SKY DIAGRAMS 1945 UNITED STATES NAVAL OBSERVATORY WASHINGTON D. C. DE12’48 SKY DIAGRAMS 1945 ♦ ISSUED BY THE NAUTICAL ALMANAC OFFICE UNITED STATES NAVAL OBSERVATORY UNDER THE AUTHORITY OF THE SECRETARY OF THE NAVY ‘J LIBRARY of Seventh day Adventist THEOLOGICAL SEMINARY TAKOMARARK WAS M , NGTON ,D r- From the Library of GRACE EDITH AMADON PRESENTED IN RECOGNITION OF HER DEVOTION TO BIBLICAL STUDY AND RESEARCH BY HER NEPHEWS Harry, Edwin, Walter, and William Gage THE LIBRARY S.D.A. Theological Seminary Takoma Park Washington 12, D.C, UNITED STATES GOVERNMENT PRINTING OFFICE WASHINGTON : 1944 For sale by the Superintendent of Documents, U. S. Government Printing Office Washington 25, D. C. • Price 15 cents mrz U. S. NAVAL OBSERVATORY Commodore J. F. Hellweg, U. S. N., Retired, Superintendent ASTRONOMICAL COUNCIL Commodore J. F. Hellweg, U. S. N., Retired...................... Superintendent Captain V. K. Coman, U. S. N., Retired..................Assistant Superintendent W. J. Eckert.................................................. Head Astronomer H. R. Morgan.............................................Principal Astronomer H. E. Burton..............................................Principal Astronomer C. B. W atts...............................................Principal Astronomer Paul Sollenberger........................................Principal Astronomer G. M. Clemence.............................................Principal Astronomer NAUTICAL ALMANAC OFFICE W. J. Eckert, Director G. M. Clemence, Assistant Director..........................Principal Astronomer Paul Herget................................................... Senior Astronomer Isabel M. Lewis........................................................Astronomer Glen H. Draper.........................................................Astronomer Ralph F. Haupt.........................................................Astronomer Charlotte Krampe............................................Associate Astronomer Jules A. Larrivee...........................................Associate Astronomer Jack Belzer.................................................Assistant Astronomer Blanche R. White............................................Assistant Astronomer Raymond H. Wilson, Jr.1....................................... Junior Astronomer Tec la Combariati Smith.....................................................Junior Astronomer Hans G. Hertz...............................................................Junior Astronomer George R. Schaefer..........................................................Junior Astronomer Nettie Rotunno.................................................Assistant Operator Martha P. Hasenstab............................................Assistant Operator Theresa E. Cooney, Sic, U. S. N. R. (JU.)......................Assistant Operator Lillian E. Strong...........................................................Junior Operator Barbara D. Scott............................................................Junior Operator 1 Absent in military service. PREFACE In 1943 it occurred to the Director of the Nautical Almanac Office that navigators might welcome a means of selecting celestial objects for navigation and of identifying them in the sky more readily than was possible by existing methods. Star finders in common use have serious scale distortion; they require setting; and do not show the Moon and planets. It was thought that a series of circular diagrams, showing the principal navigational objects on an azimuthal equidistant projection with center at the zenith, for different hours of the night and for different latitudes, might be useful. Accordingly, sets of experimental Sky Diagrams were prepared and circulated to naval activities during 1944. With the second set of diagrams there was circulated a questionnaire designed to ascertain their practical value. To date (September 1, 1944), replies have been received from 689 ships, of which all but 20 are favorable. Replies from aircraft employing celestial navigation are equally favorable. In consequence, the first regular edition of Sky Diagrams is being issued for general distribution. In addition, it is intended to incorporate the diagrams into the American Air Almanac beginning with the volumes for 1946. J. F. Hellweg, Commodore, U. S. Navy, Retired, Superintendent, Naval Observatory. Washington, September 1944- 3 PIECEWORK COMPUTERS Elsie V. Willis Lillian Feinstein Mary H. Mikesell September 1944. 2 4 EXPLANATION SKY DIAGRAMS 5 These diagrams show the appearance of the sky in various latitudes at different times of the night. They are useful in selecting the most suitable stars and planets for navigation on a given flight and for identifying prominent objects at the time of observation. The Sky Diagrams have four advantages over ordinary star charts and star finders: 1. They are ready for immediate use without settings or tables of any kind. 2. Planets and the Moon are shown as well as the stars. 3. True altitudes and bearings are shown on the diagrams without distortion. 4. The appearance of the sky for different latitudes and times is shown at one opening so the appearance for intermediate latitudes and times is easily visualized. There is a series of diagrams for each month showing the sky for six different latitudes at 2-hour intervals during the night. Those for the evening hours appear on two facing pages and those for the morning on the two following. The diagrams for a given latitude are arranged in a row and show the changes in the sky during the night. In each diagram the circular outline represents the horizon and the cross at the center the zenith. Altitudes are measured radially with a linear scale; i. e., an object one third of the way from the edge to the center has an altitude of 30°. The small circles on the diagrams are at altitudes 30° and 60°. Azimuths are measured as on the navigation chart with north at the top and east at the right. On various parts of the diagram are small curved arrows indicating the diurnal motion in that area; the length of the arrow shows the motion in one hour. The objects shown on the diagrams are the 22 navigational stars contained in the Astronomical Navigation Tables (H. O. 218), the four planets Venus, Mars, Jupiter, and Saturn, the Moon, and the north and south celestial poles. The position of a star or a planet is indicated by the symbol which also shows its brightness, the magnitude scale being the same as that of the daily diagrams in the American Air Almanac. Near each star symbol is the number in the H. 0. 218 list and near each planet symbol is its initial. The north and south celestial poles are identified by the initials NP and SP. The position of the Moon is shown by a circle with the day of the month on which it occupies that position. The positions of the stars and planets in each diagram are indicated for the 15th of the month and will usually serve for the entire month. If it is desired to allow for the motion of the stars during the month it is necessary only to remember that a given configuration will occur at the beginning of the month 1 hour later than the time indicated, and at the end of the month 1 hour earlier. In those months during which Venus or Mars moves considerably with respect to the stars the positions for the first and last of the month are shown; the position toward the west is for the first of the month. The Moon moves so rapidly with respect to the stars that its position at a given time of the night varies rapidly from night to night, and it is necessary to show on each diagram a succession of positions for various days of the month. Three or four such positions are indicated and those for the intermediate dates may be interpolated be tween those given. Since the Moon moves completely around the sky in slightly less than a month or a little over 13° in a day, it will appear on a given diagram for about half of each month. The position on the diagram for each successive night is always to the eastward, and when it disappears off the eastern edge of the diagram it will reappear on the western edge about 2 weeks later. The diagrams are particularly useful in selecting the most suitable objects for a given flight. Example 1. Select the best available objects to give a fix at 23h LCT on Feb. 10, 1945, during a flight on a true course of 210° in latitude 30° N. The required diagram, which is the fourth one in the bottom row on page 10, is reproduced here with the course of 210° marked on it. Examination of the diagram shows immediately that the best objects, giving Sumner lines perpendicular to the track and parallel to it are 20 and 10, Sirius and. Capella. Sirius is in altitude about 35°, true bearing about 210°; Capella is in altitude about 45°, true bearing about 300°. If desired the altitudes and bearings may be found more accurately with dividers 1945 FEBRUARY and the scale diagrams. The Sky Diagrams used in conjunction with the star chart.and the daily diagrams in the American Air Almanac are extremely effective in star identification, the star chart and the daily diagrams being used for detailed verification of the identification made with the Sky Diagrams. Example 2. On June 1, 1945, at the end of evening twilight, in latitude 10° S., it is desired to know what objects will be visible. The Air Almanac gives the time of sunset as 17h 45m, the duration of twilight as 23m and hence the time of ending of evening twilight is 18h 08m. Since a given configuration will occur at the beginning of a month one hour later, the diagram to be used is the one for June 1945, 10° S., 17h, which is the first diagram in the middle row on page 27. The azimuths and altitudes of the various objects visible at that time can now be read from the diagram. It must be remembered that the Sky Diagrams are to be used flat on the chart table and that they show bearings as they appear on the navigator’s chart, east to the right. The star chart and the daily diagrams in the American Air Almanac, on the other hand, are designed to be held overhead for comparison with the sky, and on them east is to the left. For some intermediate latitude, such as 40°, or for an intermediate time, such as 22h, altitudes and bearings may be taken from two diagrams and a more accurate result obtained by interpolation, but such refinements are usually not desirable. STARS 1 Achernar 12 Dubhe 2 A crux 13 Fomalhaut 3 Aldebaran 14 Peacock 4 Alpheratz * 15 Pollux 5 Altair 16 Procyon 6 Antares 17 Regulus 7 Arcturus 18 Rigel 8 Betelgeux 19 Rigil Kent 9 Canopus 20 Sinus 10 Capella 21 Spica 11 Deneb 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Jan. 1 ® “ “ •• 2 POLES N«P North, S-P South MAGNITUDE SCALE -4 -3-2-1012 A $ So.. ALTITUDE SCALE 0 30 60 90 t » » I ■_| 1 1_1—1 AZIMUTH The positions of the stars are shown for the fifteenth of the month. 609403 O - 44 STARS 1 Achernar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sirius 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Jan. 1 ® “ “ “ 2 POLES N*P North, S-P South MAGNITUDE SCALE -4 -3-2-1012 4- A $ 6 o . . ALTITUDE SCALE STARS 1 Achernar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capeila 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sirius 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Feb. 1 ® “ “ 2 POLES N-P North, S-P South MAGNITUDE SCALE -4 -3-2-1012 4- A 4 * o . . ALTITUDE SCALE 0 30 80 SO I I I I I 1 I I 1 .1 AZIMUTH The positions of the stars are shown for the fifteenth of the month. STARS 1 Achernar 2 Acrux s 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capefla 11 Deneb 12 Dubhe 18 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Feb. 1 ® “ “ “ 2 POLES N-P North. S-P South MAGNITUDE SCALE -4 -3-2-1012 4- A < So.. ALTITUDE SCALE 0 30 SO SO I » > » ■ .11 » I EVENING SKY DIAGRAMS 1945 MARCH STARS 1 Achernar 12 Dubhe 2 Acrux 13 Fomalhaut 3 Aldebaran 14 Peacock 4 Alpheratz 15 Pollux 5 Altair 16 Procyon 6 Antares 17 Regulus 7 Arcturus 18 Rigel 8 Betelgeux 19 Rigil Kent 9 Canopus 20 Sirius 10 Capella 21 Spica 11 Deneb 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Mar. 1 ® “ “ “ 2 POLES N-P North, S-P South MAGNITUDE SCALE —4 -3-2-1012 4- A 6 o . . ALTITUDE SCALE 0 30 60 90 I I I I I I I 1.1-1 STARS 1 Achemar 12 Dubhe 2 A crux 13 Fomalhaut 3 Aldebaran 14 Peacock 4 Alpheratz 15 Pollux 5 Altair 16 Procyon 6 Antares 17 Regulus 7 Arcturus 18 Rigel 8 Betelgeux 19 Rigil Kent 9 Canopus 20 Sinus 10 Capella 21 Spica 11 Deneb 22 PLANETS Vega V Venus J Jupiter M Mars S Saturn MOON ® Position on Mar. 1 ® “ “ “ 2 POLES N-P North, S-P South MAGNITUDE SCALE -4 -3-2-1012 4- A 4 do.. ALTITUDE SCALE 0 30 60 90 I I I I I I I 1 I I AZIMUTH N The positions of the stars are shown for the fifteenth of the month. EVENING SKY DIAGRAMS 1945 APRIL STARS 1 Achemar 12 Dubhe 2 Acrux 13 Fomalhaut 3 Aldebaran 14 Peacock 4 Alpheratz 15 Pollux 5 Altair 16 Procyon 6 Antares 17 Regulus 7 Arcturus 18 Rigel 8 Betelgeux 19 Rigil Kent 9 Canopus 20 Sirius 10 Capella 21 Spica 11 Deneb 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Apr. 1 ® “ “ “ 2 POLES N-P North, S-P South MAGNITUDE SCALE —4 -3-2-1012 4- A 4 6 o . . ALTITUDE SCALE 0 30 eo 90 !»»»■»!»—i_J AZIMUTH N S The positions of the stars are shown for the fifteenth of the month. MORNING SKY DIAGRAMS 1945 APRIL STARS 1 Achemar 12 Dubhe 2 Acrux 13 Fomalhaut 3 Aldebaran 14 Peacock 4 Alpheratz 15 Pollux 5 Altair 16 Procyon 6 Antares 17 Regulus 7 Arcturus 18 Rigel 8 Betelgeux 19 Rigil Kent 9 Canopus 20 Sirius 10 Capella 21 Spica 11 Deneb 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Apr. 1 ® ..........2 POLES N’P North, S*P South MAGNITUDE SCALE -4 -3-2-1012 < A $ do.. ALTITUDE SCALE 0 30 60 90 I I I I I 1 I t.-l-l AZIMUTH The positions of the stars are shown for the fifteenth of the month. 1 Achemar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb STARS 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on May 1 ® ......... 2 POLES N’P North, S*P South MAGNITUDE SCALE -4 -3-2-1012 ■4- A $ do.. ALTITUDE SCALE The positions of the stars are shown for the fifteenth of the month. 609403 O - 44 STARS 1 Achemar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega N70 EVENING SKY DIAGRAMS 1945 JUNE 19* 21* 23“ to PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on June 1 ® “ “ “ 2 POLES N«P North, S-P South MAGNITUDE SCALE -4 -3-2-1012 ■4- A 4 do.. ALTITUDE SCALE 0 30 60 90 11 I I I_1 1-L.-1-J MORNING SKY DIAGRAMS 1945 JUNE 3‘ 5“ OO STARS N70 N70 1 Achernar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on June 1 ® ......... 2 POLES N’P North, S«P South 7 MAGNITUDE SCALE -4 -3-2-1012 •4- A 4 6 o . . ALTITUDE SCALE The positions of the stars are shown (or the fifteenth of the month. EVENING SKY DIAGRAMS 1945 JULY STARS 1 Achernar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sirius 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on July 1 ® “ “ “ 2 POLES N>P North, S*P South MAGNITUDE SCALE -4 -3-2-1012 < A 4 Ao.. ALTITUDE SCALE The positions of the stars are shown for the fifteenth of the month. 19“ N70 N50 N30 N30 STARS N70 N50 1 Achemar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on July 1 ® .........2 POLES N’P North, S*P South MAGNITUDE SCALE -4 -3-2-1012 4- A $ 6 o . . ALTITUDE SCALE The positions of the stars are shown for the fifteenth of the month. MORNING SKY DIAGRAMS 1945 AUGUST STARS N70 N50 N30 1 2 3 4 5 6 7 8 9 10 11 Achemar A crux Aldebaran Alpheratz Altair Antares Arcturus Betelgeux Canopus Capella Deneb 18 14 15 16 17 18 19 20 21 22 PLANETS V Venus M Mars Dubhe Fomalhaut Peacock Pollux Procyon Regulus Rigel Rigil Kent Sinus Spica Vega J Jupiter S Saturn MOON © Position on Aug. 1 2 POLES N-P North, S-P South MAGNITUDE SCALE -4 -3-2-1012 4- A 4 do.. ALTITUDE SCALE 30 60 90 AZIMUTH The positions of the stars are shown for the fifteenth of the month. STARS 1 Achernar 2 A crux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe . 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Sept. 1 ® .........2 POLES N-P North, S-P South MAGNITUDE SCALE —4 -3-2-1012 ■$- A 4 4 o . . ALTITUDE SCALE 0 30 60 90 I i a 1 i a Lj—i—I AZIMUTH The positions of the stars are shown for the fifteenth of the month. MORNING SKY DIAGRAMS 1945 SEPTEMBER STARS 1 Achemar 12 Dubhe 2 Acrux 13 Fomalhaut 3 Aldebaran 14 Peacock 4 Alpheratz 15 Pollux 5 Altair 16 Procyon 6 Antares 17 Regulus 7 Arcturus 18 Rigel 8 Betelgeux 19 Rigil Kent 9 Canopus 20 Sinus 10 Capella 21 Spica 11 Deneb 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Sept. 1 ® “ “ “ 2 POLES N’P North, S*P South MAGNITUDE SCALE -4 -8-2-1012 4- A 4 6 o . . ALTITUDE SCALE 0 30 80 »0 AZIMUTH The positions of the stars are shown for the fifteenth of the month. STARS 1 Achemar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut • 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Oct. 1 ® “ “ “ 2 POLES N-P North, S>P South MAGNITUDE SCALE -4 -3-2-1012 A A $ do.. ALTITUDE SCALE 0 30 60 00 Il.......I ■ 1 AZIMUTH The positions of the stars are shown for the fifteenth of the month. 1 Achemar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb STARS 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sirius 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Oct. 1 ® “ “ “ 2 POLES N-P North, S-P South MAGNITUDE SCALE -4 -3-2-1012 4- A 4 do.. ALTITUDE SCALE 0 30 60 90 I ■ ■ I ■_.lilt AZIMUTH The positions of the stars are shown for the fifteenth of the month. STARS 1 Achernar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sirius 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Nov. 1 ® “ 2 POLES N»P North, S*P South MAGNITUDE SCALE -4 -8-2-1012 4- A 4 6 o . . ALTITUDE SCALE 0 so 00 90 » ■ ■ I ■_« I »_|_| AZIMUTH The positions of the stars are shown for the fifteenth of the month. STARS 1 Achemar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Nov. 1 ® “ “ “ 2 POLES N«P North, S-P South MAGNITUDE SCALE —4 -3-2-1012 4- A $ do.. ALTITUDE SCALE 0 30 60 «> I—I_i ll I I 1-A-J AZIMUTH The positions of the stars are shown for the fifteenth of the month. MORNING SKY DIAGRAMS 1945 NOVEMBER STARS 1 Achernar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega PLANETS V Venus M Mars J Jupiter S Saturn MOON ® Position on Dec. 1 ® “ “ • “ 2 POLES N-P North, S«P South MAGNITUDE SCALE -4 -3-2-1012 A $ do.. ALTITUDE SCALE The positions of the stars are shown for the fifteenth of the month. S30 STARS N10 S10 MORNING SKY DIAGRAMS 1945 DECEMBER 1 Achernar 2 Acrux 3 Aldebaran 4 Alpheratz 5 Altair 6 Antares 7 Arcturus 8 Betelgeux 9 Canopus 10 Capella 11 Deneb 12 Dubhe 13 Fomalhaut 14 Peacock 15 Pollux 16 Procyon 17 Regulus 18 Rigel 19 Rigil Kent 20 Sinus 21 Spica 22 Vega PLANETS V Venus J Jupiter M Mars S Saturn MOON ® Position on Dec, 1 ® .........2 POLES N’P North, S«P South MAGNITUDE SCALE -4 -3-2-1012 4- A $ * o • . ALTITUDE SCALE The positions of the stars are shown for the fifteenth of the month. Date Due THE ORIGIN OF THE ANCIENT EGYPTIAN CALENDAR H. E. WINLOCK Director Emeritus, Metropolitan Museum of Art {Read April 20, 1940) Abstract In 1904 Eduard Meyer stated that the Egyptian calendar was invented about 4231 b.c., and some of the principal Egyptologists of his generation adopted this theory with minor modifications. In recent years it has been realized that 4231 b.c. was far back in the prehistoric period, long before the invention of writing, and of necessity later dates have had to be advanced for the adoption of the calendar as we know it. Primitive man in Egypt regulated his life entirely by the cycle of the Nile’s stages. Nature divided his year into three well-defined seasons—Flood, Spring, and Low Water or Harvest, with the Flood Season, following the hardship of the Low Nile, the obvious starting point for each annual cycle. The Egyptian early recognized the fact that usually twelve moons would complete a Nile year, but his lunar reckoning always remained secondary to his Nile reckoning, and he never adopted solar seasons. However, by about 3200 b.c. he probably recognized the heliacal rising of the prominent star Sothis as a definite phenomenon heralding the coming flood, and he began to count the observed reappearance of the star as his New Year Day. His year he now adjusted to twelve artificial moons of 30 days each, followed by about five days in which he awaited the reappearance of Sothis. For several centuries the calendar was fixed to the star and thus was approximately correct, but the experience of generations was apparently proving that the perfect year should be 365 days long, and in 2773 b.c. a year of this length was adopted, by the simple expedient of neglecting to readjust the calendar by annual observations. Since no change was ever permitted thereafter, the Egyptian calendar was only correct once in every 1460 years. The calendar of the ancient Egyptians was one of man’s earliest experiments in almanac making. Certainly it was one of his most enduring, for in the first centuries of the Christian era it was still being used much as it had been during the pyramid age three thousand years earlier. This uninterrupted existence throughout more than half of man’s recorded history has given it an almost mysterious quality which has been so intriguing to modern scholars that within my own memory—and even within this last year or so —many an article orTits origin has appeared, all differing more or less fundamentally in the story they strive to reconstruct. The approach to this problem has usually started with a statement made by Censorinus in 238 a.d. to the effect that the Egyptian New Year Day in 139 a.d. fell on July 21, when the bright star Sothis—which we know as Sirius—after having been invisible for PROCEEDINGS OF THE AMERICAN PHILOSOPHICAL SOCIETY, VOL. 83, NO. 3, SEPTEMBER, 1940 447 448 II. E. WINLOCK a season, made its annual reappearance in the eastern sky just before sunrise. Since the Egyptian civil year was one of 365 days and that of Sothis was one of 365)4 days, this coincidence could only have happened at intervals of about 4 X 365 years, or in 1317, 2773, and 4231 b.c.1 Believing that the ancient Egyptian calendar could only have been invented on one of these occasions of coincidence, and further believing that 2773 b.c. fell in the Fourth Dynasty when the calendar was already in use, Eduard Meyer stated in 1904 that the calendar must have been introduced in 4231 b.c.2 Eventually Meyer concluded that it was not until 3200 b.c. that Menes, the first historical king of Egypt, united the Two Lands,3 yet he never altered his date for the invention of the calendar, which would thus have been in uninterrupted use for a thousand years before the beginning of Egyptian history—and equally long, we now suppose, before the development of writing. James Henry Breasted 4 accepted Meyer’s theory that the invention of the calendar in 4231 b.c. was “the oldest fixed date in history.” Evidently realizing the difficulties which this involved, Breasted eventually attributed the invention of the calendar to a predynastic “First Union” of the Two Lands, which, while it is supposed to have taken place in the forty-third century b.c. and to have lasted for eight hundred years,5 has left no written document nor any other tangible trace in history. Eventually Ludwig Borchardt6 gave Meyer’s theory a momentary support by his 1 The dates of the so-called “Sothic periods,” as given by different historians, vary slightly among themselves. Here, as in the following pages, they are uniformly made to agree with the latest corrected tables by P. V. Neugebauer in Astronomische Nachrichten, v. 261, no. 6261, 1937. I owe this reference to the kindness of Otto Neugebauer—who is not to be confused with his namesake, the compiler of the tables. 2 Aegjptische Chronologic (Philosophische und historische Abhandlungen der Koniglich preussischen Akademie der Wissenschaften, 1904), p. 41; and (in the same Abhandlungen for 1907) Nachtrdge zur agyptischen Chronologic. In the following pages the references will be cited as Meyer, Chron., or Meyer, Nachtr. In 1913 he repeated the thesis in his Geschichte des Altertums (3rd edition), § 159. 3 Die Altere Chronologic . . . Agyptens, Nachtrag num erslen Bande der Geschichte des Altertums (1931), p. 68; referred to below as Meyer, Altere Chron. This 1931 edition appeared after Meyer’s death, and a note by the editor, H. E. Stier, on page 74, calls attention to Alexander Scharff’s recent theory that the calendar was invented in 2773 b.c. 4 Ancient Records, I, pp. 25 ff.; A History of Egypt, pp. 32, 44. 5 “The Predynastic Union of Egypt,” Bulletin de I’Institut frangais d’archeologie orientate, XXX (1930), p. 709; Ancient Times (2nd edition, 1935), pp. 54, 58. He appears to have been led into this idea partly by one of Sethe’s brilliant and seemingly plausible philological exercises, Der segyptischen Ausdrucke fur rechts und links, and also by Sethe’s Urgeschichte und diteste Religion der Agypter. 6 Die Annalen und die zeitliche Festlegung des alten Reiches (Quellen und Forschungen zur Zeitbestimmung der Agyptischen Geschichte, Band 1), p. 30. Borchardt’s chronology was strongly criticized by Peet, Journal of Egyptian Archeeology, vol. VI (1920), pp. ORIGIN OF ANCIENT EGYPTIAN CALENDAR 449 attempt to place Menes close to Meyer’s date for the invention of the calendar. This combination appealed to Kurt Sethe whose study of the origin of the calendar,7 while unsatisfactory in its conclusions, is a most valuable compendium of all the available material. In recent years the various modifications of Meyer’s theory have been less generally accepted than formerly, and the tendency has been toward the more reasonable hypothesis that the calendar was a product of some later period. One of the most recent and most ingenious schemes for avoiding this difficulty—but one which unhappily was inspired, I understand, by tempting but false etymologies for the Egyptian season names—was propounded last year by Professor Jotham Johnson of the University of Pittsburg.8 He argued that the primitive Egyptian had a lunar calendar until the morning of June 18, 3251 b.c. when Sothis appeared over the eastern horizon just before the dawn of a day on which the new moon occurred. From that day onward the calendar was fixed to Sothis, but gradually the calendar became so far divorced from the terrestrial seasons that it had to be corrected by exactly one whole four-month season on June 18, 2773 b.c.—after which it became the wandering year of the historic period. Alexander Scharff of the University of Munich had long seen the difficulties inherent in Meyer’s theory, and in 1927 9 he had stated that the calendar must have been invented in 2773 b.c.—a whole Sothic period later than had usually been proposed. Before that date he assumed that the Egyptian reckoned time by some wholly different system, which he did not exactly define but which in one place he seems to say was based on a year of 320 days. 149 ff., and by Meyer, Altere Chron., p. 41, but Borchardt modified it only very slightly in Quellen, Band 2, Die Mittel zur zeitlichen Festlegung von Punkten der Agyptischen Geschichte (Kairo, Selbstverlag, 1935). So far as this refers to the XVIII Dyn., it is analyzed—unfavorably—by W. F. Edgerton in American Journal of Semitic Languages, LIII (1937), pp. 188 ff. In both parts, although Borchardt’s conclusions are unsatisfactory, he makes a great deal of important material available, but I have a feeling that the complexity with which he treats the subject would have made the ancient Egyptian’s head spin. References below will be to Borchardt, Quellen. 7 Die Zeitrechnung der alien Aegypter, in the Nachrichten der K. Gesellschaft der Wissenschaften zu Gottingen, Philologisch-historische Klasse, 1919-1920. It will be quoted below simply as Sethe, with the pagination of the Nachrichten, in which pages 287-320 are of 1919, and pages 28-55 and 97-141 are of 1920. 8 Journal of the American Oriental Society, 59 (1939), p. 403. 9 Grundziige der agyptischen Vorgeschichte, p. 54, in Morgenland; Darstellungen aus Geschichte und Kultur des Oslens, Heft 12. See note 35 below. 450 H. E. WINLOCK Two years ago Otto Neugebauer,10 now at Brown University, came out with an extremely intriguing and still more revolutionary theory. He stated that if the primitive Egyptian kept records of the days which elapsed between the successive inundations of the Nile over a period not exceeding fifty years, an average of these periods would infallibly lead to a 365 day year without the observation of any heavenly body whatever. This is unquestionably true in the light of our present day knowledge, but it is doubtful whether it was equally obvious to the Egyptian in the stone age.11 The figures which Neugebauer himself uses give differences in the lengths of the intervals between floods of as much as 80 days in a single generation, and come to exactly 365 days only once in that period.12 When one Nile year might be only 335 days long and another as much as 415, it is a question whether primitive man would ever, unaided, have arrived at the conception of an average Nile year or would have known how to calculate it, had he thought of it. Setting a calendar by the Nile flood would be about as vague a business as if we set our calendar by the return of the Spring violets. However, Neugebauer’s very interesting theory appealed to Scharff as supplying evidence on the nature of the Egyptian calendar before 2773 b.c.—and perhaps even as late as 2000 b.c.—and he now enthusiastically endorses it in part, even if not in all its details.13 Before examining the problem of the origin of the calendar afresh a digression appears to be justified on a matter which, even recently, has been the subject of discussions likely to complicate the whole question in the minds of some readers. 10 “Die Bedeutungslosigkeit der ‘Sothisperiode’ fiir die alteste agyptische Chronologic,” in Acta Orientalia, XVII (1938), pp. 169 ff. In briefer form, with additional remarks by Jean Capart, in Chronique d'Egypte, No. 28, July, 1939, pp. 258 ff. 11 This would require not only a count of the days between successive floods, but a Nilometer, sufficiently massive to withstand the erosion of the inundations, on which comparable stages of the Nile might be measured. Sethe (JJrgeschichte und alteste Religion der Agypter, §§ 109 ff.) believed that there was such a Nilometer on the Island of Roda near Memphis, as early as prehistoric times. This is pure hypothesis, as is recognized by Scharff on p. 9 of the article cited in note 13 below. 12 He uses the figures given by Sir William Willcocks for 1873-1904, before the completion of the Aswan dam. They were doubtless typical of the years before the Nile was artificially controlled. Borchardt (Quellen, I, p. 7) uses a non-continuous series of 32 high Niles between 1798 and 1888, which give comparable results. 13 Die Bedeutungslosigkeit der sogennanten altesten Datums der Weltgeschichte, read to the Phil.-hist. Abteilung der bayerischen Akademie der Wissenschaften zu Munchen in July, 1939, and (in summary) to the Archaeological Congress in Berlin in August, 1939, and published in the Historische Zeitschrift, 161, pp. 3 ff. Scharff seems to approve most of Neugebauer’s theory except that (pp. 15, 18) he hesitates to accept a 365 day year as early as the I-II Dyns. See note 35 below. ORIGIN OF ANCIENT EGYPTIAN CALENDAR 451 In modern studies on the historic Egyptian calendar one sometimes reads of a “civil” or “wandering year” and of a co-existent fixed year ” by whicji festivals might be kept in unvarying relation to the more or less true solar seasons of the inundation, agriculture, and the important reappearance of Sothis.14 It may be as well at the outset of this paper to state that the ancient Egyptians, from the Old Kingdom to the Roman Period, have not left a single trace of such a fixed calendar. Out of the thousands which have survived from dynastic Egypt, not one document gives equivalent dates in the known “wandering” year and the hypothetical “fixed” year. Furthermore, by the time that relations with the outside world were such as to result in unprejudiced foreign evidence on the customs of Egypt, we find the Egyptian both ignorant of, and unreceptive to the idea. About 600 b.c.,15 Thales of Miletus introduced the Egyptian year of 365 days to the Greeks, without hint of any correction being required, and Herodotus, when he was in Egypt about 460 b.c., heard only of a 365 day year and was under the impression that it was not only an accurate measure of time, but that it was the only accurate year devised by any contemporary people. When in 488 b.c. Darius adopted the Egyptian calendar for Persia, it was as an unmodified 365 day year, and after 120 years a whole month had to be intercalated to correct the Persian calendar. The credit for the discovery that a solar year consisted of 365J4 days was given by classical authors to Eudoxos of Knidus (408-355 b.c.) whose calculations were probably those used by the Macedonian Ptolemy III Euergetes when, by the Canopic Decree of 237 b.c., he attempted to introduce a 365^4 day year in Egypt.16 In that decree 14 Sethe, pp. 311 ff., “Das feste Jahr.” Meyer (Chron., pp. 31 ff., “Das angebliche feste Jahr,”) unanswerably refutes some of the arguments current before the appearance of Sethe’s Zeitrechnung. 15 The following paragraph is largely drawn from Sethe, pp. 315-318. 16 Meyer, Chron., p. 31; translation in J. P. Mahaffy, A History of Egypt under the Ptolemaic Dynasty (1899), pp. Ill ff., and in Edwyn Bevan, A History of Egypt under the Ptolemaic Dynasty (1927), pp. 207 ff. The decree is definite proof that a fixed calendar was unknown to the Egyptians in the III Cent. b.c. It is dated March 6, 237 b.c., when the flood and the reappearance of Sothis were expected to take place on the last of the Month Payni (95 days before New Year Day) and is an attempt to fix the calendar unalterably to the seasons as they were in that year, inconvenient though they would seem to be. It provides that an intercalary day be added, in every fourth year, to the five festivals of the gods at the end of the year, “in order that it may not occur that some of the national feasts kept in winter may come in time to be kept in summer ... as has formerly happened.” Furthermore, in order that Ptolemy Euergetes should always be credited with correcting “the former defect in the arrangement of the seasons,” it provides that this sixth god’s festival shall be named for the Benefactor Gods—Ptolemy and his wife, Arsinoe. 452 H. E. WINLOCK no reference is made to the idea being native to Egypt, and in fact it appears to have been regarded by the Egyptian people as an abhorrent foreign innovation with which they would have absolutely nothing to do, in spite of the fact that it was said to have the sanction of their own priesthood. It was only in 46 b.c. that Sosigenes of Alexandria 17 evolved for Caesar the Julian Year of 365]4 days, and twenty years afterwards Augustus imposed upon Egypt an era of Julian Years, starting with August 1st, 30 b.c., under the name of the Alexandrian year. Even this—called by the Egyptians the “Greek Year” to distinguish it from the year “according to the Egyptians,” or “according to the ancients” 18— was not used by the natives until they had given up their own religion and had adopted Christianity. In short, the whole history of a year with intercalations, as we see it in classical times, is a history of an innovation obnoxiously foreign to the native Egyptian. There is no hint in the whole four centuries and a half covered by the classical literature that the Egyptians had any memory of ever having used a fixed year or ever having recognized its desirability. The ancient Egyptian calendar of the historical period gives clear evidence that it originated in the climate of the land. Egypt has been, to all intents and purposes, rainless for many thousand years, and all living things in the Nile valley have been dependent on the fluctuations of the river. In the very occasional years when the Nile flood is average, the river is lowest at the First Cataract about the end of May and at the head of the Delta some two weeks or more later. Soon afterwards come the floods from the equatorial rains on the water-shed of the upper Nile during the preceding winter. The river rises slowly at first and then more rapidly, until it reaches its height at the First Cataract about September 1st and a month later at the Delta head where, by the middle or end of October, the highest of the flooded lands begin to emerge once more and the waters fall, until they reach their lowest again the following June. 17 It was probably Greek mathematicians in Alexandria who told Diodorus (I, 50) in 60-56 b.c. that the Egyptians “reckon . . . their month of 30 days and they add 5J4 days to the 12 months, and in this way fill out the cycle of the year.” All other evidence is against such having been the native practise at this time, but the facts were doubtless well known to the Alexandrian Greeks. 18 Meyer, Chron., p. 32. Otto Neugebauer reminds me of the fact that 200 years after the Julian Calendar reform the astronomer Ptolemy was still performing his calculations in the 365 day Egyptian year. This, however, was merely for convenience—not because of chauvanism. The Julian year is still being used in preference to the Gregorian by astronomers, sometimes to the confusion of archaeologists. ORIGIN OF ANCIENT EGYPTIAN CALENDAR 453 During the palaeolothic period, whenever the periodical rise of the Nile got under way, the settlements of the primitive Egyptians along the river banks and in the marshes, where they had been established to be near water, would have to be abandoned for others on higher ground. For a space, the Nile people would look down from the desert edge upon a broad lake covering meadows, groves, and swamps, and they would be forced to subsist on fishing, fowling, and hunting. This season in the language of their descendants, the dynastic Egyptians, was Akhet—“the Flood.” In due course the waters would fall, and the Egyptians would follow the edge of the receding flood across the alluvial plain, pasturing their flocks— once they had domesticated any—on its meadows fast growing green, themselves eating the wild fruits and vegetables which sprang up and ripened in the hot, moist soil, and—when they had learned to save the seed from the last low Nile—strewing it over the wet, black mud where it would sprout and mature very shortly under the cloudless skies. This season in the language of their descendants was Proyet—“the Coming Forth,” ‘‘the Spring.” As the waters descended, man returned to the river and to the permanent swamps where water could be had most easily, and waited for the next flood. This season was called by his descendants Shomu—perhaps meaning at first “the Low Water,” but later surely understood as “ Harvest-time.” 19 Thus the Egyptian recognized but three seasons, and when he adopted a word for “year” he chose a form of the word ronpy, “to be young,” or “fresh” as of plants, and he considered this year as beginning with the first signs of the rising water which would bring out the verdure once more. These first signs of the awaited flood would be such as primitive hunters and fishermen might learn. First the waters would turn green from the algae floating down from the swamps of the upper Nile, and the green water would last until the flood was definitely under way. The river itself and the river animals, the hippopotami, crocodiles, and fish whose actions foretold the coming flood, must have been the first harbingers of another cycle of seasons to primitive man. At this stage in his 19 Sethe, p. 294; Alan H. Gardiner, Egyptian Grammar, p. 203. The word Shomu seems to be derived from two words meaning “ deficiency ” of “water.” Later it acquires two meanings: (1) the season of low water, and (2) the harvest. Usually its “determinative” differs with the meaning, but an XVIII Dyn. ostracon found by the Metropolitan Museum’s Expedition (and shortly to be published by W. C. Hayes, Ostraca and Name Stones from the Tomb of Sen-Milt, No. 106) writes the word in a date with both determinatives. 454 H. E. WINLOCK development he probably could not count beyond the number of his fingers and surely was not interested in predictions beyond the immediate future. By the time stone-age man first felt the need of some other means of predicting the future stages of the river—probably as agriculture became his chief interest—he must already have become accustomed to counting the phases of the moon. He would early have realized that once the Nile is rising, some four moons must pass before he could sow his seed corn on the emerging mud; how at least four moons again would be required for the grain to ripen; and how a third four moons would pass before the flood would reappear again. Of course, even in the ideally normal year such a count would be only approximate. We know that each moon is theoretically about 29^4 days, and twelve moons only 354 days, and that therefore in three successive floods—aside from the irregularities of the river itself—an error of a little more than a moon would have occurred. However, the ideal flood occurs perhaps only once in a generation, and year after year the actual period between one low Nile and the next might be anywhere between 11 and 14 moons. An early or a late flood would sometimes make such a moon reckoning correct, sometimes wrong, but to primitive man the moon still would serve as a ready rule of thumb for predicting the seasons. And after all, the coming of the flood was the start of the new year, regardless of the moon count. Long after he had evolved a far more practical calendar, the Egyptian still retained some memories of his primitive lunar reckoning. It gave him his subdivision of the year into twelve parts, and the moon gave its name abod to each of those parts, as it has to our “months.” About 1850 b.c. lunar months, alternately 29 and 30 days long and totally unrelated to the then current civil calendar, still served to set the periods of priestly temple service.20 From then down to Roman times there seem to be traces of lunar months in religious calendars, and it would appear that the coronations of the kings were supposed to take place on the day of the full moon.21 In 1100 b.c. astronomical tables still had a technical term for the mid-month which appears to go back to a time when a month was literally a moon and the mid-month 20 Meyer, Chron., p. 52; Sethe, p. 301. 21 Borchardt, Quellen, II, pp.- 39 ff., 69 ff. This theory is approved by Edgerton, Amer. Jour, of Semitic Languages, LIII (1937), pp. 188 ff. He quotes, however, Cerny, Agyplische Zeitschrifl, LXXII (1936), pp. 109-118, for an emergency at the death of Ramesses III which caused his successor, Ramesses IV, to be installed immediately. ORIGIN OF ANCIENT EGYPTIAN CALENDAR 455 was full moon time.22 Even in Pliny’s 23 time it was a popular by-word that the flood might be expected on the new moon next after the summer solstice, and Vettius Valens,24 probably through some misunderstanding of a similar popular saying, supposed that the New Year was on the new moon preceding the reappearance of Sothis. However, lunar reckoning was always of secondary importance to the Egyptian. Those whose calendars are lunar count the start of each day from sunset, when the new moon, the new month, and the new year all take their beginning.25 The Egyptians, on the contrary, alone of all ancient peoples, commenced their day at dawn,26 and when their writing was invented the same ideogram stood for both the words “sun” and “day.” Nevertheless, the Egyptian never adopted solar seasons. His seasons were always those of the Nile, whose rise and fall, originating in the distant and unknown south, the prehistoric Egyptian could have had little or no reason to associate with the sun. Only during a brief period in the fourteenth century b.c. did Egyptian beliefs give full credit to the Sun for its controlling influence on terrestrial life.27 But even then the relationship of the Sun to the phases of the Nile was not clearly understood, and it was apparently only in classical times that the solstice was regarded as an omen of the coming inundation. Thus, about 450 b.c. Herodotus 28 wrote: “the Nile, at the commencement of the Summer Solstice, begins to rise and continues to increase for a hundred days and as soon as that number is passed it forthwith retires and contracts its stream, continuing low during the whole winter until the Summer Solstice comes around again.” Later Pliny was told that the river rose at the full moon next after the Summer Solstice, and similar beliefs have been current until modern times.29 22 Sethe, pp. 130, 136. 23 Natural History (ed. Bohn), Book 5, Chapter 10. 24 Sethe, p. 296. 28 Sethe, p. 119. 26 Sethe, pp. 130-138. 27 Sethe, pp. 28-30. During the reign of Akh-en-Aten (1375-1358 b.c.) the “ Hymns to the Sun” attributed to that heavenly body full control over all nature, including the Nile (Breasted, A History of Egypt, pp. 371-376; Development of Religion and Thought in Ancient Egypt, pp. 312 ff.). However, Sethe (pp. 37 ff.) is wrong in assuming an importance for the winter solstice, which actually seems to have played no part in Egyptian thought. 28 Book II, 19. 29 For Pliny, see above, note 23. For recent beliefs, see E. W. Lane, Manners and Customs of the Modern Egyptians (1836), II, pp. 254 ff.; Lepsius, Chronologic, p. 213. 456 H. E. WINLOCK Here it is important to recall certain fundamental points in our problem. First, the rise of the Nile began the new year. Second, the erratic nature of this event was too variable to be itself a measure of time for a people who were becoming more and more cultivated. Third, the moon had proved only a little better. And fourth, the sun did not seem to the Egyptian to have any connection with the question. Yet there is something in man which makes him look to the heavens for his calendar, and the Egyptian, like all others, turned to the sky for some sign that his new year was approaching. In the cloudless Egyptian nights one of the most prominent, single, heavenly bodies is the great star Sothis. As is the case with all fixed stars, there is a period in each year when Sothis has disappeared from the night sky, rising and setting in daylight. Then one morning its rising is just sufficiently earlier than the sunrise for it to be seen once more for a short time in the dawn as a prominent feature of the eastern sky. About 7000 b.c. Sothis was visible in the dawn at the head of the Nile Delta around May 21st, which was so long before even an exceptionally early flood that no possible relation could have been seen by any primitive Egyptian between the star and the rising Nile. But since about every 120 years this annual reappearance occurs a day later in the solar year, gradually the star’s rising was retarded until, in the latitude of the Delta, it took place just before sunrise on June 17 30 in 3500 b.c. Very slowly—so slowly that it took generations to make a day’s difference—the star’s reappearance was delayed further until it came on June 23 about 2800 b.c.—and the later it came the more certain it was to be regarded as a harbinger of the flood. The reappearance of this brightest of stars in the dawn is a striking sight. It must have been especially so to primitive man suffering in the fiery heat of an Egyptian June, when the Nile was at its lowest, and his longing for the flood was keenest. Gradually he began to associate the return of Sothis with the first stages of that longed-for high Nile which he grew to expect would follow soon afterwards. When it was that man became conscious of this association we shall never know. Obviously it was an idea which took shape slowly. 30 Throughout Coptic and Arab times, at least, the night of June 17 was celebrated as “the Night of the Drop ” when it was believed that a miraculous drop fell into the Nile, causing it to rise. After July 3 the flood was usually obvious enough to be proclaimed daily by criers in the streets of Cairo. Lane, loc. cit. ORIGIN OF ANCIENT EGYPTIAN CALENDAR 457 However, it is impossible to doubt the fact that, as early as the dawn of the historic period, the Egyptian was already regarding Sothis as the harbinger of the all important inundation. From one of the royal tombs at Abydos, dating from the first historic Egyptian dynasty, there comes a little ivory tablet which is now in Philadelphia in the University Museum. On it is inscribed a brief and primitive inscription which has been interpreted “ Sothis Bringer of the New Year and of the Inundation.” 31 Coming to us from a slightly later period—but in all probability repeating the words of a much earlier composition—is a passage in the Pyramid Texts describing Sothis as the creator of all green growing things, and hence of the year itself.32 Here we have statements in the very dawn of history naming Sothis, the recognized master of the annual flood, as the creator of the year—by which of course we may understand the calendar. We need have very little doubt that this association of Sothis with the year was at least as early as about 3200 b.c.—a date which, it must be realized, can only be fixed approximately—when the Egyptian communities were united by Menes, the first King of Upper and Lower Egypt.33 Menes also is credited with founding the capital city, Memphis, at the head of the Nile Delta, and it is noteworthy that it was the observation of the reappearance of Sothis at Memphis which was regarded as official throughout 31 University Museum, E 9403; Petrie, Royal Tombs, II, pls. V, 1, Via, 2; Sethe, Beitrage zur altesten Geschichte Agyptens, p. 63; Zeitrechnung, p. 294. Borchardt, who apparently never had laid eyes on the tablet, published retouched photographs of it (Quellen, I, p. 53, n. 1), gratuitously adding the hieroglyphic signs for “month 2” in the blank space in its lower right hand corner. Unfortunately for his theory, he had not noticed that the inscription on it is incised, and therefore no part of it could have faded out, as he seems to have assumed. I have examined both the tablet itself and a photograph which I received through the kindness of Dr. Hermann Ranke and can testify that the Petrie publication is accurate. More recently, Scharff has described the tablet (Altesten Datums, p. 14, note 1) as bearing the notation “the year of the cow counting,” but this gives no explanation for the hieroglyphic sign akhet, of which Sethe takes account. 