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First page of the index to Joseph Scaliger’s De Emendatione Temporum (Frankfort edition, 1593).(Courtesy of the University of Illinois, Urbana, IL.)

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Cambridge University Press978-0-521-88540-9 - Calendrical Calculations, Third EditionNachum Dershowitz and Edward M. ReingoldIndexMore information

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Index

. . . there will be few who will consider the industry, labor, vigils which we havebestowed upon [the index], or the profit and utility that may be gathered from our

labors. For it is the equivalent of a whole book.—Joseph Scaliger: Letter to Isaac Casaubon (January 7, 1604)

It requires more scholarship to make a good index than to write the book that isindexed.

—George Foote Moore: Address at a reception of the HarvardGraduate School of Arts and Sciences (1925)

Function and constant names are given in boldface, and page numbers fora function are of four types: The page with the function definition is shown inboldface. The page with the type description is shown underlined. The page withthe corresponding Lisp code is shown in italics. Pages of other occurrences aregiven in roman.

Names of people are indexed according to the guidelines of The Chicago Manualof Style: The Essential Guide for Writers, Editors, and Publishers, 14th ed., TheUniversity of Chicago Press, Chicago, 1993.

Symbols〈〉 (list construction), 22〈〉[ ] (list element selection), 22� � (ceiling function), xvi, 17� � (floor function), xvi, 17π (pi), xvi| | (absolute value function), xvi|| (list concatenation), 22∑

(summation operator), xvi, 20* (Lisp function), 361+ (Lisp function), 361- (Lisp function), 361/ (Lisp function), 361/= (Lisp relation), 361< (Lisp relation), 361

<= (Lisp relation), 361= (Lisp relation), 361> (Lisp relation), 361>= (Lisp relation), 3611+ (Lisp function), 3621- (Lisp function), 362

Aa.d. (= ante diem), 67Abdali, S. Kamal, 214, 331Abdollahy, Reza, 222Aberration, 189aberration, 189, 189, 342, 400Abraham ben David, 441Absolute value function (| |), xviAbu’l-Faraj, Gregory (= Bar Hebræus), 85

449






450 Index

AccessR , 79A.D. (= Anno Domini), 10Adam, 92Adams, John Quincy, 239adar, 91, 91, 98, 107, 110, 356, 379Adar (Hebrew month), 90, 91, 103, 106–108adarii, 91, 91, 98, 107, 356, 379Adhika month (Hindu calendar), see Leap

months, HinduAdjusted remainder function ( amod ), xvi,

19advent, 59, 59, 342, 372Advent Sunday (Christian holiday), 59, 121Afghan Calendar, 217Africa, 5Afzal, Omar, 331Age

Chinese, 266–267Japanese, 269

A.H. (= Anno Hegiræ), 84Ahargan. a (Hindu calendar), 124Ahmad, Imad ad-Dean, 331Akrami, Musa, 214Al-Azhar University, 328Alaska, 47Albumazar, see Falaki, Abu-Ma’shar al-Alexandria (Egypt), Church of, 113Ali, H. Amir, 282Ali-Ahyaie, Masahallah, 219Almagest, 25, 92, 282alt-fixed-from-gregorian, 54, 54–56, 65,

342, 370alt-gregorian-from-fixed, 55, 55, 65, 342,

370alt-gregorian-year-from-fixed, 56, 56, 342,

370alt-hindu-sunrise, 298, 298, 301–303, 342,

429alt-orthodox-easter, 116, 116, 342, 385A.M.

Anno Martyrum, 74Anno Mundi, 91

a.m. (= ante meridiem), xvamod, 342, 363Amod function, see Adjusted remainder

functionAndhra Pradesh (India), 274Anggara Kasih (Balinese holiday), 160angle, 342, 396angle-from-degrees, 24, 24, 342, 366Angles

representation, 24solar depression, 212

Annunciation (Orthodox holiday), 71Anomaly, 282, 283, 285

lunar, 199, 317solar, 199, 317

A.P. (= Anno Persico or Anno Persarum), 217Apogee, 283, 317apparent-from-local, 184, 184, 326, 342,

397approx-moment-of-depression, 208, 208,

209, 342, 408april, 48, 48, 115, 117, 270, 356, 368Arabian Peninsula, 236Arc of light, 326arccos-degrees, 342, 395arcsin-degrees, 342, 395arctan, 173, 186, 192, 213arctan-degrees, 173, 342, 395Ari the Learned, 80Aries (constellation), 127, 186

first point of, 174, 185, 186arithmetic-french-from-fixed, 243, 243,

342, 417arithmetic-french-leap-year?, 243, 243,

342, 416arithmetic-persian-from-fixed, 224, 224,

342, 412arithmetic-persian-leap-year?, 222, 222,

342, 412arithmetic-persian-year-from-fixed, 224,

224, 342, 412Arithmetical calendars, 45–169, 221–225,

231–233, 242–244Armenian calendar, 5–6, 11, 25–26

days, 5epagomenæ, 26epoch, 15, 25Lisp code, 366–367months, 26sample dates, 441

armenian-date, 342, 366armenian-epoch, 25, 25, 26, 356, 366armenian-from-fixed, 26, 26, 342, 367Arouet, Francois Marie (= Voltaire), 48arya-jovian-period, 125, 125, 126, 356, 386arya-lunar-day, 129, 129, 133, 134, 356,

387arya-lunar-month, 129, 129, 131–134, 356,

387Arya-Siddhanta (First), 126

function definition function type Lisp code








Index 451

arya-solar-month, 126, 126–129, 131–134,356, 386

arya-solar-year, 125, 125–127, 131–133,356, 386

Aryabhat.a, 126Ascension Day (Christian holiday), 119Ascension of ‘Abdu’l-Baha (Bahá’í holiday),

236Ascension of the Baha’u’llah (Bahá’í

holiday), 236Ascensional difference, 293Ash Wednesday (Christian fast), 59, 119, 121‘Ashura’ (Islamic holiday), 87Aslaksen, Helmer, xxv, 265, 272asr, 213, 213, 342, 410Asr (Moslem prayer time), 213Assumption (Christian holiday), 59astro-hindu-calendar-year, 300, 300, 302,

342, 430astro-hindu-lunar-from-fixed, 301, 301,

303, 342, 431astro-hindu-solar-from-fixed, 300, 300,

342, 430astro-hindu-sunset, 300, 300, 301, 342, 430astro-lunar-day-from-moment, 301,

301–303, 342, 431Astronomical calendars, 170–332Astronomical day numbers, see Julian day

numbersAstronomical lunar calendars, 332

classical Hebrew, 329–331Lisp code, 437–439observational Islamic, 328–329

astronomical-easter, 325, 325, 342, 438Astronomy, 171–213, 281–287

Hindu, 281–287Asura Maya, 275A.U.C. (= Ab Urbe Condita), 46, 69auc-year-from-julian-year, 70, 70, 343, 373Audette, Rodolphe, xxvaugust, 48, 48, 74, 76, 146, 270, 356, 368Augustine, Saint (= Aurelius Augustinus),

174autumn, 191, 191, 241, 356, 400av, 90, 90, 104, 356, 379Avanes, Armond, xxvAveni, Anthony F., 150Avron, Haim, xxvayanamsha, 299, 299, 343, 430ayyam-i-ha, 231, 231, 233, 235, 236, 356,

413

Ayyappa Jyothi Darshanam (Hindu holiday),304

Aztec calendar, 11, 29, 30, 138, 145–150, 479Lisp code, 390–392nemontemi, 146sample dates, 441tonalpohualli, 145, 148–149xihuitl, 145–147xiuhmolpilli, 149

aztec-correlation, 146, 146–148, 356, 390aztec-tonalpohualli-correlation, 148,

148–150, 356, 391aztec-tonalpohualli-date, 148, 343, 391aztec-tonalpohualli-from-fixed, 148, 148,

149, 343, 391aztec-tonalpohualli-name, 148, 343, 391aztec-tonalpohualli-number, 148, 343, 391aztec-tonalpohualli-on-or-before, 149, 149,

343, 391aztec-tonalpohualli-ordinal, 148, 148–150,

343, 391aztec-xihuitl-correlation, 147, 147, 150,

356, 390aztec-xihuitl-date, 147, 149, 343, 390aztec-xihuitl-day, 147, 343, 390aztec-xihuitl-from-fixed, 147, 147, 149, 343,

390aztec-xihuitl-month, 147, 149, 343, 390aztec-xihuitl-on-or-before, 147, 147, 149,

343, 391aztec-xihuitl-ordinal, 146, 146, 147, 150,

343, 390aztec-xihuitl-tonalpohualli-on-or-before,

149, 149, 343, 392aztec-xiuhmolpilli-designation, 343, 391aztec-xiuhmolpilli-from-fixed, 149, 149,

343, 391aztec-xiuhmolpilli-name, 343, 391aztec-xiuhmolpilli-number, 343, 391

BBab (= Mirza Ali Muhammad), 228, 229Babylonian calendar, 6Bach, Henri, 479Bahá’í calendar, 6, 11, 182, 229–237

days, 4, 13epoch, 15future, 187, 192, 193, 218, 229,

236–237holidays, 236–237implementation, 231–233







452 Index

leap-year rule, 229Lisp code, 413–415months, 230Near Eastern, 236–237New Year, 236, 237sample dates, 441structure, 229–231weekdays, 229Western, 231–233

Bahá’í New Year, see Feast of Naw-Ruzbahai-cycle, 343, 413bahai-date, 343, 413bahai-day, 343, 413bahai-epoch, 231, 231, 232, 235, 237, 356,

413bahai-from-fixed, 232, 232, 343, 414bahai-major, 343, 413bahai-month, 343, 413bahai-new-year, 236, 236, 343, 415bahai-year, 344, 413Baha’u’llah (= Mirza H. oseyn Ali Nuri), 229Bahula, see Month, dark fortnightBali, 5, 152, 153bali-asatawara, 344, 392bali-asatawara-from-fixed, 155, 158, 158,

344, 393bali-caturwara, 344, 392bali-caturwara-from-fixed, 155, 158, 158,

344, 393bali-dasawara, 344, 393bali-dasawara-from-fixed, 155, 157, 157,

158, 344, 393bali-day-from-fixed, 155, 155, 157–160,

344, 393bali-dwiwara, 344, 392bali-dwiwara-from-fixed, 155, 157, 157,

344, 393bali-epoch, 155, 155, 356, 393bali-luang, 344, 392bali-luang-from-fixed, 155, 158, 158, 344,

