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PAUL HERGET January 3 0, 1 908August 2 7, 1 981 BY DONALD E. OSTERBROCK AND P. KENNETH SEIDELMANN YOUTH AND EDUCATION PA U ~ H E R G ET was born on January 30, ~ 908, in Cincin- nati, Ohio. He was to live, study, and clo research there nearly all his life; he was one of the most outstanding scien- tists ever procluced in that pleasant Midwestern city. His fa- ther, Conrad Frederick Herget, had emigrated from Ger- many to Cincinnati in 1893, at the age of eighteen just ahead of a summons to military cluty, according to Paul's memory. His mother, Clara Brueckner Herget, was born of immigrant parents in the oIc! "Over the Rhine" area of Cin- cinnati, just north of downtown. By the time Paul was born, his parents were living in Fairview, a district on the brow of one of the hills overlooking the central city ant! the Ohio River. When he was four, they mover! to Oakley, an eastern suburb of the city; they stayed there until his father died in 1938. Paul was christened, in the tradition of German Prot- estantism, as Paul Frederick Ernst Herget Frederick for his father, who was called Frecl, and Ernst for an uncle. But he droppecI the miciclle names as soon as he learned to read ant! write and always signed himself Paul Herget. He liked to assert that "he was his own person anct click not want the name of someone else tagging along with him." 59

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60 BIOGRAPHICAL MEMOIRS Paul's father Fred never went to school in America; he had to go right to work to support himself, first in a laundry, where he soon became a foreman, then in a machine-too! factory. Clara Herget finisher! two years of high school; she was a firm believer in education, anct she always encouraged her only son (Paul hac! two younger sisters) to go as far as he couIcI. Paul believed that the most influential factor in his childhood was his Erector set, which stimulated his geomet- rical thinking, mechanical abilities, and sense of order. He also benefited! from his Boy Scout experiences and from the mobility and skill with tools that came from owning a bicycle. Paul's mother supported him in everything he wanted to do, especially schoolwork; he remembered his father as a harsh taskmaster, a "typical German father," who often ctisciplinec! him. Paul resented it then, but in later life felt that it tract shaped his character. Paul went to Oakley Public School and then to Withrow High School. He was a good student in all subjects, especially in mathematics. In his last two years at Withrow he was greatly inspired by his mathematics teacher, Helen Swine- forct, whom he later considered the greatest single influence on his career. Paul worked in summer jobs at the machine too! factory with his father; after he gracluated from high school in 1926 he got a temporary position as a surveyor with the Cincinnati Gas and Electric Company. That fall he en- terect the University of Cincinnati as a civil engineering stu- clent. He had never considered going anywhere else; his fam- ily had little money, and he could not afford to go away from home to college. All the students in the Engineering College of the University of Cincinnati were automatically enrolled in a "co-operative program." The program alternated terms of going to school and working in industry; students earnest their tuition and living expenses at the same time they started

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PAUL HERGET 61 putting their engineering education to practical use. Civil en- gineering was at least close to mathematics, Paul thought. But after only a few weeks he realized that it was not close enough for him. He withdrew from the university and got a full-time job as a surveyor. By rigid economy, he was able to save a thousand clolIars in one year. That sum enabled him to enter the College of Liberal Arts in 1927 as a full-time mathematics student, as he hacl wanted to clo from the first. leaching was the only tuture he could envision In math- ematics; he took a minor in education so that he couIct get a high school teacher's certificate and follow in Helen Swine- forcl's path. He disliked and resented the education courses he tract to take, but he graduatect in 1931 the worst part of the Great Depression with an A.B. degree. Paul was offerect a job as an assistant at the Cincinnati Observatory, which paid $1,020 a year. To him the job was just like a "real good fel- lowship" that wouIc! pay his living expenses and allow him to continue his education as a part-time graduate student. He snapped it up. ~ . . . . . . . . . . . GRADUATE STUDIES The Cincinnati Observatory is the oldest astronomical re- search observatory west of the Alleghenies. It was founclect in 1843 by Ormsby McKnight Mitchel under the auspices of the Cincinnati Astronomical Society and was originally funded by small contributions from the general public. Its 12-inch refractor was a big telescope by the standarcls of the time. Former President John Quincy Aciams came west to speak at its dedication; later the observatory became part of the University of Cincinnati. By 1931 the 12-inch anc! the newer ~ 6-inch refractors were not significant research instru- ments, ant] the main program of the Cincinnati Observatory was the accurate mericlian-circle measurement of the posi-

