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Biographical Memoirs

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Biographical Memoirs SETH CARLO CHANDLER, JR. September 16, 1846–December 31, 1913 BY W. E. CARTER AND M. S. CARTER SETH CARLO CHANDLER, JR., IS best remembered for his research on the variation of latitude (i.e., the complex wobble of the Earth on its axis of rotation, now referred to as polar motion). His studies of the subject spanned nearly three decades. He published more than twenty-five technical papers characterizing the many facets of the phenomenon, including the two component 14-month (now referred to as the Chandler motion) and annual model most generally accepted today, multiple frequency models, variation of the frequency of the 14-month component, ellipticity of the annual component, and secular motion of the pole. His interests were much wider than this single subject, however, and he made substantial contributions to such diverse areas of astronomy as cataloging and monitoring variable stars, the independent discovery of the nova T Coronae, improving the estimate of the constant of aberration, and computing the orbital parameters of minor planets and comets. His publications totaled more than 200. Chandler's achievements were well recognized by his contemporaries, as documented by the many prestigious awards he received: honorary doctor of law degree, DePauw University; recipient of the Gold Medal and foreign associate of the Royal Astronomical Society of London; life member

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Biographical Memoirs of the Astronomische Gesellschaft; recipient of the Watson Medal and fellow, American Association for the Advancement of Science; and fellow, American Academy of Arts and Sciences. Considering this prominence, one might ask why it is just now, three quarters of a century after his death, that Chandler's biographical memoir is being written. This is actually two questions: “Why was it not written many years ago by a contemporary?” and “Why write it now, so many years after his death?” Unfortunately, the answer to the first question is probably related to certain controversies in which Chandler became involved. Chandler 's formal education reached only graduation from high school and he had virtually no theoretical background in astronomy or physics. However, he was a talented observer and an extraordinarily adroit computer, and he reported his observational and computational results with total disregard for conflicting accepted theory. As associate editor and later editor of the Astronomical Journal, Chandler had little difficulty publishing and often included extensive commentaries in his technical papers. Chandler's comments undoubtedly proved particularly irritating to certain individuals simply because of his close association with Benjamin Pierce, B. A. Gould, and A. D. Bache. Just a few decades earlier these three scientists had joined forces in a highly publicized dispute over an attempt to develop a national observatory that ended in failure and left many personal animosities (James, 1987). The answer to the second question (Why now?) is more certain and pleasant. The recent development of very long baseline interferometry (VLBI) has improved the measurement of Earth orientation, including polar motion, length of day, universal time (UT1), precession, and nutation by two orders of magnitude. New information about the interior structure of the Earth, motions of the plates that form

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Biographical Memoirs the surface of the Earth, and improved understanding of the interactions among the oceans, atmosphere, and solid Earth have been derived from the highly accurate VLBI observations (Carter and Robertson, 1986). But contemporary researchers using high-speed digital computers and analysis techniques not even known in Chandler's day have found it difficult to develop a better model of polar motion. Recognition of the sheer volume of the computations that Chandler performed by hand and the completeness with which he was able to characterize the complexities of polar motion (not to mention the vast quantities of computations in his research of variable stars, comets, and minor planets) has brought a renewed appreciation of his achievements (Mulholland and Carter, 1982; Carter, 1987). His work has clearly withstood the test of time, and the minimal documentation afforded by this biographical memoir is long overdue. BIOGRAPHICAL INFORMATION Seth Carlo Chandler, Jr., was an eighth-generation American born in Boston, Massachusetts, on September 16, 1846. His father was a member of the firm of Roby and Company, dealers in hay, coal, and other produce. Seth Carlo, Jr., was one of six children. He attended the English High School at Boston, graduating in 1861. During his last year in high school Chandler became associated with Benjamin Pierce, of the Harvard College Observatory, for whom he performed mathematical computations. Upon graduating he became a private assistant to B. A. Gould, one of the best known American astronomers of that time. Gould was assisting the U.S. Coast Survey in developing improved procedures for the determination of astronomic longitude, and in 1864 Chandler joined the survey as an aide. In 1866 Chandler was assigned to an astronomic survey