393bali-on-or-before, 159, 159, 344, 394bali-pancawara, 159, 344, 392bali-pancawara-from-fixed, 155, 155, 157,

344, 393bali-pawukon-from-fixed, 155, 155, 344,

394bali-sadwara, 159, 344, 392bali-sadwara-from-fixed, 155, 155, 344,

393bali-sangawara, 344, 392

bali-sangawara-from-fixed, 155, 158, 158,344, 393

bali-saptawara, 159, 344, 392bali-saptawara-from-fixed, 155, 155, 157,

344, 393bali-triwara, 344, 392bali-triwara-from-fixed, 155, 155, 344, 393bali-week-from-fixed, 157, 157, 344, 394Balinese Pawukon calendar, 5, 11, 28, 29,

153–161holidays, 155, 159–161Lisp code, 392–394sample dates, 441

balinese-date, 344, 392Balkh (Iran), 216Ball, John A., 60Banaras, see VaranasiBangladesh, 328Bar Hebræus, see Abu’l-Faraj, GregoryBar mitzvah (Jewish event), 105Bar, Kfir, xxvBargeloní, Abraham bar H. iyya al- (=

Savasorda), 89, 92, 111Bat mitzvah (Jewish event), 105B.C. (= Before Christ), 14B.C.E. (= Before the Common Era), 14bce, 344, 372B.E. (= Bahá’í Era), 231Beckwith, Roger T., 120Bede, Venerable, 12, 46, 113, 193Beijing (China), 175, 250–252, 255Belize, 137Beltrami, Olivier, xxvBen-Meir, Aaron, 93Benediktsson, Jakob, 80Bengal (India), 288Berlekamp, Elwyn R., 110, 121Bernal, Ignacio, 150Berzin, Alexander, 315Beyle, Marie-Henri (=Stendhal), 241Bhutan calendar, 315Bible

Daniel, 441Exodus, 91Ezekiel, 166Leviticus, 90Psalms, 4

Bien, Reinhold, 121Bierce, Ambrose, 476Bihar (India), 277binary-search, 21, 344, 364







Index 453

binary-search (binary search macro),364

Birashk, Ahmad, 85, 87, 217–219, 221, 222,225, 227

Birkath ha-H. ama (Jewish event), 105birkath-ha-hama, 105, 105, 344, 382Birth of ‘Abdu’l-Baha (Bahá’í holiday), 236Birth of the Bab (Bahá’í holiday), 236, 237Birth of the Baha’u’llah (Bahá’í holiday),

236, 237Birthday of Krishna (Hindu holiday), 306Birthday of Rama (Hindu holiday), 306, 309Bırunı, Abu-Raih. an Muh. ammad ibn ’Ah. mad

al-, 1, 82, 92, 94, 110, 123, 129,134, 226, 275, 278, 295

Bissextile years, see Leap yearsBissextus (leap day), 66Blackburn, Bonnie, 41, 71Bloch, Abraham P., 447Blue moon, 195Bodde, Derk, 273bogus, 102, 144, 145, 149, 208–212, 266,

342–346, 352–355, 357, 362, 446Bohras, 85Bolshevik Revolution, 47Bonaparte, Louis Napoleon (= Napoleon

III), 239Bonaparte, Napoleon, 239Boncompagni, Ugo, see Gregory XIII, PopeBornstein, H. ayyim Y., 89, 111Bowditch, Charles P., 150Brady, John, 244Brainerd, George W., 150Bramsen, William, 272Brand, Stewart, 324Braude, Morris, 9Bredon; Juliet, 272Bresenham, Jack E., 32Bretagnon, Pierre, 214Brewer, David, xxiBrisson, James F., 479Bromberg, Irvin L., xxv, 96Browne, Gerald M., xxvBrownfield, Marla, xxvBuda-Cemeng (Balinese holiday), 160Buda-Keliwon (Balinese holiday), 160Buddha’s Birthday (Buddhist holiday), 264,

306, 321Buddha’s Descent (Buddhist holiday), 322Buddha’s Enlightenment (Buddhist holiday),

322

Building of the Cross (Coptic holiday), 77Burgess, Ebenezer, 282, 312Burgess, James, 134, 312Burnaby, Sherrard B., 87, 111Bushwick, Nathan, 111

CC (computer language), 18, 19, 40, 365C++ (computer language), 18, 19, 40, 365Caching, 40Cæsar, Julius, 46, 62, 69Cæsarea (Israel), 46Cairo (Egypt), 328Cajori, Florian, 112Calendar

Afghan, 217arithmetical, 45–169, 221–225,

231–233, 242–244Armenian, 5–6, 11, 15, 25–26astronomical, 170–332

lunar, 325–332Aztec, 11, 29, 30, 138, 145–150, 479

tonalpohualli, 145, 148–149xihuitl, 145–147xiuhmolpilli, 149

Babylonian, 6Bahá’í, 4, 6, 11, 15, 182, 229–237

future, 187, 192, 193, 218, 229,236–237

Near Eastern, 236–237Western, 231–233

Balinese Pawukon, 5, 11, 28, 29,153–161

Bhutan, 315Chinese, xxii, 5–7, 11, 15, 28, 30–32,

89, 182, 187, 193, 195, 207,247–273, 275, 299, 316, 333–334

Coptic, 6, 7, 9–11, 15, 73–77, 105,164–165, 217

diurnal, 4ecclesiastical, 113–121Egyptian, 6, 7, 10, 11, 15, 24–25, 140Ethiopic, 6, 7, 9–11, 15, 75–76, 217French Revolutionary, xxii, 4, 6, 7, 10,

11, 15, 182, 207, 239–244modified, 242–244original, 187, 192, 193, 239–242

Generic cyclical, 163–168Gregorian, xx, 1, 6, 7, 10, 11, 15, 16,

45–61, 70, 94–95, 104, 233, 234,275







454 Index

Hebrew, 1, 4, 6, 7, 10, 11, 15, 89–112,123, 182, 207

classical, 326, 329–331Hindu, xxii, 6, 10, 11, 15, 28, 89,

123–135, 182, 185, 186, 195, 207,247, 255, 275–313, 315

modern, 7, 182, 185, 195, 275–313old, 7, 123–135, 275, 277, 289

Icelandic, 80Islamic, 4, 6, 7, 10, 11, 15, 83–87, 89,

102, 182, 217, 222, 275observational, 11, 86, 328–329

ISO, 6, 11, 15, 79–81Jalalı, 217Japanese, 268–269Julian, 6, 7, 9–11, 15, 48, 57, 63–71,

105, 217, 479revised, 47, 70

Karaite, 329Korean, 269–271lunar, 6, 326–329lunisolar, 6, 35, 329–331Mayan, xxii, 10, 11, 15, 28, 29, 137–151

haab, 139–142, 144–145, 147long count, 138–139round, 144–145, 149tzolkin, 5, 30–31, 142–145, 148

Mongolian, 315Native American, 6, 239Nepali, 277Persian, 6, 7, 9–11, 15, 217–227

arithmetic, 221–225astronomical, 182, 187, 192, 193,

219–221Roman nomenclature, 11, 65–69Sherpa, 315solar, 6, 236taxonomy, 4–9Tibetan, 6, 10, 12, 15, 315–322Tsurphu, 315Vietnamese, 271–272Zoroastrian, 15, 26, 217

Casaubon, Isaac, 449Caso, Alfonso, 150Cassini, Jacques, 46Catholic Church, 121C.E. (= Common Era), 10ce, 344, 372Ceiling function (� �), xvi, 17cfs-alert, 211, 211Chaıne, Marius, 77

Chakravarty, Apurba K., 312Chamberlain, Basil H., 268Chandramana Ugadi, see New Year, Hindu

lunisolarChandran, Sharat, xxvChatterjee, S. K., 312Chaturvedi, Anoop, xxvChen, Jiujin, 272Chen, Shigang, xxvChesterfield, Earl of, see Stanhope, Philip D.China, see also Beijing, Nanjing, Shanxı,

and Xıan, 247, 268Chinese calendar, xxii, 5–7, 11, 28, 30–32,

89, 182, 187, 193, 195, 207,247–273, 316, 333–334

age, 266–267celestial stem names, 260days, 13epoch, 15, 258holidays, 264–266implementation, 258–260Lisp code, 417–423marriage auguries, 267–268misconceptions, 263–264month numbering, 252–258New Year, xxii, 248, 263–264, 266,

271, 332sample dates, 441sexagesimal cycle of names, 260–263solar terms, 248–251structure, 251–252terrestrial branch names, 261

chinese-age, 266, 266, 269, 344, 422chinese-branch, 344, 421chinese-cycle, 345, 417chinese-date, 345, 417chinese-day, 345, 417chinese-day-name-epoch, 262, 262, 357,

422chinese-day-name-on-or-before, 262, 262,

345, 422chinese-epoch, 258, 258–260, 264, 266,

357, 419chinese-from-fixed, 259, 259, 260, 267,

345, 420chinese-leap, 345, 417chinese-location, 248, 248, 250–252, 269,

345, 417chinese-month, 345, 417chinese-month-name-epoch, 262, 262, 357,

421







Index 455

chinese-name, 345, 421chinese-name-difference, 261, 261, 262,

345, 421chinese-name-of-day, 262, 262, 345, 422chinese-name-of-month, 262, 262, 345, 421chinese-name-of-year, 261, 261, 345, 421chinese-new-moon-before, 252, 252, 255,

258, 259, 345, 418chinese-new-moon-on-or-after, 251, 251,

253, 258–260, 345, 418chinese-new-year, 264, 264, 345, 419chinese-new-year-in-sui, 257, 257–259,

345, 419chinese-new-year-on-or-before, 258, 258,

260, 264, 345, 419chinese-no-major-solar-term?, 253, 253,

255, 258, 259, 345, 419chinese-prior-leap-month?, 255, 255, 259,

345, 421chinese-sexagesimal-name, 261, 261, 262,

345, 421chinese-solar-longitude-on-or-after, 250,

250, 251, 271, 345, 418chinese-stem, 345, 421chinese-winter-solstice-on-or-before, 251,

251, 258, 259, 345, 419chinese-year, 345, 417chinese-year-marriage-augury, 267, 267,