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62 BIOGRAPHICAL MEMOIRS tions of stars in orcler to determine their proper motions. On the recommendation of his mathematics professors, Paul Herget was hires] as a computer to reduce these observations. Paul was always fascinated by computing. As an un(ler- graduate he was intrigued by the idea of numerically evalu- ating ~ to high precision. Using what he considered the best rapidly convergent series, he took a large sheet of wrapping paper, ant! with a react pencil as his only computational device calculated ~ to thirty-two decimal places. Years later he checked it he had kept a copy, as he did of most of his computations and fount! that he had gotten the first twenty-eight places correct. As a graduate student, after studying higher-orcler interpolation, he proclucect a two- page table that gave sines and cosines of any angle correct to eight decimal places. This was his first scientific publication. Working at the Cincinnati Observatory under ctirector Ev- erett I. Yowell and Elliott S. Smith, Paul still consiclerect him- self a mathematics graduate student. He took courses from Charles N. Moore and Harris Hancock, who had recom- mended him for the assistantship at the observatory. He was strongly influenced by Louis Branct, a younger mathematics professor, who emphasized the power of vectors to express complicates] formulae in simple terms. Herget was to use them extensively in all his work, and his book, The Computa- tion of Orbits, is written completely in terms of vectors. He always claimed that spherical trigonometry is not a subject but only two vector equations, the clot anct cross product, repeated over and over again. As Paul became more proficient in the reduction of the mericlian-circle observations, he fount! himself with spare time on his hands at the observatory. He began reading re- search publications, especially the Astronomical journal. He be- came interested in orbit theory and studied it on his own. As a result, by 1933, when he received his M.A. degree, he con-

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PAUL HERGET 63 siclerecl himself a student of astronomy rather than mathe- matics. Paul was almost completely self-taught in his new sub- ject, with practically no graduate courses ancT very little in the way of guidance, except on oIct-fashioned observational methods. He was especially attracted by the papers of Leslie }. Comrie, the leading exponent of punched-card machines in astronomy, who was revamping the work of the Nautical Almanac Office in Great Britain. There were no punched-card machines at the Cincinnati Observatory in the 1930s, but Paul became an expert com- puter, using the oIc! hand-operated, mechanical clesk calcu- lators. He die] his thesis on the computation of orbits almost entirely without advice or direction, and earner! his Ph.D. in 1935. Soon afterward he married Harriet Louise Smith, his high school classmate, longtime sweetheart, ant! the daughter of Elliot S. Smith, his superior at the Cincinnati Observatory. Paul then received an Alexander Morrison Fellowship and spent one year at the University of California as a post- cloctoral research associate. Armin O. Leuschner was the heat! of the Berkeley Astronomy Department ancI a very se- nior expert in orbit computation. As a young man he had developed "Leuschner's method" for calculating the orbit of a new comet, and Herget delighted in pointing out the situ- ations in which it failed in practice and in which his own method, basest on Gauss's original scheme, was better. Leuschner in the end told Herget that he was too opinion- atect ant! that he acted as if his name were "Herr Gott" Ethe Lorct God]. Nevertheless, Herget supremely self- confidentlearnect what he couIct from Leuschner and con- tinued to go his own way. At the end of his year in California, Paul nearly got a job as a lecturer at the Griffith Planetarium in Los Angeles, which wouIct have taken him out of research. Fortunately for as- tronomy, another candidate was juciged a better speaker.

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64 BIOGRAPHICAL MEMOIRS Paul, however, let the University of Cincinnati administration know that he was thinking of going elsewhere, and they promptly raised his salary to $T,650 a year to bring him home. MINOR PLANET CENTER After his return to Cincinnati in 1936, Paul undertook the project of determining the orbit of one of the minor plan- ets discovered by lames C. Watson. A pioneer American stu- dent of asteroids, Watson hacT left in his will an endowment funs] to support research on the ones he had found. Leusch- ner tract been directing work on them over the years. Aethra (132) the most ctifficult because it had the largest eccentric- ity was the one Herget tackled first. After he had com- pleted its orbit he continued to work on one minor planet at a time, in cooperation with Gustav Stracke at the Rechen Institut in Berlin. Herget was what the Germans called a Mit- arbeiter, or collaborator. After Florid War Il. the personnel of the Rechen Institut were split between the Russian and Western occupation zones. Dirk Brouwer, president of Commission 20 of the In- ternational Astronomical Union, was responsible for getting the minor planet work organized again. After discussions with H. Spencer tones, president of the International Astro- nomical Union, Brouwer asked Herget to operate a minor planet center. Paul was familiar with what was required from his previous activities, and he readily agreed. President Ray- moncl Walters of the University of Cincinnati supported his clecision. Herget then arranged for Eugene Rabe, one of the younger Rechen Institut members in the Western zone, to join him in Cincinnati. He also obtained an appointment at the Observatory for Peter Musen, who was a native of Yu- goslavia. They began their work by recording each minor planet