32 Pyramid Texts, 965 a-b, makes the characteristically punning statement that “It is Sothis, thy beloved daughter, which has made the fresh green (‘the New Year offering’—rnp-wt) in this thy name of year (rnp-f)." Scharff, Altesten Datums, pp. 17-18, 31. 33 Meyer (Altere Chron., pp. 68-69) dates Menes, founder of Dyn. I and traditionally of Memphis, to about 3200 b.c., admitting the possibility of an error of as much as 100-200 years either way. Scharff (Die Altertumer des Vor- und Friihzeit Agyptens (1931), pp. 31-32, and Altesten Datums, pp. 21-22) dates Menes to 3000 b.c. However, he seems to approve the recent figures of Farina for the Turin Papyrus, by which the XI Dyn. begins apparently in 2143 b.c. and the I-VIII Dyns. covered 955 years. This gives a minimum date of 3097 b.c. for Menes, without making any allowance for the 18 kings of the IX-X Dyns., except insofar as the X Dyn. may have been contemporary with the first half of the XI Dyn. 458 II. E. WINLOCK Egypt during the historic period.34 With Menes began the written records of the lengths of the reigns of the kings, expressed in years, months, and days, which later annalists had no difficulty in combining with later records in the composition of the Palermo Stone, the Turin Papyrus, and the History by Manetho. And another, and most important point, each and every year on the Palermo Stone had an inundation, which would not have been the case had the civil year differed markedly from the natural year, as Scharff has suggested.35 It must be realized, however, that even when the primitive Egyptian began to recognize the reappearance of Sothis in the dawn as an omen of the coming flood, he had not immediately established what we call a “fixed” calendar. His calendar was without doubt still dependent on an annual observation of Sothis, and a successful observation of the heliacal rising without instruments presents its difficulties. Ludwig Borchardt36 attempted the observation between 1924 and 1927, with various collaborators stationed up and down the Nile between the latitudes of ancient Thebes and ancient Heliopolis under conditions simulating, as nearly as he could imagine, those of ancient times. Today the reappearance of Sothis is due early in August when a mist often hovers over the inundated valley at dawn, and in addition the modern air is likely to be befogged with chimney smoke. Furthermore, the point of the sunrise on the horizon is nearer to that of 34 This is a tradition preserved by Olympiodorus (writing in 565 a.d.), who stated that the whole land had followed the Memphite observation for the official date of the heliacal rising of Sothis. Cf. Sethe, p. 309. It should be remembered that when Sothis reappeared at Memphis on any given day, its heliacal rising had taken place at Aswan six days earlier. 35 Scharff (Grundzuge, pp. 55-56; Allesten Datums, pp. 15, 18) lays great stress upon the fact that the sum of the months and days in two adjacent regnal year spaces at a change of kings on the front of the Palermo Stone totals only 10 months and 20 days. Hence, he argues that the 365 day year was not in use in the first two dynasties. He can not, however, escape the fact that in a similar place in line 4 on the back of the stone, at the change of reign from Sahu-Re‘ to Nefer-ir-ka-Re‘, the total is only 11 months and 13 days, although the 365 day year admittedly existed in the V Dynasty. In these two places where there seem to be intervals between reigns (in the one case of 45 and in the other of 22 days) it is possible that these may be the periods between the death of one king and the coronation of the next, which had to await the presence of the successor in the capital and the occurrence of the full moon. See note 21 above. Further, Scharff forgets that if a year consisted of 320 days only, some years would have no inundation at all. 36 Ludwig Borchardt and Paul Viktor Neugebauer, Orientalistische Literalurzeit ting, 1926, cols. 309 ff.; 1927, cols. 441 ff. In the latter article the authors had the collaboration of members of the Egyptian Survey Department. These experiments (among the most enlightening contributions to the study of the Egyptian calendar) prove that primitive observers cotdd have established a 365 day year only after long experience. ORIGIN OF ANCIENT EGYPTIAN CALENDAR 459 the star rise than it was when the latter took place at the solstice, and the star is therefore more difficult to see in the growing dawn. Hence, the modern observers sometimes did not see the star for as many as five mornings after it should have been visible, and while about 3200 b.c. conditions were better, there must have been many a year when the first glimpse of the star was a day or so late— in which case it would probably be a day too early the next year. To this uncertainty of observation another day would have to be added every fourth year as we add the day to our leap years. Indeed, when the primitive Egyptian first began to keep account of the days between heliacal risings he must have been very far from believing in anything like a fixed year. Since his year was based on a primitive observation which had to be made annually, each New Year was marked with some uncertainty, but for the First Dynasty Egyptian that was surely not as great a drawback as it sounds to us. The Mohammedan months do not begin, even today, in theory, until one of the faithful has actually seen the new moon in the sunset, and I can well remember how once or twice there was a great deal of doubt, while I was still living in Egypt, as to when the month-long fast of Ramadan might be broken.37 To primitive man a day or so of doubt of this sort would have caused far less bother than it does to his modern peasant descendant, and to him it causes little bother enough. I suggest, then, that the Egyptian of the time of Menes was starting his year with an observation of the reappearance of Sothis. The divisions of the year were borrowed from prehistoric customs with, however, some important modifications. There were still the three seasons of Flood, Spring, and Harvest—now always of 120 days each. The "moons" were so convenient that they were retained as “months,” even when it was found that they could not coincide with Sothis. From now on for civil affairs they were artificially ordered, each of exactly 30 days—or three ten day “weeks”—and between one reappearance of the star and the next there were always twelve months and a few days over. These extra days “Over and above the Year” 38—which came between 37 Lane {Modern Egyptians, II, p. 229) describes how the observation of moon-rise was made in Cairo a little over 100 years ago. 38 Sethe (pp. 303 ff.) gives all the existing data on the five intercalary days, but his interpretation—that the year was originally of 360 days only—can hardly be accepted. It fits in, however, with the thesis of Scharff, Altesten Datums, p. 16. The days “Over and above the Year” at first headed the new year (Sethe, Urkunden des A. R., I, pp. 25, 27; Breasted, Ancient Records, I, §§ 218, 221); in later calendars they closed the old year. 460 H. E. WINLOCK the last month of the old year and the first of the new, and on which the reappearance of Sothis was to be awaited—were the “Birthdays of the Gods.” 39 Usually the heliacal rising came after the fifth of them, and according to the now existing texts, on them the births of five gods of the Osiris cycle were to be celebrated. Sometimes six days would pass before the star’s reappearance, and then perhaps the birthday of another god would be celebrated.40 The next year, or the year after, the star would probably be visible a day before it was expected, in which case the last of the birthdays would be lost for a year. The important thing is that none of the twelve months were ever increased or diminished, and the uncertainty was always confined to these days “Over and above the Year.” I believe this to have been the situation during the first two dynasties. The commencement of each year was dependent on the heliacal rising of Sothis being observed, with the result that while most years might be 365 days long, every fourth year was probably a day longer, and any other year might be a day or two longer or shorter, depending on the accidents of observation. Yet we know that throughout the later historical period the year differed from the star, and also from the ever variable Nile. The problem, therefore, is when was the Egyptian “wandering” year first used. Throughout the most familiar part of Egyptian history the “civil” year contained only 365 days, with the result that its New Year Day was “wandering” both in respect to the solar seasons and in relation to Sothis as well. As has been mentioned already, the civil New Year coincided with the reappearance of the star in 139 a.d. and hence, we may suppose, in 1317 b.c. From the period between 1317 and 2773 b.c. there are several items of evidence which demonstrate that the civil calendar was consistently “wandering” throughout that period. From the Eighteenth Dynasty we have calendrical dates for the reappearance of Sothis in 1469 b.c., as recorded in the Elephantine Festival Calendar of Thut-mose III,41 and in 1545 b.c. in the calendar of the Ebers Papyrus 39 Sethe, Die altaegyptischen1 Pyramidentexte, par. 1961c; only in the pyramid of Nefer-ka-Re‘ (Pepy II). See also Meyer, Chron., p. 40; Scharff, Grundzuge, p. .56. Scharff (Alt esten Datums, p. 17) states that this passage, while of the Old Kingdom, is not very ancient. 40 In the attempted calendar reform of Ptolemy III Euergetes (see above, note 16) the extra day in every fourth year was to be dedicated to Euergetes and Arsinoe in their divine quality. e 41 Sethe, Urkunden der 18. Dynastie, p. 827. The calendar is for an unrecorded year in the reign of Thut-mose III when the reappearance of Sothis took place on the 3rd ORIGIN OF ANCIENT EGYPTIAN CALENDAR 461 of the reign of Amen-hotpe I.42 In the Twelfth Dynasty the Kahun Temple Day Book of 1877 b.c. fixes the date for that year,43 and in the Eleventh Dynasty the dekan tables symbolizing the heavens on the lids of coffins give dates for the reappearance of Sothis between 2101 and 2021 b.c., which are absolutely consistent with the later dates for the same event.44 Naturally, as we go further back through the Old Kingdom, inscriptions are rarer— both due to the accidents of time and the fact that the earlier Egyptian was less literate than his descendants—and no further observations of the reappearance of Sothis have happened to survive. There are, however, other records which show that the civil calendar was shifting consistently at least as far back as 2350 b.c.45 Meyer showed that the flax harvest in the Twelfth Dynasty, about the year 1940 b.c., took place at the appropriate calendrical date in the wandering year.46 Furthermore, we know from various inMonth of Shomu, Day 28. This is 19 days later than the date given in the Ebers Papyrus calendar (see next note), and hence there must have been an interval of about 4 X 19 — 76 years between the two calendars. 42 Sethe, op. cit., p. 44; Zeitrechnung, p. 313; Meyer, Nachtr., p. 7; Edgerton, Amer. Jour, of Semitic Languages, LIII (1937), pp. 195 ff., where the calendar is dated to 1536 b.c. The calendar is for the 9th year of Amen-hotpe I when the reappearance of Sothis took place on the 3rd Month of Shdmu, Day 9. 43 Borchardt, Zeitschrift fur dgypt. Sprache, XXXVII (1899), p. 99; Meyer, Chron., pp. 51 ff. Scharff (Altesten Datums, pp. 19, 21, 31) seems to believe that observations of Sothis began only at about this time. 44 They tabulate the stars and constellations as they rose on each of the twelve hours of the night, at intervals of ten days, disregarding—probably for simplicity’s sake—the five intercalary days at the end of the year. Four coffins from Asyut (Chassinat and Palanque, Fouilles dans la Necropole d’Assiout, p. 127, pl. XXV, and p. 196; Lacau, Sarcophages anterieurs au nouvel Empire, II, p. 107; cf. Sethe, p. 306, n. 3, and p. 43, n. 1) and one from Thebes (published only in a preliminary report by Winlock, Bulletin of The Metropolitan Museum of Art, Nov., 1921, Part II, p. 50, fig. 24) set the reappearance of Sothis in the XII hour of the night between the 171st and 180th days of the year. A fifth (Chassinat and Palanque, op. cit., pp. 117-118) is of the same type but only goes to the 160th day. A sixth coffin (from Asyut; Chassinat and Palanque, op. cit., p. 145) sets the reappearance between the 181st and 190th days. The situation shown in the first group of coffins was such as existed from 2101 to 2061 b.c., when Egypt was reunited by Neb-hepet-Re‘ Mentu-hotpe. That shown in the last-mentioned coffin is the condition as it existed between 2061 and 2021 b.c. These are dates in the XI Dyn., agreeing very well indeed with our knowledge of Egyptian history and archaeology. They, furthermore, show that these Middle Kingdom dekan tables were kept up to date by periodic corrections. 45 Often we can not be certain of the exact nature of acts described in documents bearing calendrical dates, and therefore cannot use them in controlling the seasons described. Thus, builders’ marks from Lisht (Lansing, MM.A. Bulletin, April, 1933, II, pp. 5-8; November, 1933, II, p. 6) are dated between March and September, but they do not define the operations recorded sufficiently to be used as a check on the calendar of the period. 46 Meyer, Nachtr., pp. 18 ff. 462 II. E. WINLOCK scriptions that the quarrying season was from January through March in the Twelfth Dynasty, or in terms of the contemporary calendar from the 2nd Month of Akhet to the 1st Month of Proyet. In the Sixth Dynasty, when quarrying must have been done at the same season, the corresponding calendar dates were from the 2nd Month of Shomu to the 1st Month of Akhet, showing that a shift of about 125 days had taken place in the Egyptian calendar in the five centuries between about 1850 and 2350 b.c.47 At each of these several dates the calendar was at variance with the true seasons and with Sothis by about one day for every four years which had elapsed since 2773 b.c. The conclusion is—it seems to me—inescapable that in 2773 b.c. the calendar had been in agreement with the star, and in that year the observations on which this relation had depended were discontinued. The date is astronomically fixed as the start of the wandering calendar of succeeding centuries. We have not, however, sufficient knowledge to do more than guess at what was the historic occasion for this all important change. In all probability Djoser founded the Third Dynasty about 2778 b.c.,48 with the famous sage I-em-hotpe as his vizier, and Egypt entered upon one of its most flourishing periods under an all-powerful, centralized government.49 Doubtless the census takers, the tax collectors, and the hosts of royal scribes who were now managing the land found highly unsatisfactory a year whose beginning depended on the chances of an observation of a star in the dawn. The experience of centuries by now had seemed to show that the year should contain 365 days, and this definite figure was adopted for administrative purposes. But in terms of this new “civil” year the heliacal rising of Sothis gradually came later by a day every four years, until, about a century or so after Djoser’s reign, the inscriptions in the Old Kingdom mastabahs call for offerings on two separate New Year Days—Wepy-ronpet, “the Opener of the Year,” and Tepy-ronpet, 47 Meyer (Chron., pp. 179 ff.) compared these dates when his chronology placed the mean date of the VI Dyn. at 2500 b.c. and concluded that there was a difference in the quarrying season in the two periods. In the above calculation I have used 2350 b.c. as the mean date of the VI Dyn., following his Altere Chron., p. 68, and the quarrying season of the two periods becomes identical. 48 Meyer, Altere Chron., p. 68. In Geschichte, § 231, he credits Djoser with a reign of 19 years. 49 Scharff (Grundzuge, p. 57; Altcsten Datums, p. 18) believes that the 365 day calendar was invented at this time. ORIGIN OF ANCIENT EGYPTIAN CALENDAR 463 “ the First of the Year.” 50 The first of these festivals, in Twelfth Dynasty calendars, is also “the Coming Forth of Sothis”; the second festival in all likelihood was the New Year invented for the calendar when it became definitely and obviously separated from nature. In the meantime, it must not be forgotten that the date of the first appearance of the Nile flood fluctuates between very wide limits, and for several generations after the fixing of the calendar in 2773 b.c. the “civil” year would still have been, to all appearances, as closely related to the flood as ever. By the time that the flood always fell outside of the calendrical “Flood Season”—Akhet —the “civil” calendar had been so long established that no one had the temerity to do anything about it. It was perhaps at this time, while the “civil” calendar was becoming less and less dependable in foretelling the true seasons, that the conservative priesthood invented the coronation oath which called for the new king to swear—as we are informed—“never to intercalate a month or a day nor to vary a festival but to preserve the 365 days as they were ordained of old.” 51 And so for the next three thousand years the Egyptian obstinately refused to follow a fixed calendar, until he adopted the Alexandrian year with Christianity—and to this latter year the Coptic priest still adheres as uncompromisingly as his ancestors followed the ancient calendar. In conclusion, it is my belief that his calendar was not an invention made by the Egyptian on any one day at dawn, when a series of phenomena happened to coincide. On the contrary, it was a gradually developed method of predicting approximately the almost unpredictable rise of the Nile. For a few centuries before 2773 b.c. it depended on the observation of the reappearance of Sirius, and the resulting self-adjusting year was as true a measure 60 Meyer, Chron., pp. 36, 40; Sethe, p. 303. Scharff (Altesten Datums, pp. 16 and 19, note 2) seems to be sceptical of this theory of Meyer’s; firstly, because in New Kingdom inscriptions the Egyptian himself confused the two festival names; and secondly, because his own theory denies the existence of a Sothic year in the Old Kingdom. 81 So far as I am aware, we do not know of this oath before its mention by P. Nigidius Figulus of the 1st Cent. b.c. (Sethe, p. 310; Meyer, Chron., p. 31), but it unquestionably goes back to some period when there was a lively memory of such attempts and a reasonable fear of their repetition. No office holder is ever called upon to abjure a crime which has never been invented. Of course, this oath might have been inspired by the attempted reform of Ptolemy III in the III Cent, b.c., but it is unlikely that such an oath could have been wrung from a king in so enlightened a period. 464 II. E. WINLOCK of solar time as was the much later Julian year. However, as man became more civilized he felt the need of some method of time reckoning more definite than nature itself. In 2773 b.c. he dropped his New Year’s observations and took up the 365 day year, which actually brought his seasons back into their original places only once again during his whole history. ANNUAL REPORT OF THE American Historical Association FOR THE YEAR 1916 IN TWO VOLUMES VOL. I WASHINGTON 1919 WHEN DID THE BYZANTINE EMPIRE AND CIVILIZATION COME INTO BEING? By P. van den Ven. No one has ever contested the fact that the Byzantine Empire disappeared at the capture of Constantinople by the Turks, which disaster effected the complete destruction of the previous state of things in the Greek medieval world. There are in the history of mankind very few events which have brought with them so many radical changes in every branch of human life in so short a period. But disagreements are numerous when it is a question of establishing an initial date as regards the Byzantine Empire as well as the Byzantine civilization. , The division of history into periods is, as everyone knows, from its very nature, conventional and arbitrary, for history really never stops, and all the historical events are so connected with one another as to form an uninterrupted succession. But it w’ould be impossible to master the enormous mass of facts in history without marking certain halting places which correspond, within reasonable limits, to reality, that is, to the beginning and the end of a definite evolution in society, in so far as this beginning and end may be perceived. This classification has also some importance as regards specialization of historical research. Byzantine studies to-day form a special field with its own means for particular investigation, and it is of practical utility to determine the extent of this branch of learning and not to trespass on the domain of other studies. There is a risk of failing to recognize in many cases the real character of events, especially their distant causes, if the investigator has poorly classified them in their ensemble and has left to specialists in neighboring fields the care of investigating facts directly connected with those of his own concern. The difficulty of establishing a date beyond dispute, to mark the beginning of the Byzantine Empire and civilization, comes from the fact that it is hard to find an event which sets off in every aspect of life the starting point of the new evolution of the eastern world. Politically speaking, there is no fixed line of demarcation betw’een the Roman and Byzantine Empires. Those who have given special attention to the Roman structure of the eastern State, that structure 301 302 AMERICAN HISTORICAL ASSOCIATION. which remained the real basis until the end, do not perceive any beginning of a new evolution and therefore do not admit the existence of an empire distinct from the Roman. They have considered, of course, above all, the political institutions. Some who have in addition investigated the social institutions, the church, art, literature, and private life, have been led to a different view. They discover a new type of state and civilization in the beginning of the fourth century. Let us briefly examine the arguments for each position and see if it is possible definitely to determine the beginning of the Byzantine era. The supporters of the uninterrupted evolution of the Roman Empire down to the fifteenth century point with good reason to the fact that the so-called Byzantine Empire is heir and successor to the old Roman Empire. While in the west of the empire the civilization of ancient Rome was completely destroyed by the Germanic invasions, which thus prevented any continuity between the empire of Theodosius and that of Charlemagne, in the east there were for centuries no invasions, no sack of the capital by the barbarians, and therefore no interruption of the Roman life and the Roman State. There is no break in the continuity of the long series of Roman emperors from Augustus to Constantine VII, who was killed in 1453. The foundation of the Western Empire by Charlemagne has no importance in this connection, as it was an artificial creation which the legitimate emperors ruling at Constantinople never recognized, and which in turn never prevented these emperors from maintaining, theoretically at least, what they believed to be their rights over the western provinces of the old Roman State. The empire of Charlemagne did not replace the Western Roman Empire, for the latter never existed any more than an Eastern Roman Empire existed. There were sometimes several emperors, but always, theoretically and legally, only one empire. The separation made by Theodosius in 395 between the east and the west had only an administrative character, which did not at all alter the legal unity of the State. The abdication of Romulus Augustulus in 476 does not mark the end of the so-called Western Roman Empire. Its only effect was to replace the imperial authority in the hands of a single emperor—this emperor was recognized by the barbarians who dispossessed Romulus—and furthermore to reestablish the situation which existed under a sole ruler.1 Because of these facts, therefore, certain historians reject the terms “ Byzantine ” or “ Greek ” which others apply to the Roman Empire in the east after Constantine the Great or Theodosius. They con- 1 See J. B. Bury, A History of the later Roman Empire from Arcadius to Irene, I (1889), pp. v. ff. ; J. Bryce, The Holy Roman Empire (1909), pp. 23 ff., 322 ff. ; L. Hahn, Das Kalzertum (Das Erbe der Aiten, Heft VI) Leipzig, 1913, pp. 82 ff. WHEN DID THE BYZANTINE EMPIRE COME INTO BEING? 303 sider it identical with the old Roman Empire, “which endured, one and undivided, however changed and dismembered, from the first century B. C. to the fifteenth century A. D.”2 They only consent to call it late Roman, and, after the creation of a distinct western empire at Rome in 800, they call it Eastern Roman. Prof. J. B. Bury, the foremost of the historians of this opinion, maintains that all lines of demarcation which have been drawn between the Roman and Byzantine Empires are arbitrary, that “no Byzantine Empire ever began to exist, the Roman Empire did not come to an end till 1453.”3 Great as wTere the changes undergone by this State since antiquity, it never ceased to be the Roman Empire; and if it changed from century to century, it was along a continuous line of development, so that we can not give it a new name, just as we can not give a new name to a man when he enters into a new period of his life, when he passes from youth to maturity and to old age. We designate a man as young and old, and so we may speak of the earlier ard later ages of a kingdom or an empire.4 Since the publication of his excellent History of the Later Roman Empire, in 1889, Bury has not given up his point of view, as one can observe in the reading of his recent work, The Constitution of the Late Roman Empire (Cambridge, 1910), where he failed to mark any distinct period in the evolution of the form of government from the time of Augustus. Another historian, L. Hahn, who is well known for his studies on the influence of Romanism in the Greek world, has called attention only to the Roman factor in the eastern part of the empire.5 He gives preeminence to this down to the time of Justinian, and he fails to show in the slightest degree the workings of any other element. He rejects almost completely the influence of the Orient,6 -which in the mind of Er. Cumont was particularly strong from the third century of the Roman Empire,7 and he does not appear to recognize any particular event as the starting point of a new evolution. N. Jorga,8 impressed by the strength and the relative increase of the Roman element before Justinian, does not recognize Justinian*as a Byzantine ruler. During the three centuries which followed the foundation of Constantinople, the Roman institutions were translated and adapted to the Greek surroundings, and that work was still in progress under Justinian. “ The name Byzantine is given to the type of civilization slightly Roman, conspicuously Greek, and 4 most Christian’ (in the Greek sense also), which was thus pro- 2 Bury, op. cit., p. viii. 8 Ibid., p. v. * Ibid., p. vi. 8 Ludwig, Hahn, op. cit., passim. 6 Ibid., pp. 56 ff. * Fr. Cumont, Mithra, p. xi. •The Byzantine Empire (London, 1907), pp. 3 ff. 304 AMERICAN HISTORICAL ASSOCIATION. duced. The name is appropriated to the result.” Therefore, accord-। ing to Jorga, Byzantinism begins only after Justinian, when it takes the place of Romanism. Finlay, Gregorovius, Zachariae von Lin-genthal had been of the same opinion and had believed in the continuation of the Roman antiquity till the seventh century.’ Because of the lack of any racial feeling, adds Jorga, “ the empire remained what it had always been, an agglomeration of nationalities, governed according to the Roman laws and holding a political ideal which had been formed at Rome.10 11 That political Ideal slowly found a substitute in Christianity.” The Roman empire became more and more the Christian world, the true Christian wTorld, “ orthodox ” if not catholic. Rejecting the West as Arian under the Goths, as idolatrous during the dispute as to images, as perverters of dogma under the Pope, and anathematizing the Mussulmans without trying to convert them, it acquired the consciousness of holding the one and only Christian truth, and of thus being the new “chosen people” of the Lord. It is not to be denied that for centuries after Constantine Romanism was very strong, and the best advocate of the beginning of Byzantinism in the fourth century, K. Krumbacher, acknowledges it distinctly: Das gesamte Staatswesen, die Technik und die Grundsatze der Russeren und inneren Politik, Gesetzgebung und Verwaltung, Heer—und Flottenwesen lag als ungeheures Ergebnis theoretischer Studlen. praktischen Sinues und reicher Erfahrung fertig da, als der bstHche Reichsteil selbstandig wurde; und so sehr die Griechen sich bier bald als Herren im eigenen Hause fiihlten, dieses unschatzbare Erbsttick aus dem lateinischen Westen haben sie, trotz einzelner Anderungen in der Verwaltung (Themenverfassung) und anderen Teilen des Staates, prinzipiell niemals angetastet.u But, what separates Krumbacher’s opinion from the others related above, is that it is not onesided; as we shall see. it takes into account the whole question, and weighs carefully the different factors which came in force in the East in the fourth century. Bury places the beginning of the period of the history of the empire, which he calls “ late Roman ” and which others call Byzantine, in 395. It is interesting to note the reason for his adopting this date. “ In the year 395 A. D. the empire was intact, but with the fifth century its dismemberment began, and 395 A. D. is consequently a convenient date to adopt as a starting point.” 12 13 Quite logically, Prof. Bury does not take his point of departure in the history of the Eastern provinces of the empire by attributing to them a role quite distinct from that of ancient Rome; he takes his • See K. Krumbacher, Geschlchte der byzantinlschen Lltteratur, 2 ed. (1897), pp. 13 ff. w Op. cit., p. 36; see pp. 33 ff. 11 Die grlechlsche und latelnlache Litteratur und Sprache (Die Kultur der Gegen- wart (Tell I, Abtellung VIII), 1905, p. 212). 13 Op. cit., p. ix. WHEN DID THE BYZANTINE EMPIRE COME INTO BEING? 305 starting point in an event which is especially important in the annals of the empire as considered in its ancient state with Italy as its center. Tn his mind it is not the East which separates itself from the West and begins an independent existence; it is the empire as a whole which becomes dismembered by the invasion of the Western ’ provinces. Bury grants theoretically, in the beginning of the evolution of the “ Later Roman Empire,” as much importance to the western provinces as to the eastern, and his point of departure is more concerned with the destinies of the West than with those of the East. But here we find one of the weak points of Bury’s argument. Practically he treats the history of the western provinces as briefly as possible, to the extent that he feels obliged to anticipate criticism of a lack of proportion. “ I am concerned with the history of the Roman Empire, and not with the history of Italy or of ( the West, and the events on the Persian frontier were of vital consequence for the very existence of the Roman Empire, while the events in Italy were, for it, of only secondary importance. Of course, Italy was a part of the empire; but it was outlying—its loss or recovery affected the Roman Republic (strange to say) in a far less degree than other losses or gains. And just as the historian of modern England may leave the details of Indian affairs to the special historian of India, so a general historian of the Roman empire may, after the fifth century, leave the details of Italian affairs to the special historian of Italy.”13 This is an admission of the fact that after the fifth century the West had only a very secondary t importance in the destinies of the empire; that the center of gravity of the empire thereafter was in the East. In spite of the belief in the continuation of the Roman Empire—a belief which remained the same, handed down as it was by traditions, formula?, and survivals, and strongly maintained by the Roman structure of the state— the fact that Italy and Rome were no more the center about which the empire, its institutions and its civilization revolved, marks a change so radical and so far-reaching that it is difficult to understand why Bury, who has excellently w’ritten the history of this change, refuses to harmonize his general viewpoint with the facts which he brings out. It is hard to perceive why he declines to accept the appellation “ Byzantine ” so thoroughly deserved by a state which he recognizes as being so very different from the old Roman Empire. This is another weak point in Bury’s argument. When the emperors in dividing the government of the East and the West were independent of each other, or hostile, as were Arcadius and Honorius, and as a matter of fact East and West went each more and more in “ Ibid., p. xi. 23318°—19----20 306 AMERICAN HISTORICAL ASSOCIATION. its own way, Bury defends the conception of the theoretical unity of the Empire, while taking care not to affirm its unity in reality. Have not facts in history greater importance than formulae, which are the heritage of a past which has ceased to be in harmony with the present? From all this it is evident that the matter in question is not merely the judicious choice of a name, but rather a consideration of the very essence of things under that name. Is the Roman Empire really the Roman Empire down to the fifteenth century, in spite of its numerous transformations? Could it have remained for so long a period the same living creature, the nature of which does not change at the different periods of its life? Did not the transformations which it underwent, in the fourth century and later, permeate so deeply that it is proper from that time on to give it another name corresponding to its new nature? Let us examine now the arguments of those who fix the beginning of the new evolution in the fourth century and recognize its extent by giving the period the name of Byzantine. The late leader in Byzantine studies, K. Krumbacher, is the first, I believe, to have determined the various elements which have formed the Byzantine civilization, the mixed character of which differs strikingly from the unity of the old Greek culture. He recognizes four elements, the gradual intermingling of which has produced the new civilization—i. e., Hellenism, Romanism, Christianity, 1 and oriental influences.14 A great event started the whole new com-’ bination—the establishment of the capital at Byzantium (326). The importance of this event in the destiny of the Empire can not be overestimated. What, indeed, separates the Byzantine era from the Roman era is, above all, the removal of the center of the Empire from the West to the East and, consequently, the gradual substitution of the Greek language for the Latin. The first official and definite step in this course is the foundation of the new capital, Constantinople, and the second one. connected with the first, is the definitive division of the Empire into two parts—Greek East, Latin West (395)—never to be united again. The rapid growth of the capital further strengthened the Greek character of the East and gave it a center which gradually became more and more important. The natural centralizing power of Constantinople appears in many ways. For instance, in ecclesiastical matters, at the Council of Chalcedon (451) the new Rome prevailed over the older See of Alexandria. On the other hand, following the decline of the western part of the Empire, the power of the old Roman State concentrated more and more in the Greek East. At Con- 11 Die griech. und lat. Lit. und Spr., pp. 237 ff. ; Gesch. der byz. Litt., 2 ed., pp. 1 ff. WHEN DID THE BYZANTINE EMPIRE COME INTO BEING? 307 stantinople and in the central provinces the Greek element had been predominant from ancient times, especially among the people and in the church, and the number of people who spoke Latin had always been slight. Greek culture had always stood higher and the Greek language had always been universal. Now, by the much more powerful means at its disposal, the Greek element was in a way to gain the upper hand against the Roman element, which, growing for some time, had been weakening after the dismemberment of the West by the Germans. This Greek element was therefore called upon to take the place of the Roman element in the government of the state. This happened slowly but surely, so that in the centuries after Justinian the state was undergoing an Hellenization of its limbs as well as of its head. The change of the basis of the Empire from Roman to Greek, the transformation from Roman to Romaic or Byzantine was accomplished in the different branches of the organization of the state with varying rapidity. At the last the old system was destined to be more and more thoroughly broken down by the power of natural circumstances. But the great place of the Greek element in the Byzantine Empire does not destroy the force of the statement that there was neither linguistic nor national unity in the eastern world and that the Greek in the East never had in that respect the position of the Latin in the West. The existence of the old oriental civilizations in many provinces of the eastern empire and the official maintenance of the Latin as language of the state explains this to a great extent. Das ungeheure Gefiige, (lurch (lessen Festigkeit das byzantinische Reich den furchtbaren Stiirmen der Perser, Araber, Seldschuken, Slawen, Normannen, Franken, Tiirken und anderer Volker so lange widerstehen konnte, ist rdmische Arbeit. . . . Der Staatsgedanke war unendlich viel starker als das nationale und sprachliche Sonderbewusstsein. So iibernahmen die Griechen denn natiir-lich auch den Nanieu Romer. ... So wunderbar fest und fein war die Struktur des rbmlschen Staatsgebaudes, dass ein so eminent unpolitisches Volk, wie die Griechen im Altertum gewesen sind und heute sind und sicher auch im Mittelalter waren, es im Laufe vieler Jahrhunderte nicht ernstlich zu beschiidigen vermochte. . . . Die Fortwirkung der alten rilmischen, nun in griechisches Gewand gekleideten Tradition im gesamten bffentlichen und pri-vaten Leben der Byzantiner und die Art, wie die herrschenden griechischen und orientalischen Menschen sich mit der ihnen innerlich fremdartigen Staats-und Rechtsordnung abfanden wie sie sich ihr anschmiegten und wie sie mit ihr operierten, gehdrt zu den interessantesten, freilich auch zu den am wenigsten aufgekliirten Seiten der inneren Geschichte von Byzanz.16 Although by the foundation of New Rome and the division of the Empire in 395, neither Constantine nor Theodosius intended to change at all the Roman basis of the Empire and to give it the Greek character which it assumed only later, the developments occasioned “ Die griech. und lat. Lit. und Sprache, p. 242. 308 AMERICAN HISTORICAL ASSOCIATION. by these two events created the new evolution; and it may be said, w ith Krumbacher, that the foundation of Constantinople as a capital 1 really marks the beginning of that evolution, while at the same time the initial changes may have remained invisible. We have seen that the failure of perceiving those symptoms or of giving to them the importance they deserve explains the opinion of those who postpone the beginning of Byzantinism till the seventh century and see in the preceding centuries only the old age and the fall of antiquity. Simultaneously with this we notice other great changes which contributed to the making of a new era. In religion, especially, thanks to the same emperor, Constantine, Christianity officially f takes the place of paganism, and consequently represents one of the most striking differences between Byzantinism and antiquity. A good deal of the Byzantine civilization is to be explained by the influence of the Christian religion and the Christian church. As for the oriental element, it had alwrays been strong in the Greek East; and the various old oriental cultures had never ceased in their influence. The provinces of the empire where the intellectual life was most developed were in direct contact with the native civilization, and it is certain that the latter gave to Hellenism an oriental character, which from Egypt, Palestine, Syria, and Asia Minor spread to Constantinople and the European provinces. From the Orient came many of the habits of thought and customs of the Byzantines, many characteristics in literature and art, many elements of the court and the state organization, “ wie die Auffassung des Kaisertums als einer mysteridsen Macht, der Gegensatz brutaler Volksleidenschaft und grausamster Despotic, die hieratische Gran-dezza, das Eunuchentum, die blutigen Palastrevolutionen und das unheimliche Intrigenspiel, der starre Formalismus im Leben wie in der Litteratur, die Beliebtheit orientalischer Erzahlungsstoffe.” 16 There is no doubt that the political changes introduced by Constantine and Theodosius brought into action the Greek and oriental » elements. Furthermore Constantine made Christianity the state religion. Another great feature, the substitution of the bureaucracy for the military organization of the old empire, is the work of Constantine and his predecessor Diocletian.17 Therefore it seems certain that the beginning of the Byzantine Empire and civilization must be placed in the fourth century, and if a date is necessary, in the year 326, when Constantinople was founded by Constantine. This, however, does not mean the sudden disappearance of the old state of things and instant rise of the new condition of affairs. All that we have said points to an exceedingly gradual change and beginning, 19 Die griech. und lat. Lit. und Sprache. p. 250. 17 See Krumbacher, Gesch. der byz. Litt., 2 ed., p. 7. WHEN DID THE BYZANTINE EMPIRE COME INTO BEING? 309 in no way comparable to the sudden termination of the period in 1453. This argument, which was strongly developed by Krumbacher, has received careful consideration and acceptance with certain recent writers of universal histories, who have given an especial place to the Byzantine period18 and also in some general works of great value.19 Helmolt’s universal history develops the same theory, but, while emphasizing the oriental and Hellenistic elements, it neglects entirely the Roman factor, and so presents just as inaccurate a view by completely overlooking the ever recognized influence of Rome as did the earlier historians who perceived no other element.20 It is also worthy of mention that Wilamovitz-Moellendorf, in 1897, attempting to determine the end of Antiquity, places this terminus in the beginning of the fourth century: “ Die Tatsachen sind da: nur wer sie aus Tragheit oder Vorurteil ignorirt kann bestreiten, dass die Welt-geschichte um 300 an einem der Wendepunkte des grossen Welten-jahres gestanden hat, dass si ch ein Ring an der Kette der Ewigkeit schloss, und wo iiusserlich Continuitat zu sein scheint, in Wahrheit nur ein neuer Ring sich mit dem vorigen geriihrt.”21 18 Lindner, Weltgeschichte, Bd. I (1901), pp 121 ff. 18 E. g., H. Gelzer, Abriss der byzantlniscben Kaisergeschichte, in Krumbacher, Geseh. der byz. Litt., 2 ed., p. 912 ; Kesseling, Essai sur la civilisation byzantlne, Paris, 1907, pp. 13, 37 ; J. Bryce, The Holy Roman Empire (1909), pp. 321 ff., 341. 20 H. E. Helmolt, The World’s History, V (1907), pp. 27 ff. 21 Weltperloden, Rede . . . gehalten von U. v. W.—M. (1897), p. 8. Reprinted for private circulation from JOURNAL OF NEAR EASTERN STUDIES Vol. IV, No. 1, January 1945 PRINTED IN THE U.S.A. JOURNAL OF NEAR EASTERN STUDIES Volume IV JANUARY 1945 Number 1 THE HISTORY OF ANCIENT ASTRONOMY PROBLEMS AND METHODS O. NEUGEBAUER TABLE OF CONTENTS I. Introduction............................................................2 1. Scope and Character of the Paper.....................................2 2. Definition of “Astronomy”............................................2 3. Character of Ancient Astronomy.......................................3 II. Egypt...................................................................4 4. Egyptian Mathematics.................................................4 5. Egyptian Astronomical Documents .....................................4 6. Description of Egyptian Astronomy....................................6 III. Mesopotamia..............................................................8 7. The Sources of Babylonian Astronomy..................................8 8. Mathematical Astronomy in the Seleucid Period........................8 9. Babylonian Mathematics..............................................11 10. Earlier Development of Babylonian Astronomy.........................13 11. Babylonian Astrology •..............................................14 IV. The Hellenistic Period..................................................16 12. Greek Spherical Astronomy...........................................16 13. Mathematical Geography..............................................18 14. Astrology...........................................................20 15. Greek Mathematics...................................................22 16. From Hipparchus to Ptolemy..........................................23 17. Relations to Mesopotamia............................................24 V. Special Problems........................................................26 18. Social Background...................................................26 19. Metrology...........................................................27 20. History of Constellations...........................................28 21. Chronology.................................................., . . 28 22. Hindu Astronomy ....................................................29 23. Methodology of the History of Astronomy.............................30 Bibliography and Abbreviations...............................................32 1 2 Journal of Near Eastern Studies Ce qui est admirable, ce n’est pas que le champ des etoiles soit si vaste, c’est que I’homme l’ait mesure.—Anatole France, Le Jardin d’Epicure. I. INTRODUCTION 1. In the following pages an attempt is made to offer a survey of the present state of the history of ancient astronomy by pointing out relationships with various other problems in the history of ancient civilization and particularly by enumerating problems for further research which merit our interest not only because they constitute gaps in our knowledge of ancient astronomy but because they must be clarified in order to lay a solid foundation for the understanding of later periods. I wish to emphasize from the very beginning that the attitude taken here is of a very personal character. I do not believe that there is any single approach to the history of science which could not be replaced by very different methods of attack; only trivialities permit but one interpretation. I must confess still more: I cannot even pretend to be complete in the selection of topics essential for our understanding of ancient astronomy,1 nor do I wish to conceal the fact that many of the steps which I myself have taken were dictated by mere accident. To mention only one example: without having been brought into contact with a recently purchased collection of Demotic papyri in Copenhagen, I would never have undertaken the investigation of certain periods of Hellenistic and Egyptian astronomy which now seem to me to constitute a very essential link between ancient and medieval astronomy. In other words, though I have always tried to subordinate any particular research problem to a wider program of systematic analysis, the impossibility of elaborate long-range plan- i Also the bibliography, given at the end, is very incomplete and is only intended to inform the reader where he can find further details of the specific viewpoint discussed here and to list the original sources. ning has again and again been impressed upon me. The situation is comparable to entering a vast mountainous region on a single trail; one must simply follow the winding path, trying to give account of its general direction, but one can never predict with certainty what new vistas will be exposed at the next turn. 2. The enormous complexity of the study of ancient astronomy becomes evident if we try to make the first, and apparently simplest, step of classification: to distinguish between, say, Mesopotamian, Egyptian, and Greek astronomy, not to mention their direct successors, such as Hindu, Arabic, and medieval astronomy. Neither geographically nor chronologically nor according to language can clear distinctions be made. Entirely different conditions underlie the astronomy in Egypt of the Middle and New kingdoms than in the periods after the Persian conquest. Greek astronomy of Euclid’s time has very little in common with Hipparchus’ astronomy only a hundred and fifty years later. It is evident that it is of very little value to speak about a “Babylonian” astronomy regardless of period, origin, and scope. And, worst of all, the concept “astronomy” itself undergoes changes in meaning when we speak about different periods. The fanciful combination of a group of brilliant stars to form the picture of a “bull’s leg” and the computation of the irregularities in the moon’s movement in order to predict accurately the magnitude of an eclipse are usually covered by the same name! For methodological reasons it is obvious that a drastic restriction in terminology must be made. We shall here call “astronomy” only those parts of human interest in celestial phenomena which are amenable to mathematical The History of Ancient Astronomy: Problems and Methods 3 treatment. Cosmogony, mythology, and applications to astrology must be distinguished as clearly separated problems —not in order to be disregarded but to make possible the study of the mutual influence of essentially different streams of development. On the other hand, it is necessary to co-ordinate intimately the study of ancient mathematics and astronomy because the progress of astronomy depends entirely on the mathematical tools available. This is in conformity with the concept of the ancients themselves: one need only refer to the original title of Ptolemy’s “Almagest,” namely, “Mathematical Composition.” 