345, 422christmas, 59, 59, 345, 371Christmas (Christian holiday), 47, 59, 70–71,

77Christmas Fast (Orthodox fast), 71Cicero, Marcus Tullius, 79Cidenas, 92Clamen, Stewart M., xxv, xxvi, 137classical-passover-eve, 331, 331, 345, 439Clavius, Christopher (= Christoph Clau),

114, 116clock-from-moment, 23, 23, 24, 345, 366COBOL (computer language), xxCody, Aelred, 77Cohn, Berthold, 212, 214Common Lisp, see LispCompline (Christian prayer time), 213cond (Lisp function), 364Conditional expressions, 18Congo, 5Congress of the Orthodox Oriental

Churches, 47, 70Conjunction, see Moon, new

Constantine the Great (= Flavius ValeriusConstantinus), 113

Conversions, time of day of, 12Conway, John H., 110, 121Cook, Michael A., 83Cope, Leona, 41Copeland, Jeffrey L., xxvCopernicus, Nicolaus (= Mikolaj Kopernik),

179Coptic calendar, 6, 7, 9–11, 33, 35, 36, 38,

46, 73–77, 105, 164–165, 217days, 13, 73, 74epagomenæ, 73, 165epoch, 15, 74holidays, 76–77implementation, 74–75leap-year rule, 74Lisp code, 375–376months, 73sample dates, 441structure, 73–74

coptic-christmas, 77, 77, 345, 376coptic-date, 345, 375coptic-epoch, 74, 74–76, 357, 375coptic-from-fixed, 74, 74, 76, 77, 105, 346,

376coptic-in-gregorian, 76, 76, 77, 105, 346,

376coptic-leap-year?, 74, 74, 346, 375Corpus Christi (Christian holiday), 121Corr, Franz, xxvCortés, Hernán, 30, 146cosine-degrees, 346, 395Cox, Nicholas J., xxvCoyne, George V., 60Craun, Edwin D., 42Cross, John, xxvCrossley, John N., 273current-major-solar-term, 248, 248, 253,

346, 417current-minor-solar-term, 250, 250, 268,

346, 418Cycles

of days, 27–30, 367of years, 32–39simultaneous, 5, 30–32, 142–145,

153–161, 261–262Cyprus, 101

D







456 Index

d’Églantine, Fabre (= Philippe FrancoisNazaire Fabre), 239

da Silva, Hezekiah ben David, 94Dabal, Ehssan, xxvDaivajna, Gan. esa, 285Dalai Lama, see Gyatso, TenzinDanki system (Korean calendar), 270Dasra (Hindu holiday), 306Date line, international, 47Dawn, 25, 207–213

astronomical, 212Islamic, 212Jewish, 212sample dates, 441

dawn, 209, 209, 210, 298, 346, 409Day, 4–6, 17, 177, 179–185

Armenian, 5Bahá’í, 13Chinese, 13civil, 207Coptic, 13, 73, 74ecclesiastical, 13Ethiopic, 13, 75expunged, 278, 303, 304, 307, 316French Revolutionary, 4Gregorian, 13, 45, 218Hebrew, 4, 13, 89Hindu, 4, 13, 124, 276intercalated, 278Islamic, 4, 13, 83Julian, 13, 45Korean, 270leap, 49, 64, 66, 278, 281, 289, 290,

303, 316lunar, 129, 133, 134, 278, 286, 290,

298, 303–305, 307, 309nautical, 13of week, determination, 27, 56–57Persian, 13, 26, 218sidereal, 185, 187, 207, 294solar, 174, 177, 185, 187, 294subdivisions, 207tropical, 185

day-number, 52, 52, 346, 370day-of-week-from-fixed, 27, 27, 56, 81, 103,

104, 109, 346, 362Daylight saving, United States, 59daylight-saving-end, 59, 59, 346, 371daylight-saving-start, 59, 59, 346, 371days-in-hebrew-year, 98, 98, 346, 381days-remaining, 52, 52, 346, 370

daytime-temporal-hour, 211, 211, 213, 346,410

de Blois, Francois C., 87, 227de Madariaga, Salvador, 30de Ossorio, Buenaventura Francisco, 112de Santillana, Giorgio, 258december, 48, 48, 50, 59, 64, 71, 80, 316,

357, 368Deckers, Michael H., xxv, xxvii, 54Declaration of the Bab (Bahá’í holiday),

236, 237Declercq, Georges, 121Declination, 174, 186declination, 186, 186, 205, 209, 213, 346,

400defconstant (Lisp construct), 361Deferent, 282, 283, 285defun (Lisp construct), 362deg, 346, 395degrees, 346, 395degrees-from-radians, 346, 395degrees-minutes-seconds, 346, 396Delrina Technology, xxiDeo, Narsingh, 42, 61Depression angles, 212Dershowitz, Erga, xxvDershowitz, Idan, xxvDershowitz, Nachum, iii, xxvi, 214, 312Deuteronomy Rabbah, 70Dharamsala (India), 315Dickson, Stewart P., 324Dıkshit, S. Bâlkr.ishn. a, 135, 277, 306, 312Diocletian (Roman emperor), 74Dionysian cycle, 115Dionysius Exiguus, 46, 113, 114direction, 173, 173, 346, 396Dirichlet box principle, 253diwali, 308, 308, 346, 434Diwali (Hindu holiday), 306, 308Doggett, LeRoy E., 41, 60, 71, 214, 273Double-ninth Festival (Chinese holiday), 264Douglass, Robert H., xxvDragon Festival (Chinese holiday), 264dragon-festival, 266, 266, 346, 422Dù, Shírán, 273Durga Asht.amı (Hindu holiday), 306Durrani, Muhibullah, 331Dusk, 207–213

astronomical, 212Islamic, 212Jewish, 212







Index 457

dusk, 210, 210, 211, 213, 300, 326, 346, 409Dutka, Jacques, 60dynamical-from-universal, 179, 179, 346,

399

EEarth, 4, 173, 174, 177, 179, 185–187, 193,

195, 282, 283, 294, 317equator, 186orbit, 182, 186

easter, 117, 117, 121, 346, 385Easter (Christian holiday), xxii, 7, 10, 47, 59,

70, 77, 112–121, 325–326astronomical, 117–119, 325–326Gregorian, 116–117Lisp code, 385–386Orthodox, 10, 33, 114–116sample dates, 441

eastern-orthodox-christmas, 71, 71, 346,385

Eccentricity, 197Ecclesiastical calendar, 113–121

days, 13Lisp code, 385–386

Ecliptic, 174, 186, 276, 278Eco, Umberto, 22Edmundson, Munro S., 150E.E. (= Ethiopic Era), 76Egypt, see also Alexandria, Cairo, Medinet

Habu, and Thebes, 5, 24, 328Egyptian calendar, 6, 7, 10, 11, 24–25, 140

epagomenæ, 24epoch, 15, 25Lisp code, 366–367sample dates, 441

egyptian-date, 346, 366egyptian-epoch, 25, 25, 26, 357, 366egyptian-from-fixed, 25, 25, 26, 346, 366eighth (Lisp function), 361Eiseman, Fred B., Jr., 161Eiseman, Margaret, 161Ekholm, Gordon F., 150Election Day (U. S. event), 59election-day, 59, 59, 346, 371elevation, 346, 396Elevation of the Life-giving Cross (Orthodox

holiday), 71Eliyahu ben Shelomo Zalman (= Vilna

Gaon), 212Elkins, James, 41Elongation, 199, 326

elul, 91, 91, 98, 110, 357, 379Emerson, Ralph Waldo, 333end, 346, 365Epacts, 114Epagomenæ

Armenian calendar, 26Coptic calendar, 73, 165Egyptian calendar, 24Persian calendar, 26

Ephemeris, 299ephemeris-correction, 177, 177, 179–181,

346, 398Epicycle, 282, 283, 285, 286, 298, 312epiphany, 59, 59, 346, 372Epiphany (Christian holiday), 59, 71, 77epoch (Lisp constant), 363Epochs, 12, 14

Armenian, 15, 25Bahá’í, 15, 231Chinese, 15, 258Coptic, 15, 74Egyptian, 15, 25Ethiopic, xxii, 15, 76French Revolutionary, 15, 239, 242Gregorian, 15, 48Hebrew, 15, 92, 95Hindu, 15, 123, 124, 284, 288, 289Islamic, 15, 84ISO, 15, 79Julian, 15, 64julian day number, 15Mayan, 15, 138modified julian day number, 15Persian, 15, 217Tibetan, 15, 316Zoroastrian, 15

equal (Lisp relation), 362Equation of center, 283Equation of motion, 286Equation of time, 182–185, 294equation-of-time, 183, 183, 184, 346, 397Equator

celestial, 186Earth, 185

Equinox, 6, 21, 163, 171, 186, 187, 190, 191,300

autumnal, 105, 239, 241dynamical, 187sample dates, 441







458 Index

vernal, 46, 105, 113, 114, 119, 185, 192,217–219, 229, 233, 234, 236, 241,304, 325, 329

EraAlexander, 16Seleucid, 16, 89

Esslemont, John E., 229estimate-prior-solar-longitude, 193, 193,

220, 234, 241, 251, 346, 401Ethiopic calendar, 6, 7, 9–11, 75–76, 217

days, 13, 75epoch, xxii, 15, 76holidays, 77implementation, 76Lisp code, 376months, 75sample dates, 441structure, 75–76

ethiopic-date, 347, 376ethiopic-epoch, 76, 76, 357, 376ethiopic-from-fixed, 76, 76, 347, 376Euclid, 31Europe, 175Eusebius, 46, 113Eve, 92evening, 210, 210, 357, 409evenp (Lisp function), 361Everett, Steven M., 42ExcelR , xxi, 79

FFalaki, Abu-Ma’shar al- (= Albumazar), 216false, 66, 208, 357, 362Fast of the Apostles (Orthodox fast), 121Fast of the Repose of the Virgin Mary

(Orthodox fast), 71Fausett, Donald W., xxvFayyumi, Sa’adia ben Joseph al- (= Sa’adia