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Biographical Memoirs party, where he served as an observer and performed computations. He participated in a historic determination of the astronomic longitude at Calais, Maine, in which the new trans-Atlantic cable was used to relate the local clock to the master clock at the Royal Greenwich Observatory, England. His party also traveled by ship to New Orleans to make longitude determinations, again using telegraph signals to synchronize the local clock with the Coast Survey's master clock. It was an exciting period in geodetic astronomy and the young Mr. Chandler had the opportunity to learn the latest computational techniques, develop his observational skills, and acquaint himself with state-of-the-art instrumentation. When Chandler fell in love with Carrie Margaret Herman, he decided to leave the Coast Survey and accept a position in New York City, as an actuary with the Continental Life Insurance Company. In October 1870 they were married and during the next six years their first three daughters were born: Margaret Herman in 1871; Caroline Herman in 1873; and Mary Cheever in 1876. Chandler corresponded regularly with his old mentor B. A. Gould, who had moved to Argentina to establish the Cordoba Observatory. With Gould's encouragement Chandler published his first technical paper, on the development of an analytical expression for computing a person's life expectancy from his current age, an alternate method to actuarial tables. In 1876 Chandler moved his young family to Boston, where he continued his actuarial work as a consultant to the Union Mutual Life Insurance Company of Boston. In 1880 the Chandlers' fourth daughter, Elizabeth, was born. The same year Chandler renewed his association with the Harvard College Observatory, and in 1881 moved into a brand new house in Cambridge, within a short walking distance of the observatory. Three more daughters were to be born while

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Biographical Memoirs the Chandlers lived on Craigie Street: Abbie in 1883; Eunice in 1888; and Helen Osgood in 1893. Chandler spent many of the most enjoyable hours of his life at the eyepiece of his telescope, which was mounted in a cupola atop the roof of this house. It was also from this house that he carried on the duties of associate editor of the Astronomical Journal, while B. A. Gould was editor, and later as editor after Gould's death. He used his own funds to help continue to publish the journal during difficult financial periods. In 1909 he turned the editorship over to Lewis Boss, but continued to serve as an associate editor. When his father died in 1888 Chandler purchased his grandfather's place near Strafford, Vermont, and built a new summer home on the site. The Chandlers spent many relaxing times at their summer home. As a hobby Chandler designed and built model sailboats, which he raced on a small spring-fed pond on the front lawn. He relished the task of computing improved shapes for the hulls and was quite proud of his achievements. In 1904 the Chandlers moved to a new home in the small town of Wellesley Hills, today a residential suburb of Boston, where he died on December 31, 1913. The Chandler homes in Cambridge, Wellesley Hills, and Strafford all are still standing, and the latter two are still owned by his descendants. INVENTING THE ALMUCANTAR While Chandler worked at the Coast Survey he used an instrument called a zenith telescope to determine the astronomical latitude and longitude of stations. This instrument was equipped with spirit (bubble) levels to reference the readings to the local vertical. Level vials with sensitivities of 1-2 seconds of arc per division were, and even today can be, quite finicky, changing sensitivity and behavior with

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Biographical Memoirs temperature, age, stresses from mounts, and other unknown causes. Chandler set out to develop an instrument for determining astronomic latitude free of these leveling problems. His goal was to build an instrument that would automatically be aligned very precisely with the local vertical by the force of gravity. Chandler considered two possible approaches: suspending the instrument like a pendulum, and floating it on mercury. He tested instruments of both designs, concluding that the flotation approach presented lesser mechanical problems. His next step was to have a small (45 millimeter diameter objective lens), relatively inexpensive instrument built. He was quite pleased with the performance of this first instrument, concluding from his analysis of observational data that “its accuracy seemed to be limited by its optical rather than its mechanical capacity ” (Chandler, 1887). Encouraged by this success, he designed the larger aperture (100 millimeter diameter objective lens) instrument shown in Figure 1. The rectangular structure at one end of the horizontal axis was the mercury floatation bearing that kept the telescope constantly pointed to any angle of elevation set by the observer. The circle traced out in the sky when the instrument was rotated in azimuth (i.e., a small circle parallel to the horizon) is called an almucantar, and Chandler adopted this as the name of his new instrument. By the time that the full scale Almucantar was completed Chandler had moved to Cambridge, and he immediately mounted the instrument on a pier on the grounds of the Harvard Observatory, near the main dome. During the period from May 1884 through June 1885 Chandler used the Almucantar to make latitude determinations on more than fifty nights. He carefully reduced the observations and published the resulting time series, pointing out that the values “exhibited a decided and curious progression throughout