3. The study of ancient astronomy will always have its center of gravity in the investigation of the Hellenistic-Roman period, represented by the names of Hipparchus and Ptolemy. From this center three main lines of research naturally emerge: the investigation of the previous achievements of the Near East; the investigation of pre-Arabic Hindu astronomy; and the study of the astronomy of late antiquity in its relation to Arabic and medieval astronomy. This last-mentioned extension of our program beyond antiquity proper is not only the natural continuation of the original problem but constitutes an integral part of the general approach outlined here. Astronomy is the only branch of the ancient sciences which survived almost intact after the collapse of the Roman Empire. Of course, the level of astronomical studies dropped within the boundaries of the remnants of the Roman Empire, but the tradition of astronomical theory and practice was never completely lost. On the contrary, the rather clumsy methods of Greek trigonometry were improved by Hindu and Arabic astronomers, new observations were constantly compared with Ptolemy’s results, etc. This must be paralleled with the total loss of understanding of the higher branches of Greek mathematics before one realizes that astronomy is the most direct link connecting the modern sciences with the ancient. In fact, the work of Copernicus, Brahe, and Kepler can be understood only by constant reference to ancient methods and concepts, whereas, for example, the meaning of the Greek theory of irrational magnitudes or Archimedes’ integrations were understood only after being independently rediscovered in modern times. There are, of course, very good reasons for the fact that ancient astronomy extended with an unbroken tradition deep into modern times. The structure of our planetary system is such that it is simple enough to permit the achievement of relatively far-reaching results with relatively simple mathematical methods, but complicated enough to invite constant improvement of the theory. It was thus possible to continue successfully the “ancient” methods in astronomy at a time when Greek mathematics had long reached a dead end in the enormous complication of geometric representation of essentially algebraic problems. The creation of the modern methods of mathematics, on the other hand, is again most closely related to astronomy, which urgently required the development of more powerful new tools in order to exploit the vast possibilities which were opened by Newton’s explanation of the movement of the celestial bodies by means of general principles of physics. The confidence of the great scientists of the modern era in the sufficiency of mathematics for the explanation of nature was largely based on the overwhelming successes ’of celestial mechanics. Essentially the same held for scholars in classical times. In antiquity, mathematical tools were not available to explain any 4 Journal of Near Eastern Studies physical phenomena of higher complexity than the planetary movement. Astronomy thus became the only field of ancient science where indisputable certainty could be reached. This feeling of the superiority of mathematical astronomy is best expressed in the following sentences from the introduction to the Almagest: “While the two types of theory could better be called conjecture than certain knowledge —theology because of the total invisibility and remoteness of its object, physics because of the instability and uncertainty of matter— .... mathematics alone .... will offer reliable and certain knowledge because the proof follows the indisputable ways of arithmetic and geometry.”2 II. EGYPT 4. A few words must be said about Egyptian mathematics before discussing the astronomical material. Our main source for Egyptian mathematics consists of two papyri3—certainly not too great an amount in view of the length of the period in question! Still, it seems to be a fair assumption that we are well enough informed about Egyptian mathematics. Not only are both papyri of very much the same type but all additional fragments which we possess match the same picture—a picture which is paralleled by economic documents in which occur precisely those problems and methods which we find in the mathematical papyri. The Egyptian mathematical texts, furthermore, find their direct continuation 2 Almagest I, 1 (ed. Heiberg I, 6, ,11 ff.). 3 Math. Pap. Rhind [Peet RMP; Chace RMP] and Moscow mathematical papyrus [Struve MPM], For a discussion of Egyptian arithmetic see Neugebauer [1], for Egyptian geometry Neugebauer [2], and, in general, Neugebauer Vorl. The most recent attempt at a synthesis of Egyptian science, by Flinders Petrie (Wisdom of the Egyptians [London, 1940]), must unfortunately be considered as dilettantish not only because of its disregard of essential source material but also because of its lack of understanding for the mathematical and astronomical problems as such. in Greek papyri,4 which again show the same pattern. It is therefore safe to say that Egyptian mathematics never rose above a very primitive level. So far as astronomy is concerned, numerical methods are of primary importance, and, fortunately enough, this is the very part of Egyptian mathematics about which we are best informed. Egyptian arithmetic can be characterized as being predominantly of an “additive” character, that is, its main tendency is to reduce all operations to repeated additions. And, because the process of division is very poorly adaptable to such procedures, we can say that Egyptian mathematics does not provide the most essential tools for astronomical computation. It is therefore not surprising that none of our Egyptian astronomical documents requires anything more than simple operations with integers. Where the complexity of the phenomena exceeded the capacity of Egyptian mathematics, the strongest simplifications were adopted, consequently leading to little more than qualitative results. 5. The astronomical documents of purely Egyptian origin are the following: Astronomical representations and inscriptions on ceilings of the New Kingdom,5 supplemented by the so-called “diagonal calendars” on coffin lids of the Middle Kingdom6 and by the Demotic-Hieratic papyrus “Carlsberg I.”7 Secondly, the Demotic papyrus “Carlsberg 9,” which shows the method of determining new moons.8 Though written in Roman 4 The continuation of this tradition is illustrated by the following texts: Demotic: Revillout [1]; Coptic: Crum CO, No. 480, and Sethe ZZ, p. 71; Greek: Robbins [1] or Baillet [1]. For Greek computational methods in general, see Vogel [1], 5 Examples: The Nut-pictures in the cenotaph of Seti I (Frankfort CSA) and Ramses IV (Brugsch Thes. 1) and analogous representations in the tombs of Ramses VI, VII, and IX. 8 Cf. Pogo [1] to [4], 7 Lange-Neugebauer [1]. 8 Neugebauer-Volten [1], The History of Ancient Astronomy: Problems and Methods 5 times (after a.d. 144), this text undoubtedly refers to much older periods and is uninfluenced by Hellenistic methods. A third group of documents, again written in Demotic, concerns the positions of the planets.9 In this case, however, it seems to be very doubtful whether these tables are of Egyptian origin rather than products of the Hellenistic culture; we therefore postpone a discussion to the section on Hellenistic astronomy.10 The last group of texts is again inscribed on ceilings and has been frequently discussed because of their representation of the zodiac.11 There can be no doubt that these latter texts were deeply influenced by non-Egyptian concepts characteristic for the Hellenistic period. The same holds, of course, for the few Coptic astronomical documents we possess.12 It is, finally, worth mentioning that not a single report of observations is preserved, in strong contrast to the abundance of observational records from Mesopotamia. It is hard to say whether this reflects a significant historical fact or merely 9 Neugebauer [3], 10 Cf. below, p. 24. 111 know of the following representations of zodiacs: No. 1 (Ptolemy III and V, i.e., 247/181 b.c.): northwest of Esna, North temple of Khnum (Porter-Moss TB VI, p. 118); Nos. 2 and 3 (Ptolemaic or Roman) : El-Salamuni, Rock tombs (Porter-Moss TB V, p. 18); mentioned by L’Hote, LE, pp. 86-87. No. 4 (Ptolemaic-Roman; Tiberius): Akhmim, Two destroyed temples (Porter-Moss TB V, p. 20); mentioned by Pococke DE, I, pp. 77-78. No. 5 (Tiberius): Dendera, Temple of Hathor, Outer hypostyle (Porter-Moss TB VI, p. 49). No. 6 (Augustus-Trajan): Dendera, Temple of Hathor, East Osiris-chapel central room, ceiling, west half (Porter-Moss TB VI, p. 99). Nos. 7 and 8 (1st cent, a.d.): Athribis, Tomb (Porter-Moss TB V, p. 32). No. 9 (Titus and Commo-dus): Esna, Temple of Khnum (Porter-Moss TB VI, p. 116). No. 10 (Roman): Dealer in Cairo, publ. Daressy [1], pp. 126—27, and Boll, Sphaera, Pl. VI. Five other representations of the zodiacal signs are known from coffins, all from Ptolemaic or Roman times. On the other hand, the original Egyptian constellations are still found on coffins of the Saitic or early Ptolemaic periods. 12 The only nonastrological Coptic documents known to me are the tables of shadow lengths published by U. Bouriant and Ventre-Bey [1].—P. Bou-riant [1] did not recognize that the text published by him was a standard list of the planetary “houses” with no specific reference to Arabic astronomy. that we are at the mercy of the accidents of excavation. Speaking of negative evidence, three instances must be mentioned which play a more or less prominent role in literature on the subject and have contributed much to a rather distorted picture of Egyptian astronomy. The first point consists in the idea that the earliest Egyptian calendar, based on the heliacal rising of Sothis, reveals the existence of astronomical activity in the fourth millennium b.c. It can be shown, however, that this theory is based on tacit assumptions which are very implausible in themselves and that the whole Egyptian calendar does not presuppose any systematic astronomy whatsoever.13 The second remark concerns the hypothesis of early Babylonian influence on Egyptian astronomical concepts.14 This theory is based on a comparative method which assumes direct influence behind every parallelism or vague mythological analogy. Every concrete detail of Babylonian and Egyptian astronomy which I know contradicts this hypothesis. Nothing in the texts of the Middle and New Kingdom equals in level, general type, or detail the contemporaneous Mesopotamian texts. The main source of trouble is, as usual, the retrojection into earlier periods of a situation which undoubtedly prevailed during the latest phase of Egyptian history. This brings us to the third point to be mentioned here: the assumption of an original Egyptian astrology. First of all, there is no proof in general for the widely accepted assertion that astrology preceded astronomy. But especially in Egypt is there no trace of astrological ideas in the enormous mythological literature which we possess for all periods.15 13 Neugebauer [4J, Winlock [1], Neugebauer [5], 14 Sponsored especially by the “Pan-Babylonian” school. 16 It is interesting to observe how deeply imbedded is the assumption that astrology must precede as- 6 Journal of Near Eastern Studies The earliest horoscope from Egyptian soil, written in Demotic, refers to a.d. 13 ;* 16 the earliest Greek horoscope from Egypt concerns the year 4 b.c.17 We shall presently see that the assumption of a very late introduction of astrological ideas into Egypt corresponds to various other facts. 6. It is much easier to show that certain familiar ideas about the origin of astronomy are historically untenable than to give an adequate survey of our real knowledge of Egyptian astronomy. A. Pogo is to be credited with the recognition of the astronomical importance of inscriptions on the lids of a group of coffins from the end of the Middle Kingdom,18 apparently representing the setting and rising of constellations, though in an extremely schematic fashion. The constellations are known as the “decans” because of their correspondence to intervals of ten days. He furthermore saw the relationship between these simple pictures and the elaborate representations on the ceilings of the tombs belonging to kings of the New Kingdom.19 It can be safely assumed that the coffin lids are very abbreviated forms of contemporaneous representations on the ceilings of tombs and mortuary temples of the rulers of the Middle Kingdom. The logical place for these representations of the sky tronomy. Brugsch called his edition of cosmogonic and mythological texts “astronomische und astrologische Inschriften” in spite of the fact that these texts do not betray the slightest hint of astrology. 16 Neugebauer [6], 17 Pap. Oxyrh. 804. From this time until a.d. 500 more than sixty individual horoscopes, fairly equally distributed in time, are known to me. is Cf. n. 6. i’ Some of Pogo’s assumptions must, however, be abandoned, because they are based on the distinction of different types of such coffin inscriptions. A close examination of these texts (and also unpublished material) shows that all preserved samples belong to the same type. A systematic edition of all these texts is urgently needed if we are to obtain a solid basis for the study of Egyptian constellations. on ceilings explains their destruction easily enough. The earliest preserved ceiling, discovered in the unfinished tomb of Senmut, the vezir of Queen Hatshepsut,20 is about three centuries later than the coffin lids. Then come the well-preserved ceiling in the subterranean cenotaph of Seti I21 and its close parallels in the tomb of Ramses IV22 and later rulers.23 The difficulties we have to face in an attempt to explain these texts can best be illustrated by a brief discussion of the above-mentioned papyrus “Carlsberg 1.” This papyrus was written more than a thousand years after the Seti text but was clearly intended to be a commentary to these inscriptions. In the papyrus we find the text from the cenotaph split into short sections, written in Hieratic, which are followed by a word-for-word translation into Demotic supplemented by comments in Demotic. The original text is frequently written in a cryptic form, to which the Demotic version gives the key. We now know, for instance, that various hieroglyphs were replaced by related forms in order to conceal the real contents from the uninitiated reader. How successfully this method worked is shown by the fact that one such sign, which is essential for the understanding of a long list of dates of risings and settings of the decans, was used at its face value for midnight instead of evening.24 It is needless to emphasize what the recognition of such substitutions means for the correct understanding of astronomical texts. A complete revision of all previously published material is needed in the light of this new 20 Winlock [2], pp. 34 ff., reprinted in Winlock EDEB, pp. 138 ff., and Pogo [5]. The Anal publication has not yet appeared. 21 Frankfort CSA. 22 Brugsch Thes. I opposite pp. 174-75, but incomplete (cf. Lange-Neugebauer [1], p. 90). 22 Cf. n. 5. 24 Sethe, ZAA, p. 293, n. 1, and Lange-Neugebauer [1], P- 63. The History of Ancient Astronomy: Problems and Methods 7 insight into the Egyptian scheme of describing the rising and setting of stars the year round. One point, however, must be kept in mind in every investigation of Egyptian constellations. One must not ascribe to these documents a degree of precision which they were never intended to possess. I doubt, for example, very much whether one has a right to assume that the decans are constellations covering exactly ten degrees of a great circle on the celestial sphere. I think it is much more plausible that they are constellations spread over a more or less vaguely determined belt around the sky, just as we speak about the Milky Way. It is therefore methodically wrong to use these star lists and the accompanying schematic date lists for accurate computations, as has frequently been attempted. The second Demotic astronomical document, papyrus Carlsberg 9, is much easier to understand and gives us full access to the Egyptian method of predicting the lunar phases with sufficient accuracy. The whole text is based on the fact that 25 Egyptian years cover the same time interval as 309 lunations. The 25 years equal 9125 days, which are periodically arranged into groups of lunar months of 29 and 30 days. The periodic repetition of this simple scheme corresponds, on the average, very well with the facts; more was apparently not required, and, we may add, more was not obtainable with the available simple mathematical means which are described at the beginning of this section. The purpose of the text was to locate the wandering lunar festivals within the schematic civil calendar, as is shown by a list of the ‘‘great” and “small” years of the cycle, which contain 13 or 12 lunar festivals, respectively.25 Accordingly, calen- 25 The “great” and “small” years (already mentioned in an inscription of the Middle Kingdom) have given rise to much discussion (cf., e.g., Ginzel Chron., I, pp. 176-77) which can now be completely ignored. daric problems are seen to be the activating forces here as well as in the decanal lists of the Middle and New Kingdom. The two Carlsberg papyri thus give us a very consistent picture of Egyptian stellar and lunar astronomy and its calendaric relations and are in best agreement with the level known from the mathematical papyri. Before leaving the description of Egyptian science, brief mention should be made of the much-discussed question of the “scientific" character of Egyptian mathematics and astronomy. First of all, the word “scientific” must be clearly defined. The usual identification of this question with that of the practical or theoretical purpose of our documents is obviously unsatisfactory. One cannot call medicine or physics unscientific even if they serve eminently practical purposes. It is neither possible nor relevant to discover the moral motives of a scientist—they might be altruistic or selfish, directed by the desire for systematization or by interest in competitive success. It is therefore clear that the concept “scientific” must be described as a question of methods, not of motives. In the case of mathematics and astronomy, the situation is especially simple. The criterion for scientific mathematics must be the existence of the concept of proof; in astronomy, the elimination of all arguments which are not exclusively based on observations or on mathematical consequences of an initial hypothesis as to the fundamental character of the movements involved. Egyptian mathematics nowhere reaches the level of argument which is worthy of the name of proof, and even the much more highly developed Babylonian mathematics hardly ever displays a general technique for proving its procedures.26 26 See the discussion in Neugebauer Vorl., pp. 203 ff. 8 Journal of Near Eastern Studies Egyptian astronomy was satisfied with a very rough qualitative description of the phenomena—here, too, we miss any trace of scientific method. The first scientific attack of mathematical problems was made in the fifth century b.c. in Greece. We shall see that scientific astronomy can be found shortly thereafter in Babylonian texts of the Seleucid period. In other words, the enormous interest of the study of pre-Hellenistic Oriental sciences lies in the fact that we are able to follow the development far back into pre-scientific periods which saw the slow preparation of material and problems which deeply influenced the shape of the real scientific methods which emerged to full power for the first time in the Hellenistic culture. It is a serious mistake to try to invest Egyptian mathematical or astronomical documents with the false glory of scientific achievements or to assume a still unknown science, secret or lost, not found in the extant texts. III. MESOPOTAMIA 7 . Turning to Babylonian astronomy, one’s first impression is that of an enormous contrast to Egyptian astronomy. This contrast not only holds in regard to the large amount of material available from Mesopotamia but also with respect to the level finally reached. Texts from the last two or three centuries b.c. permit the computation of the lunar movement according to methods which certainly rank among the finest achievements of ancient science—comparable only to the works of Hipparchus and Ptolemy. It is one of the most fascinating problems in the history of ancient astronomy to follow the different phases of this development which profoundly influenced all further events. Before giving a short sketch of this progress as we now restore it according to our present knowledge, we must underline the incompleteness of the present state of research, which is due to the fact that we do not yet have reliable and complete editions of the text material. The observation reports addressed to the Assyrian kings were collected by R. C. Thompson27 and in the editions of Assyrian letters published and translated by Harper,28 Waterman,29 and Pfeiffer;30 much related material is quoted in the publications of Kugler,31 Weidner,32 and others. But Thompson’s edition gives the original texts only in printed type, subject to all the misunderstandings of this early period of Assyriology, and very little has been done to repair these original errors. Nothing short of a systematic “corpus” of all the relevant texts can provide us with the requisite security for systematic interpretation. The great collection of astrological texts, undertaken by Virolleaud33 but never finished, confronts the reader with still greater difficulties, because Virolleaud composed complete versions from various fragments and duplicates without indicating the sources from which the different parts came. And, finally, the tablets dealing with the movement of the moon and the planets were discussed and explained in masterly fashion by Kugler;34 but here, too, a systematic edition of the whole material is necessary.35 Years of systematic work will be needed before the foundations for a reliable history of the development of Babylonian astronomy are laid. 8 . Kugler uncovered step by step the ingenious methods by which the ephemer- 27 Thompson Rep. (1900). 29 Waterman RC. 28 Harper Letters. 30 Pfeiffer SLA. 31 Kugler SSB and Kugler MP. 32 Weidner Hdb., Weidner [1], [2], and numerous articles in the pre-war volumes of Babyloniaca. 33 Virolleaud ACh. 34 Kugler BMR and SSB. 35 Such an edition by the present author is in preparation; it is quoted in the following as ACT. The History of Ancient Astronomy: Problems and Methods 9 ids of the moon and the planets which we find inscribed on tablets ranging from 205 b.c. to 30 b.c. were computed.36 It can justly be said that his discoveries rank among the most important contributions toward an understanding of ancient civilization. It is very much to be regretted that historians of science often quote Kugler but rarely read him;37 by doing this, they have disregarded the newly gained insight into the origin of the basic methods in exact science. This is not the place to describe in detail the Babylonian “celestial mechanics,” as it might properly be called; that will be one of the tasks of a history of ancient astronomy which remains to be written. A few words, however, must be said in order to render intelligible the relationship between Babylonian and Greek methods. The problem faced by ancient astronomers consisted in predicting the positions of the moon and the planets for an extended period of time and with an accuracy higher than that obtainable by isolated individual observations, which were affected by the gross errors of the instruments used. All these phenomena are of a periodic character, to be sure, but are subject to very complicated fluctuations. All that we know now seems to point to the following reconstruction of the history of late Babylonian as- 36 The first tentative (but very successful) steps were made by Epping AB (1889). Then follow Kugler’s monumental works BMR (1900) and SSB (pub-fished between 1907 and 1924), supplemented by Schaumberger’s explanation of the determination of first and last visibility of the moon (1935) and continued by the present author with respect to the theory of latitude and eclipses (Neugebauer [8], [9], Panne-koek [2] and van der Waerden [1]). The theory of planets is treated in Kugler SSB, to be supplemented by Pannekoek [1], Schnabel [2], and van der Waerden [2], All previously published texts and much unpublished material will be contained in Neugebauer ACT. The whole material amounts to about a hundred ephemer-ids for the moon and the planets, covering the above-mentioned two centuries. 37 Abel Rey, La Science orientate avant les grecs (Paris, 1930), and E. Zinner, Geschichte der Stern-kunde (Berlin, 1931), are brilliant examples showing complete ignorance of Kugler’s results. tronomy. A systematic observational activity during the Late Assyrian and Persian periods (roughly, from 700 b.c. onward) led to two different results. First, the collected observations provided the astronomers with fairly accurate average values for the main periods of the phenomena in question; once such averages were obtained, improvements could be furnished by scattered observational records from preceding centuries. Secondly, from individual observations, for example, of the moment of full moon38 or of heliacal settings, etc., short-range predictions could be made by methods which we would call linear extrapolation. Such methods are frequently sufficient to exclude certain phenomena (such as eclipses) in the near future and, under favorable conditions, even to predict the date of the next phenomenon in question. After such methods had been developed to a certain height, apparently one ingenious man conceived a new idea which rapidly led to a systematic method of long-range prediction. This idea is familiar to every modern scientist; it consists in considering a complicated periodic phenomenon as the result of a number of periodic effects, each of a character which is simpler than the actual phenomenon.39 The whole method probably originated in the theory of the moon, where we find it at its highest perfection. The moments of new moons could easily be found if the sun and moon would each move with constant velocity. Let us assume this to be the case and use average values for this ideal movement; this gives us average positions for the new moons. The actual movement deviates from this average but oscillates around it periodically. These deviations were now treated 38 Frequently mentioned in the “reports” to the Assyrian court (e.g., Thompson Rep.). 39 A classic example is the treatment of sounds as the result of the superposition of pure harmonic vibrations. 10 Journal of Near Eastern Studies as new periodic phenomena and, for the sake of easier mathematical treatment, were considered as linearly increasing and decreasing. Additional deviations are caused by the inclination of the orbits. But here again a separate treatment, based on the same method, is possible. Thus, starting with average positions, the corrections required by the periodic deviations are applied and lead to a very close description of the actual facts. In other words, we have here, in the nucleus, the idea of “perturbations,’’ which is so fundamental to all phases of the development of celestial mechanics, whence it spread into every branch of exact science. We do not know when and by whom this idea was first employed. The consistency and uniformity of its application in the older of the two known “systems” of lunar texts point clearly to an invention by a single person. From the dates of the preserved texts, one might assume a date in the fourth or third century b.c.40 This basic idea was applied not only to the theory of the moon (in two slightly modified forms) but also to the theory of the planets. In this latter theory the main point consists in refraining from an attempt to describe directly the very irregular movement, substituting instead the separate treatment of several individual phenomena, such as opposition, heliacal rising, etc.; each of these phenomena is treated with the methods familiar from the lunar theory as if it were the periodic movement of an independent celestial body. After dates and positions of each characteristic phenomenon are determined, the intermediate positions are found by interpola- 40 The attempts to determine a more precise date (Schnabel Ber., pp. 219 ff., and Schnabel [1], pp, 15 ff.) are based on unsatisfactory methods. The generally accepted statement that Naburimannu was the founder of the older system of the lunar theory relies on nothing more than the occurrence of this name in one of the latest tablets in a context which is not perfectly clear. tion between these fixed points.41 It must be said, however, that the planetary theory was not developed to the same degree of refinement as the lunar theory; the reason might very well be that the lunar theory was of great practical importance for the question of the Babylonian calendar : whether a month would have 30 or 29 days. For the planets no similar reason for high accuracy seems to have existed, and it was apparently sufficient merely to compute the approximate dates of phenomena, which, in addition, are frequently very difficult to observe accurately. We cannot emphasize too strongly that the essential point in the above-described methods lies not in the comparatively high accuracy of the results obtained but in their fundamentally new attitude toward the whole problem. Let us, as a typical example, consider the movement of the sun.42 Certain simple observations, most likely of the unequal length of the seasons, had led to the discovery that the sun does not move with constant velocity in its orbit. The naive method of taking this fact into account would be to compute the position of the sun by assuming a regularly varying velocity. It turned out, however, that considerable mathematical difficulties were met in computing the syzygies of the moon according to such an assumption. Consequently, another velocity distribution was substituted, and it was found that the following “model” was satisfactory: the sun moves with two different velocities over two unequal arcs of the ecliptic, where velocities and arcs were determined in such a fashion that the initial empirical facts were correctly explained and at the same time the computation of the conjunctions became suffi- 41 This is shown by a tablet for Mercury, to be published in Neugebauer ACT. The interpolation is not simply linear but of a more complicated type known from analogous cases in the lunar theory. 42 For details see Neugebauer [10] and [9] § 2. The History of Ancient Astronomy: Problems and Methods 11 ciently simple. It is self-evident that the man who devised this method did not think that the sun moved for about half a year with constant velocity and then, having reached a certain point in the ecliptic suddenly started to move with another, much higher velocity for the rest of the year. His problem, was clearly this: to make a very complicated problem accessible to mathematical treatment with the only condition that the final consequences of the computations correctly correspond to the actual observations—in our example, the inequality of the seasons. The Greeks43 called this a method “to preserve the phenomena”; it is the method of introducing mathematically useful steps which in themselves need not be of any physical significance. For the first time in history, mathematics became the leading principle for the structure of physical theories. 9. It will be clear from this discussion that the level reached by Babylonian mathematics was decisive for the development of such methods. The determination of characteristic constants (e.g., period, amplitude, and phase in periodic motions) not only requires highly developed methods of computation but inevitably leads to the problem of solving systems of equations corresponding to the outside conditions imposed upon the problem by the observational data. In other words, without a good stock of mathematical tools, devices of the type which we find everywhere in the Babylonian lunar and planetary theory could not be designed. Egyptian mathematics would have rendered hopeless any attempt to solve problems of the type needed constantly in Babylonian astronomy. It is therefore essential for our topic to give a brief sketch of Babylonian mathematics. 43 E.g., Proclus, Hypotyposis astron, pos. v. 10 (ed. Manitius, 140, 21). I think it can be justly said that we have a fairly good knowledge of the character of mathematical problems and methods in the Old Babylonian period (ca. 1700 b.c.). Almost a hundred tablets from this period are published;44 they contain collections of problems or problems with complete solutions—amounting to far beyond a thousand problems. We know practically nothing about the Sumerian mathematics of the previous periods and very little of the interval between the Old Babylonian period and Seleucid times. We have but few problem texts from the latter period, but they give us some idea of the type of mathematics familiar to the astronomers of this age. This material is sufficient to assure us that all the essential achievements of Old Babylonian times were still in the possession of the latest representatives of Mesopotamian science. In other words, Babylonian mathematical astronomy was built on foundations independently laid more than a millennium before. If one wishes to characterize Babylonian mathematics by one term, one could call it “algebra.” Even where the foundation is apparently geometric, the essence is strongly algebraic, as can be seen from the fact that frequently operations occur which do not admit of a geometric interpretation, as addition of areas and lengths, or multiplication of areas. The predominant problem consists in the determination of unknown quantities subject to given conditions. Thus we find prepared precisely the tools which were later to become of the greatest importance for astronomy. Of course, the term “algebra” does not completely cover Babylonian mathemat- 44 These texts were published in Neugebauer MKT (1935-38) and in Neugebauer-Sachs MCT (1945). A large part of the MKT material was republished in Thureau-Dangin TMB (1939). For a general survey see Neugebauer Vorl. 12 Journal of Near Eastern Studies ics. Not only were a certain number of geometrical relations well known but, more important for our problem, the basic properties of elementary sequences (e.g., arithmetic and geometric progressions) were developed.45 The numerical calculations are carried out everywhere with the greatest facility and skill. We possess a great number of texts from all periods which contain lists of reciprocals, square and cubic roots, multiplication tables, etc., but these tables rarely go beyond two sexagesimal places (i.e., beyond 3600). A reverse influence of astronomy on mathematics can be seen in the fact that tables needed for especially extensive numerical computations come from the Seleucid period; tables of reciprocals are preserved with seven places (corresponding to eleven decimal places) for the entry and up to seventeen places (corresponding to twenty-nine decimal places) for the result. It is clear that numerical computations of such dimensions are needed only in astronomical problems. The superiority of Babylonian numerical methods has left traces still visible in modern times. The division of the circle into 360 degrees and the division of the hour into 60 minutes and 3600 seconds reflect the unbroken use of the sexagesimal system in their computations by medieval and ancient astronomers. But though the base 60 is the most conspicuous feature of the Babylonian number system, this was by no means essential for its success. The great number of divisors of 60 is certainly very useful in practice, but the real advantage of its use in the mathematical and astronomical texts lies in the place-value 16 Incidentally, we also have an example (Neugebauer-Sachs MCT, Problem-Text A) of purely number theoretical type from Old Babylonian times (so-called “Pythagorean numbers”); but it should be added that we do not find the slightest trace of number mysticism anywhere in these texts. notation,46 which is consistently employed in all scientific computations. This gave the Babylonian number system the same advantage over all other ancient systems as our modern place-value notation holds over the Roman numerals. The importance of this invention can well be compared with that of the alphabet. Just as the alphabet eliminates the concept of writing as an art to be acquired only after long years of training, so a place-value notation eliminates mere computation as a complex art in itself. A comparison with Egypt or with the Middle Ages illustrates this very clearly. Operation with fractions, for example, constituted a problem in itself for medieval computers; in place-value notation, no such problem exists,47 thus eliminating one of the most serious obstacles for the further development of mathematical technique. The analogy between alphabet and place-value notation can be carried still further. Neither one was the sudden invention made by a single person but the final outcome of various historical processes. We are able to trace Mesopotamian number-writing far back into the earliest stages of civilization, thanks to the enormous amount of economic documents preserved from all periods. It can be shown how a notation analogous to the Egyptian or Roman system was gradually replaced by a notation which developed naturally in the monetary system and which tended toward a place-value notation. The value 60 of the base appears to be the outcome of the arrangement of the monetary 46 Place-value notation consists in the use of a very limited number of symbols whose magnitude is determined by position. Thus 51 does not mean 5 plus 1 (as it would with Roman or Egyptian numerals), but 5 times 10 plus 1. Analogously in the sexagesimal system, five followed by one (we transcribe 5,1) means 5 times 60 plus 1 (i.e., 301). 47 Example: to add or to multiply 1.5 and 1.2 requires exactly the same operations as the addition or multiplication of 15 and 12. The History of Ancient Astronomy: Problems and Methods 13 units.48 Outside of mathematical texts, the place-value notation was always overlapped by various other notations, and toward the end of Mesopotamian civilization a modified system became predominant. It seems very possible, however, that the idea of place-value writing was never completely lost and found its way through astronomical tradition into early Hindu astronomy.49 whence our, present number system originated during the first half of the first millennium a.d. 10. We now turn to the periods preceding the final stage of Babylonian astronomy which culminated in the mathematical theory of the moon and the planets described above. It is not possible to give an outline of this earlier development because most of the preliminary work remains to be done. A few special problems, however, which must eventually find their place in a more complete picture, can now be mentioned. In our discussion of the methods used in the lunar and planetary theories, we had occasion to mention the extensive use of periodically increasing and decreasing sequences of numbers. A simple case of this method appears in earlier times in the problem of describing numerically the changing length of day and night during the year. The crudest form is the assumption of linear variation between two extremal values.50 Two much more refined schemes are incorporated in the texts of the latest period, but it seems very likely that they are of earlier origin. Closely related are two other problems: the variability of the length of the shadow of the 48 For details see Neugebauer [11] and Neugebauer Vorl., chap, iii § 4. The theory set forth by Thureau-Dangin 88 (English version Thureau-Dangin [1]) does not account for the place-value notation, which is the most essential feature of the whole system. 49 Cf. Datta-Singh HHM I and Neugebauer [12], pp. 266 ff. 60E.g., Weissbach BM, pp. 50-51. “gnomon”51 and the measurement of the length of the day by water clocks.52 The latter problem has caused considerable trouble in the literature on the subject because the texts show the ratio 2:1 for the extremal values during the year. A ratio 2:1 between the longest and the shortest day, instead of the ratio 3:2, which is otherwise used,53 would correspond to a geographical latitude absolutely impossible for Babylon. The discrepancy disappears, however, if one recalls the fact that the amount of water flowing from a cylindrical vessel is not proportional to the time elapsed but decreases with the sinking level.54 It is worth mentioning in this connection that the outflow of water from a water clock is already discussed in Old Babylonian mathematical texts.55 This whole group of texts, however, leads to nothing more than very approximate results. This is seen from the fact that the year is assumed, for the sake of simplicity, to be 360 days long and divided into 12 months of 30 days each.56 This schematic treatment has its parallel in the schemes which we have met in Egyptian astronomy and which we shall find again in early Greek astronomy; we must once more emphasize that elements from such schemes cannot be used for modern calculations, since this would assume quantitative accuracy where only qualitative results had been intended. The calendaric interest of these problems is obvious. The same is true of the 51 Weidner [1], pp. 198 ff. 52 Weissbach BM, pp. 50-51; Weidner [1], pp. 195-96. 63 Schaumberger Erg., p. 377. 64 Neugebauer [19]. 56 Thureau-Dangin [2] and Neugebauer MKT, I, pp. 173 ff. 66 This schematic year of 360 days, of course, does not indicate that one assumed 360 days as the correct length of the solar year. A lunar calendar makes correct predictions of a future date very difficult. The schematic calendar is in practice therefore very convenient for giving future dates which must, at any rate, be adjusted later. 14 Journal of Near Eastern Studies oldest preserved astronomical documents from Mesopotamia, the so-called “astrolabes.”57 These astrolabes are clay tablets inscribed with a figure of three concentric circles, divided into twelve sections by twelve radii. In each of the thirty-six fields thus obtained we find the name of a constellation and simple numbers whose significance is not yet clear. But it seems evident that the whole text constitutes some kind of schematic celestial map which represents three regions on the sky, each divided into twelve parts, and attributing characteristic numbers to each constellation. These numbers increase and decrease in arithmetic progression and are undoubtedly connected with the corresponding month of the schematic twelve-month calendar. It is clear that we have here some kind of simple astronomical calendar parallel (not in detail, but in purpose) to the “diagonal calendars” in Egypt. In both cases these calendars are of great interest to us as a source for determining the relative positions and the earliest names of various constellations. But here, too, the strongest simplifications are adopted in order to obtain symmetric arrangements, and much remains to be done before we can answer such questions as the origin of the “zodiac.” 11. Few statements are more deeply rooted in the public mind or more often repeated than the assertion that the origin of astronomy is to be found in astrology. Not only is historical evidence lacking for this statement but all well-documented facts are in sharp contradiction to it. All the above-mentioned facts from Egypt and Babylonia (and, as we shall presently see, also from Greece) show that calen-daric problems directed the first steps of 57 This name is rather misleading and is merely due to the circular arrangement. Schott [1], p. 311, introduced the more appropriate name “twelve-times-three.” Such texts are published in CT 33, Pls. 11 and 12. Cf. also Weidner Hdb., pp. 62 if. and Schott [1]. astronomy. Determination of the season, measurement of time, lunar festivals— these are the problems which shaped astronomical development for many centuries; and we have seen that even the last phase of Mesopotamian astronomy, characterized by the mathematical ephem-erids, was mainly devoted to problems of the lunar calendar. It is therefore one of the most difficult problems in the history of ancient astronomy to uncover the real roots of astrology and to establish their relation to astronomy. Very little has been done in this direction, mainly because of the prejudice in favor of accepting without question the priority of astrology. Before going into this problem in greater detail, we must clarify our terminology. The modern reader usually thinks in terms of that concept of astrology which consists in the prediction of the fate of a person determined by the constellation of the planets, the sun, and the moon at the moment of his birth. It is well known, however, that this. form of astrology is comparatively late and was preceded by another form of much more general character (frequently called “judicial” astrology in contrast to the “genethlialogical” or “horoscopic” astrology just described). In judicial astrology, celestial phenomena are used to predict the imminent future of the country or its government, particularly the king. From halos of the moon, the approach or invisibility of planets, eclipses, etc., conclusions are drawn as to the invasion of an enemy from the east or west, the condition of the coming harvest, floods and storms, etc.; but we never find anything like the “horoscope” based on the constellation at the moment of birth of an individual. In other words, Mesopotamian “astrology” can be much better compared with weather prediction from phenomena observed in the skies than with astrology in the modern sense of the The History of Ancient Astronomy: Problems and Methods 15 word. Historically, astrology in Mesopotamia is merely one form of predicting future events; as such, it belongs to the enormous field of omen literature which is so familiar to every student of Babylonian civilization.58 Indeed, it can hardly be doubted that astrology emerged from the general practice of prognosticating through omens, which was based on the concept that irregularities in nature of any type (e.g., in the appearance of newborn animals or in the structure of the liver or other internal parts of a sheep) are indicative of other disturbances to come. Once the idea of fundamental parallelism between various phenomena in nature and human life is accepted, its use and development can be understood as consistent; established relations between observed irregularities and following events, constantly amplified by new experiences, thus lead to some sort of empirical science, which seems strange to us but was by no means illogical and bare of good sense to the minds of people who had no insight into the physical laws which determined the observed facts. Though the preceding remarks certainly describe the general situation adequately, the historical details are very much in the dark. One of the main difficulties lies in the character of our sources. We have at our disposal large parts of collections of astrological omens arranged in great “series” comprising hundreds of tablets. But the preserved canonical series come mainly from comparatively late collections (of the Assyrian period) and were thus undoubtedly subject to countless modifications. We must, moreover, probably assume that the collection of astrological omina goes back to the Cassite period (before 1200 b.c.)