Gaon), 89, 93Feast of Naw-Ruz (Bahá’í New Year), 233,

236, 237Feast of Orthodoxy (Orthodox holiday), 121Feast of Rid. van (Bahá’í holiday), 236, 237feast-of-ridvan, 237, 237, 347, 415february, 48, 48, 68, 124, 258, 357, 367Feinstein, Moses, 108Feldman, William M., 111Fienberg, Richard T., 214fifth (Lisp function), 361Filipowski, Herschell, 111final, 347, 364

Finland, 115first (Lisp function), 361first-kday, 58, 58, 59, 347, 371first-quarter, 202, 202, 326, 357, 405Fixed day numbers, 9fixed-from-arithmetic-french, 243, 243,

244, 347, 416fixed-from-arithmetic-persian, 223,

223–226, 347, 412fixed-from-armenian, 25, 25, 347, 366fixed-from-astro-hindu-lunar, 302, 302,

347, 431fixed-from-astro-hindu-solar, 301, 301,

347, 431fixed-from-bahai, 231, 231–233, 347, 413fixed-from-chinese, 260, 260, 266, 267, 347,

420fixed-from-coptic, 74, 74–77, 347, 375fixed-from-egyptian, 25, 25, 347, 366fixed-from-ethiopic, 76, 76, 347, 376fixed-from-french, 242, 242, 347, 416fixed-from-future-bahai, 234, 234, 236,

237, 347, 414fixed-from-gregorian, see also

alt-fixed-from-gregorian, 49,49–53, 55, 57–59, 64, 117, 179,191, 211, 231, 232, 236, 242, 258,264, 266, 270, 316, 347, 368

fixed-from-hebrew, 99, 99–104, 106, 107,110, 331, 347, 381

fixed-from-hindu-fullmoon, 297, 297, 347,429

fixed-from-hindu-lunar, 291, 291, 297, 298,307, 347, 427

fixed-from-hindu-solar, 289, 289, 347, 426fixed-from-islamic, 85, 85–87, 347, 377fixed-from-iso, 80, 80, 347, 377fixed-from-jd, 17, 18, 18, 25, 138, 155, 347,

363fixed-from-julian, 64, 64, 65, 68, 71, 74, 76,

84, 95, 115, 124, 146, 217, 347,372

fixed-from-mayan-long-count, 139, 139,347, 388

fixed-from-mjd, 17, 17, 347, 363fixed-from-moment, 18, 18, 208, 213, 296,

308, 347, 365fixed-from-observational-hebrew, 331,

331, 347, 439fixed-from-observational-islamic, 328,

328, 347, 438







Index 459

fixed-from-old-hindu-lunar, 134, 134, 348,387

fixed-from-old-hindu-solar, 127, 127, 348,386

fixed-from-persian, 220, 220, 221, 226,348, 411

fixed-from-roman, 66, 68, 68, 69, 348, 375fixed-from-tibetan, 317, 317–319, 321, 348,

436Fleet, John F., 134Flesner, Molly, xxvFliegel, Henry F., 60floor (Lisp function), 363Floor function (� �), xvi, 17Flower Festival (Japanese holiday), 266Forsythe, George E., 337Fotheringham, John K., xxvii, 60, 71, 121fourth (Lisp function), 361Fractional part function, 18France, see also Paris, 174Francou, Gérard, 214Frazer, James G., 139Freeman-Grenville, Greville S. P., 87French Revolutionary calendar, xxii, 6, 7, 10,

11, 182, 207, 239–244days, 4decades, 240epoch, 15, 242Lisp code, 416–417modified, 242–244

implementation, 243–244leap year rule, 242–243

months, 240original, 187, 192, 193, 239–242

implementation, 241–242structure, 239–241

sample dates, 441sansculottides, 240

french-date, 348, 416french-epoch, 242, 242, 243, 357, 416french-from-fixed, 242, 242, 348, 416french-new-year-on-or-before, 241, 241,

242, 348, 416friday, 27, 27, 60, 104, 109, 110, 357, 362Friday the Thirteenth, 60Friedlander, Michael, 111Frisch, Christian, 119Fritsche, Hermann P. H., 263, 273full, 202, 202, 326, 357, 405future-bahai-from-fixed, 235, 235, 348, 415

future-bahai-new-year-on-or-before, 234,234–236, 348, 415

GGorke, Winfried, xxvGalloway, Thomas, 41Galungan (Balinese holiday), 160Galungan Days (Balinese period), 161Ganesa Chaturthı (Hindu holiday), 306Gangooly, Phanindralal, 312Ganz, Solomon, 111, 331Gardner, Martin, back cover, 185Gauss, Carl F., xxi, xxvi, 95, 102, 111, 113,

121Gautama Buddha, 264, 306, 321Gcd function, see Greatest common divisor

functionGeertz, Clifford, 153, 159Gelasius, xxviiGeneric cyclical calendars, 163–168

double cycle, 166–167single cycle, 163–166

George, Alan, 337Germany, 47, 119Gezer (Israel), 239Gilbert, Martin, 447Gilbert, William S., 45Gillispie, Charles C., 134, 312Gingerich, Owen, back coverGinzel, Friedrich K., 9, 41, 60, 77GNU Emacs, xix, xxvi, 2, 42Go-Chosun (Korea), 270Godman, Frederick D., 150Goharian, Nazli, xxvGolb, Norman, 111Goldberg, Mayer, xxvGolden number, 114Good Friday (Christian holiday), 59, 119Goodman, John T., 137, 138, 150Goodman-Martinez-Thompson correlation

(Mayan calendar), 137, 138Graetz, Heinrich H., 447Grafton, Anthony T., xxvii, 16, 41Graham, Ronald L., 41Great Britain, see also Greenwich and

London, 47Great Night of Shiva (Hindu holiday), 306,

309Greatest common divisor function, xvi, 19Greaves, John, 14, 85Greece, 70







460 Index

greenwich, 172, 172Greenwich (England), xv, 172, 174, 177, 299Gregorian calendar, xx, 1, 6, 7, 10, 11, 16,

45–61, 70, 94–95, 104, 233, 234,275

adoption of, 47days, 13, 45, 218Easter, 116–117epoch, 15, 48history, 46–47holidays, 57–59implementation, 48–52leap-year rule, 45Lisp code, 367–372months, 45New Year, xx, xxi, 47sample dates, 441structure, 45year, 47–48

Gregorian reform, 45, 47, 114gregorian-date, 348, 367gregorian-date-difference, 52, 52, 178, 179,

348, 369gregorian-epoch, 48, 48–50, 55, 56, 357,

367gregorian-from-fixed, see also

alt-gregorian-from-fixed, 51, 51,53, 60, 67, 348, 369

gregorian-leap-year?, 49, 49, 51, 67, 231,348, 368

gregorian-new-year, 50, 50, 51, 70, 77, 81,86, 106, 108, 179, 271, 304, 306,308, 309, 325, 330, 348, 369

gregorian-year-end, 50, 50, 52, 81, 321,348, 369

gregorian-year-from-fixed, see alsoalt-gregorian-year-from-fixed,50, 50–52, 55, 80, 101–104, 178,179, 226, 232, 237, 250, 264,266, 268, 330, 331, 348, 369

gregorian-year-range, 50, 50, 70, 76, 86,106, 108, 160, 308, 309, 311, 321,348, 369

Gregory XIII, Pope (= Ugo Boncompagni),45, 47

Gregory, Ruth W., 60Guatemala, see also Tikal, 137, 140, 142Guinot, Bernard, 214Guy, Richard K., 110, 121Guyot, Laurent, 238Gyatso, Tenzin (= Dalai Lama), 315

HHaab (Mayan calendar), 139–142, 144–145,

147Hademer, Nathan ben Meir, 479Hai ben Sherira (= Hai Gaon), 89haifa, 234, 234, 357, 415Haifa (Israel), 234, 236H. alaqim (Hebrew calendar), 92, 207Hale, Wayne, xxHalevy, Schulamith C., xxvHalkin, Abraham S., xxviiHalmos, Paul, 17Hamer, Mick, 244Hania (Crete), 336Hannah, Robert, xxviiHanoi (Vietnam), 271Hansch, Michael G., 119H. anukkah (Jewish holiday), 101, 103Harris, Mitchell A., xxv, 41Harvey, Oswald L., 41Haryana (India), 277Hastings, James, 41, 42, 60, 111Heaslet, Maxwell A., 61, 121Hebrew calendar, 1, 6, 7, 10, 11, 33, 35, 36,

89–112, 123, 182, 207bar mitzvah, 105bat mitzvah, 105birthdays, 105–106classical, 326, 329–331days, 4, 13, 89delays, 92–93, 96–98, 100–101epoch, 15, 92, 95history, 89, 93–95holidays and fast days, 101–105implementation, 95–101Karaite, 329leap-year rule, 91Lisp code, 378–385lo iddo rosh, 92, 108, 109molad, 92, 95–97, 479months, 90nah. ala, 105–108New Year, see Rosh ha-Shanahpossible weekdays, 108–110sabbatical year, 91sample dates, 441structure, 90–93week, 89weekdays, 89yahrzeit, 105–108

hebrew-birthday, 106, 106, 348, 383







Index 461

hebrew-birthday-in-gregorian, 106, 106,348, 383

hebrew-calendar-elapsed-days, 96, 96–98,100, 348, 380

hebrew-date, 348, 378hebrew-epoch, 95, 95, 97–99, 101–104, 357,

379hebrew-from-fixed, 99, 99, 106, 108, 331,

348, 381hebrew-leap-year?, 91, 91, 98, 107, 348, 379hebrew-new-year, 98, 98, 99, 348, 380hebrew-sabbatical-year?, 91, 91, 348, 379hebrew-year-length-correction, 97, 97, 98,

348, 380Heilbron, John L., 121Henderson, Helene, 42Henning, Edward, xxv, 315, 322Herran, Nicolas, xxvHerschel, John W. F., 16, 42Hezekiah ben David da Silva, 94Hillel II (= Hillel ben Judah), 89Hillis, W. Daniel, back cover, 324Hindu calendar, xxii, 6, 10, 11, 28, 89,

123–135, 182, 185, 186, 195, 207,247, 255, 275–313

astronomical, 299–303Lisp code, 429–432sample dates, 441

days, 4, 13, 124, 276epoch, 15, 123, 124, 284, 288, 289holidays, xxiv, 303–312karan. as, 312lunisolar, 315, 316

holidays, 304–309Lisp code, 426–427lunar day, 129, 133, 134, 278, 286,

290, 298, 303–305, 309New Year, 133, 285, 305–306sample dates, 441

modern, 7, 182, 185, 195, 275–313alternatives, 295–299expunged day, 278, 303, 304expunged month, 277, 281, 287, 303,