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Biographical Memoirs FIGURE 1. Sketch of the Almucantar used by Chandler to detect polar motion. the series” for which he could identify no instrumental or personal cause (Chandler, 1887 and 1891a). DISCOVERY OF POLAR MOTION About 1765 Leonhardt Euler, a Swiss mathematician studying the dynamics of rotating fluid bodies, developed equations that suggested the Earth might wobble slightly about its axis of rotation. Such a wobble (free nutation) would result in periodic variations of the astronomic latitudes of all points on Earth. The expected period of the variation of latitude was approximately ten months. Several astronomers attempted to detect the phenomenon during the succeeding century, without success. In 1888 German astronomer Friedrich Küstner (1888)

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Biographical Memoirs published the results of his research on the constant of aberration, reporting that his analysis indicated that the latitude of the Berlin Observatory had changed during the period of the observing campaign. Küstner's observations were made during the same period as Chandler's Almucantar observations (i.e., 1884-85), but were not continuous enough to detect any periodicity in the variation of latitude. However, he argued strongly that the apparent change in latitude was real and his evidence was sufficiently convincing that the International Geodetic Association (now the International Association of Geodesy) organized a special observational campaign to verify his discovery. Küstner subsequently refined his analysis, finding a total variation in latitude of 0.5 seconds of arc, but giving no value of the period or direction of the motion of the pole (Küstner, 1890). Chandler reexamined his Almucantar observations, as well as more recent observations made in Berlin, Prague, Potsdam, and Pulkova, and found a periodic variation of latitude, with a total range of about 0.7 seconds of arc and a period of 427 days, approximately 14 months (Chandler, 1891a and 1891b). The 40 percent discrepancy between the 305-day period predicted by theory and the 427-day observed period was quickly explained by Simon Newcomb as being the consequence of the “fluidity of the oceans” and the “elasticity of the Earth” (Newcomb, 1891). There was some level of disagreement within the scientific community, which continues today, as to who should be credited with the discovery of polar motion, Küstner or Chandler. When the Royal Astronomical Society of London awarded Chandler the Gold Medal, it specifically made note of Küstner's contribution to the discovery, and many scientists (particularly European scientists) continue today to credit Küstner. However, the 14-month wobble of the pole is universally referred to as the Chandler motion, and there is no

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Biographical Memoirs argument that Chandler illuminated the complex nature of the phenomenon, dominating the subject for decades. LEARNING THE COMPLEXITIES OF POLAR MOTION Chandler continued to analyze historical observations and in 1892 (Chandler, 1892a) reported that it appeared the period of the polar motion had changed, increasing from approximately twelve months to fourteen months, during the previous century. Newcomb (1892) responded: “The question now arises how far we are entitled to assume that the period must be variable. I reply that, perturbations aside, any variation of the period is in such direct conflict with the laws of dynamics that we are entitled to pronounce it impossible.” Chandler (1892b) vigorously defended his analysis, pointing out that the accepted theory had already been modified once to agree with the observations and suggesting that the new theory might still be incomplete. He continued his analysis of the observations without regard to theoretical constraints, but soon discarded the model that included a secular variation in the period of the free nutation in favor of a model consisting of two periodic components, the 427-day term and a superimposed 365-day (annual) term (Chandler, 1892c). The annual motion could easily be attributed to seasonal relocations of the masses of the atmosphere, ground water, and snow cover. There seems to be no record of Chandler ever revealing just how he had thought to investigate a two-component polar motion model, but it might well have been triggered by the results of a study made by his old friend B. A. Gould of variations of the latitude at the Cordoba Observatory (Gould, 1892). Gould found that he could detect the 14-month variation in the latitude that Chandler had “shown to exist at other places,” only after subtracting an annual variation. He concluded that “in the absence of any indica-