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PAUL HERGET 65 observation made after 1939 on a punched card so that all their computations couict be carried out on punched-caret equipment. To obtain observations of the minor planets, Herget loaned the 10-inch astrographic camera that the Uni- versity of Cincinnati owned to Frank Ecimondson at Indiana University. Ecimondson built a blink machine anct acquired a measuring engine so that he could provicle accurate mea- surements of asteroids upon request. This program proviclect the Inctiana students with a continuing project and a means of learning the processes of taking and measuring minor planet positional observations. From 1947 to 1978 Herget was director of the Minor Planet Center of the International Astronomical Union. During that period, 4,390 Minor Planet Circulars were pub- lished. The best computer or punched-caret equipment to which he tract access was used for the computations of the elements ancI ephemerides of the minor planets included in these circulars. U.S. NAVAL OBSERVATORY Recognizing that the astronomer Forest R. Moulton hacI contributed greatly to ballistic computations during WorIct War I, Herget sought to do the same during World War Il. He began by contacting government officials at the Ballistic Research Laboratory at Aberdeen Proving Grounds and at the Naval Weapons Center at DahIgren, Virginia. At DahI- gren he inquired about the Weapons Center's plans to use punched-caret equipment; he was toIct that punch carcis were used for preparing the payroll, "but they ain't no good" for calculations. So he figured "Boy, if you think they ain't no goocl, I'm not going to work for you." He went instead to Washington. There he joined Wallace I. Eckert at the Nauti- cal Almanac Office of the U.S. Naval Observatory from 1942 until after the war endect. Prior to Eckert's arrival in 1939,

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66 BIOGRAPHICAL MEMOIRS all calculations had been performed by hand on paper. He arranged for the acquisition of an IBM tabulator, summary punch, and sorter, which were used to prepare the Air Al- manac. Herget's job was to convert the preparation of parts of the American Ephemeris and Nautical Almanac by means of the punched-card equipment. During this period he also performed the computations for the "submarine book," a task that gave him the greatest satisfaction of his lifetime. In 1943 the losses of Allied con- voys had reached 30 percent. The German submarines would radio their headquarters when they sighted convoys. The Al- lies had 108 listening posts around the world that could pick up the directions of these radio signals. With tabulated so- lutions of about a quarter of a million spherical triangles, these observations were used to pinpoint the locations of the submarines to within five miles. Destroyers could then use sonar equipment to locate them and drop depth charges. Herget and Eckert did all the necessary calculations within three months, working only at night because the punched- card machines were in use all day on the Air Almanac and Nautical Almanac. Once the submarine book had been printed and put into use, Allied losses went down to about 6 percent. After returning to the University of Cincinnati in 1946, Her- get continued to maintain a close working relationship with the Naval Observatory. His research results "Rectangular Coordinates of Ceres, PalIas, Juno, and Vesta," "The Solar Coordinates, 1800-2000," and the "Coordinates of Venus, ~ 800-2000"were all published in the Astronomical Papers of the American Ephemeris. COMPUTER APPElCATIONS In 1928 Ernest W. Brown, the eminent celestial mechan- ician and author of Lunar Theory anc! Tables of the Moon, visited Europe. He saw that Leslie I. Comrie was using punch cards