306history, 275implementation, 287–295intercalated day, 278leap day, 278, 289leap month, 277–279, 287, 289, 290,

303, 304, 306, 307Lisp code, 424–435

structure, 275–281naks.atras, 312old, 7, 123–135, 275, 277

history, 123–124leap month, 123, 128, 129Lisp code, 386–388lunisolar, 37–39, 128–134, 167solar, 7, 126–128structure, 123–126

old lunisolarimplementation, 129–134Lisp code, 386–388sample dates, 441structure, 128–129

old solarimplementation, 126–128Lisp code, 386sample dates, 441structure, 126

Panchang, 312solar

holidays, 304Lisp code, 425–426New Year, 126, 304, 305sample dates, 441

tithi, 129, 278, 290, 292, 306, 312yogas, 312

hindu-anomalistic-month, 285, 285, 286,357, 425

hindu-anomalistic-year, 285, 285, 286,294, 295, 357, 425

hindu-arcsin, 283, 283–285, 293, 348, 424hindu-ascensional-difference, 293, 293,

295, 296, 348, 427hindu-calendar-year, 287, 287, 288, 290,

349, 426hindu-creation, 284, 284, 357, 424hindu-daily-motion, 294, 294, 295, 349,

428hindu-date-occur, 307, 307, 308, 349, 433hindu-day-count, 124, 124, 126, 127, 133,

349, 386hindu-epoch, 124, 124, 127, 134, 284, 287,

289, 291, 293, 300–302, 357, 386hindu-equation-of-time, 295, 295, 296,

349, 428hindu-expunged?, 297, 298, 298, 349, 429hindu-fullmoon-from-fixed, 297, 297, 349,

429hindu-locale, 292, 292, 295, 296, 298, 300,

357, 429







462 Index

hindu-lunar-date, 349, 426hindu-lunar-day, 349, 426hindu-lunar-day-at-or-after, 305, 305, 306,

308, 309, 311, 349, 432hindu-lunar-day-from-moment, 286, 286,

290–292, 305, 349, 425hindu-lunar-era, 289, 289–291, 302, 357,

426hindu-lunar-event, 309, 309, 349, 434hindu-lunar-from-fixed, 289, 289, 292,

297, 298, 307–309, 312, 349, 426hindu-lunar-holiday, 308, 308, 349, 434hindu-lunar-leap-day, 349, 426hindu-lunar-leap-month, 349, 426hindu-lunar-longitude, 286, 286, 309, 311,

349, 425hindu-lunar-month, 349, 426hindu-lunar-new-year, 305, 305, 349, 433hindu-lunar-on-or-before?, 307, 307, 349,

433hindu-lunar-phase, 286, 286, 287, 305, 308,

349, 425hindu-lunar-station, 309, 309, 349, 432hindu-lunar-year, 349, 426hindu-mean-position, 284, 284, 285, 294,

295, 349, 424hindu-new-moon, 305hindu-new-moon-before, 287, 287, 290,

349, 425hindu-rising-sign, 294, 294, 349, 428hindu-sidereal-month, 276, 276, 286, 357,

424hindu-sidereal-year, 276, 276, 284, 286,

287, 289, 291, 294, 295, 304, 357,424

hindu-sine, 283, 283, 285, 293–295, 349,424

hindu-sine-table, 282, 282–284, 294, 350,424

hindu-solar-date, 350, 425hindu-solar-era, 288, 288, 289, 300, 301,

357, 425hindu-solar-from-fixed, 288, 288, 350, 425hindu-solar-longitude, 286, 286–288, 291,

293, 304, 311, 350, 425hindu-solar-longitude-at-or-after, 304,

304, 306, 350, 432hindu-solar-sidereal-difference, 294,

294–296, 350, 428hindu-sundial-time, 296, 296, 297, 350, 430

hindu-sunrise, 288–290, 292, 295, 295, seealso alt-hindu-sunrise, 296, 298,305, 306, 309, 350, 429

hindu-sunset, 296, 296, 350, 430hindu-synodic-month, 276, 276, 287, 305,

357, 424hindu-tithi-occur, 308, 308, 309, 350, 434hindu-tropical-longitude, 293, 293, 294,

350, 428hindu-true-position, 285, 285, 286, 350,

424hindu-zodiac, 286, 286–290, 350, 425Hồ Ngọc Đức, 271, 273Hoang, Peter (Pierre), 273, 333Hoffman, Roy E., 331Hoffrichter, Burghart, xxvHohenkerk, Catherine Y., 215Holford-Strevens, Leofranc, 41, 71Holi (Hindu holiday), 306Holidays

Bahá’í, 236–237Balinese, 155, 159–161Chinese, 264–266Christian, 70–71, 113–121, 325–326Coptic, 76–77Easter, 47, 70, 113–121, 325–326Ethiopic, 77Gregorian, 57–59Hindu, xxiv, 303–312Islamic, 86–87Jewish, 101–105, 326, 331Julian, 70–71Korean, 271Orthodox, 70–71, 121Persian, 226Tibetan, 319–322

Hoot, Charles, xxvHoræ temporales, see Hour, temporalHorizon

geometric, 208visible, 210

Hoshana Rabba (Jewish holiday), 92, 102Hoskin, Michael A., 60hour, 350, 365Hour angle, 185Hour, temporal (= seasonal), 92, 207, 211,

306Howse, Derek, 214hr, 350, 395Huángdì (Chinese emperor), 263Hube, Douglas P., 214







Index 463

Hungry Ghosts (Chinese holiday), 264Husain, Muzhar, 86

I‘Id-al-’Ad. h. a (Islamic holiday), 87‘Id-al-Fit.r (Islamic holiday), 87Ides, 65–67ides, 65, 65, 68, 357, 374ides-of-month, 66, 66, 68, 350, 374if (Lisp function), 364Ilyas, Mohammad, 87, 214in-range?, 350, 365Independence Day (U. S. holiday), 57independence-day, 57, 57, 350, 371India, see also Andhra Pradesh, Bengal,

Bihar, Dharamsala, Haryana,Kashmir, Madhya Pradesh,Nadia, Rajasthan, Ujjain, andUttar Pradesh, 6, 85, 122, 123,128, 274, 275, 299, 328

Ingerman, Peter Zilahy, xxvInternational Astronomical Union (IAU), 172International Organization for

Standardization (ISO), 79International Telecommunications Union,

175Interpolation, 282–284, 298interval, 350, 365Inui, Shiho, xxvinvert-angular, 350, 364Iran, see also Isfahan, Khurasan, Shiraz, and

Tehran, 236Ise (Japan), 440Isfahan (Iran), 219Ishigami, Yoshiyasu, xxvIslamic calendar, 6, 7, 10, 11, 33–36, 83–87,

182, 217, 222, 275days, 4, 13, 83, 84, 89epoch, 15, 84holidays, 86–87implementation, 85–86leap-year rule, 85Lisp code, 377–378months, 84New Year, 86, 87, 263observational, 11, 86, 328–329sample dates, 441structure, 83–85week, 83–84

Islamic Shura Council of North America,328

islamic-date, 350, 377islamic-epoch, 84, 84, 85, 329, 357, 377islamic-from-fixed, 85, 85, 86, 350, 378islamic-in-gregorian, 86, 86, 87, 350, 378islamic-leap-year?, 84, 84, 85, 350, 377islamic-locale, 328, 328, 329, 357, 438ISO calendar, 6, 11, 79–81

epoch, 15, 79Lisp code, 376–377sample dates, 441

iso-date, 350, 376iso-day, 350, 377iso-from-fixed, 80, 80, 350, 377iso-long-year?, 81, 81, 350, 377iso-week, 350, 376iso-year, 350, 377Israel, see also Cæsarea, Haifa, Mount

Carmel, and Jerusalem, 93, 105,228, 236, 237

Israel Independence Day, 104Italy, see also Rome, 47iyyar, 90, 90, 98, 104, 357, 378

Jj2000, 179, 179, 185, 196, 197, 357, 397Jacob ben Meir (= Rabbenu Tam), 212Jacobi, Hermann G., 134, 290, 292, 312Jacobson, Howard, xxv, xxvii, 10J.A.D. (= julian astronomical day), 16jaffa, 330, 330, 331, 357, 439Jaffa (Israel), 330Jalalı calendar, 217Janmasht.amı, see Birthday of KrishnaJanson, Svante, xxv, 315, 322january, 48, 48, 50, 59, 65, 178, 191, 270,

357, 367Japan, see also Ise and Tokyo, 5, 268Japanese calendar, 268–269

age, 269eras, 268kigen, 268Lisp code, 423nengo, 268

japanese-location, 268, 268, 269, 350, 423Jaritz, Gerhard, 46JD (= julian day), 16jd-epoch, 17, 17, 357, 362jd-from-fixed, 18, 18, 350, 363jd-from-moment, 17, 17, 18, 350, 363jerusalem, 173, 173, 326, 357, 396







464 Index

Jerusalem (Israel), 70, 92, 94, 96, 103, 172,173, 177, 441, 446

Jesus’s Circumcision (Coptic holiday), 77Jesus’s Transfiguration (Coptic holiday), 77jewish-dusk, 211, 211, 350, 409jewish-morning-end, 213, 213, 350, 410jewish-sabbath-ends, 211, 211, 351, 409Jiéqì (Chinese calendar), 248, 249Jimmu Tenno (Japanese Emperor), 269Johnson, Samuel, xxviJones, William, 303Joshi, Murli Manohar, 123Jovian cycle (Hindu calendar), 125–126, 316jovian-year, 126, 126, 351, 386Julian astronomical day, see Julian day

numbersJulian calendar, 6, 7, 9–11, 14, 33–36, 46, 48,

57, 63–71, 105, 217, 479days, 13, 45epoch, 15, 64history, 46–47holidays, 70–71implementation, 63–65leap-year rule, 63Lisp code, 372–374months, 45revised, 47, 70Roman nomenclature, 65–69sample dates, 441structure, 63

Julian century, 179, 184, 189Julian day numbers, 9, 11, 15–17

modified, 11, 15, 17sample dates, 441

julian-centuries, 179, 179, 183, 186, 189,190, 192, 199, 203, 205, 351, 396

julian-date, 351, 372julian-epoch, 64, 64, 358, 372julian-from-fixed, 64, 64, 65, 69, 70, 351,