—a period about which our 68 A comprehensive study of the development of the astrological omina literature by E. F. Weidner is in course of publication (Weidner [2]). general information is pretty flimsy. From the Old Babylonian period only one isolated text is preserved59 which contains omina familiar from the later astrology. Predictions derived from observations of Venus made during the reign of Ammisa-duqa (ca. 1600 b.c.) are preserved only in copies written almost a thousand years later60 and clearly subjected to several changes during this long time. We are thus again left in the dark as to the actual date of the composition of these documents except for the fact that it seems fairly safe to say that no astrological ideas appear before the end of the Old Babylonian period. Needless to say, there are no astrological documents of Sumerian origin. The period of the ever increasing importance of astrology (always, of course, of the above-mentioned type of “judicial” astrology) is that beginning with the Late Assyrian empire. The “reports” mentioned previously, preserved in the archives of the Assyrian kings, are our witnesses. But here, again, a completely unsolved problem must be mentioned: we do not know how the “horoscopic” astrology of the Hellenistic period originated from the totally different omen type of astrology of the preceding millennium. It is, indeed, an entirely unexpected turn to make the constellation of the planets at a single moment responsible for the whole future of an individual, instead of observing the ever shifting phenomena on the sky and thus establishing short-term consequences for the country in general (even if represented in the person of the king). It seems to me by no means self-evident that this radical shift of the character of astrology actually originated in Babylonia. We shall see in the next section that the horoscopic practice flourished especially in Egypt. It might therefore very well be that the new tendency originated in Hellenistic times 69 Sileiko [1], "Langdon VT. 16 Journal of Near Eastern Studies outside Mesopotamia and was reintroduced there in its modified form. It might be significant that only seven horoscopes are preserved from Mesopotamia, all of which were written in the Seleucid period,61 a ridiculously small number as compared with the enormous amount of textual material dealing with the older ujudicial” astrology. It must be admitted, however, that the oldest horoscopes known are of Babylonian origin. On the other hand, at no specific place can all the elements be found which are characteristic for astrology from Hellenistic times onward. Neither Babylonian astrology nor Egyptian cosmology furnishes the base for the fundamental assumption of horoscopic astrology, namely, that the position of the planets in the zodiac decides the future. And, finally, it must be emphasized that the problem of determining the date and place of origin of horoscopic astrology is intimately related to the problem of the date and origin of mathematical astronomy. Horoscopes could not be cast before the existence of methods to determine the position of the celestial bodies for a period of at least a few decades. Even complete lists of observations would not be satisfactory because the positions of the planets in the zodiac are required regardless of their visibility at the specific hour. This shows how closely interwoven are the history of astrology and the history of planetary theories. IV. THE HELLENISTIC PERIOD 12 . Before beginning the discussion of the Hellenistic period, we must briefly describe the preceding development in 61 Two are published by Kugler SSB, II, 554 fl., and refer to the years 258 and 142 b.c., respectively. One (probably 233 b.c.) is published in Thompson AB 251. Among four unpublished horoscopes, discovered by Dr. A. Sachs, two are very small fragments, one can be dated 235 b.c., and the last was cast for the year 263 b.c.; the last is the oldest horoscope in the world. Greece. Our direct sources of information about astronomy and mathematics before Alexander are extremely meagre. The dominating influence of Euclid’s Elements succeeded in destroying almost all references to pre-Euclidean writings, and essentially the same effect was produced by Ptolemy’s works. Original documents are, of course, not preserved—one must not forget that even our oldest manuscripts of Greek mathematical and astronomical literature were written many centuries after the originals.62 It is therefore not surprising that our present-day knowledge of early Greek science is much more incomplete and subject to conjecture than the history of Mesopotamian or even Egyptian achievements where original documents are at our disposal. One point, however, can be established beyond any doubt: early Greek astronomy shows very strong parallelism with the early phases of Egyptian and Babylonian astronomy, with respect to scope as well as primitiveness. The astronomical writings of Autolycus63 and Euclid64 struggle in a very crude way with the problem of the rising and setting of stars, making very strong simplifications which were forced upon them by the lack of adequate methods in spherical geometry. The final goal is again to establish relations between the celestial phenomena and the seasons of the years; the problem is thus of essentially calendaric interest. In addition to these simple treatises, however, we do find one work of outstanding character: the planetary theory of Eudoxos, Plato’s famous contemporary. He made an attempt to explain the peculiarities of a planetary movement known as retrogra- 62 The oldest preserved manuscript of Euclid’s Elements was written about twelve hundred years after Euclid (cf., e.g., Heath Euclid, I, p. 47). 63 Autolycus, ed. Hultsch (Leipzig, 1885). 64 Euclidis opera omnia, Vol. VIII, ed. Menge (Leipzig, 1916). The History of Ancient Astronomy: Problems and Methods 17 dation by the assumption of the superposition of the rotation of two concentric spheres around inclined axes and in opposite directions. In this way he reached a satisfactory explanation of the general type of planetary movement and thereby inaugurated a new period in the history of astronomy which was marked by attempts to explain the movements of the planetary system by mechanical models. It contains the nucleus for all planetary theories of the following two thousand years, namely, the assumption that irregularities in the apparent orbits can be explained as the result of superposed circular movements. It is only since Galileo and Newton that we know that the circular orbits do not play an exceptional role and that the great successes of the Greek theory were merely due to the accidental distribution of masses in our planetary system. It is, nevertheless, of great historical interest to see how a plausible initial hypothesis can for many centuries determine the line of attack on a problem, simultaneously barring all other possibilities. Such possibilities were actually contained in the approach developed by the Babylonian astronomers in the idea of superposing linear or quadratic periodic functions. These arithmetical methods were, however, almost completely abandoned by the Greek astronomers (at least so far as we know) and survived only in the treatment of certain smaller problems. One of these smaller problems is again related to calendaric questions but also to a basic problem of mathematical geography: the determination of the geographical latitude by means of the ratio of the longest to the shortest day. We have'already mentioned the Babylonian methods of describing the change in the length of the days by means of simple sequences. These “linear” methods reappear in Greek literature and can be followed far into the early Middle Ages65 in spite of the invention of much more accurate methods.66 The term “linear” does not refer so much to the fact that the sequences in question form arithmetic progressions of the first order but is intended to emphasize the contrast with the “trigonometric” method applied to the same problem and explained in the first book of the Almagest. Here the exact solution of the problem by the use of spherical trigonometry is given. In contrast thereto, the linear methods yield only approximate results, but with an accuracy which was certainly sufficient in practice, especially when one takes into account the inaccuracy of the ancient instruments used in measuring time. Historically, however, the main interest lies much less in the perfection of the results than in the method employed and in its influence on the further development. A close investigation of early Greek astronomy and mathematics67 reveals an interesting fact. The determination of the time for the rising and setting of given arcs of the ecliptic, which lies at the heart of the question of the changing length of day and night, appears to be the most decisive problem in the development of spherical geometry. It is typical for the whole situation that a Greek “mathematical” work, the Sphaerics of Theodosius (ca. 200 b.c.), does not contain a single astronomical remark. The structure and contents of the main theorems, however, are determined by the astronomical problem in question; the methods applied constitute a very interesting link between the Babylonian linear methods and the final trigonometrical methods. Trigonometry undoubtedly has a very 65 Neugebauer [13] and [18]. 06 Almagest II, 7 and 8. Cf. also Tetrabiblos I, 20 (ed. Robbins, p. 94), 21 (ed. Boll-Boer, pp. 46, 47 ff.). 67 This investigation has been carried out by Olaf Schmidt (doctoral thesis, Brown Univ., 1943 [unpublished]) . 18 Journal of Near Eastern Studies long history. We find the basic relations between the chord and diameter of a circle already in use in Old Babylonian texts which employ the so-called “Thales” and “Pythagorean” theorems.68 In sharp contrast to the Greek models for the movement of the celestial bodies, which operate with circles and therefore necessarily require trigonometrical functions, we find no applications of trigonometry in the cuneiform astronomical texts of the Seleu-cid period which are exclusively based on arithmetical methods described above. So far as we know, spherical trigonometry appears for the first time in the Sphae-ric of Menelaos69 (ca. a.d. 100). The astronomical background of this work is much more outspoken than in Theodosius, but here, too, much is left to the reader, who must be familiar with the methods of ancient astronomy to understand all the astronomical implications. The modern scholar faces an additional difficulty, namely, the modification of the Greek text by the Arabic editors. The Greek original is lost, and what we possess is only the Arabic version made almost a thousand years later. In this interval falls the gradual transformation of Greek trigonometry, operating with chords, to the modern treatment, which uses the sine function. It is well known that this change goes back to Hindu astronomy, where the chords subtended by an angle were replaced by the length of the half-chord of the half-angle,70 i.e., our “sin a.” It is, however, a much more involved question to separate these new methods from those used originally by Menelaos; this question must be answered if we wish to understand the development of ancient spherical astronomy. This, in turn, is 68 Cf. Neugebauer-Struve [1], pp. 90-91; Neugebauer MKT, I, p. 180; and Neugebauer-Sachs MCT, Problem-Text A. 69 Krause Men. 70 Cf., e.g., Braunmiihl GT, chap. 3. necessary in order to appreciate the contributions made by the Hindu-Arabic astronomers which eventually led to the modern form of spherical trigonometry. 13. It is of great interest to see that the very same problem—the determination of rising times—leads to still other methods which are now known partly as “nomog-raphy,” partly as “descriptive geometry.” We have a small treatise, written by Ptolemy, called the Analemma.7' He first introduces in a very systematic way three different sets of spherical coordinates, each of which determines the position of a point on the celestial sphere. Then these coordinates are projected on different planes, and these planes are turned into the plane of construction, just as we do today in descriptive geometry. Finally, certain scales are used to find graphically the relations between different coordinates, again following principles which we now use in nomography. The Arabs used and developed these methods in connection with the construction of sundials.72 Another method of projection, today called “stereographic,” is given in Ptolemy’s Planisphaerium. The theory of perspective drawing in the Renaissance is directly connected with this work.73 The practical importance of the determination of the rising times or the length of the days is not restricted to the theory of sundials. The length of the longest day increases with the geographical latitude, thus giving us the means to determine the latitude of a place from the ratio of the 71 Ptolemy, Opera II, pp. 187-223. No complete translation of this badly preserved text has yet been published, but an excellent commentary has been given by Luckey [1]. These methods, using descriptive geometry, are of an older date, as is evident from the fact that they are already mentioned by Vitruvius (beginning of our era). Cf. Neugebauer [14] and Luckey [2], 72 Cf., e.g., Garbers ES and Luckey [2], 73 Ptolemy, Opera II, pp. 225-59, translated in Drecker [1]; cf. also Loria in M. Cantor, Geschichte der Mathematik, IV, p. 582. The History of Ancient Astronomy: Problems and Methods 19 shortest to the longest day. The ratio. 3 : 2 accepted by Babylonian astronomers for the ratio of the longest to shortest daylight led the Greek geographers to determine erroneously the latitude of Babylon as 35° (instead of 32|°). This error seriously affected the shape of the eastern part of the ancient map of the world.74 The precise relationship can only be established by using spherical trigonometry, but here, too, the “linear” methods were applied to various values of the basic ratio in order to give the law for the changing length of the days for the corresponding latitude. It must be remarked, however, that at this stage of affairs the concept “latitude” does not yet actually appear, but the ratio of the longest to the shortest day itself was used to characterize the location of a place. Zones of the same ratio were considered as belonging to the same “clima,” a concept which plays a great role in ancient and medieval geography. The difference in character and behavior of nations living in different climates furnished one of the main arguments for the influence of astronomical phenomena on human life.75 The second geographical coordinate— the longitude—caused more trouble. The difference in longitude between two places on the earth is essentially equivalent to the difference in local time. But there existed no clocks or signals to compare the local time at far-distant places. Only one phenomenon could be used as a time signal, namely, records of simultaneous observations of a lunar eclipse from two different places. If each observer took note of the local time at which he observed the beginning and end of a lunar eclipse, a 74 For the determination of the size of the earth by Eratosthenes (about 250 b.c.), Marinus of Tyre (about a.d. 100), and Ptolemy (about a.d. 150), see Mzik EGM, pp. 96 ff., and, in general, Heidel GM, chap. xi. Of. also Honigmann SK and Neugebauer [13]. 75E.g., Tetrabiblos II, 2. comparison of these records would then furnish the needed information. Hipparchus proposed the use of this method for an exact construction of the map of the world, but his program was never carried out. Only one pair of simultaneous observations seems to have been made, the eclipse of 331 b.c., September 20, recorded three hours earlier in Carthage than at Arbela.76 Actually the difference in local time between these two localities is much smaller, and consequently the ancient map of the world suffers from a serious distortion in the direction from east to west. Here we see one of the most essential differences between ancient and modern science at work. Ancient science suffered most severely from the lack of scientific organization which is so familiar in our own times. In antiquity, generations passed before a new scientific idea found a follower able to use and develop methods handed down from a predecessor. The splendid isolation of the great scholars of antiquity can only be paralleled with the first beginnings of the new development in the European Renaissance. It seems to me beyond any doubt that even centers like Alexandria or Pergamon during their height would appear very poorly equipped if compared with a modern university of moderate size. And these centers themselves were few and practically isolated at any particular time; and at all times they were dependent upon the mood of some autocratic ruler. No wonder that the great achievements of antiquity are either the result of priestly castes of sufficiently stable tradition or of a few ingenious men who expended tremendous energy in restoring and enlarging the structure of a science known to them from the written legacy of their predecessors. One must not think 76 Ptolemy Geographia i. 4. 2 (ed. Nobbe, p. 11). Cf. also Mzik-Hopfiier PDE, p. 21, n. 3. For Hipparchus’ program see Strabo Geography i. C. 7; also Berger GFH, pp. 12 ff. 20 Journal of Near Eastern Studies that mathematics and astronomy, like the popular philosophical systems or the art of rhetoric, were taught in the same manner from generation to generation. Three centuries separate Hipparchus from Ptolemy, one Eudoxos from Euclid, Euclid from Archimedes and Apollonius. To be sure, the literary tradition was never interrupted between these outstanding men, but most of the intermediate literature at best merely preserved and commented. This explains not only why ingenious ideas were frequently lost (e.g., Archimedes’ methods of integration) but also why it was so easy to destroy ancient science almost completely in a very short time. Astronomy alone had a slight advantage because of its practical usefulness in navigation, geography, and time-reckoning, supplemented by the fortunate accident that the Easter festival followed the lunar calendar of the Near East, thus sanctioning lunar theory when other secular sciences fell into total desuetude. The extreme paucity of scientists at almost any given time in antiquity gave rise to another phenomenon in Greek literature: the publication of commentaries and popularizing works. A work like the Almagest, written in purely scientific style, was certainly unintelligible to the majority of people who needed or wanted to know a modest amount of astronomy. Hence books were written which attempted to explain Ptolemy’s text sentence by sentence,77 or which gave abstracts accompanied by explanations of the main principles as far as this could be done without mathematics.78 We can observe the same phenomenon in geography. The first chapter of Ptolemy’s Geography™ 77 The commentaries of Pappus and Theon of Alexandria (and presumably of Hypathia) are of this type. For these texts cf. Rome CPT. 78 Represented, e.g., by Theon of Smyrna (second cent, a.d.) or Proclus (fifth cent. a.d.). 79 Edited by Nobbe (1843). The first chapter is excellently discussed by MMk and Hopfner PDE. contains a very interesting theory of map projection, whereas the remaining twelve chapters constitute an enormous catalogue of localities from all over the then known world and the corresponding values of longitude and latitude to be plotted into the network which was to be constructed according to the method explained in the first chapter. This, again, was not geography for the entertainment of the general reader. To satisfy popular tastes, there was another literature, represented by works like Strabo’s Geography. These more pleasant writings furnished serious competition to the strictly scientific literature and determined to a large extent the character of the field in late antiquity and the Middle Ages. 14. For the modern historian of ancient astronomy it is therefore of the greatest value to have an additional source of astronomical literature in which the earlier tradition was kept alive without interruption for a much longer period: the astrological texts. We have already mentioned that astrology in the modern use of the word appeared very late in antiquity. The art of casting horoscopes can be said to be a typical Hellenistic product, the result of the close contact between Greek and oriental cultures.81 We possess Greek papyri from Egypt from the beginning of our era to the Arabian conquest showing us the application of astronomical methods in a great number of specific horoscopes and in minor astronomical treatises.82 In addition, an enormous astrological literature is preserved, catalogued during the last fifty years in the twelve volumes of the Catalogus by Cumont and 30 Edited and translated in the “Loeb Classical Library” by H. L. Jones (8 vols.; 1917-32). 81 Cf., e.g., Capelle [1], who shows that only weak traces of astrological ideas in Greek literature can be followed as far back as 400 b.c. 82 Concerning horoscopes, see above, n. 17. Examples of astronomical treatises are Pap. Ryl. 27, 464, 522/24, 527/28, or Curtis-Robbins [1], The History of Ancient Astronomy: Problems and Methods 21 his collaborators.83 Finally, Vettius Valens, who wrote shortly before Ptolemy,84 and Ptolemy himself as the author of the famous Tetrabiblos, must be mentioned.85 Modern scholars have not yet made full use of this vast material. The reason is only too clear: the amount of work to be done surpasses by far the power of a single individual, and the work itself is certainly not very pleasant. The astronomical part must be extracted from occasional remarks, short computations, and similar instances submerged beneath purely astrological matter of a very unappealing character. But this work must eventually be done and will give valuable results. As an example might be mentioned the question of discovering the principle according to which the equinox was placed in the zodiac. This question must be answered, for on it depend our calculations in the determination of constellations, chronology, etc. Moreover, systematic checking of astrological computations will frequently yield information about the character of the astronomical tables used at the time. We touch here upon a point of great importance for the modern attitude toward ancient astronomy. The usual treatment of ancient sciences as a homogeneous type of literature is very misleading. It is necessary to realize that very different levels of astronomy or mathematics were coexistent, almost without mutual contact or interference. One misses the essential points in the understanding of ancient astronomy if one naively considers various documents in their chronological order. Even works by the same person must sometimes be separated from one another. Ptolemy’s Almagest is purely mathematical, the Tetrabiblos (written S3 CO AG. Of. also Boll [2], si Kroll VV. 85 Ptolemy, Opera III, 1, and “Loeb Classical Library” (ed. F. E. Robbins). after the Almagest)86 is purely astrological, and his Harmonics87 contains a chapter on the harmony of spheres employing concepts of the planetary movements which contains such strong simplification of the actual facts that one would try in vain to find similar assumptions in any of the other works of Ptolemy. In other words, it is necessary to evaluate each text in its proper surrounding and according to its traditional style. One cannot, for example, speak without qualification of the contact between Babylonian and Greek astronomy. Such a contact might even have worked in opposite directions in different fields. For instance, we have already referred to the possibility that Hellenistic astrology returned to Babylonia in the form acquired in Egypt or Syria, whereas observational material from Mesopotamia undoubtedly influenced Greek mathematical astronomy deeply. In general, it can be said that the growth of ancient sciences shows much more irregularity and stratification than modern scientists, accustomed to the fact of the uniform spread of modern ideas and methods, are prone to assume. The lack of uniformity in the whole field of ancient astronomy in general necessarily interferes also with the investigation of any special problem. We have already mentioned the fact that astrology in the Assyrian age differed considerably from the horoscopic type which prevailed in late antiquity and the Middle Ages. But there exists a third type, standing between the omina type (“when this and this happens in the skies, then such and such a major event will be the consequence”) and the individual birth horoscope, namely, the “general prognostication,” explained in full detail in the first two books of the Tetrabiblos. This type of 86 This follows from the introduction to the Tetrabiblos. During HP and PPM. 22 Journal of Near Eastern Studies astrology is actually primitive cosmic physics built on a vast generalization of the evident influence of the position of the sun in the zodiac on the weather on earth. The influence of the moon is considered as of almost equal importance, and from this point of departure an intricate system of characterization of the parts of the zodiac, the nature of the planets, and their mutual relations is developed.88 This whole astronomical meteorology is, to be sure, based on utterly naive analogies and generalizations, but it is certainly no more naive and plays no more with words than the most admired philosophical systems of antiquity. It would be of great interest for the understanding of ancient physics and science in general to know where and when this system was’ developed. The question arises whether this is a Greek invention, replacing the Babylonian omen literature, which must at any rate have lost most of its interest with the end of independent Mesopotamian rule, whether it precedes the invention of the horoscopic art for individuals or merely represents an attempt to rationalize the latter on more general principles.89 Thus we see that even in a single field of ancient astronomical thought the most heterogeneous influences are at work; the analysis of these influences has repercussions on almost every aspect of the study of ancient civilizations.90 15. The same branching-off into very different lines of thought must also be recognized in the development of Greek mathematics. The line of development characterized by the names of Eudoxus, Euclid, Archimedes, and Apollonius is to be separated sharply from writings like 88 For the whole complex of the ancient justifications of astrology, see Duhem, SM, II, 274 ff. 89 This is the assumption of Kroll [1], p. 216, for the tendency exhibited in Ptolemy’s Tetrabiblos. 90 Cf. the excellent survey of this situation in Boll [2], Heron91 and Diophantus92 or the Arithmetic of Nicomachus of Gerasa.93 Here, again, the question of oriental influence cannot be discussed as one common phenomenon. Egyptian calculation technique and mensuration were certainly continued in similar works in Hellenistic Egypt and found their way into Roman and medieval practices. At the same time, Babylonian numerical methods influenced Alexandrian astronomy. How Babylonian algebraic concepts eventually reached Greek writers like Diophantus is still completely unknown, but that it did is supported by the strong parallelism in methods and problems.94 Equally lacking is detailed information as to the revival of these methods in Moslem literature.95 On the other hand, the problems which emerged from the discovery of the irrational numbers are undoubtedly of Greek origin. It is, however, not correct to consider writings of the same person as equally representative of “Greek” mathematics. Those parts of Euclid’s Elements (the majority of the work) which deal more or less directly with the problem of irrational numbers are, as we said before, Greek. Most likely of equally Greek origin is Euclid’s astronomical treatise called Phenomena,w which is written on so elementary a level that nobody would attribute it to the author of the Elements if the authorship were not so firmly established. And, finally, Euclid’s Data'-*’1 contains the treatment of purely algebraical problems by geometrical means—which can be interpreted as the direct geometrical transla- 9 1First century a.d.; cf. for this date Neugebauer [14], pp. 21 ff. 92 Usually dated about a.d. 300; cf., however, Klein [1], p. 133, n. 23. 93 Greek text ed. Hoche (Leipzig, 1866); English translation: D’Ooge-Robbins-Karpinski Nic. 94 Vogel [2]; Gandz [3]. 96 Gandz [1], [2], [3]. 96 Opera VIII; cf. above, p. 16. 97 Opera VI. The History of Ancient Astronomy: Problems and Methods 23 tion of methods well known to Babylonian mathematics.98 These methods of “geometrical algebra” in turn determine the whole structure of Apollonius’ theory of conic sections.99 Greek mathematics is by far the best-investigated field of ancient science (and of the history of science in general) ;100 the situation with respect to the source material is very good101—except where only Arabic manuscripts are preserved.102 But one must not forget that also this tradition suffers from severe gaps. This is due not only to the destruction of manuscripts over a period of two thousand years but also to the effect of literary influence. I refer not only to the above-mentioned elimination of older treatises by the overshadowing of the great works of the Hellenistic period. The Greeks themselves contributed to the distortion of the picture of the actual development by inventing seemingly plausible stories where the real records were already lost. The oft-repeated stories about Thales, Pythagoras, and other heroes are the result.103 * We should now realize that we know next to nothing about earlier Greek mathematics and astronomy in general and about the contact with the Near East and its influence in particular. The method which involves the use of a few obscure citations’04 from 98 Neugebauer [15]. "Zeuthen KA and Neugebauer [16]. 100 Best exposition: Heath GM and MGM and Euclid. A selection of texts is given in Thomas GM W. 101 Most of the texts are edited in the Teubneriana collection. 102 Menelaos alone is now edited (Krause Men.), but Books v, vi, and vii of Apollonius’ Conic Sections are still unavailable in a modern edition. Archimedes’ construction of the heptagon is published in a free translation of the Arabic version in Schoy TLAB, pp. 74-91; cf. also Tropfke [1], 103 As an example might be mentioned the criticism of the story of the Thales eclipse by Pannekoek [3], p. 955; Dreyer HPS, p. 12, n. 2; Neugebauer [9], pp. 295-96. Cf. also Frank, Plato, or Heidel [1], 104 The fragments collected by Diels VS not only give an extremely incomplete picture of the lost writings but were certainly very much distorted by the late authors for the restoration of the history of science during the course of centuries seems to me doomed to failure. This amounts to little more than an attempt to understand the history of modern science from a few corrupt quotations from Kant, Goethe, Shakespeare, and Dante. 16 . Undoubtedly the most spectacular advances in the history of astronomy until very recent times were scored in the theory of the planets. The catch-words “Ptolemaic” and “Copernican” refer to different assumptions as to the mechanism of the planetary movement. This is not the place to underline the fact that the Copernican theory is by no means so different from or so superior to the Ptolemaic theory as is customarily asserted in anniversary celebrations,105 but we must briefly analyze Ptolemy’s own claims to having been the first one who was able to give a consistent planetary theory.106 This claim seems to contradict not only the existence of pre-Ptolemaic planetary tables in Roman Egypt as well as in Mesopotamia but also Ptolemy’s own reference to such texts. What Ptolemy means, however, becomes clear if one reads the details of the introduction to his own theory. He requires an explanation of the planetary movement by means of a combination of uniform circular movements which refrains from simplifications like the assumption of an invariable amount for the retrograde arc and similar deviations from the actual observations. Indeed, in order to remain in close agreement with the observations, Ptolemy had to overcome difficulties which Hipparchus was not able to authors from whose works they are taken. One needs only to look at the picture of oriental writings ob- tained from Greek tradition as compared with the originals. 105 The correct estimate can be found in Thorndike IIM, Vol. V, chap, xviii. 106 Almagest IX, 2. 24 Journal of Near Eastern Studies master and which led Ptolemy to a model which is very close to Kepler’s final solution of the problem, by assuming not only an eccentric position of the earth but also an eccentric point around which the movement of the planetary ecc enter appears to be uniform. The resulting orbit is of almost elliptical shape with these two points as foci.107 This whole theory is closely related in method to the explanation of the ‘'evection” of the moon (a periodic perturbation of the moon’s orbit discovered by Ptolemy) by a combination of eccentric and epicyclic movements. Both theories are real masterpieces of ancient mathematical astronomy which far surpassed all previous results. It is not surprising that Ptolemy’s results overshadowed all previous works. All that we know about his forerunners comes mainly from the Almagest itself. We hear that Hipparchus used eccenters and epicycles for the explanation of the anomalies in the movement of the sun and the moon,108 and we learn about theorems for such movements proved by Apollonius.109 This brings us to the very period (about 200 b.c.) from which the oldest cuneiform planetary texts are preserved—computed, however, on entirely different principles. These cuneiform texts cover the two centuries down to the time of Caesar. A direct continuation, chronologically speaking, but of still another type, are planetary tables from Egypt, written in IJcmotic or Greek.110 These tables give the dates at which the planets enter or leave the signs of the zodiac. Such tables were known to Cicero111 and are most likely the "eternal tables” quoted with contempt by Ptole- 107 Cf. Schumacher [1] for the Ptolemaic theory of Venus and Mercury. For the Greek planetary theory in general, see Herz GB I. 108 Almagest III, 4. 109 Almagest XII, 1 ( =Apollonius, ed. Heiberg, II, 137). 110 Neugebauer [3]. Cf. above, p. 5. 111 Cicero De divinatione ii. 6,17; cf. also ii. 71.146. my.112 We do not know how these tables were computed, and their occurrence in Greek as well as in Demotic leaves us in doubt as to their origin—showing us only the degree of interrelation we can expect in Hellenistic times. The most interesting question would, of course, be to learn more about Hipparchus’ astronomy. He is most famous as the discoverer of the precession of the equinoxes. Though this fact cannot be doubted,113 underlining its importance lays the wrong emphasis on a phenomenon which gained its importance only from Newton’s theory, which showed that precession depends on the shape of the earth and thus opened the way to test the theory of general gravitation by direct measurements on the earth. For ancient astronomy, however, precession played a very small role, requiring nothing more than sufficiently remote and sufficiently reliable records of observations of positions of fixed stars. The change in positions must then eventually become evident; and little difficulty was encountered in incorporating this slow movement into the adopted model of celestial mechanics. What we actually need to appreciate in Hipparchus’ contribution must be derived from a careful study of all relevant sections of the Almagest, not by the schematic method of obtaining "fragments” from direct quotations but by a comparison of Ptolemy’s methods and the older procedures which he frequently mentions. That such an approach can lead to well-defined results has recently been shown in the theory of eclipses.114 17. One of the most important prob- 112 Almagest IX, 2. 113 Schnabel’s attempts (Schnabel [1]) to prove that precession was taken into consideration in the cuneiform texts are, to say the least, inconclusive and in part based on mere scribal errors. 114 Schmidt [1], The History of Ancient Astronomy: Problems and Methods 25 lems in connection with Hipparchus is, of course, the problem of the dependence of Hipparchus (and Greek astronomy in general) on Babylonian results and methods. Whatever the conclusions derived from a deeper knowledge of Hipparchus’ astronomy may turn out to be, one thing is clear: the century between Alexander’s conquest of the Near East and Hipparchus’ time is the critical period for the origin of Babylonian mathematical astronomy as well as for its contact with Greek astronomy. Since Kugler’s discoveries, which showed the exact coincidence between numerical relations in cuneiform tablets and in Hipparchus' theory,115 no one has doubted Babylonian priority. It is an undeniable fact that the Babylonian theory is based on mathematical methods known already in Old Babylonian times and does not show any trace of methods considered to be characteristically Greek. The problem remains, however, to answer the question: What caused the sudden outburst of scientific astronomy in Mesopotamia after many centuries of a tradition of another sort? On what background can we understand, for example, the report116 that the “Chal-daean” Seleucus from Seleucia on the Tigris117 completed the heliocentric theory, previously proposed as a hypothesis by Hipparchus? Greek influence on late Babylonian astronomy must not be denied or asserted on aprioristic grounds, if we really want to understand a phenomenon of great historical significance. These remarks are not intended to make Greek influence alone responsible for the new developments in Mesopotamia. As a matter of fact, this answer would only raise the equally unsolved 116 Kugler BMR, p. 40. 116 Plutarch Plat, quaest. vii. 1. 1006 C (ed. Ber-nardakis, Moralia, VI, 138). Cf. also Heath, AS, pp. 305 fl. and Duhem SM, I, 423 fl. 117 Strabo xvi. 739. Seleucus may have lived about 150 b.c. question why Greek astronomy suddenly emerged from many centuries of primitiveness to a scientific system. The alternative, Greek or Babylonian, might even exclude the right answer from the very beginning. It also seems possible that the rise of mathematical astronomy in Hellenistic times resulted from the suddenly intensified contact between several types of civilization, in some respects to be paralleled with the origin of modern science in the Renaissance. In other words, neither the Greeks nor the Orientals might have been alone responsible for the new development but rather the enormous widening of the horizon of all members of the culture of the Hellenistic age. One result of this process was probably the new attitude toward the relationship between the individual and the cosmos, expressed in the new form of horoscopic astrology. In this case it is quite evident that Egypt and Greece—and perhaps Syria as well-contributed about equally much to the refinement and spread of this new creed. It is equally possible that the contact between Greek scholars, trained to think in geometrical terms which Greek mathematics had developed in the fifth century, and Babylonian astronomers, equipped with superior numerical methods and observational records, brought into simultaneous existence two closely related types of mathematical astronomy: the treatment by arithmetical means in Babylonia and the model based on circular movements in the Greek centers of learning in the eastern Mediterranean. It may well be that competition, not borrowing, was the chief contributor to the initial impetus.118 At any rate, it is clear that each detail in the development of Hellenistic astronomy which we will be able to understand better will reveal a new aspect in the fascinating process of the 118 Neugebauer [17], pp. 30-31. 26 Journal of Near Eastern Studies creation of the new world which was destined to become the foundation of the Roman and medieval civilizations. The unique role of the Hellenistic period in the field of sciences, as in other fields, can be described as the destruction of a cultural tradition which dominated the Near East and the Mediterranean countries for many centuries, but also the founding of a new tradition which held following generations in its spell. The history of astronomy in the Hellenistic age is especially well suited to demonstrate that the great energies liberated by the disintegration of an old cultural tradition are very soon transformed into stabilizing forces of a new tradition, which includes about as many elements of development as of stagnation. V. SPECIAL PROBLEMS 18. Every research program in a .complex field will face the need of constant modification and adjustment to unforeseen complications and new ramifications. Problems can arise and results be obtained without having been anticipated in the original question. The context of a mathematical text, for example, can determine with absolute certainty the meaning of a word otherwise only vaguely defined; sign-forms in a papyrus which is exactly dated by astronomical means may furnish valuable information for purely paleographical problems. From dates and positions given in Demotic astronomical texts, it follows that the Alexandrian calendar introduced by Augustus was used by Egyptian scribes only a few years after the reform,119 very much in contrast to the common opinion that the Egyptians were especially conservative in general and in calendaric matters in particular. In short, from few, but solidly established, facts we can learn more than from all general speculations. 119 Neugebauer [6], p. 119. One of the problems which at first sight lies very much outside the history of ancient astronomy is the study of social and economic conditions of the ancient civilizations. There are, however, several points of contact between these studies and astronomy. We are indebted to Cumont for a masterly investigation of the information contained in the astrological literature from Hellenistic Egypt.120 His results are not only of interest for the history of ancient civilization but also illustrate very well the background of the men who used and transmitted the astronomical material known to us from the planetary tables or from Vettius Valens. It turns out that the soil in which these practices were rooted was essentially Egyptian, in spite of the use of the Greek language in the documents. This is in perfect harmony with the close parallelism between Greek and Demotic planetary texts mentioned above and shows the constant interaction of Greek and native influences in Hellenistic Egypt. It also shows how dangerous it is to decide the authorship of Hellenistic doctrines or methods simply on the basis of such superficial grounds as the language used. The analogous question for Babylonia seems to be easier to answer. The Mesopotamian origin of the astrological omina cannot be doubted. We would, however, like to know more about the background of the astronomers of the latest period. It is well known that the names of three Babylonian astronomers appear in Greek literature121 and that two of them actually were found on astronomical tablets, though in an unclear context. For one particular place, the famous city of Uruk in South Babylonia, we can go much further. It can be shown that the scribes and owners of our texts belong to one of two 120 Cumont EA. See also Kroll [1]. 121 Cumont [1], The History of Ancient Astronomy: Problems and Methods 27 “families/’ or perhaps “guilds,” of scribes who frequently call themselves scribes of the omen-series “Enuma Anu Enlil.”122 We can follow the work of these scribes very closely for almost a hundred years until the school of Uruk ceased to exist, probably because of the Parthian invasion of Babylonia in 141 b.c. In contrast thereto, the school of Babylon survived the collapse of the Greek regime, as is proved by a continuous series of astronomical texts down to 30 b.c. This is an interesting result in comparison with the assumption that Babylon practically ceased to exist after the Parthian occupation. The grouping of our texts according to well-defined schools is also of interest from another point of view. It can be shown that two different systems of computation existed side by side for a long time. Competing schools of this sort constitute a phenomenon which is usually considered characteristic for Greek culture. 19. Countless thousands of business documents are preserved from all periods of Mesopotamian history. For the urgently needed investigation of ancient economics, a precise knowledge of the metrological systems is of the greatest importance. Unfortunately, the scientific study of Babylonian measures has been sadly neglected. Fantastic ideas about the level and importance of astronomy in the earliest periods of Babylonian history led to theories which brought measures of time and space in close relationship with alleged astronomical discoveries. We know today that all these assumptions of the early days of Assyriology must be abandoned and that Babylonian metrology must be studied from economic and related texts clearly separated according to period and region. For the determination of Old Babylonian relations between various measures, the mathematical texts 122 For this series cf. Boll-Bezold-Gundel S«S, pp. 2 fl., and Weidner [2], are of great value because they contain numerous examples which give detailed solutions of problems in which metrological relations play a major role. The consequences of such relations, established with absolute certainty, are manifold. For example, we now know from Old Babylonian mathematical texts the measurements of several types of bricks123 as well as the peculiar notation used in counting bricks. It is evident that such information is of importance for the understanding of contemporary economic texts dealing with the delivery of bricks for buildings, thus leading to purely archeological questions. Metrological relations are also needed if we wish to gain an insight into wages and prices.124 Returning to our subject, it must be said that metrology is of great importance not only for the history of the economics of Mesopotamia but also for purely astronomical problems. Distances on the celestial sphere are measured in astronomical texts by units borrowed from terrestrial metrology. The comparison between ancient observation and modern computations thus requires a knowledge of the ancient relations between the various units. This problem is by no means simple because our astronomical material belongs to relatively late periods, Assyrian and Neo-Babylonian, and the metrological system of these times is much more involved than the Old Babylonian. Mathematical texts would certainly be of great help here too, but the few tablets from this period are so badly preserved that they present us with at least as many new questions as they answer. Neo-Babylonian economic texts will therefore furnish the main point of departure for the study 123 Neugebauer-Sachs MCT, Problem-Text O and Sachs [1], 124 Waschow [1], p. 277, found, in discussing mathematical texts, that the value of the area-measure “se” must be changed by a factor 60 against older assumptions. It is obvious how such facts influence the interpretation of economic texts. 28 Journal of Near Eastern Studies of the latest phase of Mesopotamian metrology and its astronomical applications. It might be mentioned, in this connection, that theories about direct relationship between early Mesopotamian metrology and astronomy also gave rise to the rather unfortunate concept of high accuracy in the determination of weights, measures of length, etc. It is of great importance to realize that the absolute values of all metrological units are subject to great margins of inaccuracy and local and temporal variations. The first step in a historical investigation of Mesopotamian metrology must therefore be to establish from economic and mathematical texts the ratios between the units; these ratios have an incomparably better chance of showing unformity than the absolute values deduced from accidental archeological finds. 20. Closely related to metrological problems is the question of the accurate identification of ancient star configurations. Much work remains to be done before it will be possible to give a reliable history of the topography of the celestial sphere in general, or even of the zodiacal constellations.125 In spite of attempts to make Egypt responsible for many forms,126 the predominant influence of Babylonian concepts on the grouping of stars into pictures must be maintained. But neither Babylonian nor Egyptian developments are known in detail. The identification of Egyptian constellations is especially difficult, mainly because it must be based on relations between the times of rising and setting and therefore depends on elements which are grossly schematized in the texts at our disposal. The situation in Mesopotamia is slightly better because we have actual observations in addition to the 125 The best summary is given by the Boll-Gundel article, “Sternbilder,” in Roscher GRM, Vol. VI (1937), cols. 867-1072. 126 Cf. esp. Gundel DD and HT and the criticism of Schott [2], schematic lists, at least for the later periods which are of special importance for the Hellenistic forms of the constellations. For the period following the publication of the Almagest, we must take into account the possibility of still other complications. We know from explicit remarks in the Almagest that Ptolemy’s star catalogue introduced deviations from older catalogues.127 Astrological works, however, may very well have maintained prePtolemy standards both with respect to the boundaries of constellation and the counting of angles in the zodiac. We have already mentioned the stubborn adherence of astrological writers to methods of computation which were made obsolete by the development of spherical trigonometry.128 For the modern historian it is therefore of importance to establish the specific standard according to which a given document was written, especially when chronological problems are involved. 21. While metrology is a much-needed implement for economic history and the understanding of ancient astronomy, astronomy itself serves general history in chronological problems. Chronology is the necessary skeleton of history and owes its most important fixed points to astronomical facts. We need not emphasize the use of reports of eclipses, especially solar eclipses, for the determination of accurate dates to form the framework into which the results of relative chronology must be fitted. It must be underlined, however, that the available material is by no means exhausted. A better understanding and reinvestigation of the reports of the Assyrian astronomers will certainly furnish new information of chronological value. It must be stated, on the other 127 Almagest VII, 4 (ed. Heiberg, p. 37). i2s Cf., e.g., Tetrabiblos I, 20 (ed. Robbins, pp. 94-95). The History of Ancient Astronomy: Problems and Methods 29 hand, that not too much is to be expected from older material. In order to make ancient observations accessible to modern computation, a certain degree of accuracy must be granted; this accuracy seems to be missing in the earlier phases of the development of astronomy. This, for instance, makes the older Egyptian material so ill suited for chronological purposes. For later periods, however, Egypt has furnished and will furnish much information from astrological documents. It is particularly calendaric questions, such as the use of eras and similar problems, which have been illuminated by the dating of horoscopes. The great variety of calendaric systems, local eras, and older methods of dating raises many difficulties in ancient chronology. This difficulty was clearly felt also by ancient astronomers and was the cause of the early use of consistent eras in Babylonian and Greek astronomy. The Babylonian texts always use the Seleucid Era, whereas Ptolemy reduces all dates to the Nabonassar Era but uses the Old Egyptian years of constant length. This crossing of Egyptian and Babylonian influences is paralleled by the subdivision of the day into hours. The Egyptians divided the day into twelve parts from sunrise to sunset, thus obtaining hours whose length depended on the season. The Babylonian astronomers used six subdivisions of day and night, but these units were of constant length. Combining the Egyptian division into 24 hours with the Babylonian constancy of length, the Hellenistic astronomers used “equinoctial” hours for their computations and solved the problem of finding the relationship between seasonal and equinoctial hours by spherical trigonometry.129 One sees here again what a multitude of relations, problems, and methods contributed to shape concepts such as a continuous era or the 24- 129 Almagest II. 9, hour day which are so familiar to us today. Ancient chronology and the accurate analysis of ancient reports have turned out to be of interest even to a modern astronomical problem. In 1693 Halley discovered the fact130 that the moon’s position appeared to be advanced compared with the expected position as computed from positions recorded by Ptolemy. This “acceleration” can be explained by a slow increase in the length of the solar day or by a decrease in the rotational velocity of the earth. Such a decrease is caused by tidal forces,131 and it is of great interest to determine the amount as accurately as possible. For this purpose, accurate positions of the moon in remote times are of great value, and such positions can, indeed, be derived from records in cuneiform texts.132 Modern measurements of high precision can thus be supplemented by observations in antiquity. 