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Biographical Memoirs tion as to its (the annual term's) origin, it may be attributed to instrumental causes, or to terrestrial ones.” Chandler did not refer to Gould's results in defending the reality of the annual component in the variation of latitude. Rather, he argued that it was highly unlikely that seasonal variations in temperature would affect the measurements from observatories located at nearly equal latitudes but widely differing longitudes, in just such a way as to yield a consistent phase for the annual term. And, since such was the case for several observatories located in the northern hemisphere, “We may dismiss forever the bugbear which undoubtedly led many to distrust the reality of the annual component . . .” (Chandler, 1893). SECULAR MOTION OF THE POLE During the very same period that Chandler was doing the laborious computations required for him to formulate his two-component model of polar motion, and to use the model to correct historical observations (a subject to which we will return later), he also became embroiled in an argument with George C. Comstock concerning the latter's claim to have detected a secular drift of the pole (Comstock, 1892). There is not space to go into the details here, but Chandler showed that the rather large secular motion suggested by Comstock, 0.044 seconds of arc per year, was simply not supported by existent observations. He concluded that any secular motion must indeed be no larger than about one-tenth of that amount. The best estimate of the secular motion today, based on more than eighty years of observations made by the International Latitude Service, is about 0.003 seconds of arc per year in a direction roughly 130 degrees different from Comstock 's model, but consistent with Chandler's bound.

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Biographical Memoirs 1881 Comet Pechule, 1880. Science Observer 3(6):45-46. Prof. Pickering, on the variable stars of short period. Science Observer 3(7):54-55. On the telegraphic transmission of astronomical data. Science Observer 3(9-10):65-77. Elliptic elements of Comet (f), 1881-Denning. Science Observer 3(11):91. On a new variable star in the constellation Cetus. Science Observer 3(12):105-6. Elemente des Cometen b 1881. Astronomische Nachrichten 100(2384):121 Elemente und ephemeride des Cometen e 1881. Astronomische Nachrichten 100(2396):320. On the periodicity of Comet (Denning) 1881 V. 101(2406):93. 1882 Sawyer's variable. Science Observer 4(1-2):11. On some suspected variable stars. Science Observer 4(7-8):60-62. Notes on some recently discovered variable stars. Science Observer 4(11):88. On the variability of DM. +23 1599. Astronomische Nachrichten 102(2433):139. On the period of R Hydrae. Astronomische Nachrichten 103(2463):225-34. 1883 Elemente des Cometen 1883 Brooks-Swift. Astronomische Nachrichten 105(2504):127. On the variability of 36 (Uran. Argentina) Ceti. Astronomische Nachrichten 105(2517):333-36. On the outburst in the light of the Comet Pons-Brooks Sept 21-23. Astronomische Nachrichten 107(2553):131. On the possible connection of the Comet Pons-Brooks with a meteor stream. Astronomische Nachrichten 107(2561):275. Results of tests with the “almucantar” in time and latitude. The Sidereal Messenger 2(9):269-74.