373julian-in-gregorian, 70, 70, 71, 351, 373julian-leap-year?, 63, 63–65, 68, 351, 372julian-year-from-auc-year, 69, 69, 351, 373Julius Cæsar, see Cæsar, Juliusjuly, 48, 48, 57, 66, 84, 178, 264, 358, 368june, 48, 48, 358, 368Jupiter, 5, 124, 125, 199, 282Justeson, John S., 150

KKaiss, Daher, xxv

kajeng-keliwon, 160, 160, 351, 394Kajeng-Keliwon (Balinese holiday), 155, 160Kak, Subhash, xxvKalacakra calendar, see Tibetan calendarKalends, 65–67, 69, 70kalends, 65, 65, 68, 69, 358, 374Kaler, James B., 214Kali Yuga (Hindu calendar), 15, 123, 124,

129, 284, 288, 289Kamasan (Bali), 152Kaneko, Hikotaro, 440Kang Xı (Chinese emperor), 332Kantor, Mattis, 92Karaite calendar, 329Karan. a

Hindu, 309–312Tibetan, 319, 320

karana, 309, 309, 310, 351, 434Karthikai Deepam (Hindu holiday), 306Kasher, Menahem M., 111Kashmir (India), 277Kazoe doshi (Japanese age), 269kday-after, 29, 29, 58, 115–117, 325, 351,

367kday-before, 29, 29, 58, 104, 351, 367kday-nearest, 29, 29, 59, 351, 367kday-on-or-after, 29, 29, 60, 312, 351, 367kday-on-or-before, 27, 27, 29, 262, 351, 367Keiper, Jerry B., 42Kelly, Richard P., xxvKepler, Johannes, xxv, 119, 170, 282Khayyam, Omar, see Omar KhayyamKhinchin, Aleksandr Ya., 42Khowarizmı, Abu Ja‘far Mohammed ibn

Musa al-, 89, 111Khurasan (Persia), 216Kielhorn, Franz, 312Kigen (Japanese calendar), 268Kinkelin, Hermann, 121Kirchner, Claude, xxvkislev, 91, 91, 98, 107, 110, 358, 379Klein, Hyman, 111, 331Klotz, Irene, xxKnuth, Donald E., xxiv, 41, 47, 121, 361Koolish, Richard M., xxvKoran, 83, 328Korea, see also Go-Chosun and Seoul, 269Korea Astronomy Observatory, 272Korean calendar, 269–271

celestial stem names, 270holidays, 271







Index 465

Lisp code, 423solar terms, 270terrestrial branch names, 270

korean-location, 269, 269, 351, 423korean-year, 270, 270, 351, 423Kratesis (Roman festival), 70Kshaya month (Hindu calendar), see Month,

expungedKudlek, Manfred, 161Kull-i-Shay (Bahá’í calendar), 231Kuningan Day (Balinese holiday), 160K.Y. (= Kali Yuga), 124

LLabor Day (U. S. holiday), 58labor-day, 58, 58, 351, 371Lagrenée, Jean-Jacques, the younger, 238Lahiri, Nirmal C., 298Lailat-al-Bara’a (Islamic holiday), 87Lailat-al-Kadr (Islamic holiday), 87Lailat-al-Mi‘raj (Islamic holiday), 87Lalla, 126Lamport, Leslie, 60Langermann, Tzvi, 111Lantern Festival (Chinese holiday), 264last-day-of-hebrew-month, 98, 98–100,

351, 381last-kday, 58, 58, 351, 371last-month-of-hebrew-year, 91, 91, 99, 103,

106, 107, 351, 379last-quarter, 202, 202, 358, 405Lata, 275Latitude

celestial, 174, 187terrestrial, 172, 174, 293

latitude, 351, 396Laud (Christian prayer time), 213Lcm function, see Least common multiple

functionLê Thành Lân, 273Leap days

Gregorian, 49Hindu, 278, 281, 289, 290, 303Julian, 49, 64, 66Tibetan, 316

Leap months, 7, 35Chinese, 253–255, 257, 262, 263Hebrew, 90, 91Hindu, 123, 128–133, 277–279, 287,

289, 290, 303, 304, 306, 307Tibetan, 316

Leap seconds, 177Leap years, 7, 32–39

Coptic, 73, 74, 105French Revolutionary, 240, 243Gregorian, xx, 45, 49, 94, 275Hebrew, 90–94, 97, 100, 103, 105–107,

109Islamic, 84Julian, 45, 49, 63, 64Persian, 218, 223

Least common multiple function, xvi, 19Jungmin Lee, xxvLeffler, Jonathan, xxvLeiden (The Netherlands), 162Lent (Christian fast), 121Lerner, Alon, xxvlet* (Lisp construct), 363Levi, Leo, 111, 214Levin, Daniel Z., 214Lı Yăn, 273License, xxviii–xxixLilius, Aloysius (= Luigi Lilio Ghiraldi), 45,

116Line drawing, 32Linnæus, see von Linne, CarlLisp (computer language), xix, xxvi, 2, 42,

361–364, 382, 424, 439list-range, 351, 365Lists, 22–24

concatenation of (||), 22construction of (〈〉), 22element selection (〈〉[ ]), 22empty, 22

Liú Baolín, 247, 273Liu, Chung Laung, 60, 273Lo iddo rosh (Hebrew calendar rule), 92,

108, 109local-from-apparent, 184, 184, 185, 208,

351, 397local-from-standard, 177, 177, 351, 398local-from-universal, 175, 175, 177, 326,

351, 398location, 351, 396Loewinger, Yaaqov, xxvLondon (England), 172, 182, 207Long count (Mayan calendar), 138–139Long Now Foundation, 324long-marheshvan?, 98, 98, 107, 351, 380Longitude

celestial, 174, 186, 187, 276, 278, 282,284, 286, 293







466 Index

lunar, 198, 202, 283, 286, 309, 311, 446sidereal, 186, 191–192solar, 187–193, 195, 202, 234,

248–250, 286, 304, 311, 441, 446terrestrial, 172, 174

longitude, 351, 396losar, 321, 321, 351, 437Losar (Tibetan holiday), 320–321LotusR 1-2-3R , xxiLounsbury, Floyd G., 138, 150Lovering, Joseph, 239Lozowski, Edward P., 214Luang (Balinese calendar), 158Lun, Anthony W.-C., 273Lunar mansions, see Lunar stationsLunar stations, 216, 278, 309lunar-altitude, 203, 203, 205–207, 326, 351,

406lunar-anomaly, 199, 201, 201, 203, 205,

317, 351, 403lunar-diameter, 328, 328, 351, 438lunar-distance, 205, 205–207, 328, 351, 407lunar-elongation, 199, 201, 201, 203, 205,

351, 403lunar-latitude, 202, 202, 204, 205, 326,

351, 405lunar-longitude, 199, 199–201, 204, 352,

404lunar-parallax, 206, 206, 207, 352, 408lunar-phase, 198, 201, 201, 202, 299, 301,

326, 327, 352, 405lunar-phase-at-or-after, 202, 202, 326,

352, 405lunar-phase-at-or-before, 202, 202, 352,

405Lunation, see Month

MMcCarthy, Daniel P., 46McCarthy, Dennis D., 214Macler, Frédéric, 42Madhya Pradesh (India), 277Maha Shivaratri, see Great Night of ShivaMahler, Eduard, 87Maimonides, Moses (= Rambam), xix, xxvii,

89, 92, 95, 111, 212, 331Main, Andrew, xxvmajor-solar-term-on-or-after, 250, 250,

352, 418march, 48, 48, 51, 55, 57, 59, 65, 66, 68, 217,

231, 232, 236, 266, 270, 358, 367

Mardi Gras (Christian holiday), 119marheshvan, 91, 91, 98, 107, 110, 358, 379Marriage auguries (Chinese calendar),

267–268Mars, 5, 124, 282Marshack, Alexander, 42Martial (= Marcus Valerius Martialis), 477Martinez-Hernandez, Juan, 137, 138Martyrdom of the Bab (Bahá’í holiday), 236,

237Mary’s Announcement (Coptic holiday), 77Mason, Charles W., 42Matins (Christian prayer time), 213Maundy Thursday (Christian holiday), 119Mawlid an-Nabı (Islamic holiday), 87mawlid-an-nabi, 87, 87, 352, 378MAX, xvi, 20, 99, 198, 318, 319, 364may, 48, 48, 58, 66, 358, 368Mayan calendar, xxii, 10, 11, 28, 29, 137–151

epoch, 15, 138Goodman-Martinez-Thompson

correlation, 137haab, 139–142, 144–145, 147Lisp code, 388–390long count, 138–139New Year, 136round, 144–145, 149sample dates, 441Spinden’s correlation, 138tzolkin, 5, 30–31, 142–145, 148year bearer, 144, 149

mayan-baktun, 352, 388mayan-calendar-round-on-or-after, 145mayan-calendar-round-on-or-before, 145,

145, 352, 390mayan-epoch, 138, 138–140, 142, 358, 388mayan-haab-date, 352, 388mayan-haab-day, 352, 389mayan-haab-epoch, 140, 140–142, 145, 358,

389mayan-haab-from-fixed, 140, 140, 144,

352, 389mayan-haab-month, 352, 389mayan-haab-on-or-before, 141, 141, 144,

352, 389mayan-haab-ordinal, 140, 140, 141, 145,

352, 389mayan-katun, 352, 388mayan-kin, 352, 388mayan-long-count-date, 352, 388







Index 467

mayan-long-count-from-fixed, 139, 139,352, 388

mayan-tun, 352, 388mayan-tzolkin-date, 352, 389mayan-tzolkin-epoch, 142, 142, 144, 145,

358, 389mayan-tzolkin-from-fixed, 142, 142, 144,

352, 389mayan-tzolkin-name, 352, 389mayan-tzolkin-number, 352, 389mayan-tzolkin-on-or-before, 144, 144, 352,