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PAUL HERGET 67 to compute the lunar ephemeris and proceeded to support Eckert's acquisition of punched-card equipment. Herget rec- ognized the advantages of such equipment and followed Eckert's leadership. From ~ 947 to ~ 95 ~ the Cincinnati Obser- vatory had an IBM tabulator, multiplier, sorter, and repro- ducer; after ~ 95 ~ Herget used computing equipment when it was availableat the Procter & Gamble Company, the Gen- eral Electric Company, and the Cincinnati Gas & Electric Company. He worked with the computers only when com- pany employees were not using them usually at night or on weekends. He would also exchange computer time for lec- tures to the employees or technical advice on their problems. As a result of such cooperation, the Cincinnati Gas & Electric Company still uses the Julian Day Number system in prepar- ing its bills. Over the years Herget used many different models of tab- ulating equipment and computers, progressing from the multiplier through the IBM 603, 650, 1620, Naval Ordnance Research Calculator (NORC), and 360. The NORC was his favorite machine, "the greatest love of my life, after my wife and daughter." Herget found that by spending two weeks at the NORC he could get a full year's work done. Throughout his career the common thread was the application of com- puter technology to real problems. It was in this area that he advised the Air Force Mapping and Charting Laboratory and also maintained the Cancer Registry at the University of Cin- cinnati. But it also led to a number of larger projects. In 1944 and 1945 Herget was a consultant for the Manhattan Project at Oak Ridge, Tennessee. And from 1951 to 1957 he was a consultant for the Project Atlas Intercontinental Ballistic Mis- sile effort at Convair. In this effort he formulated the system for computing the ballistic trajectory for the missiles, includ- ing all the known effects that would perturb the trajectories. In 1955 President Dwight D. Eisenhower announced that

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68 BIOGRAPHICAL MEMOIRS America wouIcl have a space program. Following that an- nouncement, each of the organizations that wanted to set up and operate the satellite computing program contacted Her- get. He reasoned that only one of them was going to win, anct agreed that he would participate in the proposals from Univac, the Army Map Service, and the Naval Research Lab- oratory. That way no matter who manage(1 the program, he wouIc! be on the team. In 1959 he spent a week with IBM writing their proposal for the Mercury Project. After IBM got the contract, he set up the computer program for calcu- lating the orbits for Mercury launches. THE CINCINNATI OBSERVATORY The research of Paul Herget centered around orbit com- putations anct the use of computer programs. Early in his work he realized that the site of the Cincinnati Observatory was not ideal for observations because it was surrounclecl by a large inclustrial city. Therefore he entered into cooperative activities with Indiana University so that the required observ- ing could be clone there. He strongly supported public use of the Cincinnati Observatory; amateur astronomers came to the observatory to make mirrors, and public tours were held on a regular basis. The observatory library and punchecl-card files were well kept up, but the telescopes were maintained only to satisfy the public tour requirements. Most of the ef- fort of the personnel at the Cincinnati Observatory was di- rectec! toward! the Minor Planet Center anct related research. Herget responclect to eclucational requirements in a manner consistent with his own background anct philosophy. An outstanding research professor, Herget enjoyed the confidence and support of University of Cincinnati presi- clents Raymond Walters and Walter C. Langsam. Paul always financed his research chiefly from outside sources. His well- timed news releases and newspaper stories, his outgoing per-

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PAUL HERGET BIBLIOGRAPHY 1933 77 A table of sines and cosines of eight decimal places. Astron. I., 42: 123-25. Note on table of sines and cosines. Astron. I., 42: 196. Elements of the orbit of comet 1932c Carrasco. Astron. T., 43:39. 1934 Elements comet 1932c Carrasco. Astron. l., 43:128. A note on the computation of orbits. Astron. Nachr., 251 :53-54. 1935 Comets 1931 V Carrasco elements. Iberica (Barcelona), 21 no. 1037, suppl. 18. The determination of orbits. Astron. i., 44:153-61. Elements of Hubble Object = 1935 QN. Harv. Coll. Obs. Circ.348 and 351. (Also in: U.A.I. Circulaire 557; Nature, 6:110.) Ephemerides of Hubble Object = 1935 QN. Harv. Coll. Obs. Circ. 348, 349, 351, and 354. (Also in: Planetenzirkulare nos. 1246 and 1274.) 1936 Elements and ephemeris of Peltier's comet. Harv. Coll. Obs. Circ. 378. With D. Davis. New Delporte object. Publ. Astron. Soc. Pac., 48: 104-6. A method for determining preliminary orbits adopted to machine computation. Publ. Cincinnati Obs., 21: 1-9. Improved orbit of Biarmia (1146~. Publ. Cincinnati Obs., 21 (un- numbered). Tables for true anomaly and perihelion passage in nearly parabolic orbits. Publ. Cincinnati Obs., 21:9-11. 1937 With S. Arend. Elements and ephemeris of minor planet 1935 OA ~ ~ 1361 ~ Leuschneria). Astron. J., 45: 126 -28.

