieth century and continues to be an outstanding example of international scientific collaboration. To date forty-three observatories have in one way or other collaborated. Shortly after international agreement on the plan had been reached, its supervision was placed in the hands of an international committee of prominent astronomers; W. S. Adams, F. W. Dyson, Gill, Hale, Küstner, E. C. Pickering, K. Schwarzschild, and Kapteyn himself. The committee was later incorporated into the International Astronomical Union as one of its commissions, and progress reports on the plan are to be found in the Transactions of the union.
Dynamical Theory of the Stellar System. With the newly obtained results on stellar density distribution (the “Kapteyn system”) and the new knowledge of stellar kinematics (the peculiar motions, solar motion, and star streams), Kapteyn toward the end of his career developed a dynamical theory of the system. Such a theory aimed at explaining both observed density distribution and motions in terms of gravitational forces, and it would do this on the assumption that the system is in a state of equilibrium.
Kapteyn’s theoretical results were communicated in the 1922 paper already quoted. In considering his results we may again distinguish between two basic directions: the one toward the “pole” of the galaxy, that is, along the minor axis of the spheroidal system, and the one perpendicular to this axis, in the galactic plane.
In the first direction the galactic situation may be compared with that in the earth’s atmosphere: its scale height is such as to balance those gravitational forces that tend to flatten the atmosphere with the force of thermal motions perpendicular to the earth’s surface, which tend to increase the thickness of the atmosphere. For a given gravitational field, increased thermal velocities would lead to increased scale height, Similarly, considerations of equilibrium allowed Kapteyn to derive, from the known distribution of the components to the velocity in the direction perpendicular to the galactic plane and, from the observed “scale height” in the same direction, the strength of the gravitational field at various distances from the plane. This calculation led in turn to an estimate of the total mass density per volume, a very fundamental quantity. Kapteyn expressed the results in mean masses per star—knowing the number of stars per unit volume—and found values between 2.2 and 1.6 solar masses, well in agreement with later determinations.
The larger extension of the stellar system in the direction of its equatorial plane was explained by the occurrence of a general rotation around the polar axis. This hypothesis was related to the phenomenon of the star, streams, the assumption being that the system is composed of two subsystems with opposing directions of rotation; in that case, centrifugal force plus random motions must be balanced by the gravitational field. Here, too, Kapteyn succeeded in arriving at a coherent picture. But the concept of the Spheroidal system could not be upheld, and the phenomenon of star streams has since been given a different explanation by B. Lindblad.
Apart from these main achievements, Kapteyn made essential contributions in many other fields. Among these are his attempts, in his early years at the Leiden observatory, to improve upon the measurement of trigonometric parallaxes with the meridian telescope and his later efforts to apply photographic methods for this purpose as well as for the measurement of stellar magnitudes. In his early year he also devised a method to find the altitude of the equatorial pole which would be free of errors in the declinations of the stars and would be independent of errors in the atmospheric refraction. Kapteyn emphasized on many occasions the great need for improvement of the fundamental system of declinations and proposed observational methods to eliminate systematic errors. He demonstrated certain relations between the various spectral types of the stars and their kinematic properties and pursued especially the properties of the earliest types (the “helium stars”), for which the small ratio between peculiar velocity and solar motion allowed the determination of accurate individual parallaxes. The accounts of this latter work, in which Kapteyn’s approach to the handling of such delicate quantities as small proper motions is quite remarkable, are given in two extensive papers (Astrophysical Journal40  and 47 ; repr. in Contributions from the Mount Wilson Solar Observatory, nos. 82 and 147).
Kapten’s interest in statistical properties of natural phenomena outside astronomy is shown by his thorough studies of tree growth and other phenomena in the booklet Skew Frequency Curves in Biology and Statistics (Groningen, 1903) and in the article “TreeGrowth and Meteorological Factors (1889–1908),” in Recueil des tracaux botaniques néerlandais (1914). In the course of his researches he introduced many concepts that have come into common acceptance in astronomy, including those of absolute magnitude and color index.