390mayan-tzolkin-ordinal, 142, 144, 144, 145,

352, 389mayan-uinal, 352, 388mayan-year-bearer-from-fixed, 144, 144,

352, 390Mayr, Joachim, 87mean-lunar-longitude, 199, 200, 200, 203,

352, 403mean-sidereal-year, 187, 187, 300–302,

358, 399mean-synodic-month, 193, 193, 196, 198,

201, 202, 258, 259, 327, 329,358, 401

mean-tropical-year, 187, 187, 191, 193, 220,235, 242, 259, 260, 358, 399

mecca, 173, 173, 358, 396Mecca (Saudi Arabia), 173, 328Medina (Saudi Arabia), 84Medinet Habu (Egypt), 72Meeus, Jean, 60, 121, 214Meletios IV, 70Melhado, Evan M., 240member (Lisp relation), 361Memoization, 40Memorial Day (U. S. holiday), xxi, 58memorial-day, 58, 58, 352, 371Meng, Zhuo, xxvMercury, 5, 124, 282Meridian, 174, 185

lower, 182upper, 182

Mesha sam. kranti (Hindu Vernal equinox),see New Year, Hindu solar

mesha-samkranti, 300, 304, 304, 352, 433Meton, 7Metonic cycle, 7, 91, 114, 116, 267Metz (France), 479Mexico, 137, 146, 479Mexico City (Mexico), 146, 479

Michels, Agnes K., 41, 60, 71Microsoft, 85

OfficeR , xxiOutlookR , xxiWindowsR , xxi

Mid-Autumn Festival (Chinese holiday), 264midday, 185, 185, 213, 219, 352, 397midday-in-tehran, 219, 219, 220, 352, 411Midnight, 17, 45, 174, 182, 207, 213

civil, 247true (= apparent), 4, 184, 241

midnight, 184, 184, 213, 241, 353, 397midnight-in-china, 250, 251, 251, 252, 353,

419midnight-in-paris, 241, 241, 353, 416Midrash Tanh.uma, xxviiMilankovitch, Milutin, 47Milbrath, Susan, 150Milford-Lutzker, Mary-Ann, 152MIN, xvi, xvii, 20–22, 100, 193, 198, 219,

234, 241, 251, 284, 287–289, 292,301, 303, 307, 327, 364

Mına (Hindu month), 129, 133minor-solar-term-on-or-after, 251, 251,

266, 353, 418minute, 353, 365Mitrophanow, Igor, 272Mizner, Wilson, 42MJD (= modified julian day), 17mjd-epoch, 17, 17, 358, 363mjd-from-fixed, 17, 17, 353, 363mod (Lisp function), 363Modified Julian day numbers, 17

sample dates, 441Modulus function, xvi, 18Mohammed, 82, 84molad, 95, 95–97, 353, 379Molad (Hebrew calendar), see also Moon,

new, 92, 95–97, 109, 479Moment, 10moment-from-jd, 17, 17, 18, 353, 363moment-of-depression, 209, 209, 210, 353,

408monday, 27, 27, 58, 110, 358, 361Mongolian calendar, 315Montezuma II (= Moctezuma Xocoyotzin),

30Month, 4, 6, 193–207

anomalistic, 195Armenian, 26Bahá’í, 230







468 Index

bright fortnight, 129, 277Chinese, 251–258, 262Coptic, 73dark fortnight, 129, 277Ethiopic, 75expunged, 277, 281, 287, 303, 306French Revolutionary, 240Gregorian, 45Hebrew, 90Islamic, 84Korean, 270leap, 7, 35, 91, 123, 129–133, 195,

253–255, 262, 263, 272, 287,289, 303, 304, 306, 316

lunar, 7, 123, 124, 128, 129, 133, 247,248, 252–255, 276–279, 281, 303,315

Persian, 218sidereal, 195, 276, 278, 283solar, 126, 128, 129, 133, 195, 247,

253, 276, 277, 281, 292synodic, 193, 195, 247, 276, 281Tibetan, 315Vietnamese, 272

Moon, 5, 6, 95, 174, 179, 187, 195, 283blue, 195first quarter, 202full, 6, 113–115, 119, 195, 202, 305,

325last quarter, 202new, 6, 86, 91, 92, 95, 96, 114, 123,

128, 129, 137, 171, 193, 195–202,247, 251, 253, 263, 277, 292, 305,329

sample dates, 441Paschal, 115phase, 278visibility, 326–328

moon-node, 199, 201, 201, 203, 205, 353,403

Moore, George F., 449Moreno-Riano, Gerson, 46Morley, Sylvanus G., 150morning, 209, 209, 358, 409Moshe ben Maimon, see Maimonides,

MosesMount Carmel (Israel), 228Moyer, Gordon, 61, 121mt, 353, 395Mumm, Christine, xxv

NNabonassar (Chaldean king), 25Nabonassar era, 25Nadia (India), 303Naga Panchamı (Hindu holiday), 305Nah. ala (Jewish event), 105–108Nakayama, Shigeru, 273Naks.atras, see also Lunar stations

Hindu, 312Tibetan, 319, 320

Nanjing (China), 247Napoleon, see Bonaparte, NapoleonNapoleon III, see Bonaparte, Louis NapoleonNASA, xxNaser El-deen, Nabeel, xxvNational Spiritual Assembly, 233Native American calendar, 6, 239Nativity of the Virgin Mary (Orthodox

holiday), 71Naw Ruz

Bahá’í, 233, 236, 237Persian, 123, 226, 237

naw-ruz, 226, 226, 353, 413Needham, Joseph, 247, 273Negative years, 12–14Nemontemi (Aztec calendar), 146Nengo (Japanese calendar), 268Nepal, 314Nepali calendar, 277Neugebauer, Otto, 24, 42, 111, 331Neumann, Peter G., xxvinew, 202, 202, 326, 358, 405New moon, see Moon, newNew Year

Bahá’í, 234, 236, 237Chinese, xxii, 248, 263–264, 266, 271,

332Gregorian, xx, xxi, 47, 271Hebrew, see Rosh ha-ShanahHindu lunisolar, 133, 285, 305–306Hindu solar, 126, 304, 305Islamic, 86, 87, 263Jewish, see Rosh ha-ShanahKorean, 271Mayan, 136Persian, see Naw RuzTibetan, see Losar

New York City, xxiNew Zealand, xxinew-moon-at-or-after, 198, 198, 251, 302,

353, 403







Index 469

new-moon-before, 198, 198, 252, 302, 353,403

new-year, 39Newton, Isaac, 293next, 353, 364Nián (Chinese calendar), 248Nicæa, Council of, 113–114Nievergelt, Jurg, 42, 61nighttime-temporal-hour, 212, 212, 213,

353, 410nil (Lisp constant), 361, 362ninth (Lisp function), 361nisan, 90, 90, 99, 102, 110, 331, 358, 378Nisan (Hebrew month), 90, 331Nishizawa, Yuso, 273Nizamiah Observatory, 86None (Christian prayer time), 213Nones, 65–67nones, 65, 65, 68, 358, 374nones-of-month, 66, 66, 68, 353, 374Noon, 14, 182, 213, 218, 237

true (= apparent), 184North Pole, 186, 283Norway, 360Nothmann, Gerhard A., xxvnovember, 48, 48, 59, 358, 368nth (Lisp function), 361nth-kday, 58, 58, 59, 79, 80, 353, 371nth-new-moon, 195, 195, 197, 198, 201, 202,

353, 401Numa (= Numa Pompilius), 63Nunavut (Canada), 211Nutation, 187, 189nutation, 189, 189, 199, 353, 398Nyatri Tsenpo, 316Nychthemeron, see DayNyepi (Balinese holiday), 153

OO’Beirne, Thomas H., 119, 121O’Malley, Michael, 214Obermann, Julian, 111, 331Obliquity, 182, 184, 186obliquity, 184, 186, 186, 187, 353, 400observational-hebrew-from-fixed, 330,

330, 353, 439observational-hebrew-new-year, 330, 330,

331, 353, 439observational-islamic-from-fixed, 329,

329, 353, 438october, 48, 48, 66, 95, 358, 368

October Revolution, 47old-hindu-lunar-date, 353, 386old-hindu-lunar-day, 353, 387old-hindu-lunar-from-fixed, 133, 133, 353,

387old-hindu-lunar-leap, 353, 387old-hindu-lunar-leap-year?, 131, 131, 353,

387old-hindu-lunar-month, 353, 387old-hindu-lunar-year, 353, 387old-hindu-solar-from-fixed, 127, 127, 353,

386Olson, Donald W., 214Omar Khayyam, 217omer, 102, 102, 354, 382Omer (Jewish period), 102Ore, Øystein, 42, 150orthodox-easter, see also

alt-orthodox-easter, 115, 115,354, 385

Ottoman Empire, 83

PPakistan, 328Palaioemerologitai, 70Palm Sunday (Christian holiday), 119Panchang (Hindu calendar), 299, 312Parallax, 205paris, 241, 241, 358, 416Paris (France), 174, 175, 238, 239, 241, 441,

446, 479Paris Commune, 239Parise, Frank, xxi, xxvi, 9, 42, 273Parker, Richard A., 42Pascal (computer language), 18Pascal, Blaise, xxviPassion Sunday (Christian holiday), 119passover, 102, 102, 354, 382Passover (Jewish holiday), xxi, xxii, 70, 89,

100–103, 113, 326, 331Pasternak, Ofer, xxvPatashnik, Oren, 41Pawukon (Balinese calendar), 153–161Pedersen, Olaf, 60Pengembang (Balinese holiday), 160pentecost, 121, 121, 354, 386Pentecost (Christian holiday), 119Pepperdine, Andy, xxvPerigee, 195, 317Perihelion, 263, 277Persia, see Iran







470 Index

Persian calendar, 6, 7, 9–11, 33, 217–227arithmetic, 221–225arithmetic leap year rule, 221–223astronomical, 182, 187, 192, 193,

219–221days, 13, 26, 218epagomenæ, 26epoch, 15, 217holidays, 226Lisp code, 411–413months, 218New Year, 226sample dates, 441structure, 217–222week, 218

Persian Gulf, 236persian-date, 354, 411persian-epoch, 217, 217, 220, 223, 226, 358,

411persian-from-fixed, 220, 220, 354, 411persian-new-year-on-or-before, 219, 219,

220, 354, 411Peters, Francis E., 447Peters, Tom, xxvPeterson, Arthur E., 214phasis-on-or-after, 327, 327, 330, 354, 437phasis-on-or-before, 327, 327, 329–331,