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78 BIOGRAPHICAL MEMOIRS 1938 Elements of~upiter X. Harv. Coll. Obs. Circ. 457. Elements and ephemeris of~upiter XI. Harv. Coll. Obs. Circ. 461 and 463. Elements of~upiter X and XI. Harv. Coll. Obs. Circ. 464. Elements of Jupiter XXI. Pop. Astron., 46:509-11. Elements (1285) Julietta, (1286) Banachiewicza, and (1287) Lorcia. Astron. I., 46:39. Elements and ephemeris of (657) Gunlod = 1936 YI. Astron. I., 46:156. Elements and approximate perturbations offll 75) Margo. Astron. Nachr., 265:369-72. 1939 Elements and ephemeris of Cosik-Peltier comet. Harv. Coll. Obs. Circ. 470 and 471. Elements and ephemeris of comet Vaisala. Harv. Coll. Obs. Circ. 477. Ephemeris of~upiter XI. Harv. Coll. Obs. Circ. 491. Ephemeris ofTupiter X. Harv. Coll. Obs. Circ. 493. The orbit and perturbations of (132) Aethra. Astron. I., 47: 17-23. Filaments and general perturbations of (1274) Delportia. Astron. _ ~ J., 47:122-24. Planetary motions and Lambert's theorem. Pop. Astron., 47:310- 14. The differential correction of orbits. Astron. I., 48: 105-8. Indeterminate cases in the Laplacian orbit method. Astron. I., 48: 122-24. Orbits of the new satellites of Jupiter. Publ. Am. Astron. Soc., 9:156-57. Ephemeris of comet 1939b Vaisala. Pop. Astron., 47:282. Elements and approximate perturbations of (300) Geraldina. As- tron. Nachr., 267:1-4. On the group theory of general perturbations. Publ. Am. Astron. Soc., 9:261. 1940 Ephemeris of~upiter X and XI. Harv. Coll. Obs. Circ. 523.

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PAUL HERGET 79 1941 Ephemeris of Jupiter X. Harv. Coll. Obs. Circ. 591. Ephemeris of Jupiter XI. Harv. Coll. Obs. Circ. 592. With J. E. Kline. On the accuracy of first order general perturba- tions. Astron. I., 49: 121-24. Ephemeris of Jupiter XI. Harv. Coll. Obs. Circ. 592. (Also in: U.A.I. Circ. 885; Beobachtungzirkular der Astron. Nachr., 23:119.) Elemente von kleinen Planeten. Astron. Nachr., 272:82. 1942 Ephemeris of Jupiter X and XI. Harv. Coll. Obs. Circ. 620. The orbit of Jupiter XI. Publ. Am. Astron. Soc., 10: 164. The accuracy of approximate general perturbations. Publ. Am. As- tron. Soc., 10:225. 1943 Ephemeris of comet Oterma II. Harv. Coll. Obs. Circ. 642, 643, 649, and 654. Ephemeris of comet Schwassmann-Wachmann 1925 II. Harv. Coll. Obs. Circ. 658, 683, and 716. 1944 Ephemeris of comet 1944b Vaisala. Harv. Coll. Obs. Circ. 684. Ephemeris of comet Oterma (1943A). Harv. Coll. Obs. Circ. 687 and 741. Elements of comet Oterma (1943A). Harv. Coll. Obs. Circ. 698. Elements and ephemeris of comet Vaisala (1944A). Harv. Coll. Obs. Circ. 695. Ephemeris of comet Vaisala (1944B). Harv. Coll. Obs. Circ. 702 and 722. Search ephemeris for Adonis. Astron. l., 50:68. Elements and approximate perturbations of (657) Gunlod. Astron. J., 50:69-70. Positions of asteroids. Astron. I., 50:71. With G. M. Clemence. Optimum-interval punched-card tables. Mathematical tables and other aids to computation. Math. Tables Aids Comput., 1: 173-76.