Kapten had an almost inexhaustible capacity for scientific activity. In his attitude toward research he was extremely critical, with respect both to his own work and to that of others. He never sacrificed clarity of treatment of exposure or essential details for elegance of presentation; and, although a mathematician himself by his early training, he strongly disliked treatises in which emphasis lay more on the form of the mathematical expression than more on proper evaluation of the basic observations. It was only through his thorough knowledge of their strengths and weaknesses that he was able to draw proper conclusions from what were sometimes limited data.
In his relation to friends and colleagues, Kapteyn was very sensitive to friendship and cordiality. Having suffered in early youth from a lack of warmth and protection in his family life—his parents being fully occupied with their boarding school and perhaps having aimed at equal treatment of all their “children” —he later responded all the more readily to human relations. From his collaboration with many colleagues grew close ties of friendship, such as that with Gill (with whom a regular correspondence developed over three decades).
Kapteyn had a keen sense of justice and suffered deeply when World war I disrupted the international communication between scientists. He firmly believed in the duty of scientists to bridge the gaps caused by political developments, and therefore he urged that upon termination of the war—at least in the scientific world—reconciliation between Germany and the Allies be reestablished. He was thus deeply shocked, and protested violently, when in 1919 the Interallied Association of Academies was founded with Germany excluded. When, in spite of his and a few others’ protests, the Royal Netherlands Academy of Sciences and Letters decided to join the International Research Council (from which Germany was again excluded), he resigned his long-standing membership in the academy.
Kapteyn had a keen sense of humor and was a celebrated lecturer to audiences of all kinds. In the town of Groningen, where he lived for more than forty years with his wife and family (he married Elise Kalshoven in 1879 and had two daughters and one son), he was well remembered more than thirty years after his death.
I. Original Works. Numerous papers by Kapteyn, some of them collaborations, appeared in the main astronomical journals, especially the Astrophysical Journal, Astronomische Nachrichten, and Astronomical Journal, and in the reports of the Koninklijke Akademie van Wetenschappen of Amsterdam. A list of the principal papers is given in an appendix to the obituary by W. de Sitter (See below).
The series Publications of the Astronomical Laboratory at Groningen, created by Kapteyn, contains both treatises on the analyses of observational data and catalogues of measurements. Other important catalogues besides the Cape Photographic Durch-musterung (see text) are “Durchmusterung of the Seceleted Areas,” in Annals of Harvard College Observatory, nos. 101, 102, and 103 (1918–1924), complited with E. C. Pickering and P. J. van Rhijn; and the Mount Wilson Catalogue of Photographic Magnitudes in Selected Areas 1–139 (Washington, D.C., 1930), complited with R. H. Seares and P. J. van Rhijn.
II. Secondary Literatute. Many obituaries appeared in scientific journals after Kapteyn’s death. Of special note are A. Pannekoek, “J. C. Kapteyn und sein astronomisches Werk,” in Naturwissenschaften, 10 , no. 45 (1922), 967–980; J. J. (J. Jackson?), in Monthly Notices of the Royal Astronomical Society, 83 (1923), 250–255; W. de Sitter, “Jacobus Cornelius Kapteyn †,” in Hemel en dampking, 20 (1922), 98–110, in Dutch; C. Easton, “Persoonlijke herinneringeen aan Kapteyn,” ibid., 112–117, and 21 (1922), 151–164, in Dutch; and A. S. Eddington, “Jaconbus Cornelius Kaptey,” in Observatory, 45 (1922) 261–265.
An excellent chapter describing Kapteyn’s work in the context of developing historical insight into the structure of the universe appears in W. de Sitter, Kosmos (Cambridge, Mass., 1932), ch. 4, a lecture series at the Lowell Institute in Boston. A good detailed account of Kapteyn’s statistical treatments is given by E. von der Pahlen in Lehrbuch der Stellarstatistik (Leipzig, 1937), ch. 8, sec. ID, pp. 434–479. A biography in Dutch, J. C. Kapteyn, zijn leven en werken (Groningen, 1928), by Kapteyn’s daughter, H. Hertzsprung-Kapteyn (wife of the famous astronomer E. Hertzsprung), given a fine account of Kapteyn’s personal life, his relations with colleagues, and his scientific achievements as experienced by his family.