22 . Not only are Hellenistic astronomy and Hellenistic astrology the determining factors for the astronomy and astrology of the Middle Ages in Europe, but its influence is equally important for the development of astronomical methods and concepts in the Middle and Far East. We must therefore at least mention an enormous field which still awaits systematic research: Hindu science. This does not mean that there is not an extensive literature on this subject; indeed, even a small number of original texts are published.133 The main trouble lies, however, in the tendency of the majority of publications by Hindu authors to claim priority for Hindu discoveries and to deny foreign in- 130 Edm. Halley, “Emendationes ac notae Abatenii observationes astronomicas, cum restitutione tabularum lunlsolarum ejusdem authoris,” Philosophical Transactions, 17 (1693), No. 204, pp. 913—21. 131 Cf., e.g., Jeffreys [1], 132 P. V. Neugebauer [1], 133 For the literature until 1899, see Thibaut A A M. The best discussion of Hindu astronomy is still Burgess SS (1860). 30 Journal of Near Eastern Studies fluence, as well as in the opposite tendency of some European scholars. This tendency has been especially strong so far as Hindu mathematics is concerned,134 and it is aggravated by the inadequate publication of the original documents, from which usually only scattered fragments are cited in order to prove some specific statement. As a result, there is no means today to obtain an independent judgment from the study of the original texts which are preserved in enormous number, though of relatively late date for the most part. The situation with respect to Hindu astronomy is not much better. There can be little doubt that the original impetus came from Hellenistic'astronomy; the use of the eccentric-epicyclic model alone would be sufficient proof even if we did not also find direct witness in the use of Greek terminology.136 This fact is interesting in itself, but it may very well be that the period of reception lies between Hipparchus and Ptolemy; systematic study might therefore reveal information about pre-Ptolemaic Greek astronomy no longer preserved in available Greek sources. Hindu astronomy would in this case constitute one of the most important missing links between late Babylonian astronomy and the fully developed stage of Greek astronomy represented by the Almagest. The fundamental difficulty in the study of Hindu astronomy lies in the character of the preserved textual material. The published and commented texts consist exclusively of cryptically formulated verses giving the rules for computing certain phenomena, making it extremely difficult to understand the actual 134 Cf., e.g., Datta-Singh HHM (reviewed in Neugebauer [12]). 135 Thibaut A AM, pp. 43 ff. The Babylonian ratio 3 : 2 for the ratio between the longest and shortest days of the year also occurs in India (Thiba.ut A A M, pp. 26-27; Kugler BMR, pp. 82 and 195), though it would be suitable only for the latitude of the northern corner of India. For the planetary theory, see Kugler BB, p. 120; Schnabel [2], p. 112; Schnabel [1], p. 60. process to be followed. It is evident, on the other hand, that no astronomy of an advanced level can exist without actually computed ephemerids. It must therefore be the first task of the historian of Hindu astronomy to look for texts which contain actual computations. Such texts are, indeed, preserved in great number, though actually written in very late periods. Poleman’s catalogue136 of Sanskrit manuscripts in American collections lists about a hundred such manuscripts in the D. E. Smith collection in Columbia University in New York. In their general arrangement, these texts are reminiscent of the cuneiform ephemerids from Seleu-cid times and must reveal many details of the Hindu theory of the planetary movement if attacked by the same methods which have proved so successful in the case of the Babylonian material. The complete publication of this material is an urgent desideratum in the exploration of oriental astronomy. As mentioned above, the texts in the D. E. Smith collection are of very recent origin, only a few centuries old. This does not mean that the methods used are not of very much earlier date. This is shown by the investigation of one of these texts,137 which deals with the problem of the varying length of the days during the year. Though written about 1500, the computations are based on methods going back to a much older period. Analogous results can be expected in the remaining material, and there is no reason to assume that the D. E. Smith collection exhausts all the preserved material. 23 . In the preceding sections we have frequently touched on methodological questions. In closing, I wish to underline a few principles in a more general way. As is only natural, the study of the development of ancient science began under the 136 Poleman CIM, pp. 231 ff. See also Emeneau PIT, pp. 318 ff. 137 Schmidt [2], The History of Ancient Astronomy: Problems and Methods influence of the ancient tradition. Herodotus, Diodorus, the commentators of Plato, etc., were the sources which determined the picture of the early stages of Greek and oriental mathematics and astronomy. But while students of political history, art, economics, and law learned in the early days of systematic archeological research to consider this literary tradition about the ancient Orient as nothing more than a supplementary source to be checked by the original documents, the majority of historians of the exact sciences have remained in a stage of naive innocence, repeating without criticism the nursery stories of ancient popular writers. This is all the more surprising because many of these stories should have revealed their purely fictitious character from the very beginning. Every invention considered of basic importance is attributed to a definite person or nation: Thales “discovered” that a diameter divides the area of a circle into two equal parts, Anaxi-mandes and several others are credited with the discovery of the obliquity of the ecliptic, the Egyptians discovered geometry, the Phoenicians arithmetic—and so on, according to an obvious pattern of naive restoration of facts the origins of which had been totally forgotten. Modern authors then add stories of their own, such as the idea that the construction of the pyramids required mathematics, the assumption of supposedly marvelous skies of Mesopotamia,138 and the notion of Egyptian Stone Age astronomers industriously determining the heliacal rising of Sirius or carrying out a geodetic survey of the Nile Valley. It is clear that the replacement of the traditional stories by statements based exclusively on results obtainable from the original sources will not be very appealing. This is the inevitable result in the devel- 138 For the poor conditions of actual observation cf. Koldewey WB, p. 192; Vogt [1], pp. 38-39; cf. also Boll [1], pp. 48 and 157. 31 opment of every science; for increased knowledge means giving up simple pictures. In the history of science, an additional element must be added to the steady increase of complexity resulting from a better understanding of our sources. Not only do we learn to interpret our material more accurately but we also learn to see everywhere the immense gaps in our preserved sources. We will more and more be forced to admit that many, and essential, steps in the development of science are hopelessly destroyed; that we, at best, are able to sketch mere outlines of the history of science during certain sharply limited periods; and that many of the driving forces might actually have been quite different from those which we customarily restore on the analogy of later periods. One consequence of this situation seems to me to be evident: unless the history of science now enters the stage of specialization, it will lose all value in the framework of historical research. It must be clearly understood that the history of science must work with methods and must consider its problems from viewpoints which correspond to the methods and standards of other branches of historical research. The idea must definitely be abandoned that the history of science must adapt its level to the alleged requirements of the teaching of the modern fields of science. The intrinsic value of this research must be seen in its contribution to our understanding of the historical processes which shaped human civilization, and it must be made clear that such an understanding cannot be reached without the closest contact with the other historical fields. The call for specialization is not very popular. I am convinced, however, that a well-founded insight into the details of a single essential step in the development is at present of higher value and more fascinating than any attempt at general syn- 32 Journal of Near Eastern Studies thesis. It is ridiculous to believe that we are anywhere able to reach “final” results in the study of the development of human civilization. But the overwhelming richness of all phases of human history can be appreciated only if we occupy ourselves with the real facts as accurately as possible and do not attempt to hide their manifold aspects under the veil of hazy generalizations or let our judgment be guided by the naive idea of human “progress.” Every synthesis written fifty years ago is now completely antiquated and at best enjoyable for its literary style; the careful study of the original works of the ancients, however, will reveal to everyone and at any time the development of their achievements.139 The call for specialization must not be misunderstood as a plea for the disregard of the general outlines of the historical conditions. On the contrary, specialized work can be accomplished successfully only if the points of attack are selected under constant consideration of possible interference from other problems and other fields. It is indeed the most gratifying result of detailed research on a well-defined problem that it necessarily uncovers relationships which are of primary importance for the understanding of larger 139 An excellent example is Delambre HA A, published in 1817 and still not surpassed or even equaled because of its direct contact with the original sources. historical processes. The actual working program, however, needs restriction and minute detail work. The most essential task is that of making the original sources accessible as easily as possible in their best available form. By the indefatigable work of Heiberg, Hultsch, Tannery, and many others, we possess today a great part of the extant writings of the Greek scientists in excellent editions. We owe to Sir Thomas Little Heath many brilliant commentaries and translations of Greek mathematicians.140 To make Greek and oriental source material more generally accessible, supplemented, of course, by modern translations and commentaries, will be the foremost problem of the future. The extension of this program to include medieval material, on the one hand, and Middle Eastern documents, on the other, appears as a logical consequence, worthy of the serious efforts of all scholars who wish to contribute to the understanding of the past of our own culture. Brown University 140 On the other hand, much remains to be done to repair the harm caused by classical philologists who made their editions inaccessible to modern scientists by translating them into Latin instead of a modern language. Great opportunities have been spoiled by this absurd attitude. It has fortunately never occurred to Orientalists to translate their texts into Hebrew. It should be mentioned, however, that the Arabic version of Euclid’s Elements was published in Latin(!) translation by Besthorn, Heiberg, and others (Copenhagen, 1897-1932). AJP AJSL Almagest AN Baillet [1] BASOR Berger GFH Boll, Sphaera Boll [1] Boll [2] Boll-Bezold-Gun-del &S BIBLIOGRAPHY American Journal of Philology. American Journal of Semitic Languages and Literatures. See Ptolemy. Astronomische Nachrichten. . Baillet, J. “Le Papyrus mathematique d’Akhmim,” Mem. publ. par les membres de la mission arch, frang. au Caire, Vol. 9, Fasc. 1 (1892). Bulletin of the American Schools of Oriental Research. Berger, H. Die geographischen Fragmente des Hippar ch. Leipzig, 1869. Boll. F. Sphaera. Leipzig, 1903. Boll, F. “Antike Beobachtungen farbiger Sterne,” Abh. K. Bayerischen Akad. d. JPtss., Philos.-philol. u. histor. KI. 30, No. 1 (1918). Boll, F. “Die Erforschung der antiken Astrologie,” Neue Jahrbucher fur das klassische Altertum, 21 (1908), 103-26. Boll, F.; Bezold, C.; and Gundel, W. Sternglaube und Sterndeutung. 4th ed. Leipzig, 1931. The History of Ancient Astronomy: Problems and Methods 33 Bouriant, P. [1] Bouriant, P. “Fragment d’une manuscripte copte de basse epoque ayant contenu les principes astronomiques des arabes [cf. n. 12].” Journal asiatique, 10. ser., 4 (1904), 117-23. Bouriant, U.-Ven- Bouriant, U., and Ventre Bey. “Suf trois tables horaires coptes,” Me- tre Bey [1] Braunmuhl GT moires presentes a I’institut egyptien, 3 (1900), 575-604. Braunmuhl, A. v. Vorlesungen uber Geschichte der Trigonometric. Leipzig, 1900. Brugsch, Thes. 1 Brugsch, H. Thesaurus inscriptionum aegyptiacarum, I. Astronomische and astrologische Inschriften. Leipzig, 1883. Burgess »S'S Burgess, E. “Translation of the Surya-Siddh&nta,” J AOS, 6 (1860), 141— 498. Reprinted, Calcutta, 1935 [with introduction (45 pp.) by P. C. Sengupta]. Capelie [1] Capelle, W. “Alteste Spuren der Astrologie bei den Griechen,” Hermes, 60 (1925), 373-95. CCAG ■Catalogus codicum astrologorum Graecorum. Edited by Boll, Cumont, et. al. 12 vols. Bruxelles, 1898-1936. Chace RMP Chace, A. B.; Manning, H. P.; and Archibald, R. C. The Rhind Mathematical Papyrus. 2 vols. Oberlin, 1927-29. Cicero De div. Cicero, M. T. De divinatione. (English trans, by W. A. Falconer, “Loeb Classical Library.”) Crum CO CT Cumont EA Cumont [1] Crum, W. E. Coptic Ostraca. London, 1902. Cuneiform texts from Babylonian tablets, etc., in the British Museum. Cumont, F. L’Egypte des astrologues. Bruxelles, 1937. Cumont, F. Comment les grecs connurent les tables lunaires des chaldeens: Florilegium ... dedies a M. Ie marquis Melchior de Vogue ... , pp. 159-65. Paris, 1910. Curtis-Robbins [1] Curtis, H. D., and Robbins, F. E. “An Ephemeris of 467 a.d.” Publ. of the Daressy [1] Observatory of the Univ, of Michigan, 6 (1935), 77-100. Daressy, G. “Notes et remarques 181,” Rec. trav., 23 (1901), 126-27. Datta-Singh HHM Datta, B., and Singh, A. N. History of Hindu Mathematics. 2 vols. Lahore, 1935-38. Delambre HAA D ’ Ooge-Robbins- Kar pinski Nic. Delambre, J. B. J. Histoire de l’astronomie ancienne. 2 vols. Paris, 1817. D’Ooge, M. L.; Robbins, F. E.; and Karpinski, L. C. Nicomachus of Gerasa. “Univ, of Michigan Studies: Humanistic Series,” No. 16. Ann Arbor, 1926. Drecker [1] Drecker, J. “Das Planisphaerium des Claudius Ptolemaeus,” Isis, 9 (1927), 255-78. Dreyer HPS Dreyer, J. L. E. History of the Planetary Systems from Thales to Kepler. Cambridge, 1906. During HP During, I. Die Harmonielehre des Klaudios Ptolemaios. “Gbteborgs Hbgsko-las Arsskrift,” No. 36 (1930). During PPM During, I. Ptolemaios und Porphyrias uber die Musik. “Gbteborgs Hbgsko-las Arsskrift,” No. 40 (1934). Duhem SM Duhem, P. Le Systeme du monde; histoire des doctrines cosmologiques de Platon a Copernic. 5 vols. Paris, 1913-17. Emeneau PIT Emeneau, M. B. A Union List of Printed Indic Texts and Translations in American Libraries. “Amer. Oriental Series,” Vol. 7, 1935. Epping AB Epping, J. Astronomisches arcs Babylon. “Stimmen aus Maria-Laach, Ergan-zungsheft,” No. 44. Freiburg, 1889. Euclid Euclidis opera omnia, ed. J. L. Heiberg and H. Menge. 8 vols. Leipzig, 1883-1916. Frank, Plato Frank, E. Plato und die sogenannten Pythagoreer. Halle, 1923. 34 Frankfort CN4 Gandz [1] Gandz [2] Gandz [3] Garbers ES Ginzel Chron. Gundel DD Gundel HT Harper Letters Haskins MS Heath AS Heath Euclid Heath GM Heath MGM Heidel GM Heidel [1] Herz GB Honigmann SK JAGS Jeffreys [1] JNES Klein [1] Koidewey WB Krause Men. Kroll [1] Kroll VV Kugler BB Kugler BMR Kugler MP Kugler SSB Journal of Near Eastern Studies Frankfort, H. The Cenotaph of Seti I at Abydos. 2 vols. “Egypt Explor. Soc., Memoir,” No. 39 (1933). Gandz, S. “The Sources of al-Khowarizmi’s Algebra,” Osiris, 1 (1936), 263-77. Gandz, S. “The Algebra of Inheritance,” Osiris, 5 (1938), 319-91. Gandz, S. “The Origin and Development of the Quadratic Equations in Babylonian, Greek, and Early Arabic Algebra,” Osiris, 3 (1937), 405-557. Garbers, K. “Ein Werk Tabit b. Qurra’s uber ebene Sonnenuhren,” QS, A, 4 (1936). Ginzel, F. K. Handbuch der mathematischen und technischen Chronologic. 3 vols. Leipzig, 1906-14. Gundel, W. Dekane und Dekansternbilder. “Studien d. Bibi. Warburg,” No. 19 (1936). Gundel, W. “Neue astrologische Texte des Hermes Trismegistos,” Abh. d. Bayerischen Akad. d. IFfss. Phil.-hist. Abt. (N.F.), 12 (1936). Harper, R. F. Assyrian and Babylonian Letters Belonging to the Kouyunjik Collection of the British Museum. 14 vols. Chicago, 1892-1914. Haskins, C. H. Studies in the History of Mediaeval Science. 2d ed. Cambridge: Harvard University Press, 1927. Heath, T. L. Aristarchus of Samos. Oxford, 1913. Heath, T. L. The Thirteen Books of Euclid’s Elements. 3 vols. 2d ed. Cambridge, 1926. Heath, T. L. A History of Greek Mathematics. 2 vols. Oxford, 1921. Heath, T. L. A Manual of Greek Mathematics. Oxford, 1931. Heidel, W. A. The Frame of the Ancient Greek Maps: With a Discussion of the Discovery of the Sphericity of the Earth. New York, 1937 ( = Am. Geographical Soc., Research Series No. 20). Heidel, W. A. “The Pythagoreans and Greek Mathematics,” AJP, 61 (1940), 1-33. Herz, N. Geschichte der Bahnbestimmung von Planeten und Kometen, 1: Die Theorien des Altertums. Leipzig, 1887. Honigmann, E. Die sieben Klimata und die Poleis episemoi. Heidelberg, 1929. Journal of the American Oriental Society Jeffreys, H. “The Chief Cause of the Lunar Secular Acceleration,” MN, 80 (1920), 309-17. Journal of Near Eastern Studies. Klein, J. Die griechische Logistik und die Entstehung der Algebra,” QS, B, 3 (1934-36), 18-105, 122-235. Koldewey, R. Das wiedererstehende Babylon. 4th ed. Leipzig, 1925. Krause, K. “Die Spharik von Menelaos aus Alexandrien in der Verbesserung von Abu Nasr Mansur b. All b. Iraq,” Abh. Ges. d. Wiss. zu Gottingen, Phil.-hist. Ki., 3. Folge, No. 17 (1936). Kroll, W. “Kulturhistorisches aus astrologischen Texten,” Klio, 18 (1923), 213-25. Kroll, W. Vettii Valentis anthologiarum libri. Berlin, 1908. Kugler, F. X. Im Bannkreis Babels. Munster, 1910. Kugler, F. X. Die babylonische Mondrechnung. Freiburg, 1900. Kugler, F. X. Von Moses bis Paulus. Munster, 1922. Kugler, F. X. Sternkunde und Sterndienst in Babel. 2 vols. Munster, 1907-24. Ergdnzungen, in three parts (Part III by J. Schaumberger) . Munster, 1913-35. The History of Ancient Astronomy: Problems and Methods 35 Langdon VT Lange-Neugebauer [1] L’Hote LE Luckey [1] Luckey [2] MN Mzik EGM Mzik-Hopfner PDE Neugebauer ACT Neugebauer MKT Neugebauer Vorl. Neugebauer [1] Neugebauer [2] Neugebauer [3] Neugebauer [4] Neugebauer [5] Neugebauer [6] Neugebauer [7] Neugebauer [8] Neugebauer [9] Neugebauer [10] Neugebauer [11] Neugebauer [12] Neugebauer [13] Neugebauer [14] Neugebauer [15] Langdon, S.; Fotheringham, J. K.; and Schoch, C. The Venus Tablets of Ammizaduga, Oxford, 1928. Lange, H. 0., and Neugebauer, 0. "Papyrus Carlsberg No. 1,” Kongl. Danske Vidensk. Selskab, Hist.-fil. Skrifter, Vol. 1, No. 2 (1940). L’Hote, Nestor. Lettres ecrites d’Egypte en 1838 et 1839 ... . Paris, 1840. Luckey, P. "Das Analemma von Ptolemaus,” AN, 230 (1927), 18-46. Luckey, P. "Tabit b. Qurra’s Buch liber die ebenen Sonnenuhren,” QS, B, 4 (1937), 95-148. Monthly Notices of the Royal Astronomical Society. Mzik, H. v. Erdmessung, Grad, Meile und Stadion nach den altarmenischen Quellen ( = Studien zur armenischen Geschichte No. 6). Wien, 1933. [Reprinted from Handes Amsorya, Z. f. armenische Philologie, 4R (1933), cols. 283-305, 432-59, 559-82.] Mzik, H. v., and Hopfner, F. Des Klaudius Ptolemaios Einfuhrung in die darstellende Erdkunde, 1. Wien, 1938 ( = Klotho 5). Neugebauer, 0. Astronomical Cuneiform Texts. (In preparation.) Neugebauer, 0. Mathematische Keilschrift-Texte. 3 vols. (QS, A, 1 [1935-38].) Neugebauer, 0. Vorlesungen uber Geschichte der antiken mathematischen Wissenschaften, 1: Vorgriechische Mathematik. Berlin, 1934. Neugebauer, 0. "Arithmetik und Rechentechnik der Agypter,” QS, B, 1 (1930), 301-80. Neugebauer, O. "Die Geometrie der agyptischen mathematischen Texte,” QS, B, 1 (1931), 413-51. Neugebauer, 0. "Egyptian Planetary Texts,” Trans, of the Amer. Philos. Soc., 32 (new ser., 1942), 209-50. Neugebauer, 0. "Die Bedeutungslosigkeit der ‘Sothisperiode’ fiir die al-teste agyptische Chronologic,” Acta orientalia, 17 (1938), 169-95. Neugebauer, 0. "The Origin of the Egyptian Calendar,” JNES, 1 (1942), 396-403. Neugebauer, 0. "Demotic Horoscopes,” JAOS, 63 (1943), 115-26. Neugebauer, 0. Review of Kugler SSB Erg. (Schaumberger), QS, B, 3 (1935), 271-86. Neugebauer, 0. "Untersuchungen zur antiken Astronomie, II: Datierung und Rekonstruktion von Texten des Systems II der Mondtheorie,” QS, B, 4 (1937), 34-91. Neugebauer, O. "Untersuchungen zur antiken Astronomie, III: Die baby-lonische Theorie der Breitenbewegung des Mondes,” QS, B, 4 (1938), 193-346. Neugebauer, 0. "Jahreszeiten und Tageslangen in der babylonischen Astronomie,” Osiris, 2 (1936), 517-50. Neugebauer, O. “Zur Entstehung des Sexagesimalsystems,” Abh. d. Ges. d. Wissenschaften zu Gottingen, Math.-phys. KI. (N.F.), 13, No. 1 (1927). Neugebauer, 0. Review of Datta-Singh HHM I (QS, B, 3 [1936], 263-71). Neugebauer, 0. "On Some Astronomical Papyri and Related Problems of Ancient Geography,” Trans, of the Amer. Philos. Soc., 32 (new ser., 1942), 251-63. Neugebauer, 0. "Uber eine Methode zur Distanzbestimmung Alexandria-Rom bei Heron,” Kongl. Danske Vidensk. Selskab, Hist.-fil. Meddel., Vol. 26, No. 2 (1938). Neugebauer, 0. Zur geometrischen Algebra ("Studien zur Geschichte der antiken Algebra,” III) (QS, B, 3 [1935], 245-59). 36 Neugebauer [16] Neugebauer [17] Neugebauer [18] Neugebauer [19] N eugebauer-Sachs MCT Neugebauer-Struve [1] N eugebauer-V ol-ten [1] Neugebauer, P. V. [1] Pannekoek [1] Pannekoek [2] Pannekoek [3] Pap. Oxyrh. Pap. Ryl. Peet RMP Pfeiffer SLA Pococke DE \ Pogo [1] Pogo [2] Pogo [3] Pogo [4] Pogo [5] Poleman CIM Porter-Moss TB Ptolemy Journal of Near Eastern Studies Neugebauer, 0. Apollonius-Studien (“Studien zur Geschichte der antiken Algebra,” II) (QS, B, 2 [1932], 215-54). Neugebauer, 0. “Exact Science in Antiquity,” University of Pennsylvania Bicentennial Conference: Studies in Civilization, pp. 23-31. Philadelphia, 1941. Neugebauer, 0. “Some Fundamental Concepts in Ancient Astronomy,” University of Pennsylvania Bicentennial Conference: Studies in the History of Science, pp. 13-29. Philadelphia, 1941. Neugebauer, 0. “The Water-Clock in Babylonian Astronomy” (to be published in Isis in 1945). Neugebauer, 0., and Sachs, A. Mathematical Cuneiform Texts (to be published in “Amer. Oriental Series,” New Haven, 1945). Neugebauer, 0., and Struve, W. “Uber die Geometrie des Kreises in Babylonien,” QS, B, 1 (1929), 81-92. Neugebauer, 0., and Volten, A. “Untersuchungen zur antiken Astronomic, IV: Ein demotischer astronomischer Papyrus (Pap. Carlsberg 9),” QS, B, 4 (1938), 383-406. Neugebauer, P. V. “Eine Konjunktion von Mond und Venus aus dem Jahre -418 und die Akzeleration von Sonne und Mond,” AN, 244 (1932), cols. 305-8. Pannekoek, A. “Calculation of Dates in the Babylonian Tables of Planets,” Koninkl. Akad. van Wetensch. te Amsterdam, Proceedinqs, 19 (1916), 684-703. Pannekoek, A. “Some Remarks on the Moon’s Diameter and the Eclipse Tables in Babylonian Astronomy,” Eudemus, 1 (1941), 9-22. Pannekoek, A. “The Origin of the Saros,” Koninkl. Akad. van Wetensch. te Amsterdam, Proceedings, 20 (1917), 943-55. Grenfell, B. P., and Hunt, A. S. The Oxyrhynchus Papyri. London: Egypt Exploration Fund, 1898 ff. Hunt, A. S., and Roberts, C. H. Catalogue of the Greek and Latin Papyri in the John Rylands Library, Manchester. 3 vols. 1911-38. Peet, T. E. The Rhind Mathematical Papyrus. Liverpool, 1923. ' Pfeiffer, R. H. State Letters of Assyria. “Amer. Oriental Series,” No. 6. New Haven, 1935. Pococke, R. A Description of the East and Some Other Countries. 2 vols. London, 1743-45. Pogo, A. “Calendars on Coffin Lids from Asyut,” Isis, 17 (1932), 6-24. Pogo, A. “The Astronomical Inscriptions on the Coffins of Heny,” Isis, 8 (1932), 7-13. Pogo, A. “Three Unpublished Calendars from Asyut,” Osiris, 1 (1935), 500-509. Pogo, A. “Der Kalender auf dem Sargdeckel des Idy in Tubingen,” in Gundel DD, pp. 22-26. Pogo, A. “The Astronomical Ceiling-Decoration in the Tomb of Senmut,” Isis, 14 (1930), 301-25. Poleman, H. I. A Census of Indic Manuscripts in the United States and Canada. “Amer. Oriental Series,” Vol. 12. 1938. Porter, B., and Moss, R. L. B. Topographical Bibliography of Ancient Egyptian Hieroglyphic Texts, Reliefs and Paintings. 6 vols. Oxford, 1927-39. Cl. Ptolemaeus, Opera. I. Syntaxis mathematica, ed. J. L. Heiberg. 2 vols. Leipzig, 1898-1903. German translation by K. Manitius. 2 vols. Leipzig, 1912-13. The History of Ancient Astronomy: Problems and Methods 37 QS RA Rec. trav. Revillout [1] Robbins [1] Rome CPT Roscher GRM Sachs [1] Schaumberger Erg. Schmidt [1] Schmidt [2] Schnabel Ber. Schnabel [1] Schnabel [2] Schott [1] Schott [2] Schoy TLAB Schumacher [1] Sethe ZAA Sethe ZZ Sileiko [1] Struve MPM Thibaut AAM II. Opera astronomica minora, ed. J. L. Heiberg. Leipzig, 1907. Ill, 1. Apotelesmatica, ed. F. Boll and Ae. Boer. Leipzig, 1940. Tetrabiblos, ed. and English trans, by F. E. Robbins (“Loeb Classical Library” [1940]), and Opera, III, 1. Geographia, ed. Nobbe. Leipzig, 1843. Harmonics. See During. Quellen und Studien zur Geschichte der Mathematik, Astronomic und Physik. Revue d’assyriologie. Recueil de travaux relatifs a la philologie et a Varcheologie egyptiennes et assyri-ennes. Revillout, E. Melanges sur la metrologie, Veconomic politique et I’histoire de I’ancienne Egypte avec de nombreux textes demotiques, hieroglyphiques, hie-ratiques ou Grecs inedits ou anterieurment mal publies. Paris, 1895. Robbins, F. E. “A Greco-Egyptian Mathematical Papyrus,” Classical Philol., 18 (1923), 328-33. Rome, A. Commentair es de Pappus et de Theon d’Alexandrie sur VAlmagest. 2 vols. ( = “Studi e testi,” Vols. 54 and 72). Roma, 1931—36. Roscher, W. H. Ausfuhrliches Lexikon d. griechischen u. rbmischen Mytholo-gie. Leipzig, 1884-1937. Sachs, A. J. “Some Metrological Problems in Old-Babylonian Mathematical Texts” BASOR, 96 (1944), 29-39. See Kugler SSB. Schmidt, O. “Bestemmelsen af Epoken for Maanens Middelbevsegelse i Bredde hos Hipparch og Ptolemaeus,” Matematisk Tidsskrift, B (1937), pp. 27-32. Schmidt, 0. “The Computation of the Length of Daylight in Hindu Astronomy” (to be published in Isis in 1945). Schnabel, P. Berossos und die babylonisch-hellenistische Literatur. Leipzig, 1923. Schnabel, P. “Kidenas, Hipparch und die Entdeckung der Prazession,” ZA, 37 (1927), 1-60. Schnabel, P. “Neue babylonische Planetentafeln,” ZA, 35 (1924), 99-112. Schott, A. “Das Werden der babylonisch-assyrischen Positionsastronomie und einige seiner Bedingungen,” ZDMG, 88 (1934), 302-37. Schott, A. Review of Gund'el HT, in QS, B, 4 (1937), 167-78. Schoy, C. Die trigonometrischen Lehren des persischen Astronomen Abud-Raihdm Muh. ibn Ahmad al-Blrunt. Hannover, 1927. Schumacher, C. J. Untersuchungen uber die ptolemaische Theorie der unteren Planeten. Munster, 1917. Sethe, K. “Die Zeitrechnung der alten Aegypter,” Nachr. Ges. IFfs-s. zu Gottingen, Phil.-hist. KI., 1919, pp. 287-330; 1920, pp. 28-55, 97-141. Sethe, K. Von Zahlen und Zahlworten bei den alten Agyptern ( —Schriften der Wissenschaftlichen Gesellschaft Strassburg, No. 25). Strassburg, 1916. Sileiko, V. “Mondlaufprognosen aus der Zeit der ersten babylonischen Dynastie,” Comptes-Rendus de V Academic des Sciences de I’URSS, 1927, B, pp. 125-28. Struve, W. W. “Mathematischer Papyrus des staatlichen Museums der schonen Kiinste in Moskau,” QS, A, 1 (1930). Thibaut, G. “Astronomie, Astrologie und Mathematik” (art.) in Grundriss d. Indo-Arischen Philologie und Altertumskunde, HI, 9 (1899). 38 Thomas GMW Thompson AB Thompson Rep. Thorndike HM Thureau-Dangin S'S' Thureau-Dan-gin TMB Thureau-Dan-gin [1] Thureau-Dan-gin [2] Tropfke [1] van der Waer-den [1] van der Waer-den [2] Vettius Valens Virolleaud ACh. Vogel [1] Vogel [2] Vogt [1] Waterman RC Weidner Hdb. Weidner [1] Weidner [2] Weissbach BM Winlock [1] Winlock [2] Winlock EDEB ZA ZDMG Zeuthen KA Journal of Near Eastern Studies Thomas, I. Selections Illustrating the History of Greek Mathematics. 2 vols. 1939-41. (“Loeb Classical Library.”) Thompson, R. C. A Catalogue of Late Babylonian Tablets in the Bodleian Library, Oxford. London, 1927. Thompson, R. C. The Reports of the Magicians and Astrologers of Niniveh and Babylon. 2 vols. London, 1900. Thorndike, L. A History of Magic and Experimental Science. 6 vols. New York, 1923-41. Thureau-Dangin, F. Esquisse d’une histoire du systeme sexagesimal. Paris, 1932. Thureau-Dangin, F. Textes mathematiques babyloniens. Leiden, 1938. Thureau-Dangin, F. “Sketch of a History of the Sexagesimal System,” Osiris, 7 (1939), 95-141. Thureau-Dangin, F. “La Clepsydre chez les Babyloniens,” RA, 29 (1932), 133-36. Tropfke, J. “Archimedes und die Trigonometric,” Archivf. Gesch. d. Math., d. Naturwiss. und d. Technik, 10 (1928), 432-63. van der Waerden, B. L. “Die Voraussage von Finsternissen bei den Baby-loniern,” Berichte d. math. phys. KI. d. sacks. Akad. d. TlT-s.s. zu Leipzig, 92 (1940), 107-14. van der Waerden, B. L. “Zur babylonischen Planetenrechnung,” Eudemus, 1 (1941), 23-48. See Kroll VV. Virolleaud, Ch. L’Astrologie chaldeenne. 4 vols. Paris, 1908-12. Vogel, K. “Beitrage zur griechischen Logistik,” Sitzungsber. d. Bayerischen Akad. d. JFiss., Math.-nat. Abt., 1936, pp. 357-472. Vogel, K. “Bemerkungen zu den quadratischen Gleichungen der babylonischen Mathematik,” Osiris, 1 (1936), 703-17. Vogt, H. “Der Kalender des Claudius Ptolemaus” ( = F. Boll, Griechische Kalender, V), Sitzungsber. d. Heidelberger Akad. d. IFfss. Philos.-hist. KI., 1920, p. 15. Waterman, L. Royal Correspondence of the Assyrian Empire. 4 vols. “Univ, of Michigan Studies: Humanistic Series,” Vols. 17-20. Ann Arbor, 1930-36. Weidner, E. F. Handbuch der babylonischen Astronomic, I: Der babylonische Fixsternhimmel ( = Assyriologische Bibliothek, 23). Leipzig, 1915. [Only 146 pages are published; pp. 147-80 were printed but not published.] Weidner, E. F. “Ein babylonisches Kompendium der Himmelskunde,” AJSLL, 40 (1924), 186-208. Weidner, E. F. “Die astrologische Serie Enuma Anu Enlil,” Archiv fur Orientforschung, 14 (1942), 172-95 [to be continued], Weissbach, F. H. Babylonische Miscellen. Leipzig, 1903 ( = JFiss. Verbffentl. d. Deutschen Orient-Ges., 4). Winlock, H. E. “The Origin of the Egyptian Calendar,” Proc, of the Amer. Philos. Soc., 83 (1940), 447-64. Winlock, H. E. The Egyptian Expedition, 1925-1927. Section II of the Bulletin of the Metropolitan Museum of Art, 1928, pp. 3-58. Winlock, H. E. Excavations at Deir el Bahri. New York, 1942. Zeitschrift fur Assyriologie. Zeitschrift der Deutschen Morgenldndischen Gesellschaft. Zeuthen, H. G. Die Lehre von den Kegelschnitten im Altertum. Copenhagen, 1886. Reprinted for private circulation from Journal of Near Eastern Studies Vol. I, No. 4, October, 1942 PRINTED IN THE U.S.A. 0. NEUGEBAUER THE ORIGIN OF THE EGYPTIAN CALENDAR O. NEUGEBAUER Probably no calendaric institution has continued over a longer period than the Egyptian calendar. After its uninterrupted use during all of Egyptian history, the Hellenistic astronomers adopted the Egyptian year for their calculations. Ptolemy based all his tables in the Almagest on Egyptian years; even as late as a.d. 1543 Copernicus in De revolutionibus orbium coelestium used Egyptian years. The explanation of this fact is very simple: astronomers are practical-minded people who do not connect more or less mystical feelings with the calendar, as the layman frequently does, but who consider calendaric units such as years, months, and days as nothing but conventional units for measuring time. And because the main requirement of every measuring unit is, of course, its constancy, the Egyptian calendar is an ideal tool: twelve months of thirty days each, five additional days at the end, and no intercalation whatsoever. It is no wonder that the Hellenistic astronomers preferred this system to the Babylonian lunar calendar with its very irregularly changing months of twenty-nine and thirty days combined with a complicated cyclic intercalation—not to mention the chaos of Greek and Roman calendars.1 The ideal simplicity of the Egyptian calendar, however, raises serious problems for the historian. Should we assume that astronomers, for the sake of their own calculations, imposed on the rest of the population a calendar with no respect for sun and moon? No scholar will accept this viewpoint, even if he does not hesitate to speak (in cases of no consequence) of Egyptian “astronomers” or Egyptian Kalendermacher. Only one other solution seems to remain: the simplicity of the Egyptian calendar is a sign of its primitivity; it is the remainder of prehistoric crudeness, preserved without change by the 1 It may be remarked that for the same reason modern astronomy does not use the Gregorian calendar for computations but Julian years instead (the continued use of Egyptian years would be inconvenient because of the discrepancy of about one and a half years with the adopted historical chronology of our times). 396 The Origin of the Egyptian Calendar 397 Egyptians, who are considered to be the most conservative race known in human history. Even this second solution, however, is by no means satisfactory. I do not have in mind the sophisticated argument that one of the strongest foundations for the belief in the extreme Egyptian conservatism is the very maintenance of the calendar and should therefore not be used as an explanation of the calendar. What I mean is the fact that there is no astronomical phenomenon which possibly could impress on the mind of a primitive observer that a lunar month lasts 30 days and a solar year contains 365 days. Observation during one year is sufficient to convince anybody that in about six cases out of twelve the moon repeats all its phases in only 29 days and never in more than 30; and forty years’ observation of the sun (e.g., of the dates of the equinoxes) must make it obvious that the years fell short by 10 days! The inevitable consequence of these facts is, it seems to me, that every theory of the origin of the Egyptian calendar which assumes an astronomical foundation is doomed to failure. Four years ago I tried to develop the consequences of this conviction as far as the Egyptian years are concerned. I showed2 that a simple recording of the extremely variable dates of the inundations leads necessarily to an average interval of 365 days. Only after two or three centuries could this “Nile calendar” no longer be considered as correct, and consequently one was forced to adopt a new criterion for the flood, which happened to be the reappearance of the star Sothis. I do not want to repeat the discussion here, but I should like to state that I still think that this theory is in perfect agreement with the structure of the Egyptian calendar, which has only three seasons, admittedly agricultural and not astronomical, and which has no reference to Sothis at all.3 I did not see, at that time, any satisfactory 2 O. Neugebauer, “Die Bedeutungslosigkeit der Sothisperiode fur die altere aegyptische Chronologie,” Acta orientalia, XVII (1938), 169-95. 31 wish to take this opportunity to make some remarks about an interesting paper by H. E. Winlock, “The Origin of the Egyptian Calendar’’ {Proceedings of the American Philosophical Society, LXXXIII [1940], 447-64), where the problem of the Egyptian year is treated independently of my paper. The most important point seems to me that Winlock reached the same conclusion, namely: the classical theory that both Nile and Sothis are responsible for the beginning of the years must be abandoned. The old story of the “creation” of the Egyptian calendar in 4231 b.c. can now be considered as definitely liquidated. An objection has been raised against my theory of a “Nile-year” resulting from averaging the strongly fluctuating 398 Journal of Near Eastern Studies explanation of the second characteristic element of the Egyptian calendar—the months of invariably 30 days’ length. How are we to explain these artificial months, seemingly so contradictory to all our experience with ancient calendaric systems? The solution which I finally believe to have found for this problem is nothing but the radical abandoning of the concept that the 30-day months should be explained by some kind of primitive astronomy and the clear insight into the fact that the 30-day months are by no means peculiar to Egypt but play a very important role also in Mesopotamia, the classical country of the strictly lunar calendar. I can best start by quoting two sentences from Sethe’s Zeitrech-nung: “Bei den Aegyptern haben so wo hl Lepsius als Ed. Meyer und Andere die Existenz eines Mondjahres ffir die Urzeit als a priori selbstverstandlich vorausgesetzt .... und Brugsch wollte sogar das Fortbestehen eines solchen Mondjahres in geschichtlicher Zeit neben dem Siriuswandeljahr aus zahlreichen Angaben fiber Mondstande intervals between the inundations. This objection is that there is no proof of the existence of “Nilometers” at so early a period (ibid., p. 450, n. 11). However, no precise Nilometer is required for my theory. The sole requirement is that somebody recorded the date when the Nile was clearly rising. As a matter of fact, every phenomenon which occurs only once a year leads to the same average, no matter how inaccurately the date of the phenomenon might be defined. The averaging process of a few years will automatically eliminate all individual fluctuations and inaccuracies and result in a year of 365 days. Fractions, however, would be obtained only by much more extensive recording and by accurate calculation. The actual averaging must, however, be imagined as a very simple process based on the primitive counting methods as reflected in the Egyptian number signs: the elapse of one, two, or three days recorded by one, two, or three strokes. After ten strokes are accumulated, they are replaced by a ten-sign, thereafter ten ten-signs by a hundred symbol, etc. This is the well-known method of all Egyptian calculations. This method finally reduces the process of averaging to the equal distribution of the few marks which are beyond, say, three hundred-signs and five ten-signs; in other words, there is no “calculation” at all involved in determining the average length of the Nile-years. Of course, we need not even assume the process of counting all the single days every year: the averaging of the excess number of days over any interval of constant length (say twelve lunar months) gives the same result. This equal distribution of counting-marks finally makes it clear that no fractions will be the result of the process. Winlock’s own theory assumes the prediction of the flood at an early epoch according to lunar months (pp. 454 ff.). Thereafter, Menes is credited with having begun to determine the beginning of the years by observing the Sothis star (pp. 457-58), the seasons still being of variable length because of their composition by lunar months (p. 459). Finally, Djoser around 2773 b.c. is supposed to have dropped the actual New Year’s observations by installing the year of “12 times 30 +5 days” because “experience of centuries by now had seemed to show that the year should contain 365 days” (p. 462). I cannot see how experience from observing Sothis could have created this assumption of the length of the year because Sothis after one hundred years of 365 days each rises 25 days too late! This obvious contradiction between the year of 365 days and any astronomical observations seems to me just the most striking argument in favor of looking for another phenomenon which leads to a 365-day year—the flood of the Nile. The Origin of the Egyptian Calendar 399 .... schliessen.”4 But, he goes on, “schwer liesse sich von einem solchen alten Mondjahre die Briicke zu dem geschichtlichen Wandel-jahre .... schlagen.” This conclusion of Sethe is obviously the generally accepted viewpoint. However, how can one justify the total ignoring of the textual evidence amply collected, for example, by Brugsch in his Thesaurus,6 which shows clearly a great interest in the real lunar months? Indeed, Brugsch’s assumption of the. existence of real lunar months has only been confirmed since his time.6 I admit, of course, that Borchardt7 overemphasized the importance of the fullmoon festivals for the coronation ceremonies and that his chronological construction, based on this theory, requires checking. The fact remains, however, that at all periods of Egyptian history the real lunar months had their well-defined religious significance. One need only recall the countless passages where we are told about the loss and restitution of the moon’s eye, of its magical importance, etc. Indeed, one should be surprised that the behavior of the real moon should have been totally disregarded and have been replaced by meaningless intervals of 30 days. Moreover, we now know that the “short” and “long” years mentioned in the list of offerings at Beni-hasan8 (Twelfth Dynasty) are the years containing either twelve or thirteen lunar festivals (say, new moons), respectively; this is shown by a Demotic' papyrus in which a simple cycle of twenty-five years is developed according to which one can tell whether a certain year contains twelve or thirteen new moons and on what dates in the civil calendar they can be expected.9 In other words, we have to admit the coexistence of real lunar months and of the civil calendar with its 30-day months. Sethe’s contradiction then disappears, and we no longer need astronomy to explain the 30-day months: all “astro- 4 K. Sethe, Die Zeitrechnung der alten Aegypter (“Nachr. Ges. Wiss. Gottingen, Phil.-hist. KI.,” 1919, pp. 287-320, and 1920, pp. 28-55, 97-141), pp. 300 and 301. 5 H. Brugsch, Thesaurus inscriptionum aegyptiacarum, Vol. I: Astronomische und astrologische Inschriften altaegyptischer Denkmaler (Leipzig, 1883). 6 Winlock, op. cit., pp. 454 f. 7 L. Borchardt, Die Mittel zur zeitlichen Festlegung von Punkten der agyptischen Ge-schichte und Hire Anwendung (Cairo, 1935). 8 Urkunden d. aeg. Altertums, VII, 29, 18=P. E. Newberry, Beni Hasan I, p. 25, 11. 90 f. 9 Neugebauer-Volten, “Untersuchungen z. antiken Astronomie. IV: Ein demotischer astronomischer Papyrus (Pap. Carlsberg 9),” Quellen u. Studien z. Gesch. d. Mathematik, Abtl. B, IV (1938), 383-406. 400 Journal of Near Eastern Studies nomical” interest is restricted to the actual observation of the real moon with no resultant influence on the civil calendar. But how are we to explain the coexistence of the schematic 30-day months side by side with the real lunar months? The answer sounds paradoxical at first but is actually very simple: schematic months are the natural consequence of a real lunar calendar. Here the analogy with the situation in Mesopotamia enters the picture. The actual behavior of the moon is so complicated that not before the very last centuries of Babylonian history was a satisfactory treatment of the movement of the sun and the moon developed sufficiently accurate to predict the length of the lunar months for an appreciable time in the future. In other words, only a highly developed theoretical astronomy (today we would say “only celestial mechanics”) is able to determine the further course of a lunar calendar. Private and public economy require the possibility of determining future dates regardless of the irregularity of the moon and the inability of the astronomers to predict the outcome. A simplified calendar is'equally useful also for the past because it eliminates the necessity of keeping exact records of the actual length of each month. It is amply testified from Babylonian sources how this natural demand was met: beside the real lunar calendar there was a schematic calendar of twelve months of 30 days each, regardless of the real moon. A few well-known examples are sufficient to prove this statement: contracts for future delivery were dated in this schematic calendar, regardless of the actual outcome in the particular year,10 past expenses11 and rents are calculated according to a 360-day business year and to 30-day months,12 etc. But it is interesting to see that this schematic year was also in use in astronomical texts. Solstices and equinoxes are listed as falling on the fifteenth of the Months I, IV, VII, and X, although everybody knew that the dates in the real lunar calendar would be totally different in almost all cases. The same holds with 10 Thureau-Dangin, RA, XXIV (1927), 188 ff. These examples belong to the Old Babylonian, Persian, and Neo-Babylonian periods. 11 Kugler, ZA, XXII (1908), 74 f. 12 Neugebauer, Jlfathem. Keilschrift-Texte, III, 63. The Origin of the Egyptian Calendar 401 the lengths of day and night,13 the shadow length,14 rising and setting of fixed stars,15 etc.16 This use of the schematic calendar in an astronomical context is especially important; it demonstrates clearly that the schematic dates do not represent an attempt to approximate as closely as possible the real facts but merely constitute a way of expressing future dates in round numbers according to a general scheme whose exact relation to the real lunar calendar remains to be established later on when actually needed. It is evident that the analogous situation in Egypt is sufficient to explain analogous consequences. No one was able to predict exactly the moon’s behavior, and a schematic calendar was therefore quite necessary wherever economic life demanded regularity and simplicity. “The” Egyptian calendar is therefore ip all respects the result of practical needs alone, and “astronomy” is restricted to the simple fact that the real lunar festivals were regulated by direct observation, with no attempt to influence the civil calendar, and vice versa. It is only a slight difference in emphasis which brought about the almost total eclipse of the schematic calendar in Babylonia and of the lunar calendar in Egypt. The deeper reasons for this difference in emphasis can perhaps be found in the difference of social and economic structure of the two countries. In unified Egypt with its centralized administrative system the schematic calendar naturally had a much higher importance for the life of the whole country17 than in the 13 E.g., Weissbach, “Bab. Miscellen,” Wiss. Veroff. DOG, IV (1903), 50 f., and Kugler, Sternkunde, Erganzungsheft, 88 fl. 14 Weidner, AJSL, XL (1924), 186 if. 43 CT, XXXIII, 1-8. 16 It is very possible that many dates in cuneiform sources are actually meant in the schematic calendar, but we have no means to prove it. It would be, however, equally difficult to prove that the real lunar calendar is meant. 17 When I reviewed the content of this paper at the meeting of the American Oriental Society in Boston, Professor H. Frankfort asked whether the institution of the schematic calendar could be assumed to belong to the reign of Djoser. I think that no serious objection can be raised against such an assumption, because the only condition for the creation of the schematic calendar is a sufficiently well-organized and developed economic life. On the other hand, means to determine such a date by astronomical considerations do not exist. The problem of the invention of the schematic months must not be confused with the problem of the period at which-the 365-day year was introduced. The two institutions are absolutely independent—at least in principle. The 365-day year must have been created 402 Journal of Near Eastern Studies city-states of early Mesopotamia, where each community enjoyed the right of having a calendar of its own.