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Biographical Memoirs 1884 Elemente und ephemeride des Cometen 1884 II. Astronomische Nachrichten 109(2606):223. Elements of Comet 1884 Wolf. Astronomische Nachrichten 110(2625):143. On a convenient formula for differential refraction in ring-micrometer observations. Astronomische Nachrichten 110(2628):177-80. 1885 Dr. Gould's star in sculptor. Astronomische Nachrichten 111(2661):333. On the latitude of Harvard College Observatory. Astronomische Nachrichten 112(2672):113-20. On the right ascensions of certain fundamental stars. Astronomische Nachrichten 112(2687):381-88. Berichtigung zu on the right ascensions of certain fundamental stars in nr. 2687. Astronomische Nachrichten 113(2690):17. 1886 On the light-variations of Sawyer's variable in Vulpecula. Astronomical Journal 7(145):1-3. Elements and ephemeris of the Comet 1886 f (Barnard, Oct. 4). Astronomical Journal 7(147):23. Elements and ephemeris of the Comet 1886 f (Barnard, Oct. 4) (continued from number 147). Astronomical Journal 7(148):30. On a new short-period variable in Cygnus. Astronomical Journal 7(148):32. On a new variable of the Algol type. Astronomical Journal 7(149):40. On the new Algol-variable in Cygnus. Astronomical Journal 7(150):47-48. On the light-ratio unit of stellar magnitudes. Astronomische Nachrichten 115(2746):145-54. On the variable 10 Sagittae 19h49m25 + 16 15'4 (1855). Astronomische Nachrichten 115(2749):217-20. 1887 Note on an inaccuracy in the development of a differential refraction formula. Astronomical Journal 7(151):53. Notes on some places of Auwer's fundamental catalogue. Astronomical Journal 7(155):81-83. On the orbit of the Great Southern Comet 1887 a. Astronomical Journal 7(156):92-95.

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Biographical Memoirs On the orbit of the Great Southern Comet 1887 a. Astronomical Journal 7(157):100. Elements and ephemeris of Comet 1887 e (Barnard, May 12). Astronomical Journal 7(157):104. Improved elements and ephemeris of Comet 1887 e. Astronomical Journal 7(160):121-22. Investigation of the light-variations of U Ophiuchi. Astronomical Journal 7(161):129-33. Investigation of the light-variations of U Ophiuchi. Astronomical Journal 7(162):137-40. Ephemeris for minima of the two new Algol-variables. Astronomical Journal 7(162):144. On the two new Algol-type variables Y Cygni and R Canis Majoris. Astronomical Journal 7(163):150-51. Ring-micrometer observations of Comet e 1887. Astronomical Journal 7(163):152. Observations of X Cygni. Astronomical Journal 7(164):159-60. The almucantar. In : Annals of the Astronomical Observatory of Harvard College, vol. 17. ( Cambridge, Massachusetts: University Press, John Wilson and Sons ) : 222. 1888 On the period of Algol. Astronomical Journal 7(165):165-68. On the period of Algol (continued). Astronomical Journal 7(166):169-75. On the period of Algol (continued). Astronomical Journal 7(167):177-83. On the observation of the variables of the Algol-type. Astronomical Journal 7(168):187-89. On a new variable of long period. Astronomical Journal 8(171):24. Ephemeris of variables of the Algol-type. Astronomical Journal 8(173):40. Ephemeris of variables of the Algol-type. Astronomical Journal 8(182):107-8. Ephemeris of variables of the Algol-type. Astronomical Journal 8(188):159. Catalogue of variable stars. Astronomical Journal 8(179-80):81-92. On the observation of the Fainter Minima of the telescopic variables Astronomical Journal 8(183):114-17. On some remarkable anomalies in the period of Y Cigni. Astronomical Journal 8(185):130-32.