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80 BIOGRAPHICAL MEMOIRS With G. M. Clemence. Editorial changes in scientific papers. Sci- ence, 99:241. Multiplication of Fourier series. Astron. J., 51:20. Comet 1943b 0terma = 1942 VII. Harv. Coll. Obs. Circ. 741. (Also in: U.A.I. Circ. 1036.) 1946 Catalogue of 2300 stars for the equinox 1925.0. Publ. Cincinnati Obs., 22. Numerical integration with punched cards. Astron. I., 52:115-17. The orbits of comet 1925 II (Schwassmann-Wachmann) and comet 1943a (Oterma). Astron. I., 52:124. 1947 Comet Schwassmann-Wachmann 1925 II ephemeris. Harv. Coll. Obs. Circ. 777. Comet Schwassmann-Wachmannfl), 1925 II. Br. Astron. Assoc. Handb. 1948 :48-49. Comet Oterma (1943A) ephemeris. Harv. Coll. Obs. Circ. 812. Comet Oterma 1942 VII (= 1943a). Br. Astron. Assoc. Handb. 1948:49-50. A device in satellite perturbation computations. Astron. i., 52: 177- 78. Approximate general perturbations of (1361) Leuschneria. As- tron. J., 52: 198 - 200. On the higher order effects of a differential rotation. Astron. I., 53: 15-16. Elements and ephemeris of comet Schwassmann-Wachmann 1925 II. Astron. J., 53:16-17. The orbit of comet 1943a (Oterma). Astron. I., 53:18-21. 1948 Ephemeris of Otermascher comet (1942 VII). Br. Astron. Assoc. Handb. 1948. (Also in: Int. Astron. Union Circ. 1162.) The Computations of Orbits. Ann Arbor, Mich.: Edwards Brothers, Inc., Press. ix + 177 pp. Ephemeris of erster Schwassmann-Wachmann comet (1941 VI). Br. Astron. Assoc. Handb. 1949. (Also in: Nachrichtenblatt As-

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PAUL HERGET 81 bon. Zentralstells 2, 26, and 32; Int. Astron. Union Circ. 1183 and 1193.) Comet Oterma, 1942 VII (= 1943a). Br. Astron. Assoc. Handb. 1949:56-57. 1949 Ephemeris of erster Schwassmann-Wachmann (1941 VI). Nach- richtenblatt Astron. Zentralstells 3 and 25. (Also in: U.A.I. Circ. 1228; Astr. Circ. UDSSR, 82:7; Astr. Circ. UDSSR, 90/91:13.) With G. M. Clemence and Hans G. Hertz. Rectangular coordinates of Ceres, Pallas, Juno, Vesta 1920 - 1960. Astron. Pap. Am. Eph. 11, part 4. Washington, D.C.: U.S. Government Printing Office. 67 pp. 1950 Reports on the progress of astronomy. Minor planets. Mon. Not. R.Astron.Soc.,110:167 - 69. Solutions of the wave equation. In: Proceedings Seminar on Scien- tiic Computation, Nov. 1949, pp. 79-86. New York: International Business Machines Corporation. Current minor planet problems. Astron. i., 55:165. 1951 Notes on magnitude. Minor Planet Circ. 603. Reports on the progress of astronomy. Minor planets. Mon. Not. R. Astron. Soc., 111: 232 - 33. The constructions of tables. In: ProceedingsComputation Seminar, Dec. 1949, pp. 62-66. New York: International Business Ma- chines Corporation. Coordinates of the Sun. Astron. I., 56: 128. 1952 Reports on the progress of astronomy. Minor planets. Mon. Not. R. Astron. Soc., 112:332. Methods for minor planet perturbations. Astron. J., 57: 13. 1954 Reports on the progress of astronomy. Minor planets. Mon. Not. R. Astron. Soc., 114:358.

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82 BIOGRAPHICAL MEMOIRS 1955 Solar coordinates, 1800-2000. Astron. Pap. Am. Eph. 14. xi + 735 PP Coordinates of Venus, 1800-2000. Astron. Pap. Am. Eph. 15, part 3.x + 523 pp. 1956 Reports on the progress of astronomy. Minor planets. Mon. Not. R. Astron. Soc., 116:218. Resume of minor planet perturbation computations at the Cincin- nati Observatory. Minor Planet Circ. 1423-31. The computation of minor planet perturbations. Minor Planet Circ. 1504-6. 1957 With G. M. Clemence and R. L. Duncombe. Ephemeris of satellite 1957 A 2. Int. Astron. Union Circ. 1626. With G. M. Clemence and R. L. Duncombe. Satellite 1957 A 2 ephemeris. Harv. Coll. Obs. Circ. 1380. The return of comet Pons-Brooks 1884 I. Astron. I., 57: 160. 1958 The computation of minor planet perturbations. Minor Planet Circ. 1695. With P. Musen. A modified Hansen lunar theory for artificial sat- ellites. Astron. i., 63:430-33. Opposition dates for new minor planets. Sonderdruck Real Acad. Ciencias Artes Barcelona, 1957. With R. L. Duncombe. Elements of satellite 1958A. Int. Astron. Union Circ. 1640. With R. L. Duncombe. Satellite 1958 A elements. Harv. Coll. Obs. Circ. 1393. 1959 With P. Musen. The calculation of literal expansions. Astron. J., 64:11-20. Partial astronomical refraction. Astron. I., 64:334-35. General theory of oblateness perturbations. In: Proc. Symposium Ap- plied Math., 9:29-35.