* is * * 18 It is worth noticing that the parallelism between the Babylonian and Egyptian situation also holds for the astronomical documents which we possess from the Twelfth Dynasty and from the New Kingdom. The decanal lists in the coffins from Asyut19 represent the same type of schematic astronomical calendars as do the Babylonian texts,20 and the same holds for the star calendars around the figure of Nut in the cenotaph of Seti I and in the tomb of Ramesses IV.21 Here again, < as in Babylonia, we see that astronomy in its earlier stages of development makes no attempt to give exact dates but applies simple schemes which strongly idealize the real facts.22 To summarize, both the Egyptian and the Babylonian calendaric concepts display a higher complexity than usually admitted by modern scholars. One point needs special stressing: this complexity must not be considered as the struggle of two or three competing calendaric systems in the modern sense of the word but represents the peaceful coexistence of different methods of defining time moments and time intervals in different ways on different occasions. The situation is here very much the same as in ancient metrology: no need is felt to measure, e.g., grain and silver and fishes by the same units of at a period when the inundation coincided roughly with the season called “inundation.” Such a coincidence held for the centuries around 4200 and again in the centuries around 2800. The latter date (i.e., the time of Djoser) has been considered by Winlock (op. cit. p. 462) as the date of the definite establishment of the Egyptian year. The analysis of all available evidence for the use of the 365-day year by A. Scharff (e.g., Historische Zeit-schrift, CLXI [1939], 3-32) also shows that there is no reason to maintain the earlier date (as I was still inclined to do in my paper in Acta orientalia). is Cf., e.g., N. Schneider, “Die Zeitbestimmungen der Wirtschaftsurkunden von Ur III,” Anal. Or., Vol. XIII (1936). is Cf., e.g., Pogo, Isis, XVII (1932), 16-24, and Osiris, I (1935), 500-509. 20 Of course, only as far as the method is concerned; the content is totally different. 2i For the astronomical and mythological interpretation of these texts see Lange-Neugebauer, “Papyrus Carlsberg I”, Kgl. Danske Vidensk. Selsk. Hist.-fil. Skrifter, Vol. I, No. 2 (1940). It is a methodical mistake to use these documents as astronomically precise and to calculate their date under this assumption—not to mention the fact that there does not yet exist a satisfactory explanation of essential features of the “diagonal calendars” on the coffin lids. 22 The same can be observed in early Greek astronomy, e.g., in Autolycus (ca. 300 b.c.), De ortibus et occ. II, theorem 6 (ed. Hultsch, p. 118). The Origin of the Egyptian Calendar 403 weight, nor is an attempt made to establish well-defined relations between these measures. Exactly in the same sense all modern talk about ancient “luni-solar calendars” constitutes an anachronism: some elements of ancient life are regulated according to the seasons; others, according to the moon (and in Egypt also according to the Nile and Sothis). But no Egyptian thought about a Sothis-lunar calendar or any analogous construction. The key to understanding the origin of the Egyptian calendar seems to me to be the insight into the independence of all its elements which we still see in existence in historical times: the Nile, the Sothis star, the fiscal calendar, and the moon. Brown University MAC ROB I VS FRANCISCVS EYSSENHARDT ITERVM RECOGNOVIT ADIECTAE SVNT TABVLAE LIPSIAE IN AEDIBV8 B. G. TEVBNERI MDCCCLXXXXIH 10 SAT. LIBRI I monem adducitis nihil ex omnibus quae a ueteribus elaborata sunt aut ignoratio neget aut obliuio sub-trahat, superfluum uideo inter scientes nota proferre. sed nequis me aestimet dignatione consultationis grauari, quidquid de hoc mihi tenuis memoria sug- 5 gesserit, paucis reuoluam.’ post haec, cum omnes para-tos ad audiendum erectosque uidisset, ita exorsus est. 2 M. Varro in libro rervm hvmanarvm, quern de diebvs scripsit, homines inquit qui ex media nocte ad proximam mediam noctem his horis 10 uiginti quattuor nati sunt, uno die nati dicun- 3 tur. quibus uerbis ita uidetur dierum obseruationem diuisisse, ut qui post solis occasum ante mediam noctem natus sit, illo quern nox secuta est — contra uero qui in sex noctis horis posterioribus nascitur, eo 15 die uideatur natus qui post earn noctem diluxerit. 4 Athenienses autem aliter obseruare idem Varro in eodem libro scripsit, eosque a solis occasu ad solem iterum Occident em omne id medium tempus unum diem esse dicere: Babylonios 20 porro aliter: a sole enim exorto ad exortum eiusdem incipientem id spatium unius diei nomine uocare: Vmbros uero unum et eundem diem esse dicere a meridie ad insequentem 5 meridiem, quod quidem inquit Varro nimis ab- 25 surdum est. nam qui kalendis hora sexta apud Vmbros natus est, dies eius natalis uideri de-bebit et kalendarum dimidiatus et qui post G kalendas erit usque ad horam eius dici sextam. populum autem Romanum ita, uti Varro dixit, dies so singulos adnumerare a media nocte ad mediam proximam multis argumentis ostenditur. sacra sunt enim 1 mducitif P a om. B’ P; que uetenbuf P, supra qu£ add. nich cor P2 4 dignatione * (fait m) B 8 marcuf BP 10 *"oril P 11 quatuor P 13 diuidiffe B' 14 quemox nox B fequuta P 20 babilomof BP 21 exortom B' 29 oram _B' eiufdem P 31 annumerare P III 2-10 11 Romana partim diurna, alia nocturna, et ea quae diurna sunt ♦**♦♦*♦♦♦♦♦ ab hora sexta noctis sequentis nocturnis sacris tempus impenditur. ad hoc 7 ritus quoque et mos auspicandi eandem esse obserua-5 tionem docet. nam magistratus, quando uno die eis et auspicandum est et id agendum, super quo processit auspicium, post mediam noctem auspicantur et post exortum solem agunt, auspicatique et egisse eodem die dicuntur. praeterea tribuni plebis, quos nullum 8 10 diem integrum abesse Roma licet, cum post mediam noctem proficiscuntur et post primam facem ante mediam noctem sequentem reuertuntur, non uidentur afuisse diem, quoniam ante horam noctis sextam regressi partem aliquam illius in urbe consumunt. 15 Qvintvm quoque Mvcivm iureconsultum dicere 9 solitum legi lege non isse usurpatum mulierem, quae, cum kalendis lanuariis apud uirum matrimonii causa esse coepisset, a. d. IIII kalendas lanuarias sequentes usurpatum isset: non 20 enim posse impleri trinoctium, quo abesse a uiro usurpandi causa ex duodecim tabulis deberet, quoniam tertiae noctis posteriores sex horae alterius anni essent, qui inciperet ex kalendis. 25 Vergilivs quoque id ipsum ostendit, ut hominem 10 decuit poeticas res agentem, recondita atque operta ueteris ritus significatione 'torquef inquit 'medios nox humida cursus et me saeuus equis oriens addauit anhelis.’ 27 Vergilius Aen. V 738 2 post flint est -jfr pictum in P, lacunam expleuit Carrio 4 aufpicoudi ut uid. B' 6 preceffit B 8 aufpicatiq. * * & * * | eodem egiffe die P 12 mediam noctem proficifcuntur et poft om. P 13 di* {fuit die) P fexta * | P 16 legi add. Pont anus non iffe JP3: nouiffe P ufui'patu 18 cgpiffet P addiem quartum BP 19 effet B poCCet b 22 pofteriorif B' 25 uirgihuf BP 28 corfuf P' 29 afflauit bP f; THE ATTIC NIGHTS OF AULUS GELLIUS WITH AN ENGLISH TRANSLATION BY JOHN C. ROLFE, Ph D., Litt.D. UWITKRUFTT or I'KMNSTLVANIA IN THREE VOLUMES 1 LONDON : WILLIAM HEINEMANN NEW YORK : G. P. PUTNAMS SONS MCMXXVIT library S. D A. THEOLOGICAL SEMINARY VKC MA PARK; WASHIN -TON. n. f;_ ATTIC NIGHTS OF AC LUS GELLIUS BOOK III. n. 9-14 10 lueescit. A<1 hoe ritus quoque et mqs auspicandi eandem esse observationen) docet; nam magistrates, quando uno die eis auspicandum est et id super quo auspicaverunt agendum, post1 median) noctem auspicantur et post meridiem sole magno agunt,2 auspicatique esse et egisse eodein die dicuntur. 11 1’raeterea tribuni plebei, quos nullum diem abesse Homa licet, cum post median) noctem proficiscuntur et post primam facem ante mediam sequentem rc-vertuntur, non videnlur afuisse unmn dien), quoniam, ante horam noetis sextain regressi, parte aliqua illius in urbe Roma sunt. 12 Q.3 quoque Mucium iureconsultum dicere solitum legi, non esse usurpatam mulierem, quae, cum Kalen-dis lanuariis apud virum matrimonii causa esse coe-pisset, ante diem IV. Kalendas lanuarias sequentes 13 usurpatum isset; non enim posse impleri trinoctium, quod abesse a viro usurpandi causa ex Duodeeiin 1 abulix deberet, quoniam tertiae noetis posterioris sex horae alterius anni essent, qui inciperet ex Kalendis. 14 Istaec autem omnia de dierum temporibus et finibus ad observationen) disciplinamque iuris antiqui pertinentia cum in libris veterum inveniremus, non dubitabamus quin \ ergilius quoque id ipsuni osten- 1 cum post, Puleanus ; dum post, Danish!. 2 meridiem sole magno agunt, Hertz ; meridiem solem agnum (sole magnum, F), w ; meridialem solem agunt, Hosiux. 3 Q. added bg Macrob. 1 Fr. 7, Huschke ; Jur,. Civ. iv. 2, Bremer. 2 Dec. 27th ; January at that time had twenty-nine days. 3 vi. 4. 4 Posterioris is nom. pl. See Varro De Ling. Lat. viii. 66. 242 over, the ceremony and method of taking the auspices point to the same way of reckoning; for the magistrates, whenever they must take the auspices, and transact the business for which they have taken the auspices, on the same day, take the auspices after midnight and transact the business after midday, when the sun is high, and they are then said to have taken the auspices and acted on the same day. Again, when the tribunes of the commons, w ho are not allowed to be away from Rome for a whole day, leave the city after midnight and return after the first lighting of the lamps on the following day, but before midnight, they are not considered to have been absent fora whole day, since they returned before the completion of the sixth hour of the night, and were in the city of Rome for some part of that day. I have read that Quintus Mucins, the jurist, also used to say 1 that a woman did not become her own mistress who, after entering upon marriage relations with a man on the day before the Kalends of January, left him, for the purpose of emancipating herself, on the fourth day before the Kalends of the following January ; 2 for the period of three nights, during which the Tire tee Tables3 provided that a woman must be separated from her husband for the purpose of gaining her independence, could not be completed, since the last4 six hours of the third night belonged to the next year, which began on the first of January. Now since I found all the above details about the duration and limits of days, pertaining to the observance and the system of ancient law, in the works of our early writers. I did not doubt that Virgil also a 2 243 ATTIC NIGHTS OF AULCS GELLIUS derit, non ex|M>site atque aperte, sed. ut hominem decuit poeticas res agentem, recondita et quasi operta veteris ritus significatione : 15 I orquet (inquit) niedios nox umida cursus Et me saevus equis oriens afflavit anhelis. 16 His enim versibus oblique, sicuti dixi, admonere voluit, diem quem Romani “civilem” appellaverunt a sexta noctis hora oriri. Ill l)e noscemlis exploramlisque Plauti comoediis, quoniam promisee verae atque falsae nomine eius inscriptae fenin-tur ; atque inibi, quod Plautus in pistrino1 2 et Naevius in carcere fabulas senptitarint. 1 \ erum esse comperior quod quosdain bene littera- tos homines dieere audivi, qui plerasque Plauti comoedias curiose atque contente lectitarunt, non indicibus Aelii nec Sedigiti nee Claudii nee Aurelii nee Accii nec Manilii super his fabulis quae di-cuntur “ ambiguae ” crediturum, sed ipsi Plauto 2 moribusque ingeni atque linguae eius. Hae enim iudicii norma Varronem quoque usum videmus. 3 Nam praeter illas unam et viginti quae “ Varronia-nae ” voeantur. quas idcirco a ceteris segregavit, quoniam dubiosae non erant set consensu omnium Plauti esse censebantur, quasdain item alias probavit 1 in pistrinum (pistrino, a), added in 1 Aen. v. 738. 2 Crediturum seems an archaism for crediluros; see i. 7. 244 BOOK 111. ii. 14 hi. 3 indicated the same thing, not directly and openly, but. as became one treating poetic themes, by an indirect and as it were veiled allusion to ancient observance. He says :1 For dewy Night has wheeled her way Far past her middle course; the panting steeds Of orient Morn breathe pitiless on me. For in these lines he wished to remind us covertly, as I have said, that the day which the Romans have called “ civil ” begins after the completion of the sixth hour of the night. Ill On investigating ami identifying the comedies of Plautus, since the genuine and the spurious without distinction are said to have been inscribed with his name ; and further as to the report that Plautus wrote plays in a bakery and Naevius in prison. I am convinced of the truth of the statement which I have heard made by men well trained in literature, who have read a great many plays of Plautus with care and attention : namely, that with regard to the so-called “ doubtful ’ plays they wotdd ■ trust, not the lists of Aelius or Sedigitus or Claudius or Aurelius or Accius or Manilius, but Plautus himself and the characteristic features of his manner and diction. Indeed, this is the criterion which we find Varro using. For in addition to those one and twenty known as “ Varronian,” which he set apart from the rest because they were not questioned but by common consent were attributed to Plautus, he accepted also some others, influenced by the style and humour of their language, which was 245 ATTIC NIGHTS OF AULUS GELLIUS necessum est atque in sese colendo non aeque esse 13 parcum. Nam si avaritia sola smnma oinnes hominis jwirtes affectionesque occupet et si ad incuriam usque cor|M>ris grassetur, ut per illam imam neque virtutis neque virium neque corporis neque aniini cura adsit, turn denique id vere dici potest effeminando esse et animo et corjiori, si1 qui neque sese neque aliud 14 curent, nisi pecuniam.” Turn Favorinus “ Aut hoc,” inquit, “ quod dixisti, probabile est, aut Salluslius odio avaritiae plus quam |>ar fuit2 earn criminatus est.” II Queninam esse natalein diem M. Varro dicat, qui ante noctis horam sextain postve earn nati sunt ; atque inibi de tempo-ribus terminisque dieruin qui civiles nominantur et usque-quaque gentium varie observant ur ; et praeterea quid Q. Slucius scripserit super eamulierequae a* marito non iure se usurpavisset, quod rationem civilis anni non habuerit. 1 Quaf.ri solitum est, qui noctis hora tertia quartave sire qua alia nati sunt, uter dies natalis haberi appellarique debeat, isne quern nox ea consecuta 2 est, an qui dies noctem eonsecutus est. M. Varro in libro lierum Humanarum, quern De Diebus scripsit, “homines,” inquit, “qui inde a4 media nocte ad 1 si, added by H. J. Muller. 1 par fuit, suggested by Hosius; potuit, MSS.; decuit, Damste. 3 quae a, Erbius ; quia, w. 4 inde a, Hertz ; n, a>; ex, Maer. i. 2. 3. 1 The reading of the MSS., potuit, might perhaps be 238 BOOK III. 1. u-n. 2 other things as well, and cannot be equally niggardly in his care of himself. For if extreme avarice, to the exclusion of everything else, lay hold upon all a man's actions and desires, and if it extend even to neglect of his body, so that because of that one passion he has regard neither for virtue nor physical strength, nor body, nor soul—then, and then only, can that vice truly be said to cause effeminacy both of body and of soul, since such men care neither for themselves nor for anything else except money.” Then said Favorinus : “ Either what you have said is reasonable, or Sallust, through hatred of avarice, brought against it a heavier charge than he could justify.”1 II Which was the birthday, according to Marcus Varro, of those born before the sixth hour of the night, or after it; and in that connection, concerning the duration and limits of the days that are termed “civil” and are reckoned differently all over the world; and in addition, what Quintus Slucius wrote about that woman who claimed freedom from her husband's control illegally, because she had not taken account of the civil year. It is often inquired which day should be considered and called the birthday of those who are born in the third, the fourth, or any other hour of the night ; that is, whether it is the day that preceded, or the day that followed, that night. Marcus Varro, in that book of his Human Antiquities which he wrote On Days, says : 2 “ Persons who are born during the supported by such expressions as Catull. Ixxvi. 16, hoc facias, sire id non pote, sire pote. 2 xiii. Frag. 2, Mirsch. 239 ATTIC NIGHTS OF AULUS GELLIUS proximain inediam noctem in his horis viginti quat-3 tuor nati sunt, uno die nati dicuntur.” Quibus verbis ita videtur dieruin observationem divisisse, ut qifi post solem occasion ante inediam noctem natus sit, is ei dies natalis sit. a quo die ea nox coeperit; contra vero, qui in sex noctis horis posterioribus nascatur, eo die videri natuin, qui post earn noctem diluxerit. 4 Athenienses autein aliter observare, idem Varro in eodem libro scripsit, eosque a sole occaso ad solem iteruin occidentein omne id medium tempus unum 5 diem esse dicere. Babylonios porro aliter; a sole enim exorto ad exortum eiusdem incipientem 1 totum G id spatium uniusdiei nomine appellare; multos vero in terra Umbria unum et eundem diem esse dicere a meridie ad insequentem meridiem ; “quod quidem,” inquit, “ nimis absurdum cst. Nam qui Kalendis hora sexta apud Umbros natus est. dies eius natalis videri debebit et Kalendaruni dimidiarum et qui est post Kalendas dies ante horam eius dici sextain.” 7 Populum autem Romanuni ita, uti Varro dixit, dies singulos adnumerare a media nocte ad mediam 8 proximain, multis argumentis ostenditur. Sacra sunt Romana partim diurna, alia nocturna, sed ea quae inter noctem hunt diebus addicuntur, non noctibus; 9 quae igitur sex posterioribus noctis horis fiunt, eo die fieri dicuntur qui proximus earn noctem in- 1 insequentem, Damste. 1 xiii. Frag. 3, Mirsch. 2 That is, according to -the Roman reckoning. Ry the alleged Umbrian reckoning, the first day of the month would begin at midday and end at the next midday. 240 BOOK III. 11. 2 9 twenty-four hours between one midnight and the next midnight are considered to have been born on one and the same day.’ From these words it appears that he so apportioned the reckoning of the days, that the birthday of one who is born after sunset, but before midnight, is the day after which that night began ; but that, on the other hand, one who is born during the last six hours of the night is considered to have been born on the day which dawned after that night. However, Varro also wrote in that same book 1 that the Athenians reckon differently, and that they regard all the intervening time from one sunset to the next as one single day. That the Babylonians counted still differently ; for they called by the name of one day the whole space of time between sunrise and the beginning of the next sunrise; but that in the land of Umbria many said that from midday to the following midday was one and the same day. “ But this,” he said, “ is too absurd. For the birthday of one who is born among the Umbrians at midday on the first of the month will have to be considered as both half of the first day of the month and that part of the second day which conies before midday.” 2 But it is shown by abundant evidence that the Roman people, as Varro said, reckoned each day \* from midnight to the next midnight. The religious/ ceremonies of the Romans are performed in part by day, others by night; but those which take place by night are appointed for certain days, not for nights ; accordingly, those that take place during the last six hours of the night are said to take place on the day which dawns immediately after that night. More- 241 vol. 1. H Reprinted for private circulation from JOURNAL OF NEAR EASTERN STUDIES Vol. Ill, No. 4, October 1944 PRINTED IN THE U.S.A. THE TETRAGRAMMATON: AN OVERLOOKED INTERPRETATION WILLIAM A. IRWIN The problem of the tetragrammaton has been given renewed attention in recent months. In this Journal, III (1944), 1-8, Raymond A. Bowman advanced the view that the name is derived from a root meaning “to speak”; and in the Journal of Biblical Literature, LVII, 269 ff., Julian Morgenstern adduces the usage of Second Isaiah to show that the word hv? was understood as a divine title. In this he was anticipated by Samuel I. Feigin, whose discussion in his Missitrei HeavaB is such as to merit its being presented to readers who may not have seen it in the Hebrew original. He says (pp. 355 and 430-31): “The name Yahweh is an imperfect from H’H in the ancient form which had pathah with 1 New York: Hebrew Publication Society of Palestine and America, 1943. the preformative yod and waw as the second radical instead of the later yod. It appears also as the first person n'HX when God speaks on his own behalf [Exod. 3:14; Judg. 6:16; Hos. 1:9]. “Perhaps, too, the participial form of the verb HT1, namely Xin [HuJ, is used to signify Yahweh.2 Compare, ‘I, I am He [HuJ, and 2 [The form is a passive participle with stative meaning. As is contracted to inTIIZ?"1!, so (later was contracted to and finally X1H, probably under the influence of the third person pronoun. While H1H expresses the existence of temporary things (Eccles. 2:22) and H^lH (Exod. 9:3) expresses God’s power acting temporarily, the passive form X17I expresses constant existence which is befitting as an epithet of God. For the passive participle expressing constant action compare ~Jahuze hereb (Song of Songs 3:8), “constant holders of sword”; bafuah 258 Journal of Near Eastern Studies there is no god with me’ (Dent. 32:39) with the verse in Isaiah, ‘I, I am Yahweh, and beside me there is no saviour’ (Isa. 43:11). The word Hu3 in Deuteronomy means Yahweh. The same meaning attaches to the verse, ‘I, I am He [Hu3] who wipes out your transgressions for my own sake, and your sins I will not remember’ (Isa. 43:25), namely,\‘I am Ya’h-we'U.^S^ljke^ej/I^I- aa^ He [JJu?] whoksdpi-i forts you’ (Isa. 5T:12), namely, T, Yahweh, comfort you..’ Alsct in the verses, ‘I, Yahweh, .^amYhe fifst, and withlhe la^t I aja He [Hu3]’ (Isa. 41:4), T am He [Hu3], and none can deliver from my hand’ (Isa. 43:13), ‘And unto old age I am He [Hu3], and unto gray hairs I will carry’ (Isa. 46:4), T am He [Hu3], I am the first, yea I am the last’ (Isa. 48:12)—in all these verses one can interpret ‘I am Yahweh.’ Also the verse, ‘For my mouth, it [Hu3] has commanded, and his spirit, it [Hu3] has gathered them’ (Isa. 34:16), which Professor David Yellin explains as an ellipsis for ‘His mouth, it has commanded’ (Hiqre Miqra? on Isaiah [1939], p. 36) is to be interpreted, ‘For the mouth of Yahweh’; Hu3 serves in place of Yahweh. “Also some proper names which end in Hu3 are to be explained as compounded of the participle of JTFI, standing for Yahweh, and another element. At times Hu3 is shortened still further. Compare, for example, Abihu, son of Aaron, and Abiyahu or Abiyah, king of Judah. Both are one, but in Abihu the name of God is expressed by the participle of TTH, (Isa. 26:3), “it is constantly trusting”; hassedudah (Pss. 137:8) “the professional robber”; we'azub (Deut. 32:36) “permanent ruler and helper.” The use of intransitive verbs in passive participle to express stative meaning is common in the Mishnah. For another contraction of T compare “O, “branding,” from (Isa. 3:24). For contraction of N compare JY”! (Mesha Stone, 1. 12) for “gazing stock.” For contraction of " compare FA*] for “friendship.” For other examples of contraction of 1 compare “swim,” from sahw (Gesenius-Buhl, 16th ed., p. 781), “pasture” from Jahw, which is still found in Aramaic ““IHS? (Onqelos Gen. 41:2, 18). Compare also itfIFI'1 “it will be” (Eccles. 11:3) for with additional —S.I.F.] while in Abiyah the name of God appears in the regular form. The name is to be interpreted as ‘Yahweh is my God.’ So too, Elihli (I Chron. 26:7; 27:18), Elihu3 (Job 32:2, 5, 6; 34:1; 36:1; I Sam. 1:1; I Chron. 12:20), and Elijah [3Eliyah and ’Eliyahu]: the interpretation of both is ‘Yahweh is my God.’ “The name Solomon, too, is to be explained as compounded of Shalom and Hu3, ‘Peace of Yahweh,’ but the name of Yahweh is written as the participle Hu3, which can be shortened to Hu, and, finally, waw falls out and only he with mappiq is left, from which at length the mappiq also falls out as if a pronominal suffix were before us. And, indeed, Nathan called Solomon by the name Jedidiah (II Sam. 12:25), for the two names have the same meaning, ‘The peace of Yahweh’ and ‘Beloved of Yahweh.’ Compare the names Shele-miah and Shelemiahu, in which the tetragram-maton is preserved in shortened form. “Sometimes the name is compounded of two divine names. The name Dodawahu (II Chron. 20-37) is compounded of Dod and Hu, and even the waw connecting the two names is preserved. But in the name Dodo (I Chron. 11:12, 26, etc.) not alone is the waw connecting the names lost but also the root Hu is contracted to 6, as at the beginning of names Yahu is reduced to Y6.3 “The Dwdh, mentioned in the stela of Mesha, the 3r’Z of which Mesha carried into the city of Ataroth and dragged before Chemosh in Keriath (Inscription of Mesha, 11. 12-13), was, it seems, compounded of Dwd and an abbreviation of the participle of 7TH, signifying Yahweh. We have here a divine name compounded of Dwd and Hu3, but each one appearing in its own right. Professor Albright in his latest book, Archaeology and the Religion of Israel (1942), explains 3r3Z as a proper name, Uriel; Dwdh he explains as dodah with mappiq— her dod, namely of Ataroth (p. 218, n. 86). But he gives a completely new meaning to the word dwd; that it is ‘chief.’ Against this one may note that the noun does not appear with this meaning anywhere in Hebrew............Accord- 3 [For two deities used as a personal name compare I-li-u-dSamas, l-li-u-dSin, dSin-u-dSamas (see J. J. Stamm, Die akkadische Namengebung [1939], p. 135).—S.I.F.] The Tetragrammaton : An Overlooked Interpretation 259 ingly it seems preferable to explain yrd as an object of the cult which stood in the eyes of Mesha for Yahweh, and he dragged it before 4 [Ibid. For MP as the divine name see James A. Montgomery, “The Hebrew Divine Name and the Personal Pronoun hu” (JBL, LXIII [1944], 161-63). Professor Montgomery adduces other examples where MP stands for Yahweh. The phrase ON (II Kings Chemosh his god. Dwdh, then, is the name of a deity, Dawidhu — Dawid + Hu.”1 2 3 4 * University of Chicago 2:14) is possibly to be read X'HH “Where is Hu,” namely, Yahweh. Very instructive is the verse Jer. 5:12, where XTI N'b, “there is no Hu,” is parallel to denying Yahweh,—S.I.F.] (Montgomery’s article appeared since the above was written.—W. A. I.) THE ORIGIN OF -ELOH, “GOD,” IN HEBREW SAMUEL I. FEIGIN as is well known the name 'Aloh, “God,” is ex-plained either as an enlargement of 3eZ or as derived from a special root dh.1 It seems to me that we have in Jeloh a compound name of 3eZ, “God,” and Jah a shortened form for ^ahyeh, “I shall be,” the designation of Yahweh in the first person (Exod. 3:14; Judg. 6:16; Hos. 1:9). As Yahweh the third person is related to ^ehyeh, originally ^ahweh the first-person qal of the root hwy,2 also 'Jah abbreviation of ^ahyeh in the first person is related to yah shortened form of Yahweh in the third person.3 The which was lost in the combination is recompensated by lengthening the vowel a, as the lost a3 is recompensated by lengthening the preceding vowel in syllables ending with \ Thus baraJ became bard, “he created”; raA, “head,” became rdsim, “heads,” finally rds; and yaPmar, “he will say,” becomes *yamar, finally ydmar, so also ^elaAh became ^elah. The form ^eldh is preserved in Aramaic and in Hebrew becomes, as usual, ^eldh. In cuneiform both forms are preserved ilahi and iluha.1 For such a combination of deities compare Dwdh,4 namely, Dawid + Hu.6 In the same region is found also Ishtar-Kemosh.6 It is in 1 See Gesenius-Buhl, Hebrdisches und aramaisches Handworterbuch (16th ed.; 1915), p. 39. 2 See Missitrei Heavar, p. 355, and above, p. 257. The origin of it is “I shall be with you,” as is explained in Exod. 3:12. 3 For ydh being shortened from Yahweh see Gese-nius-Buhl, op. cit., p. 289. 4 Mesha Inscription, 1. 12. 6 See Missitrei Heavar, pp. 430-31, and also above, p. 258. Professor Irwin calls my attention to the compound deity Qntyhw (A. Cowley, Aramaic Papyri of the Fifth Century [1923], No. 44:3). 6 Mesha Inscription, 1. 17. teresting to note that in both cases the other element precedes the element of the national deity, Ishtar before Kemosh, Dawid before Hu = Yahweh. Moreover, both may have some connection with the deity of love, Ishtar being the well-known deity of love in Babylonia and the West, and Dawid, judging from the name ddd, means love also. Whether Dwdh was regarded as a separate deity or was only a manifestation of Yahweh as god of fertility is hard to decide. The two elements of 3eZ and ^ah, of which the name 'jelah = Jeldh is compounded, may have been originally two special deities, 3eZ being the deity of earth and Jah = Yahweh the deity of heaven and the national deity of the Hebrews in general and of Israelites in particular.7 But Professor G. Cameron pointed out to me that DeZ may have been a kind of determinative “god” in general and has no specific designation as “god of the earth.” The singular Aldh, pronounced ^eldah, is used in plural form Aldhim, originally “gods,” but later “God” in the singular. This interchange between “god” and “gods” to designate the same divinity was found also in the old period in nAmurru, “the god Arnurru” and iUAmurru (dingir.dingir.mar.tu). Also, Bacal appears as Becdlvm, cAshtdreth as cAshtdrdth, cAnath as cAndthdth, the manifestations of the deity in various places and in various functions.8 University of Chicago 7 Cf. the interesting article of Professor G. Levi della Vida, “El Qelyon in Genesis 14:18—20,” JBL, LXIII (1944), 1-9. 8 Cf. W. F. Albright, From the Stone Aye to Christianity (1940), p. 161. 39° Traclatips de Confecratione Calendarum, id tute facias ipfe licet: Itemque fi curfum medium dierum viginti, triginta, quadraginta, ufque ad centefimum cupias no-tari charatoribus. Explicata enim atque explorata ratio eft , ubi curfum medium unius diei notum habeas. Confentaneum eft autem illud cognitum & comprehenfum animo habere , medius ille folis motus quid intervalli perluftrct novem & viginti dierum fpatio, quid trccentis & quatuor fupra quinqua-ginta diebus , quibus efficitur annus ille lunaris, cujus lunt or-dine difpofiti menfcs, qui annus adeo ordinatus dicitur. Hos enim curfus medios qui rite cognorit, is facile rationes illas percepcrit, ex quibus dilucidc pcrfpiciatur, luna nova quando le aperiat. Nam a nocfc menfis ea, qua primum luna nova fe aperit, ad proximi menfis illam notom qua rurfus aperiatur luna nova, dies toti intercedunt viginti novem. Nec omnino contingit unquam, ut plures, pauciorefve in-tcrfint dies folidi. Atqui hoc unum eft, quod hike rationibus quxrimus, luna videlicet nafcens quando primum aperiatur. Turn ex quo certa quxdam luna nova hoc anno apperiatur, ufque dum anno vertente luna nova aperiatur eadem, aut abit omnino tempus id , quod annum diximus ordinatum, aut uno die plus: atque eadem eft annorum omnium ratio. Curfus igitur iblis ifte medius novem & viginti diebus perluftrat duo-detriginta gradus, partes quinque & triginta, & fecundam u-nam: character eft 28. 35*. 1. anno autem ordinato trecentos & quadraginta oto> gradus , partes quinque & quinquaginta , atque deceni & quinque fecundas : charator eft 348. yy. ry. Solis in orbe fic, ut in reliquorum circulis planctarum, punctual eft certum, quo cum planeta commearit, tarn eft remotus a terris, quam cum maxime. Et tanquam id, quod eft-in folis orbe, puntom, ita quod in cxtcris planetaruni (luna ta-men excipitur) orbibus inert, tequabiliter movetur, atque an-nis feptuaginta unum fere gradum conficit. Atqui hoc punctual, quod idefi folis altitudo nominatur, diebus decern femper tinarn & dimidiatam fecundam conficit, quae dimidia tertian funt triginta : diebus. centum fecundas quindecim : mille dierum partes duas, & fecundas triginta : decern millibus dierum conficit quinque & viginti partes. Ex quo intelligitur idem puntom diebus viginti novem perluftrare fecundas quatuor & eo de Ratione Intercalandi. co amplius: & anno illo ordinato fecundas tres fupra quinqui-ginta: DiCtum a nobis ante eft,hujufceratiociniiftirpemrepeti ab ineunte noCte quinta hebdomads:, 8c eadem tertia mentis Nifan , anni videlicet quater millefimi, nongentefimi, triceft-mi obtavi poft conftitutum mundum. Ad hujus ratiocinii principium iftud confecerat motio folis media gradus feptenos, ternas partes, atque duas & triginta fecundas ex ariete: character eft 7. 3. 32. & hxc folis altitude quae vocatur, fex 8c vi-ginti gradus , infuper partes quinque & quadraginta , & oCto fecundas e geminis: character eft 26. 45. 8. Ergo fi quando libeat fcirc lol ubi fit fecundum motum medium, primd nume-rum dierum, qui a principio hujus ratiocinii ufque ad id tern-pus prseterierint, notum cllenecefte eft, 8c convcrhonem folis mediam his diebus confeCtam, quam ex iis, quae pofui, fig-nis cognofci licet, fic addere ad ftirpem hujus computationis, ut fuo quazque partium genera generi conjungantur. Nam ubi convcrfionis ejus erit terminus, ibi tunc temporis fol ex curfu medio locum habebit. Placet autem rei adjungere exemplum. Si quazreretur , ubinam ex medio curfu fol diet in anno primo hujus computationis, ineunte noCte fabbati, qui dies erat de-cimus & quartus menfis Tamuz, fiquidem ab ftirpe ad principium ejus diei, quo quazritur locus folis, intercedebant dies centum, curfus folis medius his centum diebus definitus fume-retur, oporteret, nempe gradus oCto& nonaginta, tres fupra triginta partes, & fecundx tres 8c quinquaginta : qua: adde-rentur ad gradus feptenos, partes.ternas, duas & triginta fecundas Arietis, ubi fol erat initio hujus computationis. Ex qui-bus una colleCtis fumma fieret centum & quinque graduum , partium feptem & triginta, & fecundarum viginti *quinque : character eft 107. 37. 27. Itaque prima ilia noCte fabbatica fol ex medio curfu in Cancro exiftebat, in feptima & tricefima parte gradus decimi & fexti. Quod autem quotidianus folis curfus medius interdum prima noCte ipfa determinetur, inter-dum ante folis occafum hora una, nonnunquam etiam tantundem poll folis obitum , id omnino in exponendo motu folis , quatenus ad lunte rationcm pertinet, ne attingimus quidem. At in explicando medio lunte curfu locus ille ftudiose traCtabi-tur, Atque hujus motus inveftigandi ratio temper eft eadem, nam Traftatut de Confecratione Calendar um\ nam & mille poft annos fi fubducendis & addendis fpatiis ex-curfis reliquoruni fumma fiat, eamque adjungas ad eum locum, quern fol lecundum motum medium obtinebat in principio hu-jus ratiocinii, certo cognofcas ubinam fol turn motu illo medio feratur. Idem de lunx motione media dicendum: idem-que de cujufque ftellx. Cum ejus quotidianam motionem mediam cognoveris quanta fit, fciafque motionis ejus principium urtde ducatur, poft annos, aut dies tot, quot libuerit, certo com-perias ea ubi feratur motione ilia media , fi curfum medium hifce diebus aut annis confeftum adjicias ad ilium locum, qui ftellie erat ab initio. Eadem ratio in ilia altitudine folis eft. Si ad eum, ubi initio erat altitudo folis, locum addas & fpati-um diebus aut annis prateritis confe&um , quovis die folis ubi fit altitudo reperias. Si quis autem primum alicujus cycli aut feculi annum malit efle hujus computations caput, quam eum annum, qui fuit a nobis propofitus, datur illi eligendi optio. Atque caput iftuc five id antecedat, five multis annis fubfequa-tur hoc , quod eft a nobis, perfpicuum eft quid oporteat fieri. Namque explicatum eft, quern curfum fol definiat ordinato anno toto , quern diebus novem & viginti, quern denique die uno. Demonftratum eft etiam annum, cujus fint pleni menfes, uno die efle longiorem eo, qui ordlnatus nominatur : annum autem ilium, qui completur menfibus cavis, uno die minorem efle, quam ordinatum. Jam de anno intercalari, ilium, fi menfes ejus fint ordine difpofiti, majorem efle anno communi & eodem ordinato diebus triginta : fin autem illius fint pleni menfes, fore, ut ordinatum annum communem fuperet diebus uno & triginta : ciim verb habeat menfes cavos, eundem novem 8c viginti diebus efle majorem anno illo ordinato. Quibus rebus perlpedfis & cognitis, facile eft folis inveftigare ac confe-fequi curfum medium in quot vifum fuerit dies aut annos: quern cum addideris ad id, unde nos hujus ratiocinii ftirpem repetiimus, curfum medium folis cognoveris ad quern volue-ris annum & diem ftirpem noftram fubfequentem, quern tu diem feceris computationis principium. Hunc autem fi detraxe-ris huic eidem, unde nos computationis duximus initium, medium folis curfum cotnpertum habueris in quern libuerit aut annum, aut diem ftirpem noftram antecedentem, a quo tu die exordium & de Ratione Intercalaiidi. 393 exordium computation is ceperis. Et quae in medio curfu folis, eadem eft tencnda ratio in lunse ac reliquorum notorum ftde-rum motu medio. Ac de folis quidem medio curfu quccrendo ciim in diem venientem, turn in prccteritum fatis di&um eft. CAPUT DECIMUM ET TERTIUM. Zft in quemvis diem verus folis curfus invejligari poffit ? Naw-que indidem (£> ver am cardinum anni commijftonem cognofci. §. I. QEquitur, ut agamus de folis curfu vero: hunc quovis O die tibi cognitum efle velis, primum in diem eun-dem'ita, ut expoluimus, folis inveftiges curfum medium: deinde folis etiam altitudinem: turn hanc fubducas e medio folis curfu, ex quo quod reliquum fuerit, id propria folis via di-citur. II. Porro videndum eft hcec propria folis via quot fit gra-duum. Nam fi pauciorum eft, quam centum & odoginta, e confedo medio folis curfu fubducenda eft etiam hujus propria via portio: fin autem plurium eft, ufque dum trecentorum 8c fexaginta fit graduum, ad folis confedum curfum medium portio hujus vice propria addatur, necefte eft. Quibus ita fubduc-tis aut additis, inde quod erit, folis erit curfus verus. §. III. Tenendum eft autem hanc folis viam propriam, cum fit aut ipforum centum & odoginta, aut trecentorum & fexaginta graduum, portione turn omnino carere, atque folis eun-dem efte curfum verum, & medium. IV. At propricehujufee vice portioqueenam eft ilia tandem? Nimirum fi gradus occupat decern, portio ejus eft viginti partes: fi occupat viginti, portio eft partes quadragence : fitriginta, portio eft partes odo & quinquaginta: fi quadraginta, pro portione debetur gradus unus, & partes quindecim: fi quinquaginta, gradus unus, & novem & viginti partes pro portione debentur: fi fexaginta,portio erit gradus unus,& partes una & quadraginta: fi feptuaginta, erit portio gradus unus, atque una & quinquaginta partes: ft odoginta , portio erit gradus unus, & partes E e e fep- 324 Tr attains de Confecratione Calendavum, feptem & quinquaginta j fi nonaginta, portio erit gradus unus, & undefexaginta partes: fi centum, gradus unus, & ocfto ac quinquaginta partes erit portiofi centum & decern, portio gradus unus erit, & partes tres ac quinquaginta : fi centum & viginti, portio gradus unus, ac quinque & quadraginta partes erit t fi centum & triginta, portio gradus item unus erit, atque partes tres & triginta : fi centum & quadraginta, erit portio gradus unus, & partes undeviginti: fi centum & quinquaginta, portio gradus unus, & una pars erit: fi centum & fexagin-ta , portio erit duae & quadraginta partes: fi centum & fep-tuaginta, portio erit partes viginti una: fin autem centum & o&oginta ipfos occupat gradus, portio, ficut docuimus, erit om-tlino nulla : fed curfus medius folis erit idem, atque verus. V. Cum verd via ifta propria fit longior gradibus centum & o&oginta, turn illius longitude tota detrahetur e trecentis & fexaginta gradibus, atque ejus portio cognofcetur: ut fi ifta propria via graduum fit ducentorum, hoS e trecentis & fexa-ginta fubduci gradibus oporteat, unde reliqui fiant gradus centum & fexaginta, quorum, ut ante diximus, portio eft partes dure & quadraginta: eadem eft igitur & ducentorum graduum portio. §. VI. Similiter fit propria via ifta trecentorum graduum, hi fubducentur de gradibus trecentis & fexaginta : reftabunt fexaginta , quorum quidem jam cognovifti portionem efte gradual unum, & unam & quadraginta partes, qux eadem trecentorum etiam eft portio, graduum. Eadem eft ratio in reli-quis numeris tenenda. §. VII. Jam fi via ilia propria quinque & fexaginta ft graduum, quoniam portio fexaginta graduum gradus eft unus, & tana & quadraginta partes: feptuaginta verb graduum portio eft gradus unus & una & quinquaginta partes: turn ilia: por-tiones duae diflerunt inter fe partibus decern , confoquens eft , ut unufquifque gradus pro rata portione partem unam habeat: ex quo id efticitur , portionem propria: via: ejus, quee gradus obtinet quinque & fexaginta, efte gradual unum, & partes fex & quadraginta. §. VIII. Ergo illius, qua: gradus obtineat feptem 8c fexa-gihta , propria: via: portio erit gradus unus, & partes otfto & quadra- 395 & de Ratione Intercalandi. quadraginta. Atque idem crit modus fervandus in omni ejuf-modi via, cum graduum decadibus unitates erunt adjundti, cum in folis, turn in ratione Juno?. §. IX. Harum rerum exemplum ejufmodi ponatur. Si quis folis inveftiget curfum verum qualis eHet primo noftro ratioci-nii hujus anno , prim a noefte fabbatica , qua: erat quarta deci-mamenfis Tamuz, prius idem quxrat qualis eflet turn curfus Iblismedius, quern cum, ficut oftendimus, compererit centum & quinque graduum fuifle, partiumque feptem & tri-ginta , ac quinque & viginti fecundarum , folis etiam quaerat altitudinem : nempe reperietur ca fuifle fex & oeftoginta gra-duum, partium quinque & quadraginta , & fecundarum tri-um & viginti: turn fubducat hanc altitudinem ex folis curfu medio , relinquetur via duodeviginti graduum , partium dua-rum & quinquaginta , & duarum etiam fecundarum : character eft 18. yz. z. Verum in omni hujufmodi via nunquam partium habetur ratio , cum fint pauciores quam triginta : & triginta fi colligantur, vel plures, pro gradu uno putantur, ifque cseteris via: gradibus additur: qua ratione via haze erit graduum undeviginti: unde fit, ut illius fit portio fie, ut diximus, partes duodequadraginta. X. Atque ha:c via cum fit minor gradibus centum & oc-toginta, nimirum oportet partes duodequadraginta portionem ejus ex folis medio curfu detrahi. Itaque ex eodem relinquen-tur gradus centum & quatuor, undefexaginta partes, & fe-cundx viginti quinque: character eft 104.5'9. 2 5'. Ergo prima ilia nocte fabbatica verus folis curfus e Cancro confecerat gradus quindecim, quinque & triginta fecundis minus : fed & in exquirendo folis & lunx curfu vero, & in reliquis calculis ad eorum cognitionem ducentibus habenda ratio eft non fecundarum, fed partium: nifi fecundas fere triginta colligas, quee pro parte una funt ducendae, atque in earum ponendse numero. §. XI. Solis igitur cum liceat curfum verum cognofcere qualis fit quolibet tempore , facile eft quorumeunque anni car-dinum inveftigace horam ipfam five fubfequentium ftirpem hanc, ex qua nos exordium hujus ratiocinii duximus, five *mul-tis annis antecedentium. ' . ; . . ; ■ .* «... • C '■> ■> Z /; ± 1 < - < Eeez CAPUT Trattaiws de Confecratione Calendarum, CAPUT DECIMUM ET QUARTUM. Luna medios curfus ejfe duosnam ipfam in exiguo quo dam orbe ferri , & exiguud hunc in majori or be orbem converti .• con-verfionem exigui or bis vocari luna curfum medium. Quantum hie curfus medius fpatii conficiat uno die, diebus decern, die-bus-undetriginta, diebus centum, anno illo ordinato qui dici-tur, diebus item mtlle , & decern millibus dierum ? Et al-terum via curfum medium nuncupari ; quantum fpatii perlu-ftret ifte his definite temporibus ? Qualis ejfet curfus luna medius ad epocham hujus ratiocinii ? Et quis effet turn via curfus medius ? Nam his cognitis in quemvis diem curfum luna medium facile cognofci proinde, ac Jolis. §. I. T UNA medios -curfus definit duos. Nam ipfa exiguo ,1, t in orbe convertitur, qui quidem orbis non globum terrenum complexu fuo coercet & continet omnem, ejufque in eo orbe curfus medius , vise curfus medius efie dicitur. exi-guus enim hie orbis & ipfe movetur etiam in orbe majore, qui terram comple&itur totam. Atque hujus orbis exigui majo-rem ilium circulum conficientis mqtio media ea eft, quam lu-nx medium curfum vocitent. Hie igitur lunx curfus medius fingulis diebus conficit gradus decern & tres, atque decern partes, & fecundas quinque & triginta : character eft 13. 10. 3 5. §. II. Igitur diebus decern conficit centum atque unum & triginta gradus, partes quinque & quadraginta, quinquagin-ta fecundas : character eft 131. 4?. 50. Ita diebus centum id fpatii conficit, ut ex eo fi fubducantur, quoad eju§ fieri pof-fit, gradus trecenti & fexaginta , reftent feptem gradus , & triginta, & ducenti, partes duodequadraginta, tres&vigin-ti fecundx: character eft 237. 38. 23, Quod igitur fpatium conficit mille dierum, ex eo fi fimilis fiat detra quatore gradus tres & viginti, & dimidiatum fere gradum. Rurfum a capite Cancri figna fenfim infledhmtur ad xquato-rem ufque ad principium Librae, quod in ipfo infiftit sequato-re. Ab principle autem Librae ufque ad initium Capricorni figna fic ab sequatore recedunt in auftralem mundi partem, uti tandem Capricorni principium ad auftrum verfus ab xquatore fit disjun&um gradus tres fupra viginti, & dimidium circiter gradum. Atque ab initio Capricorni ad Arietis initium figna lenfim ad xquatorem etiam accedunt. ' 42 2 Tr attains de Confecratione Calendaruni y V. Qupniam igitur principium Arietis & Libra? in ipfo infiftit cequatore, fequitur, cum ad alterutrum fol commearit, ilium neque in mundi plagam auftralem, neque in aquilona-rem inclinare: fed his duabus mundi partibus intcrjeftum medium oriri & obire: ut in omnibus, qua: habitantur, terris dies & noftes inter fe fint aequales. * §. VI. Ex his igitur videre licet fignorum unumquemque gradum aut ad feptentriones inclinatum efle, aut ad meridiem; ita, ut fuum quccque habeat inflexio modum alia majorcm, alia minorem, nec excedat vigefimum tertium & dimidium fere gradum, cum fit quam maxima. §. VII. Sic igitur res eft, modum amplificat graduum multitude, & numerandi capitur initium ab Ariete. Gradus au tern decern habent inflexionem quatuor graduum : viginti gradus inflexionem altero tanto majorem. Habent triginta gradus inflexionem undecim graduum & femiflis: quadraginta, inflexionem quindecim graduum : quinquaginta, duodevi-ginti graduum : fexaginta, graduum viginti: feptuaginta gra duum inflexio duobus iftam gradibus fuperat : hanc etiam in-ftexio graduum o&oginta fuperat uno gradu : porro nonagin-ta graduum inflexio dimidio gradu major eft ifta. VIII. Quod ft decadibus unitates adjun&ae funt, earum portionem ex eo , quod inter duas inflexiones proximas inter-cedit, inflexionis diferimine collegeris eodem modo , atque in folis & lunsc ratione docuimus. Exempli caufa quinque gradus inflexionem habent duorum graduum; itaque tres & vi-ginti gradus habent inflexionem novem graduum. Similis eft ratio reliquarum * decadibus adjunftarum unitatum. §.IX. Utque graduum inflexionem noris a primo adnona-gefimum, omnium omnino graduum inflexionem cognoveris item , ut & de luna? latitudine difleruimus. Cum enim gradus funt plures , quam nonaginta , idque ufque ad centum & ■oifoginta, graduum numerus eft de. centum & o&oginta exi-mendus. Nam fi fint plures, quam centum & oftoginta gradus §. VIII. Decadibus adjunflarum unitatum. antiquioribus autem editionibus vox DP Hie in editione recentiore correfte legitur defideratur. rrnwpn ay jw annxn in & de Ratione Tntercalandi. dus, idque adducentos& feptuaginta, ex eorurn numero de-mendi funt gradus centum & oftoginta. Si graduum numerus fuperat etiam ducentos & feptuaginta, ufque ad trecentos & fexaginta, eorum numerum ex trecentis & fexaginta detrahe-tur : turn facile erit reliquorum cognofcere graduum inflexio-nem, qua: eadem fine ulla aut acceflione, aut deceflione, inflexio ell ejus numeri, de quo quxritur. X. Si quis igitur fcire expetit quot gradus ab xquatore fit inflexa luna vel ad aquilonarem mundi partem, vel ad au-llrum, primum id quxrat, quxnam fit inflexio gradus ejus, in quo luna: curfus verus volvitur, & quam in partem mundi fit converfa ad feptentriones, an ad meridiem : deinde luna: latitu-dinem primam videat quanta fit & qualis, an aquilonaris, an auftralis: turn fi latitude luna: prima, & ejus, in quo volvitur luna: curfus verus, gradus inflexio vergit in eandem mundi partem vel aquilonarem, vel aullralem, fimul agregentur : fin autem altera in feptentriones, altera fit in meridiem converfa, harum minor c majori eximatur. Ac turn demum quod fuper-erit fpatium, id omnino luna ab xquatore eft inflexa in earn mundi partem, in qua major illarum fuit inventa. §. XI. Quxratur igitur quantum ab xquatore converfa luna eflet epochali nofte ilia fecunda menfis Jar, prxfentis hujus anni, a quo nos initium hujufee ratiocinii repetimus. Gra-dum, in quo turn lunx volvebatur curfus verus, oftendimus fupra Tauri fuifle undevigefimum, cujus gradus inflexio quaff duodeviginti graduum erat ad feptentriones verfus: lunx verb latitudo prima graduum fere quatuor erat, eaque auftralis. Jtaque fi de majori numero minor eximatur, reliqui flent gradus decern & quatuor. Tantum videlicet erat turn ab x-quatore inflexa luna ad feptentriones, fiquidem in ea parte mundi fita erat ilia inflexio duodeviginti graduum, qui numerus duorum major erat. Sed hxc quidem ratio, quoniam ad ki-nx vifionem perfpiciendam nihil juvat, non eft accurate inita & fubdu&a. §. XII. Jam fi quis fcire velit, lunx quorfum erunt obverfa cornua, fitum ejus etiam ad xquatorem comparer. Nam fi kina aut in ipfo inhxreat xquatore, aut ab eo duos omnino, trefve gradus abierit ad feptentriones, vel ad meridiem, e regions 424 TraEiatus de Confecratione Calendarum, gione medii occidentis collocata efle videbitur, & ejus cornua folis ipfum ad ortum converfa. §. XIII. Sin autem ab xquatore longius receflerit ad feptentriones , videbitur inter occidentem & feptentrionem elle fita, & ejus cornua ab oriente inclinata in meridiem. §. XIV. Sin ab xquatore fit remota procul ad auftrum ver-fus , inter occidentem & meridiem fita videbitur , & ejus cornua ab oriente ad feptentriones inflexa, pro magnitudine ejus ab xquatore diftantix atque inflexionis. §. XV. Atque ex his, qui de luna nafcente renunciarent, ten-tandx fideicaufa , quxrebatur etiam & illud, luna quam alte ferebatur. Id cognofcitur ex area wifionis , qui fi brevior eft , curfus lunx propius a terra volvi, fi longior, luna moveri vi-detur altius. Ut enim vifionis arcus longus eft, ita lunam ocu-li al tarn a terra percipiunt. §. XVI. Explicate funt rationes omnes, qux requiruntur ad perfpiciendam lunx vifionem, & interrogandos eos , qui veni-•ebant lunx nuncii fic, ut intelligentibus hxc omnia promta . fint, & aperta. Etenim nulla prorfus do&rinx ratio a Lege noftra excluditur. Ut igitur hxc de luna do&rina percipiatur, confugiendum eft non ad alienorum hominum monumenta, fed ad hunc librum divinum: ille, ille leditandus eft : nihil enim in eo defideratur. INDEX (425) INDEX RERVM P R/EC IPV A RV M Quae in hoc Libro continentur. Nimi er us Paginam, Litera n Notam indicat A. A Damns & ejus lileri qualem put a rent cult urn & honorem Deo facrificiis faciendis adhilere ? 