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Biographical Memoirs On the square bar micrometer. Memoirs of the American Academy of Arts and Sciences, Vol. XI. Cambridge: University Press John Wilson and Sons. On the colors of the variable stars. Astronomical Journal 8(186):137-40. 1889 Note on the equation of the meridian transit instrument. Astronomical Journal 8(187):147. Contributions to the knowledge of the inequalities in the periods of the variable stars. Astronomical Journal 8(189):161-66. Contributions to the knowledge of the inequalities in the periods of the variable stars. Astronomical Journal 8(190):172-75. On the general relations of variable star phenomena. Astronomical Journal 9(193):1-5. On the light-variations of U Cephei. Astronomical Journal 9(199):49-53. Note on the variable Y Cigni. Astronomical Journal 9(204):92-93. On the period of U Coranae. Astronomical Journal 9(205):97-99. On the action of Jupiter in 1886 upon Comet d 1889 and the identity of the latter with Lexell's Comet of 1770. Astronomical Journal 9(205):100-103. Elements of Comet 1889 (Brooks, July 6). Astronomische Nachrichten 123(2935):111. 1890 Contributions to the knowledge of the inequalities in the periods of the variable stars. Astronomical Journal 9(208):126. Supplement to first edition of the catalogue of variable stars. Astronomical Journal 9(216):185-87. Elements of Paul's Algol-type variable, S Antliae. Astronomical Journal 9(216):190-91. Ephemeris of S Antliae. Astronomical Journal 10:10. Contributions to the knowledge of the inequalities in the period of the variable stars. Astronomical Journal 10(229):103. On the present aspect of the problems concerning Lexell's Comet. Astronomical Journal 10(231):118-20. On Jupiter's perturbation of Comet 1889 V in 1922. Astronomical Journal 10(232):124-25.

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Biographical Memoirs On the period of 2100 U Orionis. Astronomical Journal 10(233):133. Address before the Section of Mathematics and Astronomy, Indianapolis meeting, American Association for the Advancement of Science, August 1890. Proceedings of the American Association for the Advancement of Science , vol. 39. 1891 Definitive orbits of the companions of Comet 1889 V. Astronomical Journal 10(236):153-59. Definitive orbits of the companions of Comet 1889 V. Astronomical Journal 10(237):161-63. On the orbit of Comet 1887 IV. Astronomical Journal 10(237):166-67. On the rigorous computation of differential refraction. Astronomical Journal 10(239):181-82. Contributions to the knowledge of the inequalities in the periods of the variable stars. Astronomical Journal 11(242):14-15. On the variation of latitude, I. Astronomical Journal 11(248):59-61. On the variation of latitude, II. Astronomical Journal 11(249):63-70. On the variation of latitude, III. Astronomical Journal 11(250):75-79. On the variation of latitude, IV. Astronomical Journal 11(251):83-86. 1892 On the supposed secular variation of latitudes. Astronomical Journal 11(254):107-9. Contributions to the knowledge of the variable stars. Astronomical Journal 11(255):113-16. Contributions to the knowledge of the variable stars. Astronomical Journal 11(256):121-26. Note on secular variation of latitude. Astronomical Journal 11(257):134-35. On the Washington prime-vertical observations. Astronomical Journal 11(262):174-75. On the variation of latitude, V. Astronomical Journal 12(267):17-22. On the variation of latitude, VI. Astronomical Journal 12(272):57-62. On the variation of latitude, VI (continued). Astronomical Journal 12(273):65-72. On the variation of latitude, VII. Astronomical Journal 12(277):97-101.

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Biographical Memoirs A device for eliminating refraction in micrometric or photographic measures. Astronomical Journal 12(271):51-52. Sweeping ephemeris for bodies moving in the Biela-orbit. Astronomical Journal 12(281):133-34. 1893 On the influence of latitude-variations upon astronomical constants and measurements. Astronomical Journal 12(284):153-55. On the constant of aberration. Astronomical Journal 12(287):177-79. On the nomenclature of recently discovered variables. Astronomical Journal 13(290):12-13. On the constant of aberration, II. Astronomical Journal 13(293):33-36. Contributions to the knowledge of the variable stars VII. Astronomical Journal 12(294):45-47. On the constant of aberration, III. Astronomical Journal 13(296):57-61. Systematic correction of the declinations of the fundamental catalog for variations of latitude. Astronomical Journal 12(296):63-64. On the constant of aberration, IV. Astronomical Journal 13(297):65-70. On the constant of aberration, V. Astronomical Journal 13(298):76-79. Second catalog of variable stars. Astronomical Journal 13(300):89-110. On the variation of latitude, VIII. Astronomical Journal 13(307):159-62. Ephemerides of long-period variables for 1894. Astronomical Journal 13(308):172-73. On the nomenclature of recently discovered variables. Astronomische Nachrichten 132(3161):283-86. 1894 On the observations of variable stars with the meridian-photometer of the Harvard College Observatory. Astronomische Nachrichten 134(3214):355-60. On the Harvard photometric observations. Astronomische Nachrichten 136(3246):85-90. Schreiben von Herrn S. C. Chandler an Prof. H. Kreutz Betr. Z Herculis. Astronomische Nachrichten 136(3260):331-33.