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Jacobus Cornelis Kapteyn
Jacobus Cornelis Kapteyn
The Dutch astronomer Jacobus Cornelis Kapteyn (1851-1922) founded a unique astronomical data analysis laboratory, helped compile a monumental star catalog, discovered the two star streams, and constructed a model of our galaxy.
Jacobus Kapteyn was born on Jan. 19, 1851, in Barneveld. At 18 he entered the University of Utrecht and 6 years later obtained his doctorate in physics. He became a professional astronomer somewhat accidentally: just as he received his doctoral degree, the position of observer at the Leiden Observatory became vacant. He applied and obtained it, a decisive event in his life, for it appears likely that it was during his subsequent 3 years at Leiden that he resolved to try to understand the structure of the universe. In 1878 he became professor of astronomy, calculus of probabilities, and theoretical mechanics at the University of Groningen. The following year he married Catharina E. Kalshoven; they had three children.
The University of Groningen had no observatory, and for years Kapteyn unsuccessfully attempted to secure funds to establish one. However, he found a unique solution to the problem: in 1896 he established at Groningen not an observatory but a laboratory, where stellar photographs taken elsewhere could be analyzed. In 1903, after several years at a temporary location, his laboratory found a permanent home in the mineralogical laboratory of the university; it is now known as the Astronomical Laboratory Kapteyn.
In 1885 Kapteyn took upon himself a prodigious task: he offered to help David Gill measure and reduce the photographs Gill had taken of the southern sky from his observatory at the Cape of Good Hope. The project took 14 years. The resulting star catalog contained almost a half million entries; this work alone would have put generations of astronomers in Kapteyn's debt.
By 1889 Kapteyn had developed new methods for determining stellar parallaxes, or distances. This work soon evolved into studies on stellar proper motions, and by 1896 he found indications that, contrary to accepted belief, stars do not move about at random in space. By 1904-1905 he had proof that they do not. He discovered, by photographically sampling limited portions of the night sky—a technique that made him the founder of modern statistical astronomy—that stars tend to move in two diametrically opposed directions in our galaxy, the Milky Way, toward the constellations Orion and Scutum. His discovery of these two "star streams" was one of the most significant astronomical discoveries ever made.
While it was not until much later that a correct explanation of the star streams was offered, it was immediately obvious to Kapteyn that it was of the greatest importance for understanding the structure of the universe. Accordingly, in 1906 he proposed the Kapteyn Plan of Selected Areas for enlisting the help of astronomers throughout the world to determine the apparent magnitudes, parallaxes, spectral types, proper motions, and radial velocities of as many stars as possible in over 200 patches of sky. On the basis of the results he proposed a model of our galaxy, now known as the Kapteyn universe. The solar system was pictured to be nearly centrally embedded in a dense, almost ellipsoidal, concentration of stars which thinned out rapidly a few thousand light-years (a relatively small distance in astronomy) away from the center.
Between 1908 and 1914 Kapteyn was a research associate at Mt. Wilson Observatory in southern California during the summers. He died in Amsterdam on June 18, 1922.
A. Van Maanen's obituary of Kapteyn is in the Annual Reports of the Smithsonian Institution (1923). General accounts of some of Kapteyn's contributions are in Hector MacPherson, Makers of Astronomy (1933), and Otto Struve and Velta Zebergs, Astronomy of the 20th Century (1962).
The life and works of J. C. Kapteyn, Dordrecht; Boston: Kluwer Academic, 1993. □
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Kapteyn, Jacobus Cornelius
Jacobus Cornelius Kapteyn (yäkō´bəs kôrnā´lēəs käptīn´), 1851–1922, Dutch astronomer. He was an authority on the Milky Way, of which he made notable statistical studies; he constructed a model of the galaxy known as the "Kapteyn universe." He computed the positions of the stars of the Southern Hemisphere photographed by Sir David Gill and in 1904 announced the discovery of two streams of stars moving in opposite directions in the plane of the Milky Way.
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