291, & 295”. Adipe leftiarum ad rem diuinam faciendam aptarum inter die-turn ejfe feilittt : at fer arum, quoniam non erant ad rem di* vinam idonea ; adipe aeque, ac carne vefei fas effe, 147. n. Alpha menfura quid caperet ? 114. Agitatio facrorum quo loco fie ret ? 197. Aliunde qui petit aliquid, ejus eft caujam dicere, quare fuum fit* 92, & 96. Allegatus perfonam fuftinet allegant is, iy. n. Alterius causa fee I us admit tit nemo, 8y. Alt it udo folis Q Alfts VYimo, Aux Arabibws diciturj quid fit* & quam conuerftonem confciat ? 390, & feq. Ancilla defponfata in literis facris commemorat a queenam ejfet ? ip. n. Animal femiferum feu hylridam e[fe quilufdam Hcbrxis id quod dicitur, 147. Animantes , catteraque rerum genera in Lege nominatim edifta , cur rei d'rvinat deligerentur ? 235, & icq. Animantis foetus ante, quam olio dies totos compleverat, ejeo tioms loco due ebat ur, 77.0. I i i Anni CKONOLOGIA HISTORICA Scritta in lingua Turca, Perfiana, & Araba, D A HAZI HALIFE' MUSTAFA’, E tradotta nell’Idioma Italiano DA GIO: RINALDO CARLI NOBILE J U S T I N O POLI T A N O, e Dragomano della Sereniflima Republicadi Venezia. CONSACRA TA All' Illuftrijfimo , & Eccellentiffimo Sig. GIO: BATTISTA DONADO IN VENETIA, M. DC. XCVII. Appreflb Andrea Poletti, all'Italia. CON LJCENZA De SUPERIOR/. io6 CRONOLOG1A di'Ini valli penfieri. Formato dunque un numerofo , e valido EfercU toufcirono unici inCampagna , enefle pianuredi Hirat venuti col fudecco IbcA Han a battaglia, reflarono abbattuti. Il Principe Jacup Marini forprefe, dcoccupd in Africa la Citti di Meracchies. Pafso Tahir BibersSultano d’Egitto allavihta del Pellegrinaggio della Meca lanno 668 Il Sultano d’Egitto liberd dalli Franchi le Ci tea di Hufmiechrat, & Achie Reftoquafi tutta fommerfa laCittAdi Damafcoda un diluviodi pioggia. Fu da Ibni Jemen SerifFo della Sacra Meca interfetto in un com-bacrimentoil Principe IdrisCatade 1’anno 669^ Fudalli Tartari diftrutta, edefolata la Provincia diHaran» Il Principe Ahmet fececon provefondatiflime conflare nella Citta del Cairo FArbore della fuadifeendenza, derivarc legittimamentc dalla Profapia AbbaflianaJa quale per il corib di cinquecento anni belI’lmperio di Babilonia regno in qualitadi Halife, in di cui virtu glifu preHata da tutta la Cortequel rifpetto, eveneratione , che fi afpettava ad’un Halife, & ad una nafeita tanto fublime,.difcendendo da un Zio Paterno dello Heflb Maometto 1’anno 670 Cinta dalli Tartari la Citta di Beierizich fituata Copra TEufrate d’un ftretto afledio,. fuquefta dal Sultan d’Egitto foccorfa, & obligati li Tartaria ritirarfi. Occupata da Mahmut Cahani 1’lfbla di Ormus comincid come difpoticoSovrano adominarlal’anno 671 La famiglia d’Abdulmumin principid a regnare nelli Regni di Barbaria . Pafso nella Citta d’Iconia all’altra vitail celeberrimo Prelate M.ul-laHunchiar fondatore della Religion de’Derviili 1’anno 672 675 674 Nel Regno d’Albiftan venuto a giornatail Sultan d’Egitto con li Tartari di Mogul refto vincitore. Altre Trupe Tartare di Mogul azzuffatefi colie Greche le batterono. Manco di vita in CairoSeid Ahmet Elbedevi venerate, e ftimato come perfona pia Tanno 675 Mono Tahir Bibers Sultan d’Egitto, fu nella fuavece efaltato, li Principe Seid Mehmet fuo figliuolo 1’anno 676 677 Pafsoall’altro MondoSeidMehmetnuovo Sultan d’Egitto, efu occupata quella Corona da Calavun 1’anno 678 679 Menchiut Temer Principe Scita, correndocolli fuoi Tartari per invader x c faccheggiar la Citta diHamus, fu axtaccato dall’Efler-' 7 cit£x HISTORIC A. io7 eitoEgkio, e con grande fvantaggio delle fuoTruppe neceflitato a ritirarfi. II PrincipeRucnedinGauriano s’impatronidel Regnodi Cande-. bar. Manco di vita in qrieft’anno Erdpgrul Gasi Padre di Ofmano primp cm a Principe dit quefta Imperial Profapia,chiamato ancheegh per fbprano’ 1°• me il GuerrieroTanno 680 cMottom^ Il Principe Ibca Han delli Tartari di Mogul, e figliuolo di Hella-hiii Han, inqueft’annoprofefsola Legge Maomettana, e perdar parte di quefta lua converfione, fpedi Allamei Sirafi in qualid d’Am-bafciatorEftraordinarioal Sultand’Egitto, partecipandoli pure haver tmitato il nome primiero in quello d’Ahmet. Mori il Principe Menchiut Temer Scita 1’anno 681 Da un diluviodi pioggia accaduto nella Citt£ di Damalcoaccrefciutt ifiumi, che irrigano quella Citd ,nefeguironodanni notabilk In un conflitto fucceflb nell’Armenia Maggiore fra il Principe Hufreu AliSelzuch, eliTartari, reftdil primo interfetto, &efaf-tatoa quel Dominio il Principe Mefliiud Chiechiavus Ali Selzuch 1’anno 682, Il Principe Ibca chiamato Ahmet Handel Regno di Mogul, per eflerficonvertito al Munfulmanefmo nacque ad inftigatione di A trail-muluchfuo Vefiro una follevatione di tuttoil Popolo contro la fua perfona, onde rimafe morto ’, & efaltato in luoco fno il Principe Argum Atteifta della profapia ftefla . Fuda Calavun Sultan d’Egitto liberata dalli Franchi la Citta di Mercab 1’anno 684 685 686 Nacque Sultan Orhan mentre Sultan Ofman Gasi fuo Genitore, ow*™* -data nelle Campagned’EneghiuI nella Bittinia la battaglia all’infede-liGreci, redo Trionfante, in cui perd fit interfetto Ghiundus Elp Soggetto delli piii qualificati, eValorofi, chefeco havefle : Spinte poile fue Truppe all’aflediodelleGittad’Affion,eCara Hiflar se 1’ac-quifto 1’anno 687 Comincio lafamiglia di Sabanghiare a regnare nella Perfia^ome So* vrana. Calavun Sultan d’Egitto fpoglid li Frandhi del pofleflbdi Tripoli di Soria . In queft’anno la Real Profapia d’Ali Selzuch invid al Princrpe Ottoman© un’Infegna Reale, concui lo dichiaravaper Principeindi-pendente 1’anno • 688 Moriil PrincipeCalavunSultand’Egitto, efu nellafua veceefal- >tato il Principe Efrcf. O z Ed io8 CRONOLOG1A Fii privata la famiglia di Finis Sah del Dominio, che teneva nell* Indie Tanno 689 Il Principe Efref nuovo Sultan d’Egitto fpoglid la famiglia di Benieiup dello Scato, e Citta d’AIeppo,la quale la fece egli reilaurar, emunir; Ri volte poi le fue Armi, controAchie, ftaltreCitta, e Cai tell i pofleduti dai Franchi fopra le Rippe del Mare, e fpettanti alia Soria li ricuperd tutti, e fece anche abbandonare per timore la Citt£ di Sattalia. Principiarono gl’Infedeli Franchi 1’anno Maomettano 490. A invader li Regni d’Egitto, Soria, e Palellina con fortuna tanto propitia, chefi erano quail fatti aflbluti Padroni delli medefimi, fenon fofle fucceffo alia Corona d’Egitto il Principe Selahedin, con il di cui valo-re, &ottima condotta contrapesole loro forze , arend i loro pro-grefli, e ravvivo il perduto coraggio alii Monfulmani; I di lui Succef-foripure calcati i fuoi velligii, feppero ancheefli difcacciarli dalle tanteCitt^, eFortezze, che s’eranoacquiftate 1’anno 690 - Fu occupatadal Sultan d’Egitto la Qttadi Rum ibpra 1’Eufrate Fanno 691 Occorfe un’improvifo incendioalla Citta di Medina . La famiglia d’Alizenghis fu privata del Regno di Turan 1’an-no 692, Morto il Principe EfrefSultan d’Egitto fu innalzato a quella Corona Chitga . Fu fpogliata la Profapiadi Attabechian del Dominio di Loriflan. Eflendoil Regnodi Perfia oppreflo d’unaeftraordinaria careilia decretdquel Sovrano, per follievodel fuo Popolo, che fopra una Carta quadrata fi dovefle imprimer il fuoNome, e tefla quellacorrer in vecedella primiera Moneta 1’anno 695 L’efler fcarfamente crefciute Facque del FiumeNilo, fu caufa, che il Regnod’Egitto, provo una grande penuria. Mancatodivita ilPrincipeCutlai Handel Regnod'Usbech fuin fuo luoco efaltato il Principe Timur Han. In quefto anno tutto il Popolo del Regno di Mogul profefsd la Legge Maomettana 1’anno 694 Li Regni d’Egitto, e Soria patironouna grande care ilia. Volendo il Principe FirusSah tentare la ricupera delli da lui perdu-ti Regni nell’Indie, venne nelle vicinanze del Fiume Hidafpe a gior-natacol fuo ufurpatore, in cui facrifico colla perdita la propria vita 1’anno 695 Fu fpogliato un Rampollo della famiglia Chiachiviechiamata A t-tebechian del Dominio, che teneva in Perfia; Fa HISTOR IC J. log Fit levato dal Tronoil Principe Ghifca,Sultan d’Egitto, Scefal-tato Manfur Lacin. L’anno 688. comincid il Principe Ottomano impugnaril Scettro diSovrano, e come tale nelTefpugnata Citta di Cara Hiflar fece ch’il °‘icmano Cadidalui fbllituico, officiaflepublicamentequellorationi nelle Mo-fchee, cheli pratticano implorare per li Principi, che fono indi-pendenti, & aflbititi; Perb fufliftendoal Thora la Real Profapia d’A li Selzuch, nell’auge delle fue forze , ecoronata di moki Regni , e di-pendendo eflb da quelja, non voile farfi conofcer per aflblutoSovra-nolino 1’anno 696. che quella Reggia famiglia rimafe eftinta 1'an-no 696 Il Principe Ganan HanScita, doppo haver nella Citta di Tebris, formatoun Magnificodiflegno per conltruirvi unSepolcro Reggio, feneparti, elafcibin qualitadi Sovranodi quel Regno il Principe Ailadin Chieicubat 1’anno 697 Fii facto ftrozzare il Principe Manfur Lacin Sulrano d’Egkto, -& a quella Corona efakato il Principe Nadir Mehmet. S’attaccbunafiera battaglia verfoil Fiume Neilufer, che irigala Bittinia, fra il Principe Ottomano, & il Principe J arhiflar con la per-dita di quefti, e fchiavitii della propria figliuola Tanno 698 Spintelefue Truppeil Principe GafanHan de’Tartari contro la Soria, corfe fubitoil Sultano d’Egitto conic fueal riparo, enelle Campagne, che giacciono fra le Citta di Hamus, eSeleme , incon-tratifi ambiduegl’ElTerciti,feguiunfanguinofocombattimento , con la perdita dell’Egittio, con che il Tartaro li refe Padrone del Domi-nio di Damafco. Coll’acquiftofattodal Principe Ottomano delle Citta di Eneghiul, eBilezich nella Bittinia, fifece Padrone difpoticodi tuttala Grecia Afiatica l’anno 699 Inqueftanno fu inftkukodal Principe Mehmet figliuolo di Ca-lavunSultanod’Egitto, ilcoftume dell’invito , che fi prattica an-chealprefentefoprale Torri delle Molchee conalta voce, accioil PopoloaH’hore dellinate intervenga a farle lorodivotioni, e per diftinguer il giorno di Veneredidagl’altri feriali,prefcri(Te,che in queflo unitefi diverfe voci, doveflero fopra le fudette Torri con Nobil armo-nia can tare , e chiamare la gente alle Mofchec. Il Principe A li Caramano Ipoglibdel Regno di Loriftan il Principe Attabecchian Tanno 700 Si pretefe in queft’anno inflituiruna nuova Epoca , ma quella non hebbe fufliftenza. Fii prohibito da IbniNimcReligiofo di pia vita Soriano che non fi dovef- IIO c RONOLOGIA *d la dovefleroinavvenirepraticarcerteOrationi,ches’ufavan farfilanotte r*' delli 27. della Lunadi Ramafan,come contravenienti alia Maometta-na Legge. Segui una (anguinofa battaglia fra 1’Eflercito dell’Han del Regno di Mogul, e quello del Principe Alladin R£ dell’Indie con la rotta total di quefto. Accade anche nella Caramaniain vicinanza di Coin Hiflar frail BeNicofo Principe Ottomano, eliGrecian fierocombattimento,in cui quefti furono rotci, e fugati. Mancarono di vita Hacchimbiemirullah Principe della Real Pro-fapia Abba (Tiana, & il Principe Ebutemi Mehmet Seriffo della Me-ca Tanno 701 Spinfe il Principe Gafan Han de’Tartari le fue Truppe alTinva-lion della Soria, doveattaccatedalSultanod’Eggito, furono vinte, e fugate. Il Sultano d’Egirto accennato libero dalli Franchi Tlfola d’Auret Addafli, ch e pofta in faccia di Tripoli di Soria. In Egitto fuccefle un terribile Terremoto. Fu efpugnaca dal Principe Ottomano la Fortezzadi Chipte Tan- no 702 Fu opprefla grandemente 1’Afia tutta dall’infettion del malcontag-giofo, & un mal fimile fece ftrage degTAnimali Bruti. Nella Citta di Hamedan maned di vitail Principe Gafan Han de’ Tartari, e fu aflunto in fuo luoco il Principe Mehmet Hudabende Tanno 705 704 Il Principe Hudabende nuovo Handel Regnodi Mogul, volen-do colie fue Armi invader il Regno di Chilian, ricevc cola una fan-guinofa rotta. Mancatodivitail Principe RucchnedinSultand’Egirto, fucon-vocata la Confultadalli Principal!di quel Regno, per maturarein e(Ta lafcielta delSoggetto, chefiflimava conferenre all'efaltatione di quella Corona , edoppo varii dibattimenti, furono in fine propo-fli due Principidi Reggia Profapia, che ivi rifliedevano, Tuno Ibni Nime Abbafliano, e Taltro Fahredin Gauriano, il quale fu preferi-to al primo, per la di luimaggiorcapacita Tanno 705 Fu fpeditodal Sovranodi Barbaria fotto la condorta del Principe JuflufMarini il fuo Eflercito alTerpugnationedellaCittadi Tillim-fah, e gti fu dal valore deg 1 a fled i a t i, in una fortita toka la vita. ruoi div Cai. Principe Ghiafledin Sovrano delli Chiurti fu fpogl iata la fa mi-glia d’ A liberach del pofTefl'odel Regno di Chirman Tanno 706 Ibni Marhar feppe si bene infinuare al Principe Hudabende Han di HISTORIC J in Ji i dogmi della Setta Perfiana, che Findufle di procurare a dat-tutto luo potere la propagation di quella. per trema , Il Prcncipe Ottomano fi refe Padrone delFliola di Marmara l’an-//4"'f * errori ne'qu.i- no 707 li in ct rr eno Doppo haver li Franchi efpugnata 1’Ifola di Rodi tenuta dalli ^nd0 la lo~ Greci, portarono le loro Armi verfo Coftantinopoli contro 1’Im- rO(>1>,>t,one * peracorNicefbroi Dal Principe Ottomano furono occupateleCitta diLeuchie, 6c Ac Hiflar 1’anno 708 Fane! Regnodi Granata dal Principe Naflir figliuolo di Mehmet battuto FEflercito Spagnuolo, Erefle il Principe Hudabende Han del Regno di Mogul nella Citta di Tcbris un fontuofo, e Magnifico Palaggio 1’anno 70^710 Fuin queft’anno terminate il ludetto Reggio Palaggio facto con-flruir dal prenominato Principe Hudabende 1’anno 711 Il Principe Ottomanofi refePadrone dellaCitta diChieive Jan- na 7I2, Efpugndil Principe Orhano figliuolo del mentovato Principe Ottomano l’Armigero, la Citta chiamata Adriano Fan no 715 Accade fra liSeriffi Hamas, eRamiefrattelinella Citta dellaMe-ca una Guerra ci vile^iella quale rimafe il primo vin to,. & interfet-to 1’anno 714 Dal Vicegerente di Damafco/udattoil Sacco all’Ifola di Maka. Si perfettiond in queft’anno lafabrica della reftauratione di Cefa-rea Tanno 715 Mancatodi vita il Principe Hudamende Han di Mogul fiiefaltaco alia Corona di quelli Regniil Principe Ebuflaidil quale fubito fece nafeer un divieto, che nelli fuoi Stati non fofle permeflo 1’efercitio Publico della Setta Perfiana, tantoaumentata dal fuo Predeceflore. Eflendofi eftinta la Real difeendenza da Ali Selzuch, si nella Gre-cia Afiatica , come in akri Regni, e Principati ch’erano commanda-tidaGovernatoriadeflafubordinati, ogn’unodiquefti, perlaman-canza del legitcimo Sovrano afliinfe del medefimo, ildilpotico Domi-niol’anno 716 Pafsoil Principe Ottomano conle fue Truppe nella Bittinia, e per precluder tuttele vie alia Citta di Burfia, erefle nell’Eminenza d’un Colle un Forte,col quale veniva a dominarla. Furono nel Regno di Granata dalli Monfulmani battuxi li Chri-flianil’anno 717 Fiiin queft’anno loStatodiZefire dauna grande careftia angus-ftiato*. Coir 112 C RO NO LOG 1 A ColTaffcnfodeiSogecti pin fapicnti, e virtuofi dellaCitta diDa-mafco, fii interdettolodudiodeli’Ailro!ogia. La Famiglia TaditSahie fpoglioquelladiHalizie dclli Dominii, che pofledeva nell'Indie l’anno 718 Venutinel Regnodi Granatanuovamcntea giornata gl’Eflerciti del Principe Bamirullahfigliuolod’Ahmer, ede’SpagnuoliJi Mon-fu Imani col facrificio facto di dodecimilladi quegli al furor della loro Sciabla, rcftaronotrionfanti 1’anno 719 II Principe Time AbbalTiano, che concorreva alia Corona d’Egitto fu obligato alle Carceri del Caliello di Damafco Tanno 720 721 722 723 Li Ottomani prefero laProvincia d’Achova toccante alia Bittinia Kanno 724 La famiglia di Beni Amar comincid a regnare nella Barbaria. Li Ottomani ncli’Anacolia occuparono le Cict& di Bolli > e Candri Tanno 725 Redo dalTefcrefenza eftraordinaria del Fiume Tigri dannificata tutta la Citta di Babilonia. Mancato di vita Tacbitfahie Re dell’Indie, fu efaltato aquella Corona Ulug Han fuo Hgliuolo l’anno 726 Pafsoin queft’anno all alrro Mondo il Principe Otromano , &rl Principe Orhan, prefo ch’hebbe leRedini delGoverno, porto Ie fue Armi contro la Citti di Burfia , e Jallach Abbat, e Tefpugnd. Lo deffo Principe Orhan fece trafportar Tacqua , che fcaturiva dal Monte Arifaccontiguoalia Meca in quella Citta l’anno 727 Furono cot mezzo del perfpicaceintendimentodi Altadin Pafsa elle-fi li Canoni,& inftituite Ie Leggi dell’Imperio Ottomano. Da Sultan Orhan fu fpeditoinqualitadi Generale Achce Coza all’ acquidodella Mi ilia. Fii da Ulug Han Re dell’Indie battuto ChisluHan RedelRegno di Multan l’anno 728 Sono date dilatate le Mura della Meca. La famiglia di Benizirban occupo la Corona delTArmenia Mag* giore. Abdulrahman Generale di Sultan Orhan acquidd la Citta d’-Aidos. Il Principe Ibni TimeAbbafliano, morinelle Carceri nella For-tezza di Damafco, dovefurinchiufo l’anno 729 Furono inqueft’anno dalla prudenza d’Alladin Pafsa inftittiite Ife divife del veftir della Militia Ottomana, ecominciofli anco far batter le Monete col nome della medcfima Cafa Tanno 730 Fii HISTORIC J. n3 Fu inftitnito 1’ordine della militia de1 Gianizzeri Tanno 731 La penuria grande d’acqua nclla Citta d’Aleppo portava non poco pregiuditio al Publico Errario,edoppoeflerfltentatemol-te viewer introdurvi quella del FiumeSazur,in fineriulcial Suka no d’Egitto in queft’annotale intraprefa conmolto vantaggio di quella Citta. Sultan Orhan I’Armigero occupola Liconia con la Citta diNi-cea. . LiSeriffi della Meca ripugnarono di preftar ubbidienza al Sultan Orhano, anzi tutti unitificontro diluiriflolferofaraflalirlaCarava-na de’Pellegrini, che dalli fuoiStati s’incaminava alia vilita della Meca , e diftruggerli tutti con il loro Capo principalelan no 732 Sotto la condotta del General Suleiman Pafsa glOttomani fi re-fero Padroni delle Citta di Mudurli, eGhioimuch 1’anno 733 Comincid la famiglia di Alimuzaffer aregnarein Perfia. Fu occupata dagl’Ottomani la Cittadi Ghiemleich Tanno 754 Gl’Ottomani efpugnarono Ie Citta di Pollicaftri, Carafli , e Per-gamo 1’anno ' 73$ GTOttomani prefero laCitta di Tusia eftiftente Tulle fponde del cioi.delle s Mare Bianco, e nellaCittadiBurfia fondaronouna MagnificaMo- ‘ ‘5' fchea. Mancatodi vita il Principe Ebuflaid figliuolodi Hudabende Han di Mogul fu eTaltato a quel Trono il Principe Erhan. Trova nd oft fette fratelli della Real famiglia d’Alizenghis, & ha-vendo quefti fmembrato 1’Imperio, che godeva il Padre in fette Dominii, venne la loro primiera grandezza, &auttorita moltoa fcemarfi 1’anno 736 Gl’Ottomani occuparono la Frigia. La Cafa di Bihdaran comincid come Sovrana a reger il Dominio di Sebrevar. Doppo haveril Principe Haflan Ilhanie acquiftato il Regnode’ Parti, pafsoalfimprefadi quello di Babilonia, de Armenia Maggiore Tanno • 737 Gl’Ottomani occuparono la Caria , &le Citta di Armudili , & Anahor Tanno 738 La Citta di Tripoli di Soria fu rovinata dalle fcofle d’un Terre-moto. Paflarono all’altro Mondo in Cairo li Principi Muftagfi, eSuIei-man fratelli difeendenti dalla Real Profapia A bbafliana 1’anno 739 Furono da tin prodigiofo fuoco calato dal Cielo inccnerite la maggior parte dellj Caftelli, e Citta attinenti allo Stato diDamafco P 1’an- 174 C RO NO LOG baizan , e doppo haverli regnato tre Principi di quefta difcendenza fet-tancafeianni, rimafeprivadeH’ottqcento , etredici. L’anno 750 La Zellaviana domino il Regno di Mafinderan, e doppo haverlo poffeduto fette Principi di quella fchiata cento, e cin* quanta anni , li fu levatodel novecento , e nove. L’anno 760 Quella di Beni Abdulvadfi refe Padronadel Regno di Tillimfan, edoppo haverlodominate tre Principi di quel flipite trentacinque anni , ne fit fpogliata del fettecento, e novanta cinque. L’anno 771 La famiglia Tamerlana Georgiana occupo liRegni di Semercanda, edell’Indie, e viregnaronoinefli fucceffivamente vinti quattro Principi di quefla fchiata. L’anno 773 Quella di Chiezurat s’acquiflola Corona del Domi-niodi Chiezurat, edoppohaverlapofleduta quattordeciPrincipi di quefta difcendenza cento, e novanta fette annija perde del novecento, e fettanta. L’anno 774 LaServaniana fi refe Sovrana nel Dominio diServan , e doppo haverlo regnato otto Principi di quefla difcendenza cento, e fettanta urianno, li fu levato del novecento, equaranta cinque. L’anno 777 La Caracoiunlidomino il Regnodi Diarbecchir, e doppo haverlo pofleduto quattro Principi di quefla famiglia novanta fette anni lo perde dell’ottocento, e fettanta quattro.. L’anno 78a Quella di Zulcadries’acquiftdil Regno di Marras,e doppo haverlo dominate dieci di quei Principi cento,equarantaun anno, ne fu privata del novecento , e venti . L’anno fudetto Quella di Beni Ramafans’impadronidel Domi-niod’Adena e doppo haverlo goduto otto diqueiPrincipi cento, e novanta anni, li fit levato del novecento, e fettanta. L’anno 783 La Nation Circaflaflfece Sovrana nelli Regni d’E-gitto, e Damafco, e doppo haverli regnato vinti quattro Principi di quella Natione cento „ equarantaanni, ne rimafe priva nel novecento, eventitre. L’anno 809 La famiglia di Accoiunli occupo la Corona di Azer* baifan, e doppo haverla pofleduta novedi quei Principi novanta nove anni, li fu levata nel novecento > e otto. L’anno 839 Quelladi Sebicchie nella Citta di Semercanda fl fece Sovranadel Regno de’Sciti, edoppo haverlo dominato dieci fette Principi di quella Profapiaduecento, edieci fetteanni,ne fu fpogliata nel mille, e cinquanta fei . L’anno 858 Quella di Ali Tahir occupo il Dominio di Jemen , e doppo haverlo regnato quattro Principi di quella difcendenza felfanta cinque HISTORIC A. i7f cinque anni, venne a perderlo nel novecento, e vent! tre. L’anno 876 QuelladiBeni Vetass’impadronidel RegnodiFes, e doppohaverlo dominate fette di quei Principi fettanta nove anni, fii privatadel novecento, ecinquanta cinque. L’anno 890 Li Principi del Regno di Chilian, doppo haverlo otto di quei Principi pofleduto cento, etrentacinque anni, ne furono fpogliati nel mille, eventi cinque. L’anno 906 La famiglia Ifmailita occupola Perfia, ftAzerbai-zan, e vi regnarono fette Principi di quella Profapia. L’anno 911 La Nobil Profapia delli Seriffi Soccupo la Corona del Regno di Fes, e fette Principi di quel ftipite fuccefli vamente la poC. federono. L’anno 95^ Quattro Principi della difeendenza di ImamamSaidic dominarono T Arabia Felice. L’anno 957 Cinque Principi della Profapia Chieumers occuparo-noilTronodelliRegnidiRuftemdar, eTaberiflan. In fomma fi raccoglie dalle Croniche antiche , e modeme, che furono regnati vintifei Dominiidafeicento, ecinquanta Principiprima delli Monfulmani, e che da quefti furono occupati cento, e dieci Regni, lo Scecro de’ quali fu fuccefli vamente con difpotica Sovrani* ta impugnato da mille duecento, equindeci Principi Maomettani, ondein tutto fi calcolano cento, e trentafeifr^Regni,eProvin-cie, e mille ottocento, e fettanta cinque Sovrani. Dtfcrittibne degVImperatori Ottomam. SUltan Ofman figliuolo d’Odogrul chiamato il Propagator della Ottoman* < Legge Maomettana nacque l’anno 657,fuefaltatoal Trononel 699, e doppo haver regnato anni 27 maned di vita nel 726 Sultan Orhan figliuolo d’Ofman detto pure il Propagator,nacque l’anno 680/ii portatoal Trononel 727, e doppo haver regnato cren-ta fette anni mori nel 761 Sultan Murad figliuolo d’Orhan 1’Eroe nacque l’anno726, fu inco-ronatonel 761,6 doppo ha ver regnato trenta unanno morinel 791 Sultan Baiafit detto il Fulmine figliuolo di Sultan Murad Han, nacque l’anno 76 i,fuaflbnto al Trononel 791,6 doppo ha ver regnato quatordeci anni pafsd al 1’altro Mondo nel 805 Sultan Mehmet Han figliuolodi Sultan Baiafit Han il Fulmine, nacque l’anno 781,‘fu incoronato nel 816 edoppo haver regnato otto anni mori nel 824 Sultan Murad Han figliuolo di Sultan Mehmet Han, nacque Tan- no [Reprinted from Journal of the American Oriental Society, Volume 63, Number 2 (1943), Pages 115-127.] DEMOTIC HOROSCOPES 0. Neugebauer Brown University While working on Demotic astronomical texts, I sorely felt the need of palaeographical resources for astronomical symbols. Spiegelberg’s attempt in this direction appeared to be incomplete and occasionally unreliable.1 Moreover, since several of the documents are horoscopes, one could hope to obtain more definite chronological information about the palaeographical material in question by dealing with these texts astronomically. This resulted in finding a very close relationship between five of these horoscopes—so close that a join of one of Spiegelberg’s and one of Sir Herbert Thompson’s ostraca could be made. As to palaeographical problems, already Spiegelberg assumed a connection between medieval zodiacal and planetary symbols and Demotic forms. This hypothesis is in itself very plausible 2 but very difficult to prove in detail. I hope to have succeeded at least in one particular case, the sign =a=, opening a new possibility to explain the origin of such a symbol. For the majority of signs the main difficulty consists in the complete lack of epigraphic studies in this field as far as Greek papyri and medieval manuscripts are concerned. Before going into details, I wish to express my warmest gratitude to Dr. G. R. Hughes of the Oriental Institute of the University of Chicago. I owe to him many very valuable suggestions and corrections in my readings and translations. He furthermore drew my attention to the two ostraca published by Thompson and to the papyri Cairo 31222 and 50143. The discovery of the symbol □ for Saturn is one of his results. Finally, Dr. Hughes investigated the approximately 2500 Demotic ostraca in the Oriental Institute with respect to astronomical texts and succeeded in finding one new horoscope, which is published here with the kind permission of the Oriental Institute. 1 Spiegelberg [3] Pl. IV twice shows the “knife” as the symbol of the zodiacal sign “ Leo,” although it means “ Leo ” only once, but “ Mars ” in the second text (see below Pls. 2 and 4). 2 As early as 1708, B. de Montfoucon speaks in his Palaeographia Graeca (p. 373) about the Egyptian origin of the astronomical symbols, at this time, of course, without any actual epigraphical evidence. § 1. Horoscopes 1. Beside the five ostraca discussed below, only one additional horoscope in Demotic writing is known to me, namely, horoscopic notices on a coffin-lid discovered by Brugsch in 1857 at Luxor.3 The lid shows inside a large figure of Nut surrounded by pictures of the twelve zodiacal signs. Among these signs, the names of the planets are indicated in cursive writing, obviously later additions of the purchaser of the sarcophagus, the priest Het er, ( )? indicating the constellations on the day of his birth. These notes are as follows:4 u f hr-p-sth n ( hr-ph-kh n my v. phwy n Tip hr-tsr Nf. sbk thdl.t x. above Scorpius: ph r'-h? y. between Scorpius and Sagittarius: ph ntr dwh z. above Sagittarius: nty >t(li> Jupiter (and) Saturn in Leo end of TTg: Mars Mercury in Scorpius the ascendant the morning star u. n: both n refer to my, written only once because of lack of space.—v. 1Tg: written by ideogram only.— v. phwy; w. dl.t: these readings were suggested to me by Dr. Hughes.—x and z: reading very doubtful. Such a complete horoscopic constellation is amply sufficient to determine its date within the narrow limit of some days;5 the result is 93 A. d., middle of October.6 Because we know that the owner died at the age of 31| years,7 the horoscope must have been written at the latest in the beginning of the year 125 a. d. 2. We turn now to a uniform group of Demotic ostraca, which will henceforth be cited by the following abbreviations: 3 Brugsch, Rec. I Pl. 34 and 35 and ZDMG 14 (1860) p. 15 ff. 4 Citations u, v, . . . etc. according to Brugsch. 5 A simple graphical method proved to be very useful to find in a few minutes the year in question. 8 The calculated longitudes for 93 A. D. Oct. 16 are: Jupiter in ff 11, Saturn in ff 21, Mars in ug 25, Mercury in =0:18 (instead of TIL), Venus in 11. About 3 or 4 degrees should be added in order to get Egyptian longitudes (cf. Neugebauer [1] p. 230). 7 Brugsch [1] p. 16. 115 116 Neugebauer: Demotic Horoscopes Os. 1 Chicago M. H. 3377 (see below Pl. 1) Os. 2 Strassburg (Spiegelberg [3] p. 150) Os. 3 upper part: coll. Thompson 1 (Thompson [1] Pl. 28) lower part: Strassburg (Spiegelberg [3] p. 149) Os. 4 Strassburg D 270 (Spiegelberg [2] col. 223/224)8 Os. 5 coll. Thompson 2 (Thompson [1] Pl. 28). 8 Cf., furthermore, Muller [1] and [2]. Oefele [1] p. 24 contains a rather phantastic treatment of Os. 4 which does not deserve serious consideration. The most complete form is represented by Os. 3 which gives not only the planetary constellation but accounts for the influence of all twelve zodiacal signs. Os. 1, 2 and 4 restrict themselves to the first part only; Os. 5 is only fragmentarily preserved. 3. The parallelism between these horoscopes is made evident by the following transliteration, with the exception, of course, of the lower part of Os. 3 and the differences due to the special constellation in each case.—The use of modem symbols for the zodiacal signs indicates that only the ideograms are used in the text. Os>. 1. Os. 2. Os. 3. Os. 4. 11 hl.t sp 43 K hl.t-sp 4-f II Ih.t sw 9 pl ty 11-f rhwy i- hl.t-sp 4-t III [pr] . 11 pl ty 4-t n rhwy ... *• hl. t-sp 21 III smw sw 13 pl ty H-t [n pl hrw] 2- tpy Ih.t sw 16( ?) pl ty n 2- pl r* n tl ihy 2- pl r* n nl tbty.w hr-pl-st 2- pl r' n pl gnhd, sbh 3- pl hrw i'h n(?) 3- i'h n pl hl n 16 hr-ds 3- i'h n pl nty 1th... 3- i*A n pl nty 1th n 1 4- pl r* n tl Tl# sbh pl(?) r'-h' n(?) tbty. w 4- pl r'-h' tl ihy 4- pl f-h' tl ihy 5- i'h n pl hl 21 5- pl r'-htp n( ?) TTJ n( ?) ntr dwl 5- pl r'-htp pl isw 5- pl r'-htp pl isw 6- pl r'-h' pl nty 1th hr-ds 6- pl sy p.t pl nty-lth 6- pl sy p.t pl gnhd 6- pl sy p.t pl gnhd 7- pl r'-htp nl X 7- pl sy dl.t nl X ’l- tl dl.t pl hr-nh hr-pl-hl 7’ [P’] sy dl.t pl hr-nh 8- pl sy p.t tl TTJ2 8- pl swsp n 10 tl dl 8- pl swsp n mtr W X 8- pl swsp n mtr nl X 9- tl dl.t nl tbty.w 9- pl swsp n wbt ( ?) pl mly 9- pl swsp n wbt( ?) n (?) [tbt]y Q 3 v 3 p> swsp n wnm nl tbty.w 10- swsp n 10 tl dl hr-pl-hl tl ihy.t 10‘- hr-pl-st 10- pl swsp n wnm pl mw 10- pl swsp n wnm tl TT£ 10- [_pl s]wspnwbt(?) tlTVS, u- pl swsp n wnm pl mly 12- [p> sw]sp n wbt( ?) pl mw 1S- pl twr n wnm tl TTR 14- pl twr wbt( ?) pl hr-nh 15- pl * shn 'nh pl hr-nh u- [p’ t]wr [n] wnm destroyed u- pl twr n wnm pl isw 12- pl twr wbt ( ?) pl mw pl mly 13- pl' shn 'nh [£’] dl 14- tl dny ,t sn pl nty-lth 15- tl dny .t it pl hr-'nh 16- tl dny. t sry pl mw sbh 17- tldny.thnenl tbt.w 18- tl dny. t shne pl isw 19- * shn mt pl hl hr-ds 20- tl dny. t ntr nl X 21- prntr.t^) pl gnhd 22- pl sy pl mly 23- pl ssr tl Tip 111 i] wr n wnm pl isw 12- [pl twr] wbt ( ?) pl mly pl [*] 1S- [sAn 'n]h tl dl Neugebauer: Demotic Horoscopes 117 The following translation consistently substitutes modern names for the planets and zodiacal signs, even where the Egyptian expressions are very different, as “ Horus the bull ” for Saturn etc. Os. 1. 1 Year 43 2 month I, day 16 (?), 8 o’clock of 3 the day. The moon in(?) 4 The sun in TTg (and) Mercury. 5 The moon in Taurus 21°. 6 The ascendant: Sagittarius (and) Mars. 7 The descendant: X 8 The lake of the sky: TTR 9 The Dwat: Pisces 10 The middle swsp: Scorpius (and) Saturn. Libra10a J upiter 11 The right (== western) swsp: Leo. 12 [The] left (= eastern) swsp: Aquarius 13 The right (= western) twr: TTg 14 The left (= eastern) twr-. Capricornus. 15 The house of provision of life: Capricornus. Os. 2. 1 Year 4, month II, day 9, 11 o’clock in the evening. 2 The sun in Libra. 3 Moon in Taurus 16° (and) Mars. 4 The ascendant: Pisces. 5 The descendant: Tip (and) Venus. 6 The lake of the sky: Sagittarius. 7 The lake of the Dwat: X 8 The middle swsp: Scorpius. 9 The left (=== eastern) swsp: Leo. 10 The right (= western) swsp: Aquarius. 11 [The] right (= western) twr: TTJ2 destroyed Os. 3. 1 Year 4, month VII, (day) 1, 4 o’clock in the evening........... 2 The sun in Pisces (and) Jupiter. 3 Moon in Sagittarius 1°(?) 4 The ascendant: Libra. 5 The descendant: Aries. 6 The lake of the sky: Cancer. 7 The Dwat: Capricornus (and) Saturn. 8 The middle swsp: X 9 The left (= eastern) swsp: Pisces. 10 The right (= western) swsp: Tip 11 [The] right (= western) twr: Aries. 12 [Theleft (= eastern)] twr: Aquarius(!) Leo. 13 The house of provision of life: Scorpius. 14 The part of the brother: Sagittarius. 15 The part of the father: Capricornus. 16 The part of the child: Aquarius (and) Mercury. 17 The part of ( ?) : Pisces 18 The part of the fate: Aries. 19 The house of provision of death: Taurus (and) Mars. 20 The part of god: X 21 The house of the goddess: Cancer. 22 Psais: Leo. 23 The evil spirit: TIR Os. 4. 1 Year 21, month XI, day 13, 7 o’clock [of the day]. 2 The sun in Cancer (and) Mercury. 3 Moon in Saggit-tarius 1° 4 The ascendant: Libra. 6 The descendant: Aries. 6 The lake of the sky: Cancer. 7 [The] lake of the Dwat: Capricornus. 8 The middle swsp: X 9 The right (= western) swsp: Pisces. 10 [The] left (== eastern) swsp: 11 [The] right (= western) twr: Aries. 12 [The] left (== eastern) [twr] : Leo. The [house] 13 [of provision of li]fe: Scorpius. 118 Neugebauer: Demotic Horoscopes Os. 1. 2. 16(7): Reading of 10 clear; it follows a group which is either 5, 6 or 8. The position of the moon, given in line 5 as & 21, would be exactly correct if one would read 16.—3. i'h: mention of the moon here (cf. line 5) seems to be meaningless.—3. n(1): The photograph shows at the end of this line a dark stroke. Dr. Hughes, however, carefully inspected the original and found that the “ sign ” in question is not ink at all but only a small depression in the surface of the clay. There follows, however, a short stroke of ink (like n) immediately after i'h.—10. swsp: no traces of p’ visible. —10. 10: cf. the same writing for mtr in Os. 2 line 8. —10a: Written between lines 10 and 11.—14. twr wbt: without n, as in Os. 3 line 12. Os. 2. 1. 4-t: t omitted by Spiegelberg.—1. }h.t: Spiegelberg reads smw, which is astronomically excluded because, according to line 2, the sun was in Libra.— 1. 11-t: Spiegelberg reads 11 n.—1. rhwy: 11 o’clock “in the evening” could be understood as 11th hour of the daytime i. e. one hour before sunset. In Os. 3, 1 however, occurs 4 o’clock “ in the evening ” which must be the 4tl> hour of the night. Hence rhwy must be interpreted as “ night.”—4. p} ( J) : looks like an r.—4. n ( ?) : merely a point.—5. n( ?) : merely a point.—5. ntr dw%: Spiegelberg reads n (7) tu-ntr.—8. n: omitted by Spiegelberg.—8. 10: 10 = md stands here for mtr, as Spiegelberg [3] p. 150, note 4 remarks. Cf. Os. 1, line 10.— 9 ff. n: disregarded by Spiegelberg. Os. 3. 1. [pr].t 1: Thompson reads pr ss 1. Both pr.t and %h.t would be compatible with the remains but the reading ^h.t is eliminated by the following line, which says that the sun stood in, Pisces. The following large stroke must represent the first day (without Q), as is frequently the case in the planetary texts.—1. rhwy: cf. Os. 2, 1.—1. . .. traces, probably meaningless. —3. . .. : according to photograph traces (disregarded by Thompson) which might be interpreted as n 1 (i. e. “ first degree ”).—9. [tbtpy: sic, without the plural w.— 11, 12, 13. The break between upper (Thompson) and lower part (Spiegelberg) crosses these lines.—12. twr wbt: cf. Os. 1, line 14. — p% mw: error, corrected by adding p^ m^y.— 13. shn = provision: sic, according to Thompson; Spiegelberg read 2.—14. &n: this reading according to Thompson; Spiegelberg read mwt.— 14 ff. dny.t: Spiegelberg f.—17. hne — ( ?) : Spiegelberg translated “ Trennung,” probably because of the subsequent line.—18. shne — fate: cf. the discussion by Thompson [1] p. 230; Spiegelberg translated “ Vereinigung.” — 19. *: written over t} dny.t. 19. shn: cf. line 13. Os. 4. l.^w: omitted by Spiegelberg.—13: Spiegelberg reads 13 and translates 15.—7-t: left-hand part of the numeral is broken off.—3. n 1: disregarded by Spiegelberg.—8 ff. swsp: Muller [2] col. 9 proposes to read only sws, considering the last sign as determinative. Spiegelberg [3] p. 150, note 1 opposes this assumption.—8. n, X: Spiegelberg p} (t) k} but correct in [3] Pl. IV.—9. n}: Spiegelberg p}.—12. p? [‘J : p, disregarded by Spiegelberg. 4. From these four ostraca we can derive the following scheme according to which they were composed. The first step consists in giving the date (regnal year, month, day and hour) and the position of the sun, the moon and the planets. The next part consists in giving the four “ Kf.vTpa,” the three “ swsp ” and the two “ twr” The “ Kevrpa ” are the rising and setting signs (r*-A' and r'-htp) and the lake of the sky and Dwat, respectively.8 9 The swsp correspond to the dnoKXtpMTa of Greek astrology,10 i. e. the signs inclined in the direction of the daily rotation, thus preceding the three upper KevTpa by 30 degrees. The “ left- ” and “ right-hand ” twr^s define a parallel line to the left and right swsp (cf. Fig. 1). I do not know the Greek analogue to this latter concept, except that the two swsp constitute the corners of a “ tri-gonon.” The last step consists in enumerating the “ houses ” in their relationship to the zodiac in its special position at the given moment. The first 8 This fact was recognized already by Thompson [1] p. 228 and has been confirmed independently and based on entirely different textual material (commentary to the Nut-picture in the cenotaph of Seti I and the tomb of Ramesses IV) by Lange-Neugebauer [1] p. 57 ff. 10 Cf. e. g. Bouche-Leclercq AG p. 273 and Thompson [1] p. 231. house is not repeated because it is the ascending sign, already mentioned before. The next sign is the ' slin 'nA “ house of provision of life ” 11 (the 11 lucrum” of classical astrology); the knowledge 11 Thompson [1] p. 230. Cf. Bouche-Leclercq AG p. 280 ff. or Boll-Bezold SS p. 62 f. See furthermore the new text Gundel, Dek. p. 410. Neugebauer: Demotic Horoscopes 119 of this sign determines the rest according to the known scheme, which is therefore only once completely given (Os. 3), while the other ostraca restrict themselves to the * shn lnh alone. Not one of these ostraca indicates the conclusions drawn from these elements. There exist different small discrepancies between this general scheme and the 'text in the ostraca. Ostraca 2 and 3 interchange “ right ” and “ left ” in indicating the swsp’s but give the tor’s correctly. Ostracon 1 turns all swsp’s and tor’s 90 degrees towards the east, obviously by erroneously calling the left hand swsp the “ middle ” one and then modifying all the rest accordingly. All these errors, however, are only due to carelessness and do not disprove the above-given rules. 5. We turn now to the problem of dating the four ostraca. The easiest case is No. 1, where the regnal year 43 points to Augustus as the only possibility. This is fully confirmed by the planetary positions (cf. the table given on p. 120). The position of the moon (8 21), however, can only be accounted for if we interpret the dates in terms of the Alexandrian calendar, using “ Julian years,” and not as dates in the Old-Egyptian wandering year which would give a totally different value (^ 22) for the moon’s longitude. Os. 3 is also easy to date because the positions of both of the slowly moving planets, Jupiter and Saturn, are given. Here again the position of the moon shows that the Alexandrian calendar was used. All positions given in the text accordingly agree perfectly with modern calculation for the year Tiberius 4 = 18 A. D. More difficult is the dating of the two remaining ostraca because of missing information about the two outer planets. In Os. 4 the regnal year 21 points to Augustus or Tiberius. Assuming Augustus, the moon does not agree with the sign Sagittarius, regardless of whether we use the Egyptian or Alexandrian calendar. Tiberius 21, however, brings the moon into the right place if we interpret the date in the Alexandrian calendar. Sun and Mercury then also become correctly placed. Os. 2 requires a longer discussion. From the positions given for the sun (=2=) and the moon (8 16), it follows that the moon must be about three days after opposition. Assuming the Alexandrian calendar, we find October 3 (±lday) as the date of full moon. Investigating all regnal years 312 and 4 between, say, 40 b. c.13 and 160 A. d. as to full-moon dates we find that only Tiberius 3, Domitianus 3 and Hadrian 4 remain possibilities. All these dates are, however, ruled out by considering Mars, which is far from & in all these dates. We are, therefore, forced to abandon our assumption of Alexandrian calendar and to interpret the date as Egyptian. Doing so, we obtain perfect agreement with the text for the year Tiberius 4 not only so far as sun and moon are concerned but also for Venus and Mars. The table on p. 120 shows the results obtained. Comparing text and calculation, one must keep in mind that the Egyptian limits of the zodiacal signs must not necessarily coincide with ours (true vernal point) ; as a matter of fact, the Demotic planetary tablets show that 4° or 5° should be added to calculated values in order to get Egyptian longitudes.14 In the given dates, (a) means Alexandrian calendar, (e) Egyptian, (j) Julian. The small deviations in the case of moon (daily movement from 11 to 15 degrees!) and Mercury are easily accounted for, because all these horoscopes are of course based on calculation and not on actual observation. The fact that three of these ostraca use the Alexandrian calendar and one the Egyptian is in itself of interest. It shows on the one hand how early the Augustan new order was adopted by Egyptian scribes, and on the other hand, how unstable the calendarical rules were. This is underlined by experience with other texts. The Alexandrian calendar is the basis for the Stobart planetary tables, covering the years from 71 A. d. to 143 a. d., but the Egyptian calendar is employed both in the planetary tables of Pap. Berlin 8279, written after 42 a. d., and in the moon tables of Pap. Carlsberg 9, written after 144 A. d.15 * That Ptolemy and his successors (from Pappus and Theon to Copernicus) base all their calculations on Egyptian years is well known. 12 The reading 3 would be even better than 4. The same sign form occurs, however, as 4 in the date of Os. 3 and in Pap. Carlsberg 9. 13 Among the approximately 50 published horoscopes on Greek papyri and ostraca, the oldest is from 4 B. c. (P. Oxyrh. No. 804; erroneously printed A. D. instead of B. c.), and only five belong to the first cent. A. D. 14 Cf. Neugebauer [1] p. 230. 16 Cf. Neugebauer [1] p. 229 and Neugebauer-Volten [1] p. 398. 120 Neugebauer: Demotic Horoscopes 05. 1 Qs. 2 Os. 3 Os. 4 text catcut. text calxut. text calcul. text Calcut. 0 V ry 19 «=a=. =rA~= 1 )( )(5 Q S 12 c 0 21 0 IL 0 16 0 24 //(?) nj 2i / 1 / 21 s ? > X 18 s ® 6 $ 5?-S' 0 0 6 0 0 23 4- -A-r 18 K )( II "1 m 15 3 5 /2 date text (Auqu.stu.s) 43 Z(a) M 8 k Ji. (Tiberius) 4 Xie) 9 //** n. (Ti berius) 4 MCa) 1 n. (Tiberius) 2/ 31(a) /3 7fc J. e^uiv. + /3 ix(j) 13 +■ >7 lA(j) 26 + 18 JLlj) 25 + 35 S(J) 7 6. The dates obtained in the preceding section show that all four ostraca give horoscopes for men living in the first half of the first century of our era. As to the place of origin, Os. 1 was found in the campaign of the Oriental Institute of the University of Chicago during 1929/30 at Medinet Habu. Os. 4 was purchased in 1899 by Spiegelberg J[p’ t] n p’ t’OiWOi 2 [?A n] pl kl 17(?) 3 [p’ r']-A‘ pl hr-nh ^01 4 pl r'-htp pl gnhd ... 6 pl sy tl p.t tl 6 pl sy tl dl.t 7 pl iswe ifi 8 iOiS pr(?) p> sy p’J sp-sy' or L * J as Dr. Hughes recognized. — d’.t: Thompson thought 18 Spiegelberg [2] col. 223 note 1. in Gurna,16 Os. 2 and the lower part of Os. 3 ten years later by Wreszinski in Luxor.17 This makes it very probable that all four texts were written by the same man at Medinet Habu. It is possible that also the last horoscope, Os. 5, belongs to the same group, but it is too badly preserved to be dated. One can read the following:18 [The sun] in Taurus [Moon in] Taurus 17°(?) [The] ascendant: Capricornus The descendant: Cancer The lake of the sky: =^= The lake of the Dwat: Aries, nt house (?) of sy.t house (?) of] sp-sy.t that the latter part of the line did not belong to the word d’.t, as dots in his transcription indicate. Dr. Hughes, however, pointed out to me that we have here only a full spelling of d’.t. — 7. Thompson hesitatingly read my, but Dr. Hughes recognized that iswe becomes clear if one eliminates the long tail of the sign sy reaching down into line 7 from line 6. 17 Spiegelberg [3] p. 149. 18 Cf. Thompson [1] p. 232 f. Neugebauer: Demotic Horoscopes 121 Lines 1 to 7 indicate beside the positions of sun and moon the four Kevrpa s E ?. One should now expect the three swsp ? X HR, but line 7 mentions without explanation Tq, which would be the left twr. Also the two following “houses,” mentioned in the two last lines (8 and 9), do not fit into the regular scheme as given by Os. 3. § 2. The date of origin of Egyptian astrology and the symbol =£j= 7. It is well known that there is no trace of astrology in Egypt before the Hellenistic period. Moreover, as Kroll pointed out,10 the doctrine going under the name of Nechepso and Petosiris reflects circumstances in Egypt and Syria existing in the middle of the second century b. c. It seems possible, however, to discover traces of a phase approximately a hundred years older by using the relationship between the zodiac and the Egyptian calendar established in ostracon D 521 of the Strassburg collection, published 1902 by Spiegel-berg.18 * 20 This text is as follows: 1 pl wn pl 5 syw *nh hr-pl-kl pl syw 2 pl d ply hr-ds pl syw mie-hs ply 3 sbkl pl syw thwty ply pl ntr-twy 4 hr si is. t ply hr-pl-ste pl syw imn ply 5 pl rn n pl 5 syw lnh irm, ntrw nb 6 r ir rnw drw ... pl wn nl syw nty sr 7 pl ibd 12 ... II pr.t pl isw III pr.t pl kl 8 IV pr.t nl htrw tpj smw pl knhd 9 II smw pl mle III smw tl rpy 10 IV smw tl ihy.t tpy Ih.t dll 11II ih.t pl III ih.t pl hr-nh 12 IV Ih.t pl ( ?) n pl mw 13 tpy pr.t nl tbt.w 14 dmd syw 12 pl ibd 1[2 ^’^0^] 15 r pl ibd 2. mle hs: “ the fierce lion ” — god Ap/itvais (cf. Spiegel -berg [1] col. 8 note 3 and WB II p. 12). — 3. the Stobart tablets alternate between s&fc and sbky, cf. Neugebauer [1].—4. Hr s’ is.t: Greek Ap Boll [1]. In Egypt we have the following orders: according to synodic period in the planetary tables (cf. Neugebauer [ 1 ]), according to “ houses ” in the Hathor temple of Dendera (outer hypostyle; Porter-Moss VI p. 49) and according to “ exaltations ” in the same temple (eastern Osiris-chapel; Porter-Moss VI p. 99), as discovered by Boll (Sphaera p. 232 ff.). Cf. furthermore the article “ Hebdomas ” by Boll in RE 7 col. 2547-2578. 22 Cf. Neugebauer [1] p. 246. 23 Muller [1] and [2] assumed an erroneous etymology which substituted mhy.t by %h.t. But this is in itself very unlikely and contradicts both spelling and ideogram in all texts. Cf. Spiegelberg [3] p. 147 note 6. 24 This distinction, e. g., frequently in the Tetrabiblos (cf. e.g. I, 9 ed. Robbins p. 50/51). There exists even a glyptic representation of the claws alone, namely on a reused block in the Panhagia Gorgopico or Hag. Eleu-therios church in Athens. Cf. G. Thiele, Antike Himmels-bilder (Berlin 1898) p. 57 ff. and L. Deubner, Attische Feste (Berlin 1932) p. 248 ff. esp. Pl. 40 no. 41. The date of this frieze is uncertain; Deubner quotes argu- of the) balance,” Latin “libra,” appears rather late in Greek literature: only once in Hipparchus’ writings (ca. 150 b.c.),25 more frequently in Geminus (first cent. b. c.) and afterwards, but more in Roman works than in Greek.26 On the other hand, the constellation “ balance ” is already known in Old-Babylonian times, but in the series “ mul-apin ” also the equivalent “ sting of the scorpion ” appears.27 The cuneiform ephe-merids from the Seleucid period keep “ balance ” (nn) and “scorpion” (gir-talD) strictly separated.28 The latter statement holds equally for the Egyptian representations of the zodiac, the earliest preserved examples being at Dendera (time of Tiberius). In the pictorial representations a clear balance is always given and nothing like a “ horizon.” How can this contradiction be explained ? I think one must first try to discover a reasonable motive for calling a zodiacal sign “horizon.” Such a reason can be found in the special situation which is assumed by the correspondance between zodiacal signs and months, given in ostracon D 521, discussed above, where the sun is supposed to travel in “ Scorpius ” during the first month of the Egyptian calendar. From this assumption follows, namely, that the preceding sign “ balance ” was rising heliacally at the beginning of the year —sufficient reason, indeed, to be called “(being in the) horizon.” Such an emphasis on the quality of a constellation to indicate the beginning of the civil year by its heliacal rising would certainly be nothing surprising in Egypt; moreover this sign is, so to speak, the “ Horoscope ” of the year.29 * * If one considers this explanation of the name “ horizon ” as plausible, one can accept the fol ments for dates from the third cent. B. c. to the third cent. a. d. 25 Ed. Manitius p. 222, 9. This passage is therefore considered as suspicious. 20 Cf. the articles “ Libra ” and “ Scorpios ” by Gundel in RE 13, 116-137 (1926) and A3, 588-609 (1927); furthermore the article “ Sternbilder ” in Roscher GRM 6, 963-967 (1937) by Boll and Gundel. 27 CT 33, 2 obv. II, 11 m^zi-ba-an-na si mu}gir-tab. Cf. Jensen [1], 28 This follows from all moon and planetary tablets published by Kugler and is only confirmed by unpublished material. The “ sting of the Scorpion ” appears, however, in the horoscope AB 251 obv. 3 (Thompson CBL plate 2). 29 One might remark that the decans are called the 36 (bpoaKOTToi in P. Brit. Mus. No. 98 line 15 (Kenyon GP I p. 128). Neugebauer: Demotic Horoscopes 123 lowing outline of the development. When, during the third cent. b. c., Babylonian and Greek astrological concepts were introduced into Egypt, the more or less precisely defined belt of 36 decanal configurations, was replaced by the twelve zodiacal signs.30 The Greek names were translated into Egyptian, but since the “ Scorpio ” extended over two twelfths, it was felt so inconvenient that the Babylonian order Scorpius-Libra was adopted so far as pictorial representations are concerned. Simultaneously, the horoscopic character of this star group leads to an original Egyptian name which is the only one preserved in Demotic documents. 