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Biographical Memoirs On Pond's double-altitude observations, 1825-35. Astronomical Journal 14(313):1-6. Note on Nyren's vertical-circle observations, 1882-91. Astronomical Journal 14(314):13-14. On Pond's double-altitude observations, 1825-1835. Astronomical Journal 14(315):17-20. Supplement to second catalogue of variable stars. Astronomical Journal 14(319):51-53. Variation of latitude from the Greenwich mural-circle observations, 1836-51. Astronomical Journal 14(320):57-60. On the inequalities in the coefficients of the law of latitude-variation Astronomical Journal 14(322):73-75. On some further characteristics of the polar rotation. Astronomical Journal 14(323):82-84. Ephemerides of long-period variables for 1895. Astronomical Journal 14(327):118-19. On a new variable of the Algol-type, 6442 Z Herculis. Astronomical Journal 14(328):125 Further proof of eccentricity in the annual component of the polar motion. Astronomical Journal 14(329):129-32. On a new variable of short period. Astronomical Journal 14(329):135. Elements of the polar motion from all published observations from 1889.0-1894.5. Astronomical Journal 14(330):141-43. The variation of terrestrial latitudes. Publications of the Astronomical Society of the Pacific 6:180-82. 1895 On the parallax of B Cassiopeae. Astronomical Journal 14(333):163. Orbit of Comet e 1894. Astronomical Journal 14(333):167-68. Note on the investigations of Gonnessiat upon the variations of latitude observed at Lyons. Astronomical Journal 14(334):174. Improved elements of Comet e 1894 IV. Astronomical Journal 15(338):10. On Comet e 1894 and its identity with DeVico's (1814 I). Astronomical Journal 15(338):13-15. On the annual term of the latitude-variation from the Lyons observations Astronomical Journal 15(344):60-61. Revised supplement to second catalogue of variable stars. Astronomical Journal 15(347):81-85. The latitude-variation tide. Astronomical Journal 15(351):127-28.

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Biographical Memoirs On a new variable of peculiar character, 8598 U Pegasi. Astronomical Journal 15(358):181. Assignment of notation for recently discovered variables. Astronomical Journal 15(358):184. Tables of the trajectory of the pole, for computing variations of latitude. Astronomical Journal 15(360):193-96. On a new determination of the constant of nutation. Astronomical Journal 16(361):1-6. 1896 On standard systems of declination and proper motion. Astronomical Journal 16(364):28-29. Elements and ephemeris of Comet a 1896. Astronomical Journal 16:56-72. Notation of recently discovered variables. Astronomical Journal 16(369):71-72. Elements of variation of 8598 U Pegasi. Astronomical Journal 16(374):107-8. Third catalogue of variable stars. Astronomical Journal 16(379):145-72. On the companions of the periodic Comet 1889 V. Astronomical Journal 17(385):1. Corrected ephemeris of the component C of the periodic Comet 1889 V. Astronomical Journal 17(386):14. Ephemeris of long-period variables for 1897. Astronomical Journal 17(387):17-20. 1897 Trajectory of the pole, for computing latitude-variations in 1897 Astronomical Journal 17(392):63. Notation of recently discovered variables. Astronomical Journal 17(392):64 Revised elements of 320 U Cephei. Astronomical Journal 17(396):94. On Nyren's vertical-circle observations, 1882-91. Astronomical Journal 17(400):125-27. Revised elements of 5190 R Camelopardalis. Astronomical Journal 17(400):128. Elements of the annual component of the polar motion from recent observations. Astronomical Journal 17(402):141-42.