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PAUL HERGET 83 With P. Musen. Erratum: A modified Hansen lunar theory for ar- tificial satellites. Astron. J., 64:73. 1960 The elements and ephemeris of comet Wirtanen 1948b. Astron. i., 65:385-86. Parabolic orbit calculations on the IBM 650. Astron. T., 65:491-92. 1961 The orbit of comet Schwassmann-Wachmann 1. Astron. }.,66:266- 71. Keeping track of the minor planets. I.C.S.U. Rev., 3: 125-29. 1962 On the variation of arbitrary vectorial constants. Astron. J., 67: 16- 18. 1963 With C. Bardwell. Potter object = 1963A. Harv. Coll. Obs. Circ. 1629. Rectangular coordinates of Ceres, Pallas, Juno, Vesta, 1960-1980. Astron. Pap. Am. Eph., 16:341-95. 1965 Computation of orbits. Astron. I., 70: 1-3. 1966 The Minor Planet Center at the Cincinnati Observatory. Bull. Cin- cinnati Hist. Soc., 24: 175-87. With C. I. Van Houten and I. Van Houten-Groeneveld. Periodic comet Van Houten. Int. Astron. Union Circ. 1973. With F. Barlein, S. Lauret, C. Bertaud, I. Verdier, A. D. Andrews, S. J. Arend, and L. E. Cunningham. Andrews object. Int. As- tron. Union Circ. 1900. 1967 Revised plate constants for the Bordeaux astrographic zone. As- tron.J.,72:575 - 81.

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84 BIOGRAPHICAL MEMOIRS 1968 Ephemerides of comet Schwassmann-Wachmann 1 and the outer satellite of Jupiter with text. Publ. Cincinnati Obs., 23:1-62. The outer satellites of Jupiter. Astron. i., 73:737-42. Revised orbit of comet Schwassmann-Wachmann 1. Astron. I., 73:729-30. 1969 Index to minor planet elements. Minor Planet Circ. 3001-3007 . 1970 With C. }. Van Houten, I. P. Van Houten-Groeneveld, and T. Geh- rels. The Palomar-Leiden survey of faint minor planets. Astron. Astrophys., Suppl. Ser., 2:339-448. The physical distortion of Schmidt Plates. In: I.A. U. Colloquium No. 7: Proper Motions, ed. W. J. Luyten, p. 93. Minneapolis: Univer- sity of Minnesota. The solution of overlapping plates by iteration. In: I.A.U. Collo- quium No. 7: Proper Motions, ed. W. J. Luyten, pp. 94-95. Min- neapolis: University of Minnesota. With H. l. Carr. The probable error of mass determination. Bull. Am. Astron. Soc., 2:245-46. Minor planet circulars. Cincinnati Obs. 3023-3126. Comet 1957 I. Schwassmann-Wachmann 1. Int. Astron. Union Circ. 2295. 1971 The work at the Minor Planet Center. In: Physical Studies of Minor Planets, NASA SP-267, ed. T. Gehrels, pp. 9-12. Washington, D.C.: NASA SP-267. Seth Barnes Nicholson. In: Biographical Memoirs of the National Academy of Sciences, vol. 42, pp. 201-27. Washington, D.C.: The National Academy of Sciences. An analysis of the AGK3 companion star positions. In: Conference on Photographic Astrometric Technique, ed. H. Eichhorn, pp. 169- 71. Washington, D.C.: NASA CR-1825. 1972 On the differential correction of nearly parabolic orbits. In: The Motion, Evolution of Orbits, and Origin of Comets, ed. G. Chebo-

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