9. The further development can be traced with a much higher degree of certainty than the beginnings. Since Roman times,31 astrology became in Egypt what we understand today by this word, deeply influencing the life both of the native and the Hellenistic-Roman population. Undoubtedly, every astrologer was familiar with the Egyptian symbols for the zodiacal signs and the planets, and it is therefore not surprising to find Egyptian forms used as sigla in the professional writings. Obviously, the Hieratic-Demotic sign —*32 in this way became a representation for the Greek “claws of the Scorpion.” We have, however, a very interesting bit of evidence that still was pronounced “x’/Aat.” Hephaistion of Thebes, an astrological author of the 4th cent. a. d. says:33 To p-era ryr UcqoSevov SwScKaT^pjopwv wpio/xauav ot TraAatorepot Trarres £vyov Kai tovtov crr)}j,e~t.ov Trotovvrai to8e =£=, 6 UtoXc/mzIos yyAas Ka'L to {npjbdov avrov tomvSc , % , “All the older ones called the sign after Virgo the Balance and used the following symbol: =o=; Ptolemy, however, called it the claws and used the sign X .” The statement about the use of the words “ balance ” and “ Claws ” gives, as we have seen, the inverse order; but the 30 The earliest representation of the zodiac in Egypt known to me is the ceiling in the temple of Khnum north-west of Esna (about 200 B. c.; cf. Porter-Moss VI p. 118). . 31 It might be repeated that there exists, at least to my knowledge, not a single horoscope in Egypt (either in Greek or Demotic) earlier than 4 b. c.! (Cf. above note 13.) 32 The second line in =0= might have its origin in forms like Cf., e.g., P. Cairo 50143 (Spiegelberg DD II Pl. 59). 38 CCAG 8, 2 p. 43 (P 57, 1). This codex was written in the XVth cent. (cf. CCAG 8, 2 p. 11, No. 21). essential point in our discussion is the fact that the combination of the “horizon” and the abbreviation x for x’yAaf existed at least as early as the 4th century a. d. or even actually in Ptolemy’s time, the very period of some of our Demotic astronomical texts. That this combination of the two symbols was not an isolated incident is proved by the fact that it is actually used in one of the codices of the Tetrabiblos, namely in the Cod. Vatican 2 0 8 34 written in the XIVth cent.35 Hence we have at least one thousand years of continuous tradition down to Hephaistion. His testimony finally bridges the short gap to the extant Demotic papyri and ostraca. On the other hand, the Greek terminology was more and more replaced by Latin, in which “libra” always was the preferred notation. So it happened that the sign =o= was not only called but also was interpreted as the picture of a balance— which is still the explanation in common use today. § 3. The Zodiacal and Planetary Symbols 10. If one wishes to investigate the history of the medieval and modern symbols used for zodiacal signs and planets, then the signs used in Demotic documents are undoubtedly the earliest known symbols—cuneiform ideograms like hun, mid, etc. are of course out of the question.36 * 38 However, to follow the history of these sigla into Greek and Latin documents meets the greatest difficulties, not so much by lack of documents but by the combined efforts of classical scholars in virtually extinguishing all traces of the palaeographical situation. The astronomical symbols have been treated with the greatest disregard, symbols being 341 owe photocopies of the pages 150 r., 151 v. to the courtesy of the Library of the University of Michigan; they correspond to ed. Boll-Boer p. 73, 22-76, 33 and ed. Robbins p. 152-158. 36 This codex belongs to family 7 according to Boll- Boer p. xiv (codex B = codex A Robbins). 38 Agnes M. Clerke says in the article “ Zodiac ” on p. 998 of the 11th ed. of the Encyclopaedia Britannica (1911): The origin of the zodiacal symbols “is unknown; but some, if not all of them, have antique associations. The hieroglyph of Leo, for instance, occurs among the symbols of the Mithraic worship ” quoting “ Lajard, Culte de Mithra Pl. 27 fig. 5 ” where a Babylonian cylinder seal is published. This seal (which, of course, has no relationship whatsoever to the worship of Mithra) is republished by E. Douglas Van Buren AfO 9 (1933/34) p. 168 fig. 4 (I owe this quotation to Miss E. Porada). The symbol in question (looking like the modern symbol for the ascending node) is, however, shown by Mrs. Van Buren to be a symbol of the goddess Ninbursag and has no relation to the configuration “ Leo.” 124 Neugebauer: Demotic Horoscopes replaced by words and vice versa. It is therefore absolutely impossible to give today more than a few examples accidentally collected from published photographs. I was not even able to verify a statement of Cumont that the zodiacal symbols “sont deja employes dans les papyrus et remontent au moins a 1’epoque hellenistique.”37 The earliest forms of the planetary symbols known to me 38 are taken from (I) Cod. Laur. 28, 34 fol. 132v. (Xl-th or X-th cent.)30 and the zodiacal signs from (II) Cod. Vatican. 1594 fol. 155r. (IX-th cent.).* 38 39 40 For more recent forms I used (III) Cod. Paris. 2424 fol. 189r. (XlV-th cent.)41 (IV) Cod. Vatican. 208 fol. 150v., 151r. (later XlV-th cent.)42 but I must repeat that these examples can by no means be considered as more than mere accidentally selected forms. 11. The Demotic sources used in the following sign-lists will be quoted as follows: (1) to (5) Ostraca 1 to 5; horoscopes;43 (Medi-net Habu about 50 a. d.). (6) Ostracon D 521 44 87 Daremberg-Saglio, Vol. V p. 1046 b note 3 but without citation. 38 The examples quoted by V. Gardthausen, Griechische Palaeographie II (2nd ed., Leipzig 1913) are even as late as the XVth cent. Only the symbols for sun and moon and (^) are very frequent in astrological papyri. A list of zodiacal and planetary symbols from Greek manuscripts of unknown date can be found in the plate attached to the article “ Abbreviations grecques copiees par Ange Politien ” by H. Omont in the Revue des etudes grecques 7 (1894) p. 81-88. 39 CCAG 1 (cod. 12) plate. For the date, cf. p. 70 note 1. Horn-d’Arturo [1] attempted to derive the planetary and other symbols from the Hindu-Arabic numerals applied to the almost complete conjunction of all planets in the year 1186. This hypothesis is disproved by the date of the codex mentioned. 40 Peters-Knobel [1] Pl. IV. This is the first page of Ptolemy’s star catalogue, ed. Heiberg, opera I, 2 p. 38, 1 to p. 44, 15. 41 Tannery, Mem. sci. IV Pl. I (between p. 356 and 357). 42 Cf. above note 34. 43 Above p. 116 and 120. 44 Above p. 121. (7) P. Berlin 8279; planetary tables (Fayum; after 42 a. d.)45 (8) P. Cairo 31222; 46 astrological. (9) Coffin of Het er-, horoscopic inscription (Thebes, about 120 a. d.)47 (10) Stobart tablets; planetary tables (Thebes, after 134 a. d.) 48 (11) P. Carlsberg 9; moon tables (Fayum, after 144 A. d.) 49 (12) P. Carlsberg 1; Nut and decans (Fayum)50 (13) P. Berlin 8345; astrological treatise (Fayum)51 (14) P. Cairo 50143;52 astrological fragment.53 The above list seems to be complete so far as published Demotic54 sources are concerned.55 They are closely related to the Ptolemaic-Roman monumental representations and to the vast Greek astrological literature. The only Demotic text which refers to the totally different original Egyptian “ astronomical ” concepts known to us from the royal tombs of the XIXth and XXth Dynasty is the P. Carlsberg 1. It seems to me of importance to emphasize very strongly that the astronomical as well as the religious and social back- 45 Neugebauer [1] p. 212 ff. and Pls. 17 ff. 48 Spiegelberg DD II Pl. 129. 47 Above p. 115. 48 Neugebauer [1] p. 221 ff. and Pls. 23 ff. 49 Neugebauer-Volten [1]. 60 Lange-Neugebauer [ 1 ]. 51 Spiegelberg DPB Pl. 97. 82 Spiegelberg DD III Pl. 59. 83 What I am able to read is only pl ntr mh 6 swgl ply Ml * p? The constellation at the beginning of the second line must be either Gemini or Pisces because of the determinative. | . Gemini, Libra and Aquarius are known from the Tetrabiblos (I, 18 ed. Robbins p. 86/87) as constituting the triplicity (rplyovov) of Mercury and it is therefore evident that we have here the same arrangement. Mercury is the sixth “ planet ” only if one counts from outside and includes the sun. To call the planets Oeol is not rare in Greek; e.g., P. Brit. Mus. No. 130 speaks about “ the movement of the seven gods ” (Kenyon GP I p. 133, 7f.). 84 All these texts contain many Hieratic sign forms, included here. 88 [After the preparation of this manuscript, Dr. Hughes discovered the symbol for Sagittarius also in P. Cairo 31222 (text (8) of our list). In lines 3 and 5 occurs the upturned arrow in a form similar to (7) I, 4 in our Pl. 3, but with the added star determinative. In line 1, the star determinative is almost completely gone, but the preceding signs are probably to be read pl nty Ith, as Dr. Hughes observes.] Plate 1 Ostracon Chicago M. H. 3377 Neugebauer: Demotic Horoscopes 125 ground of the Hellenistic material is at least as different from the Egyptian material of the New Kingdom (and its predecessors of the Middle Kingdom) as from the Babylonian sources. The world of Hellenism is in every respect a world of its own, being much more the beginning of the medieval world than the conclusion of the ancient. BIBLIOGRAPHY AND ABBREVIATIONS aZ. Zeitschrift fur aegyptische Sprache und Altertums-kunde. Boll [1]. F. Boll, Neues zur Babylonischen Planeten-ordnung. ZA 28 (1913) p. 340-351. Boll, Sphaera. F. Boll, Sphaera, Neue griechische Texte und Untersuchungen zur Geschichte der Sternbilder, Leipzig, Teubner, 1903. Boll-Bezold SS. F. Boll-C. Bezold-W. Gundel, Sternglaube und Sterndeutung. 4th ed., Berlin-Leipzig, Teubner, 1931. Boll-Gundel [ 1 ]. F. Boll and W. Gundel, Article “ Sternbilder, Sternglaube und Sternsymbolik bei Griechen und Romern ” in Roscher, Lexikon d. griech. u. rom. Mythologie, Leipzig, Teubner, vol. 6, col. 867-1072. Bouche-Leclercq AG. A. Bouche-Leclercq, L’astrologie grecque, Paris, Leroux, 1899. Brugsch [1]. H. Brugsch, uber ein neu entdecktes astro-nomisches Denkmal aus der thebanischen Nekropolis. ZDMG14 (1860) p. 15-28. Brugsch, Rec. I. H. Brugsch, Recueil de monuments egyptiens etc. vol. I, Leipzig, Hinrichs, 1862. Brugsch, Thes. I. H. Brugsch, Thesaurus inscriptionum aegyptiacarum, I. Astronomische und astrologische Inschriften altaegyptischer Denkmaler, Leipzig, Hinrichs, 1883. Brugsch, WB. H. Brugsch, Hieroglyphisch-Demotisches Worterbuch, Leipzig, Hinrichs, 1868-1882. CCAG. Catalogus codicum astrologorum graecorum, Bruxelles, Lamertin, 1898 ff. CT. Cuneiform texts from Babylonian tablets etc., in the British Museum. Cumont, EA. F. Cumont, L’Egypte des astrologues, Bruxelles, 1937, Fondation 6gyptol. reine Elisabeth. Daremberg-Saglio. Ch. Daremberg-E. Saglio, Dictionnaire des antiquitds grecques et romaines. Paris 1877-1919. Frankfort [1]. H. Frankfort, The Cenotaph of Seti I at Abydos, The Egyptian Exploration Society, Memoir 39 (1933). Ginzel, Chron. F. K. Ginzel, Handbuch der mathema-tischen und technischen Chronologic, Leipzig, Hinrichs, 1906-1914 (3 vols.). Griffith, Ryl. III. F. LI. Griffith, Catalogue of the Demotic papyri in the John Rylands Library, Manchester, Vol. Ill, Manchester, Univ. Press, 1909. Gundel, Dek. W. Gundel, Dekane und Dekansternbilder. Studien d. Bibliothek Warburg 19, Gliickstadt-Hamburg, T. T. Augustin, 1936. Horn-d’Arturo [1]. G. Horn-d’Arturo, Numeri arabici e simboli celesti. Pubblicazioni dell’ Osservatorio astronomico della R. University di Bologna. Vol. 1 No. 7 (=p. 183-204 of Vol. 1), Roma, 1925. Jensen [1]. P. Jensen, Zibanitu, die Wage. ZA 6 (1891) p. 151-153. Kenyon GP I. F. G. Kenyon, Greek papyri in the British Museum1 I, London 1893. Lange-Neugebauer [1]. O. H. Lange-O. Neugebauer, Papyrus Carlsberg No. 1, Ein hieratisch-demotischer kosmologischer Text. Kong. Danske Videnskabernes Selskab, Hist.-filol. Skrifter vol. 1, nr. 2, 1940. Muller [1]. W. M. Muller, Zu dem neuen Strassburger astronomischen Schultext, OLZ 5 (1902) p. 135 f. Muller [2]. W. M. Muller, Zur Geschichte der Tierkreis-bilder in Aegypten. OLZ 6 (1903) p. 8 f. MVAG. Mitteilungen der Vorderasiatischen Gesellschaft. Neugebauer [1]. O. Neugebauer, Egyptian planetary texts. Trans. Am. Philos. Soc., New Series 32 (1942) p. 209-250. Neugebauer [2]. O. Neugebauer, On some astronomical Michigan Papyri and related problems of ancient geography and astronomy. Trans. Am. Philos. Soc., New Series 32 (1942) p. 251-263. Neugebauer-Volten [ 1 ]. O. Neugebauer-A. Volten, Untersuchungen zur antiken Astronomie IV. Ein demo-tischer astronomischer Papyrus (Pap. Carlsberg 9). QS Abtlg. B vol. 4 (1938) p. 383-406. Oefele [1]. F. v. Oefele, Die Angaben der Berliner Planetentafel P 8279 verglichen mit der Geburts-geschichte Christi im Berichte des Matthaus. MVAG 8, 2 (1903). OLZ. Orientalistische Litteraturzeitung. Peters - Knobel [1J. Ch. H. Fr. Peters - E. B. Knobel, Ptolemy’s Catalogue of stars, a revision of the Almagest. Carnegie Institution of Washington, Publication No. 86 (1915). Porter-Moss. B. Porter-R. Moss, Topographical bibliography of ancient Egyptian hieroglyphic texts, reliefs and paintings, 6 vols., Oxford 1927-1939. PSBA. Proceedings of the Society of Biblical Archaeology. Ptolemy, Opera I. Claudii Ptolomaei opera I, 1 and 2: Syntaxis mathematica, ed. Heiberg, Leipzig, Teubner, 1898-1903. Ptolemy, Tetrabiblos. Ed. Boll-Boer, Claudii Ptolemaei opera III, 1. Leipzig, Teubner, 1940. Ed. Robbins, Loeb Classical Library, 1940. QS. Quellen und Studien zur Geschichte der Mathe-matik, Astronomie und Physik. RE. Real-Encyclopadie der classischen Altertumswissen-schaft. Roscher GRM. Roscher, Lexikon d. griechischen u. ro-mischen Mythologie. Schott [1]. A. Schott, Das Werden der babylonisch-assyrischen Positionsastronomie. ZDMG 88 (1934), 302-337. Schram KCT. R. Schram, Kalendariographische und chronologische Tafeln, Leipzig, Hinrichs, 1908. 126 Neugebauer: Demotic Horoscopes Servius. Servii grammatici qui feruntur in Vergilii Bucolica et Georgica commentarii ed. G. Thilo, Leipzig, Teubner, 1887. Sethe, Biirgschaftsurk. K. Sethe, Demotische Urkunden zum aegyptischen Biirgschaftsrechte, Abh. d. phil.-hist. Klasse d. sachs. Akad. d. Wiss. 32 (1920). Spiegelberg [1]. W. Spiegelberg, Ein aegyptisches Ver-zeichnis der Planeten und Tierkreisbilder. OLZ 5 (1902) p. 6-9. Spiegelberg [2]. W. Spiegelberg, Ein neuer astrono-mischer Text aut einem demotischen Ostrakon. OLZ 5 (1902) p. 223-225. Spiegelberg [3]. W. Spiegelberg, Die aegyptischen Na-men und Zeichen der Tierkreisbilder in demotischer Schrift. AZ 48 (1910) p. 146-151. Spiegelberg [4]. W. Spiegelberg, Demotische Miscellen. AZ 37 (1899) p. 18-46. Spiegelberg DD. W. Spiegelberg, Die demotischen Denk-maler. Musee des antiquites egyptiennes, Cairo. Catalogue general des antiquites egyptiennes du Musee du Caire. Spiegelberg DPB. W. Spiegelberg, Demotische Papyrus aus den Koniglichen Museen zu Berlin, Leipzig u. Berlin, Giesecke u. Devrient, 1902. Spiegelberg Gr. W. Spiegelberg, Demotische Grammatik. Heidelberg, Winter, 1925. Tannery, Mem. sci. P. Tannery, Memoires scientifiques, Paris, 1912 ff. Tetrabiblos. See Ptolemy. Thompson [1]. Sir H. Thompson, Demotic Horoscopes. PSBA34 (1912) p. 227-233. Thompson CBL. R. C. Thompson, A Catalogue of the Late Babylonian Tablets in the Bodleian Library, Oxford. London, Luzac, 1927. WB. A. Erman-H. Grapow, Worterbuch der aegyptischen Sprache, Leipzig, Hinrichs, 1926 ff. ZA. Zeitschrift fur Assyriologie. ZDMG. Zeitschrift der Deutschen Morgenlandischen Gesellschaft. Plate 2 Plate 3 Plate 4 WATERMAN, I, p. 21 LETTER 2U Mardukshakinshun to King Esarhaddon In regard to (the fact) that on this, the thirteenth day, sun and moon were seen together, there are rites pertaining to it which are to be performed. Let Nabugamll come that I may instruct him, that he may perform (them)j and to Arad-Anu (give orders) that he also may assist. WATERMAN, I, p. 27. " LETTER 36 Ishtarshamereah to King Esarhaddon right anc^elFt bT the god Sin (?)j and at the same time let them station "the images of the sons of th© king ay lord *Sofore Mn th© lord of the crown, every month without ceasing, rising and setting, for the prolongation ofdays, the strengthening oftKe tlirone and the b'estowSl of his power upon the king my lord, will not forsake the" sl'Jc of the king (?) ....... WATERMAN, I, p. 39 LETTER 50 Akkullanu to King Esarhaddon Let me hear of the welfare end the health of the king my lord by a reply to my letter. In regard to the appearance of the moon and sun in conjunction and Its signification, in the month Tebet, the fourteenth day •»••••* i’ov. .,...........will appear and the misfortune of the land of Akkad ... Elam and the land of Amurru. , When a storm bursts in the month Tebet, it will be an eclipse of the lands. WATERMAN, I, p. 53 LETTER 78 Bales! and Nabuaheriba to King Ashurbanipal (?) The king our lord is long-suffering. One day has passed that the king has denied his appetite, (and) has not eaten a morsel. nHow long” (runs) his Inquiry. Th® king may not eat food today. The king (feels himself) a poor serf. Were it the beginning of the month, the moon would appear. (The king speaks), saying, ’’Release me. Kev” have I not wited (long enough)? It is the beginning of the month, I will eat food, I will drink win®/’ Now is Jupiter (perhaps) the moon? WATERMAN, I, p. 55« LETTER 81 Nabuaheriba to King Esarhaddon To the king my lord, your servant Nabuaheriba. May it be well with the king my lord. May Habu (and) Marduk be gracious to the king my lord. The thirteenth day the gods appeared together. 4. WATERMAN, I, p. 67. LETTER 100 Tabshar-Ashur to King Sennacherib (?) Regarding that which I sent from the palace, saying, "Let thorn cross the rivers# Let them proceed to the city of Blrte. Let them make a ferry aow Arbailai th© third mounted messenger has 'spolcon, saying, ’"fW river Tigris is in flood (?) I can not .... advance ....... witK th© riding horses over it and Ve'fore me I have sent* WATERMAN, I, p. 95* LETTER 137 Zakir to King Ashurbanipal (?) On the fifteenth day of the month Tebet in th© middle watch, there was an eclipse of the moon. It began on the east (side) and turned to the west. The evil disturbance, which is in the land of Amurru and its territory, is its own harm. WATERMAN, I, p. 97. LETTER 1U Nabua to the King Kev* We keep the watch. On the fourteenth day th© sun and moon appeared together. WATERMAN, I, p* 107• LETTER 157 Ishtarduri to King Sargon Exceedingly much rain has fallen. The harvest is auspicious. Hxy the heart of the king my lord be of good cheer. WATERMAN, I, p. 16$. LETTER 2hl Ashurbelusur to the King Fifty oxen, lambs *••••• which for Babylon .«. • • are levied upon us annually, in the month Nisan we have given them. The king ny lord has spoken, saying, "Deliver them in the month Tishri." Just now the cattle and the lambs arc being brought in. Because of the cold and the (condition of the) streams, they have not delivered them. According as the king also has spoken, in the month Tishri we have given them. Now we are bringing down th© lambs. They are rounding them up according as the king ay lord speaks, and when the king comes to Babylon, I shall come with a chariot for the purpose of greeting the king. waterman, 1, p. 187. LETTER 276 Kiidurru to King Esarhaddon After the king ray lord went to the land of Egypt, in the month Tammuz an eclipse took place. There were none of my men left among them for the protection of the land of Assyria. It scattered them right and left. WATERMAN, X, p* 209* LETTER 302 Proclamtion of King Ashurbanipal (?) to Kabusharoheshu In regard to the horses of the former contingent of which you have written* *It is made up and within the month Adar w shall send it,” come. If the governor acts craftily w shall devastate. In the midst of the month Shebat w wrotet 'cv* nja every attack of the cold, 1. e., In cold wind, in the cold they would die.” About the middle of the month Shebat we sent again (?) s ”For the month Adar they will bring them. Ho will come that they may come, that they may arrive in the month Nisan.” WATERMAN, I, p. 2141. LETTER 3I46 The Scribes of Kaksi to the King The watch of Sin we have kept. On the fourteenth day, the moon and sun were seen together* It is well. i"ev* May Nabu and Marduk be gracious to th© king. On account of th® levy of compulsory service, the watch of the king we cannot continue* The official ....... waterman, 1, p* 2^5. LETTER 355 Bales! to the King Eserhaddon In regard to the raven, of which the king my lord has written, if a raven brings anything into a"'manfs house, that loan’s hand will' attain ”something that is not.” If a falcon or a raven drops something It has taken, at the house, or before the man (himself), that house will have a way— ’’way” means riches. If a bird drops at a man’s house meat or (another) bird Rev* or anything It has taken, that men will live sumptuously. WATERMAN, I, p. 21tf. LETTER 355 Balas! to King Esarhaddon ... As to the signification of th© nano of the months—how this is—one is not emal to another. In succession Rev* they receive their signification, thus it Is if it is complete. The signification, that Is, of the earthquake is thlst since it has taken place, let then perform whatever the rites are for an earthquake. WATERMAN, I, p. LETTER 356 Balas! to King Esarhaddon • • • If It is not agreeable to the king during this month, (then) in the month Nisan, at the beginning of the year, in case the moon completes its course (on the thirtieth day) in the month Nisan, let him enter into the presence of the king. WATERMAN, X, p. 251* UTTER 359 Adadshuimisur to King Esarhaddon (?) In regard to the image of th© king, of which the king my lord has written, saying, "How many days should it abide?" in expectancy of the eclipse of the sun we manned the watch# The eclipse of the sun did not take place. Nov; if on the fifteenth day the gods R<3V* are seen together, on the sixteenth day let it come for a possession# Now if it is pleasing to the king 115* lord, let it complete one hundred days# WATERMAN, I, p. 255. LETTER 361 Adadshumusur and Arad-Ea to the Planter Our service now is in Nippur (?)# I of the itinerary and Arad-Ea ;’v * serve before Enlll, we enter Into the shrine# The rites of the month Elul (?) with the (ordinary) rites I have performed# The burnt-offering I have’Turned# We have made the atonement. To the kalu priest, who is here, accompanied by a conjurer, I have entrusted (the matter). I have given him command as follows, "Tarry six days (then) carry out th© atonement according to this instruction." WATERMAN, I, p# 28J# LETTER l|07 Nabuaheriba to King Esarhaddon This is a day of sinister import, I could not send a blessing# The eclipse drew off from the east unto the west# -.’voxything has been regular# The planets Jupiter (and) Venu® stood within the eclipse until it set theta free# It is favorable for the king ry lord. It is evil concerning Amurru. Tomorrow the report of the eclipse of the moon I shall forward ihe "king my lord# WATERMAN, I, p. 295* LETTER 1|523 Ishtamadlnaplu (?) to King Ashurbanipal To the king my lord, your servant Ishtamadlnaplu (?), the chief of the shrine of th© scribes of th© city of Arbela. May "It be well with the king lay lord# May Nabu (and) Marduk be gracious to the king my lord# On the twenty-ninth day I. kept the watch. Kev* On account of the- appearance of clouds, w did not see th©**noon. (Dated) 1 the monthAcTar," tHc "first day, ’Before' 'bbe first day. WATERMAN, I, p# 299# LETTER U?2 The Keeper of the Shrine to the King To the king my lord, your servant, the keeper of the shrine (?) of the city of Arbela. May it be well with the king my lord. May Nabu (and) Marduk be gracious to the king my lord#* On thirteenth (?) ^@v* in the morning watch, the eclipse took place. I WATERMAN, I, p. J05- LETTER U57 Mar-Ishtar to King Ashurbanipal The eclipse of the moon approaches, the gods are (nigh). It will not apply to the land. If it is acceptable to the king my lord, as formerly let him appoint an overseer (?) for the shatamnii officials. Let his bring the regular offering before the shrine, on the day of the feast, for the welfare of the house. WATERMAN, I, pp. J29, 331. LETTER U70 ........ to King Esarhaddon Akkulanu has reported, saying, ’’hhen the sun arose, It came to pass that an eclipse took place of about two fingers (in width).n It has no releasing incantation. It is not th© same as with the moon. If you command, its signification I shall write down and cause it to be brought to you. WATERMAN, I, p. 337* LETTER i|77 to the King In regard to th© eclipse of the sun, of which th® king has written, saying, "Will It take place or will It not take place? Send a definite reply," the eclipse of the rm as well as that of the mon does not occur at my oermnd. ev* Th® sign Is not clear and I am cast down. I do not understand it. Row because of the (period of) the month, a watch of the sun is (kept) and the king (is concerned) about it, and I have sent to the king regarding It, saying, "Let the king consider also, how it is and how it la not." WATERMAN, I, p. 355. LETTER 306 Ashipa to King Ashurbanipal (?) ?,0V* With respect to the straw of which the king my lord has written, in the month Tammuz a heavy rain fell (and) the second officer (and) aTi Bw city rulers came down. Straw was laid down and wine was set forth. As much as there was they gave (to them). WATERMAN, I, pp. 359, 3&1. LETTER 51U Bel(?)iddina to the King * • • SS, W lord ha8 showQ ^avor to his servant, saying, "Before Sin the rites a socond time on this day I aa to perform," on the morrow I shall complete (them). A sacrificial lamb without blemish before Sin I shall bring, for the king my lord I shall pray. 6 WATERMAN, I, p. $65. LETTER $19 Ishtarshuneresh to King Esarhaddon Wen Mars on its return course from the head of Leo passes over Cancer and Gemini, this is its signification: End of the rule of the king of Araurru. This (also) is not of a definite series. It is unfavorable. It signifies* Since recently the location of the position of Mars has changed, that indicates evil. Since it has completely changed its later position, its significance cannot be otherwise. And with respect to Jupiter, when it Is thus, if it turns aside clearly from the breast of Leo, (and) passes away from this, in the series it is written* "When Jupiter advances on Regulus and has put (?) him behind-—or as Regulus advances on him and. has put him in his broadest part, (and) stands with him, so another will rise up and kill the king, and seize the throne. This signifies* Since recently the location of the position of Jupiter has changeT/it indicates evil. Since it has completely changed its later position, Its significance cannot be otherwise. In case there be a servant of the king (who speaks) concerning this, that it Is naught, then as for me, declare before the king ray lord* Saturn is clone favorable this month but (even this) is not completely so. And regarding that which the king ray lord has written, saying, "Watch in order that no evil take place," so I keep watch. Whatever it is (that happens) I shall send to the king my lord. WATERMAN, I, p. UOl. LETTER 565 to the King Jupiter stands behind the moon. This is its signification* stands behind the moon, there will be hostility Tn the land. When Jhpiter WATERMAN, I, p. 109. LETTER 629 Mar-Ishtar to King Esarhaddon This eclipse, which took place In the month Tebet, pertains to the land of Anairru. The king of the land of Amurru will die. His land shall be reduced, a second time It shall be destroyed. An arny will at once be against Ainurru. Whoever speaks to the king ray lord (about) th® land of Amurru or the land of the Hittites or the land of Sutu, or again of the land of Chaldea, whoever brings to the king ny lord this sign against the kings of the land of the Hittites or the land of Chaldea ReVw or the land of Aribi, It it well. The king my lord shall attain his wish. WATERMAN, I, p. 1+57. LETTER 657 Adadshunaisur to King AahurbanipaL As for the eclipse of the sun, it did not take place> It is over. The planet Venus la approaching the constellation Virgo. The appearance of the planet Mercury is approaching. Great wrath will come. Adad has opened his mouth. May tho king my lord know. 7 WATERMAN, I, p. I465. LETTER 671 Ishtarshumeresh to King Ashurbonipal On the twenty-ninth day we kept eVo the watch# We did not see the moon# (Dated) the second day of the month Tammuz in the eponym year of Belshunu, governor of the city of Hindanu. WATERMAN, I, pp# 1|69* LETTER 679 Akkullam to King Esarhaddon The piftge'k ^ars has ontered the path of Enlil# It was observed at the feet of Gemini. Y€ appeared faint# It was high. On the twenty-sixth day of Iyyar I observed until it was high, thereupon I sent its signification to the king my lord. As for the planet Mars, when Gemini approaches there will be war in Amurru, brother will"" slay hl s' '"brother la the palace# WATERMAN, I, p# U73* LETTER 687 Balasi to King Esarhaddon Hev. ja to the watch of the sun, of which the king my lord has written, It is (now) the month of the watch of the sun# On the second there is its watch# On the twenty-sixth day of Marcheshvan (and) on the twenty-sixth day of Kisleu we shall keep the watch# Accordingly we shall keep the watch of the sun for two months. WATERMAN, II, p. 21. LETTER 7hU Mar-Ishtar to King Ashurbauipal On the twenty-seventh day the moon disappears# On the twenty-eighth, twenty-ninth, (and) thirtieth days we kept the watch of the eclipse of the sun# It passed by, the eclipse did not take place. On the first day the moon appears, the (opening) day of the month Tammuz is fixed# In regard to Jupiter, of which formerly I wrote to the king my lord, saying, ”It appears in th© path of Rev* Am, In the region of the star Sibziama, it is low In the haze (?); I do not understand it,” they spoke, saying, wIt is in the path of Am, Its signification I shall send to the king my lord.” Nw it Is lifted up, it Is understood, it stands below the constellation of th© Chariot in the path of Mill# In relation to the Chariot, it la surely cast down# Its signification I have completed, but the signification of Jupiter, which is in the oath of Am, about which I wrote earlier to the king my lord, I have not completed# Hay the king my lord know. WATERMAN, II, p# 37- LETTER 765 Belnasir to the King In regard to the watch of the moon, there was no eclipse. On the eighteenth day an eclipse of the sun took place# In the eighth monBTTEere vail be an TintffiTfflHfi-ji.- r^KWnanmwnMi T-j.rr. iWitii#wr.tr WS eclipse of the moon# 8 wmmii, ii, p. 73. LETTER 816 Nabushumiddln to the Planter On the fourteenth day the watch of Sin we kept. Rev* The eclipse of the moon took place• waterman, il, p. 75. LETTER 818 Nabua to the King The watch we have kept. On the fourteenth day the moon and sun appeared together. WATERMAN, II, p. 75. LETTER 821 Nabua to the King On the thirteenth day we kept the watch. At the same time that a cloud covered the sun, a cloucT likewise covered the moon. Onthe~ f c^rtcwntK TaTwon and sun were seen together. WATERMAN, II, p. 75 LETTER 822 Nabua to the King Be kept the watch on the thirteenth day, when the moon and sun appeared together. WATERMAN, II, p. 75- LETTER 82J Nabua to the King On the twelfth day we kept the watch. On the thirteenth day moon and sun appeared together. WATERMAN, II, p. 77* LETTER 386 Nabua to the King On the thirteenth day (and) the fourteenth day, we kept the watch, On the fifteenth day moon (and) sun appeared together. WATERMAN, II, p. 77* LETTER 827 Nabua to the King On the twenty-ninth day we kept the watch. We saw the moon. 9 WATERMAN, II, p. 77* LETTER 829 Ishtaraadinaplu to King Ashurb&nipal To the king rny lord, your servant Ishtaraadinaplu, the chief of the shrine of the scribes of Arbela. Fay it be well with the king my lord, May Habu, Marduk, (and) Ishtar of Arbela be gracious to the king my lord. On the tvmnty-ninth day ' ev* we kept the watch. On account of the appearance of a cloud, we did not see the moon. First day of the month Shebat, eponym year of Belharrenshadua. WATERMAN, II, p. 87* LETTER 8l|2 Ahulu... to the King ... On the fifth day of second Adar I shall go forth from Itar-Sharrukln. Before the month Nisan, the face of the king may I see (?). WATERMAN, II, p. 105. LETTER 869 ......... to the King Regarding that which the king my lord has written, this night in the morning watch (is) its watch. The eclipse will take place in the morning watch. WATERMAN, II, p. 113- LETTER 881 Baushumiddin to the King In regard to the watch, of which the king ny lord hat written, as for the toon, the eclipse was not seen. As for the watch, cause an order to com® up ev* from the king ay lordj let them proclaim it. On the fifteenth day, god will be seen with god. WATERMAN, II, p. 123* LETTER 89U Adadshumusur to King Esarhaddon I saw the moon on the thirtieth dayj it was high. When on the thirtieth day, directly it is high, according as it continues on the second day, if it is pleasing before the king ny lord, ”ov* let the king wait before the city of Asshur, and thereupon lot the king my lord establish the day. Accordingly the king my lord (will speak), saying, "Why do you not observe, thereupon I .... to ...... the scribe ...... the dominion .... days ..... bet ore ....... to *•»*.. WATERMAN, II, pp. 123, 125. LETTERS 895 Belushezib to King Ashurbanipal Rev. gxgng and the officials, the sign of the eclipse. In the month Adar and in the month Nisan it cam®. I have reported everything to the king my lord and although (?) the king has not abandoned the freeing incantations from the eclipse, which are perfowned in order offset any sin whatever, the 10 great gods who dwell in the city of the king ny lord overcast the sky and did not permit (me) to see the eclipse, May the king mjr lord know that this eclipse is not against the king my lord nor his land, May the king rejoice. In the month Mean, Adad upholds peace. The grain, to be grown, will not be reduced. WATERMAN, II, p. 16?. LETTER 956 In regard to the duration of the year of which the king spoke, saying, ”The month Siu 1 decided (?) tho dividing (?) ...TT.T^Ke king my lord in regaru to Rcv* ••••••«..• knows the . • • day of the month Taskritu, the man wEo 1Is weak will clothe himself, On the eighthcay the gate of according as the month Shebat ««»••«• the way was seen (?) «• • • * of Dur .. • • • when Anu and ... what • • • • • let the king ay lord decide. From the hands of MarJulcaharusur and the bo^-»guard official seek a inistworthy man. He" .r.. • the smith •••«•*• WATERMAN, II, p. 181. LETTER 976 to King Ashurbenipal (?) To Darisharru, to to Aradilu, to Kisir-Atshur, to let the king my lord promulgate the command. We have come, let them out (?) their hands to the task. Unto the shepherd of the sacrificial iamhs of the "city of he will accomplish nothing ••*«« The king my lord knows how their hands one day the people ,,,* Fev. abode (?). WATERMAN, II, pp. 197, 199. LETTER 1006 Mannabite to King Ashurbanipal The report of the eclipse I have not caused the king my lord to hear from my own lips? I have, however, written instead (and) sent it to the king iiy lord. Regarding the eclipse, its evil up to the very month, day, watch, end exact point where it began and where the moon pulled and drew off its eclipse—these pertain to its evil. The month Sivan is Amurru and a decision is given to Ur. Its evil (applies to) the fourteenth day, of which they declare 1 ”The fourteenth day is Elam.” The exact point where it began we do not know, the area of its eclipse drew off toward the southwest. It is evil for Elam and Amurru. From th© east and north, according as it is bright, it is propitious for Subartum and Akkad. One says of it that it augurs favorably. • • • omen is favorable and the heart of the king my lord may be of good cheer. Jupiter stands in the eclipse? it signifies peace for th© king? his name will be honorable and unique ..... 11 WATERMAK, II, p. 207. LETTER 1015 Tabsilesharra (?) to King Sargon (?) To king BL *ord» yo**** servant «••••••• May It be well with the king qy lord.“*lday Ashur luesTTlnlil Ke gracious to the king ry^lord. In regarT to Ihe ravens, of which tlw king iiy lord “Kas written, saying, "SentT^en We ravens Tarry (?) help Is destroyed” «•• (?) he is proud (?), saying, at the appointed time his rebellion will go forth for him. Since a letter from the palace hag not come to me', I gent by ••••• the city ....... a report the ravens ....... help is destroyed. He is proud(?), saying, wAt KKe appointed time IT wil l go forth for him, will Ke not cause him to revolt? WATERMAN, II, p. 21+3 • LETTER 1069 ••••••• We have observed. Regarding the moon*3 halo I have written to the king my lord. In regard to the watch or the eclipse of the moon, of which the king ry lord has written .... its watch • •••• Belerlba......of the sun is large ®eVt ....... words ...... these ••• proceeded • ••• the months .... its watch now of the month Klsleu we keep, for th© watch •••«••• WATERMAN, II, p. 251. LETTER 1080 the earth quaked ...... its interpretation is after this fashion* When the earth quakes In the month Sivan, the overthrown ruin sites shall be inhabited, R0V# by the word of Eni11. Regarding the eclipse, when it Is evil, let them seek, let them remove, let whoever goes into Nineveh .........* • In order that they may lift up (?) ••*«••• WATERMAN, II, p. 255. LETTER 1087 •••«•••*• to the King The lambs continually (?) which the king uy lord, for the temples, gathered in on© flock (?J,' to'The'city of laru ............... Rev* not •***••• in the palace ...... saying, "A woman .... I spoke (?) «••••• and went (?) • •••• now saying ..... WATERMAN, II, pp. 255, 257. LETTER 1089 to King Ashurbanipal . • • Our hands are lifted up Rov< toward the king our lord. In the present month I^yar let the king our lord send us troops for campaigning, and the land to that of the king will turn end we your servants shall live. Many peoples set their faces against the king their lord, but they give hood to the troops of the king, to the campaigning of the troopsj and may the king our lord and his army quiet the confusion end bloodshed. The land of the Pukudu and the Gurasimmu will wait upon the welfare of the king our lord 12 WATERMAN# II, pp. 269, 271 LETTER 1106 Nabuushabshi (?) to King Ashurbanlpal • • « And the king rry lord well knows, since the king gave the Sealand to Nebuchadressar my brother. This is not well pleasing to Belibni the heir of Nebuchadrezzar. He hates us for this reason. He speaks abusive words. The king should not give heed to the words of his mouth.......a man, they connect with Nebuchadrezzar, as a servant they fear *•••# of the father of the king in Uruk they seise him .... his word (?) extend. Now ............ the chief of the store- house of the Sealand • •••. his face before the king ..••••••• with me a word WATERMAN# II, p. 275 LETTER 1115 ......... to the King The king lord has sent, saying, "The planet Mars has been observed. Why have you hoireported?1*' * The plaasv ^ars is visible in the month Ab, behold it is with the constellation Libra. At the left it is dark. It is approaching. Rov* When it draws near it# I shall send its omen to the king my lord. That which is now seen is th® planet Mercury in the constellation Capricorn. Regarding Mars ....... WATERMAN, II, pp. 291, 293- UTTER lljU to the King ..... one life of the evening against When a star on any day, this the land will have an enemy ....... the twenty-ninth day of the month Iyyar from .... this word until the ... day whenever this is established ..... of Shamash is fallen. According to this is its interpretation........ • and you know • •. • • I do not know • • • • • the kingof the land, Shamash with him The king fears the king of Akkad .... the flesh of (?) his life that is cast down (?), as we hear •••••• is not. He has spoken of the failing of the brightness# saying, ttIs it not an eclipse, and the failing of th© brightness of the eclipse is extreme. Ita sign is ReVe exceedingly unfavorable. Mars is inclosed in the constellation Capricorn. It is brilliant (?)• The brightness is great, it is lifted up. According to this Is its interpretation .... The constellation Capricorn •••**» Is favorable. WATERMAN, II, p. 295* The watch we LETTER 1157 Nabua to the King On the fifteenth day the sun end moon appeared together. 13 WATEW-H, II, pp. 295, 897- LETTER llhO • to the Fing propitious • •••• the gods they fear • •••• propitious* Th© favorable days of which the king (I) lord has spoken, (are) the tenth, the fifteenth, the sixteenth, the eighteenth, the twentieth, the twenty-second, the twenty-fourth, (and) "ev* the twenty-sixth, a total of eight days of the month of Iyyar—^whieh are propitious for making requests (and) reverencing the deity. (Of these,) th© tenth day is favorable for judgment, the fifteenth day (for) carrying out an attack, the sixteenth day (for) rejoicing the heart, the eighteenth day (for) interpreting the futures?), the twentieth day let him slay a serpent (?), th® twenty-second day one may make a journey, the twenty-fourth day is good (?) for making (?) a request (?) ......... WATERMAN, II, p. 505. LETTER 1156 to the King On the twenty-ninth day we kept the watch* Rev> We observed the moon. WATERMAW, II, pp. 509, 311• LETTER 1168 • • • which I seised ««.,« day, the sixth day, the .... day, the thirteenth day, the ... day, the thirteenth day, •••«••• day, the twenty-fourth day, the ... day, the thirtieth day are favorable. These favorable days •••••. a rest day • *••••• let him write, we have don© it ...... which we do now (?) and my god .»..«••• WATERMAN, II, p. $27. LETTER 1195 to King Ashurbanipal The message is as follows: Tammaritl, king of Elam, his men •••• will they make a raid,a vicious attack upon the territory of Assyria? Is the message true (and) reliable? •••*•« From this day, the first day of this month Adar, of this year unto the first day of the coming month •••••. of the current year, will the men with Tansnarlti, king of Elam, advance to make war with battle end defeat .... will they cone for a raid, for a vicious attack upon the territory of Assyria or upon Nippur? WATERMAN, II, p. 329. LETTER 1197 •••«.*«•• to the King • «*«...* from • «••• of the city of • ar® established. The month Iyyar, the sixth day Adad drew near, In th® festal house he dwelt. The kalu priest rests. Kev* Regarding that which the king my lord • •••• Adad ..... in his house 1U WFWI, II, p. 5U1- LETTER 1214 ........ to King Sennacherib (?) In the south Ta®au&, on the night of the tenth day, the constellation Scorpio approaches the moon. Its signification is as follows* Whan* at the appearance of the moon, the constellation Scorpio stands within its right horn, in this year locusts will swam, they will eat up the harvest. Regarding the jTng of Elam, in that year they will kill him. Ms reign will come to an end. An enery will attack and plunder in the midst of his lend* For the king of Akkad they Tavis lifted up, his reign will be long, as for the ene ry who attacks him, the fell of his ener.y will take place. In the month Tashritu on the Wnth day, the planet Venus will stand In the constellation UR-GAB. WATERMAN, II, p. ^>5* LETTER 1285 ***** to King Ashurbanipal (?) • • ♦ May Bhamash, the light of heaven and earth, fix his attention to judge your faithfulness* WATERMAN, H, p. h09. LETTER 1505 ..... * .... unto him they restore. If he does not make an uprising against him, proceed (?). In the middle of the month Shebat do you raise it up. WATERMAN, XI, p. U57* LETTER 1575 Belushezib to King Ashurbanipal(?) When the moon appears on the first day, the word is established, the heart of the land will be of good cheer, '.hen the day according to its measure is long, there will be a reign of far extendeddays. When the moon at its appearance rreers a crown, the king will core to his supremacy. WATERMAN, II, p. W* LETTER 1583 Nabuaherlba to King Esarhaddon • . . The (present) month is favorable. This day is favorable. The planet Mercury the crown prince ...... with the star ......... appears, when the planet Venus appears in (?) Babylon, the moon in the month Nisan, on any day It does not draw near, at W© same time, it is favorable. TUTERMAW, II, p. U73- LETTER 1591 When Shanamma str-mds before (or) approaches Bel, the heart of the land will be satisfied* Shanamma is Mars* There is favor for the king my lord* When Mars culminates dimly and its brilliance becomes pale, in that year the king of Elam will be your servant. When Nergal becomes small and white in appearance, (and) like a star of heaven becomes especially dim, he will have mercy on Akkad* The forces of my army will stand and slay the enemy. The army of the enery will not be able to stand before ny amy. The cattle of Akkad will lie down securely in the fields* Sesame and dates will prosper* The gods will show mercy to Akkad* When Mars appears In the month Iyyar, the enemy will be the unrighteous Umman-Manda. The Unnan-Kanda are the Cimmerians. MTERWI, II, p. LETTER U1O8 •**«»«♦»»»•»•! ..•••• and the yoke an eclipse of the sun will take place the ••»** day the moon appeared ••••• of the eleventh day **.*•• the moon went forth • «..* the eleventh day • ••.. will be great, the new «•••» of the twelfth day •••«•* the moon arose KGV# the thirteenth (?) day cloudiness prevailed. The whole of the fourteenth the moon did not appear «•••• the night of th© thirteenth day ••*.*•* the moon arose the thirteenth cloudiness prevailed, it did not appear •«•*•••*•* the night of 'tHe"/ourtoenth day *•••• the moon arose, it turned, it did not go down (?) ....... the thirteenth day «•••• before the king he will come (?). watermah, ii, p. 505. LETTER 11M *•*•••*.* to the King ...••••• to the king «•••••• in the glov,- of their (?) ••*•* Sin th© god who brings in hostility is established. In the south it is established. In the south it cleared. On the right it was beclouded. Rev* In the region of the constellation Scorpio It was beclouded* Wen the star KUMARU of the constellation UTU-KA-GAB-A was on the meridian an eclipse two fingers broad took place. WATERMAU, II, p. W• LETTER O .».**.. to the King When (the moon) completes the day In the month Iyyar, on the fifteenth day sun and moon will be seen together. On the thirteenth day (and) the night of th© fourteenth day was the time of the watch, and the eclipse did not take place. One-seventh of the front and side was ’bitten out.’ The eclipse did not take place* A word of decision Y have sent to the king* 16 watermo, n, p. 519* LETTER II466 *•««»••«• to King Sargon On the thirtieth day of the month Adar I entered. One day (?) •••••• the people of Sibushki #«•* in the land of Wbushki «•«*«•«< •«•*•••«••# we spoke, saying, Sal *••# in the heart of •«•••« house of (?) •«••••••#•* bring# THE VENUS TABLETS OF AMMIZADUGA □64 MA8HMATIKHZ 2YNTASE0S BIBAION A. C II A P I T R E VIL DE I.EPOQUF DFS MOTENS MOUVEMFNS DE LONGITUDE ET d’aNOMAI IF. DE LA LUNE. Vour rEduire ces epoques au midi du premier jour du mois Egyptien Thoth de la premiere annee de Nabonassar, nous avons pris I'intervalle de temps E> oulE de ce jour au milieu de la seconde des trois premieres et plus proclies Eclipses, laquelle est arrivee, commenous l’a-vons dit, la seconde annEe de Mardocem-pad , du 18 au 19 du mois Egyptien de 1 hoth , a 7 et | d'une heure Equinoxiale avant minuit, ce qui fait une espace de 27 amices Egyptiennes 17 jours et 11 7, heures a tres-peu pres , tant simplement qu’exactement; et en rejettant les cir-conferences entjeres , 123d 22' de longitude , et io3d 35' d’anomalie. Si nous retranchons respectivement ces quantiles, des lieux du milieu de la seconde Eclipse, nous aurons pour la premiere annEe de Nabonassar au premier jour du mois Egyptien de Thoth a midi, le lieu moyen de la lune sue nd 22' du taureau en longitude et A 268d 49' d anomalie depuis l apogEe de lepicycle, e’est-a-dire a 70** 37' d’Elongation , le so-lt:l,comme il a EtE prouvE, Eta nt alors sur ou des poissons. KEGAAAION Z. IIEP! THX EIIOXIIX TAN OMAAQN THZ ZEAHNHX KlNHZEnN MHKOrZ TE KAI ANUMAAIAX. Ina Ji TaC ffurwaw- pt&a lij to avTo' TrpwTOE tro< NaCo-taaaapou tear’ Alywriouc a r~; pr~*, tAaCoptt toe tVrivS'iE £po~ ror pt%pi rou pttrau riic J'turtpac txAt<- TtJr TrpurcDV >(cp iyytiTtpwt rpiair, nr if, uc tQaptt , ytyott r£ /turtpai trti MapJ'oKtpTraJou tar' Aiywriouc &ai& in tic tre i0 ‘wpo' c y" piac tvpac iffnptpirnc rot/ ptaotuiriou. Zutaytrai (Of np-tpait 1^ VH atpat drAaic rt dupiCuc ty-yi^o- let r . x.ai 'orapantitrai rtu TOffoura X(>ova> /zi0’ oAouc xt/xAov? tTrovaiac ptn-xouc pit p.dipai pay x(3, draiuaAiac /i palpal py At • de iat diptAaiptt rat it ret ptaa %pota> riic dwriqac exAf/-4««c tTro^ut, txartpat dtp' ixartpac oixnfft^c, t^optrtic roTrparot trof NaCovaaadpou xut’ Go;S- a Tn; pter.p- Pf'ac , it poipac 0 pt. u65 CH A PITRE VIII. COMPOSITION MATH EM A TIQUE, LIVRE IV. KE4>AAA1ON H. nEPi thz AiopenxEnz tan kata fiaatoz ME ZAN TIAPOAAN THZ ZEAHNHZ KAI TAN EIIOXAN AYTAN. T Al /xir ouv rov /bcvtLouf >&j rUc dvu-fxaAiat yrtpiod/xat xirriatif, r&j tri rdf iyro^dt etuTar, did Tut toioutuv i$o-duv auft^naa/utt&a,' iir) dt ru> nard TrAarot , TT^onpor /Uir dixna^Tavopiv avToi avy%puptvai Kara, Tor iTTTrap^ov ru Tviv arAxmr t^axooiaxi; /z»r 7rlr" THKorraxic xarayuerpt/r To'r ‘idiov nuxAov, cDf di <«/' H/uioaxit Tor trc axia< xara/cirpi/r xcrra to iv ra7( av-^uyiaif fxtvov dtfofti/xa. Tovtuv yap u'&ox.ti/utruv , r&f twc TniAiKornrot twc •yxA/aia; rov Ao%ou xuxAou rwc fl’iAx-r»c, oi rar Kara juipot avrUc ixAti-^tuv opoi didovrai. Aa/ucGdvovTtt our diafdatit txAi/TTixa? , i(af diro rov /uvyi&out Tar nard Tout ptiaout Xpdvout i'rrianoTwtuv rat dxpiCtlt Kara TrAaTOt i-w) tou Ao-%ou xuxAou tfapodout , dip' oTrortftou Tar auvdiv^uv tTriAoyi^o/Lttvoi, dia ti Trit a'Trodrdtiyfjitrnt xard T«r ava/zaAiar diaipopat, a7ro Tar axgr€ar iraqoduv rat Trtyodtnat diaxpivovTtt, outu Tat ti iara Tout ptffovt %povout tuv ixAti-4«»» tTTO^dt TOU TTtpiodlXOV TtAaTOUt tupioxopitv, nflif Tx'r ir Ta pitTa^t) %poru jutG’ oAot/t xuxAouc i