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Biographical Memoirs Correction of the 336 Pulkowa Hauptsterne for latitude-variation. Astronomical Journal 17(402):143. Synthetical statement of the theory of the polar motion. Astronomical Journal 17(406):172-75. On the proposed unification of astronomical constants. Astronomical Journal 18(410):15-16. Note by the editor. Astronomical Journal 18(415):54. 1898 Ephemeris of long-period variables for 1898. Astronomical Journal 18(420):94-96. Elements and ephemeris of Comet a 1898. Astronomical Journal 18(424):127. Nature of the variation of U Pegasi. Astronomical Journal 18(426):140-41. Trajectory of the pole for computing latitude-variations in 1898. Astronomical Journal 18(426):144. The aberration-constant of the French conference. Astronomical Journal 18(427):149-52. Note by the editor. Astronomical Journal 18(429):165. Additional correction to Newcomb's aberration from Küstner's observations. Astronomical Journal 18(430):179. Determination of the aberration-constant from right-ascensions. Astronomical Journal 19(444):89-92. Comparison of the observed and predicted motions of the pole, 1890-1898, and determination of revised elements. Astronomical Journal 19(446):105-10. Elements and ephemeris of small planet DQ. Astronomical Journal 19(450):148. Elements and ephemeris of small planet DQ. Astronomical Journal 19(451):155. The small planet DQ at the opposition of 1893-4 and 1896. Astronomical Journal 19(452):160-62. The areal velocities in the annual component of the polar motion. Astronomical Journal 19(452):163-64. 1899 Aberration-constant from right-ascension observations. Astronomical Journal 20(462):46.

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Biographical Memoirs 1901 Changes in the annual elliptical component of the polar motion. Astronomical Journal 21(489):65-71. On a new component of the polar motion. Astronomical Journal 21(490):79-80. On the assignment of the nomenclature and the formation of a new catalogue of variable stars. Astronomical Journal 21(492):96. On a new component of the polar motion. Astronomical Journal 21(494):109-12. Definitive formulas for computing variations of latitude. Astronomical Journal 21(495):119. The period of Algol. Astronomical Journal 22(509):39-42. The Greenwich reflex zenith-tube. Astronomical Journal 22(511):57-60 The observations of Algol by Argelander, Schmidt, and Schonfeld. Astronomical Journal 22(511):60. Variation of latitude from Molyneux's and Bradley's observations. Astronomical Journal 22(513):71-75. 1902 Variation of latitude from Bessel's and Struve's observations. Astronomical Journal 22(515):89-91. Aberration-constant from Pond's observations, 1825-36. Astronomical Journal 22(515):91-92 The constant of aberration from the San Francisco and Waikiki observations of 1891-92. Astronomical Journal 22(517):105-6. The aberration-constant from Davidson's San Francisco and Waikiki observations. Astronomical Journal 22(519):124. Aberration-constant from Kasan, Prague, Potsdam and San Francisco observations. Astronomical Journal 22(520):128-31. Aberration-constant from Pond's observations of Polaris 1812-19. Astronomical Journal 22(520):131-33. New study of the polar motion for the interval 1890-1901. Astronomical Journal 22(522):145-48. On the possible existence of still another term of the polar motion Astronomical Journal 22(523):154. Note on Kimura's suggestions in A. J., 517. Astronomical Journal 22(524):164.

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Biographical Memoirs The probable value of the constant of aberration. Publications of the Astronomical and Astrophysical Society of America 1:192. 1903 The probable value of the constant of aberration. Astronomical Journal 23(529):1-5. Questions relating to stellar parallax aberration and Kimura's phenomenon. Astronomical Journal 23(530):12-15. Period of 320 U Cephei. Astronomical Journal 23(552):227-28. 1904 Revision of elements of third catalogue of variable stars. Astronomical Journal 24(553):1-7. Elements of 6189 U Ophiuchi. Astronomical Journal 24(559):63-64. Elements of 2610 R Canis Majoris. Astronomical Journal 24(559):64. Ephemerides of long-period variables 1903-1910. Astronomical Journal 24(560):65-73.