354, 437Philippines, 47Phugpa calendar, see Tibetan calendarPhukluk calendar, see Tibetan calendarpi, 358Pigeon-hole principle, 253Pillai, Dewan Bahadur L. D. Swamikannu,

277, 287, 312Pingree, David, 134, 312Pirkei Avoth, 192Pisces (constellation), 186, 276Pleiades (star cluster), 6Plutarch, 69p.m. (= post meridiem), xvPolaris (star), 186poly, 354, 364poly (polynomial evaluation macro), 364Pongal, see Ayyappa Jyothi DarshanamPoole, Robert, 61Portugal, 47Position, 172–174positions-in-range, 160, 160, 354, 394possible-hebrew-days, 109, 109, 110, 354,

384

Poznanski, Samuel A., 111Precession, 185–186, 293precession, 191, 191, 192, 300, 354, 401Presentation of Christ in the Temple

(Orthodox holiday), 71Presentation of the Virgin Mary in the

Temple (Orthodox holiday), 71Pridie (= day before), 66Prime (Christian prayer time), 213Ptolemy (Claudius Ptolmæus), 25, 92, 282Ptolemy III Euergetes, 76Puckett, Barry, 42Purewal, Pal Singh, xxvpurim, 103, 103, 354, 382Purim (Jewish holiday), 103Purple Mountain Observatory (Nanjing),

247, 273

QQibla, 174Qıng dynasty, 207, 247qing-ming, 266, 266, 354, 422Qıngmíng (Chinese solar term/holiday), 266Qıqiao (Chinese holiday), 264Qıxı (Chinese holiday), 264Quadragesima, see LentQuartodecimans, 113Quiché, 140Quinn, Terry J., 214Quintus Curtius Rufus, 217quotient, 354, 363

RRabbenu Tam, see Jacob ben Meirradians-from-degrees, 354, 395Rajasthan (India), 277rama, 309, 309, 354, 434Rama Navamı, see Birthday of RamaRamadan (Islamic fast), 87, 328Ramasubramanian, K., xxvRambam, see Maimonides, MosesRamses III, 72Rashi, see Solomon ben IsaacRata Die, 10R.D. (= Rata Die), 10rd, 11, 11, 354, 362rd (Lisp function), 363Read, Kay, 145, 150Recursion, 40Reese, Ronald L., 42Regulagedda, Akshay, xxv







Index 471

Reingold, Deborah H., xxvReingold, Edward M., iii, xxvi, 41, 42, 61,

214, 227, 312Reingold, Eve M., xxvReingold, Leah S., 471Reingold, Rachel N., xxvReingold, Ruth N., xxvRemainder function, see Modulus functionRepose of the Virgin Mary (Orthodox

holiday), 71Resnikoff, Louis A., 111rest (Lisp function), 361Revatı (star), 276, 279Rhodes, Ida, xxviRichards, Edward G., back cover, 42, 71Richards, Nigel, xxvRickey, V. Frederick, 61Rieb, Jean-Pierre, 479Right ascension, 174, 186right-ascension, 186, 186, 205, 354, 401Roegel, Denis B., xxvRogation Sunday (Christian holiday), 119Rolf, John C., xxviiRolle, Theodore M., xxvRoman calendar

days of the month, 65–69ides, 65–66kalends, 65–66Lisp code, 374–375nones, 65–66pridie, 66sample dates, 441years, 69–70

Roman Republic, 5roman-count, 354, 374roman-date, 354, 374roman-event, 354, 374roman-from-fixed, 66, 68, 68, 354, 374roman-leap, 354, 374roman-month, 354, 374roman-year, 354, 374Rome (Italy), 46, 74Romme, Gilbert, 242Rosh ha-Shanah (Jewish holiday), xxi,

90–93, 98–102, 108Rosh H. odesh (Jewish holiday), 104Roth, Arthur J., xxvRoth, Cecil, 111, 447round, 24Round (Mayan calendar), 144–145, 149Round function, xvi, 18

Routh, Martin, 168Ruggles, Clive L. N., 80Russia, 5, 47, 70

SSa’adia Gaon, see Fayyumi, Sa’adia ben

Joseph al-Sabbath (Jewish), 211Sachau, C. Edward, 110, 123, 134sacred-wednesdays, 311, 311, 354, 435sacred-wednesdays-in-range, 311, 311, 312,

354, 435Sagarin, Jeff, xxvSahillıoglu, Halıl, 83Saka Era (Hindu calendar), 288Sakai, Ko, xxvSalama, Ahmed, 331Salvin, Osbert, 150Sam. kranti (Hindu calendar), 304Samoa, 47Sampson, Russell D., 214Samuel, Alan E., 71Samvatsara, see Jovian cycleSansculottides (French Revolutionary

calendar), 240Sarasvatı (Hindu deity), 306Sarasvatı Puja (Hindu holiday), 306Satterwaite, Linton, 150saturday, 27, 27, 103, 108, 110, 358, 362Saturn, 5, 124, 282Saturnalia (Roman festival), 70Saudi Arabia, see Mecca and Medina, 328Saunders, Robert A., xxvSavasorda, see Bargeloní, Abraham bar

H. iyya al-Savoie, Denis, 214Saw, Swee-Hock, 273Scaliger, Joseph Justus, xxii, xxvii, 0, 16, 62,

63, 90, 162, 448, 449Scaliger, Julius Cæsar, 16Schram, Robert G., 9, 42, 123, 135, 312Schuh, Dieter, 322S.E. (= Saka Era), 288Search, 20–22, 40, 364

bisection, 20–22, 287, 304, 328linear, 20

Season, 191sec, 354, 395second (Lisp function), 361Second Empire (France), 239seconds, 354, 365







472 Index

secs, 354, 396Seidelmann, P. Kenneth, back cover, 41, 60,

71, 214, 215, 273Sengupta, Prabodh C., 312Seoul (Korea), 269september, 48, 48, 58, 242, 358, 368Septuagesima Sunday (Christian holiday),

119, 121Serbia, 70seventh (Lisp function), 361Sewell, Robert, 134, 135, 277, 306, 312Sexagesima Sunday (Christian holiday), 119,

121Sext (Christian prayer time), 213Sh’ela (Jewish event), 105sh-ela, 105, 105, 354, 383Shakespeare, William, 20, 27, 32, 65, 163,

325, 329Shallit, Jeffery O., 61Shanks, Thomas G., 214Shanxı (China), 246Sharma, Shriramana, xxvShaukat, S. Khalid, xxv, 326–328, 331Shavuot (Jewish holiday), 70, 102Shemini Az.eret (Jewish holiday), 102Sherpa calendar, 315shevat, 91, 91, 107, 110, 358, 379shift-days, 109, 109, 354, 385Shiraz (Persia), 228shiva, 309, 309, 354, 434Shiva (Hindu deity), 306short-kislev?, 98, 98, 107, 354, 380Shrove Monday (Christian holiday), 119, 121Shrove Sunday (Christian holiday), 119, 121Shrove Tuesday (Christian holiday), 119, 121Shushan Purim (Jewish holiday), 103sidereal-from-moment, 185, 185, 205, 354,

397sidereal-solar-longitude, 192, 192, 299,

300, 302, 354, 401sidereal-start, 192, 300, 300, 358, 430sidereal-zodiac, 300, 300–302, 355, 430sigma, 355, 364sigma (summation macro), 364Sign function, xvi, 18Signum, 18Simh. at Torah (Jewish holiday), 102Simon, Jean-Louis, 214sin-degrees, 355, 395sine-offset, 208, 209, 209, 355, 408Singer, Isaac Bashevis, 325

Singer, Isidore, 111, 447Sinnott, Roger W., 214Sirius (star), 6Sivakumar, G., xxvsivan, 90, 90, 358, 378Sıvıs year (Ottoman Empire), 83sixth (Lisp function), 361Skeel, Robert D., 42Skiena, Steven S., xxvSlonimski, H. ayyim S., 111Sobel, Dava, 215Sodhya (Hindu calendar), 285Sohn, Sangmo, 269Solar cycle, 105Solar terms

Chinese calendar, 239, 248–251Japanese pronunciation, 248Korean calendar, 270

solar-anomaly, 199, 201, 201, 203, 205,355, 403

solar-longitude, 189, 189–193, 201, 209,213, 219, 234, 241, 248, 250, 251,299, 355, 399

solar-longitude-after, 190, 190, 191, 250,325, 330, 355, 400

Solomon ben Isaac (= Rashi), 185Solstice, 6, 21, 163, 171, 187, 190, 191, 441

sample dates, 441winter, 247, 251, 304

Sornes, Rasmus, 360Sosigenes, 46Soviet Union, 47Sowramana Ugadi, see New Year, Hindu

solarSpain, 47Spectrum (of a real number), 36Spica (star), 276Spier, Arthur, 111Spinden, Herbert J., 137, 138, 150, 151spring, 191, 191, 219, 220, 234, 325, 330,

358, 400Spuler, Bertold, 87Stallman, Richard M., xxvi, 42standard-day, 355, 364, 365standard-from-local, 177, 177, 184, 185,

209, 210, 355, 398standard-from-sundial, 212, 212, 213, 296,

308, 355, 410standard-from-universal, 177, 177, 191,

250–252, 355, 398standard-month, 355, 364, 364







Index 473

standard-year, 355, 364, 365Stanhope, Philip D. (= Fourth Earl of

Chesterfield), xxiv, 171start, 355, 365Stavroulakis, Nicholas, 336Steel, Duncan, 42Steele, Guy L., Jr., xxvi, 42, 439Stein, Michael R., xxvStendhal, see Beyle, Marie-HenriStephenson, F. Richard, 215, 273Stern, Sacha, 89, 111Stewart, Ian, back coverStillingfleet, Benjamin, 240Stolz, Otto, xxvSuddha, see Month, bright fortnightSuì (Chinese calendar), 252Sukkot (Jewish holiday), 70, 102Sullivan, Arthur, 45sum, 355, 363sum (summation macro), 363, 364Summation operator (

∑), xvi, 20, 40

summer, 191, 191, 358, 400Sun, 4, 5, 95, 174, 179, 185–187Sun Yat-sen, 263sunday, 27, 27, 59, 80, 103, 104, 108–110,

115–117, 325, 358, 361Sunrise, 4, 12, 124, 126–129, 134, 138, 182,

207–213, 217, 276, 278, 292–295,298, 305, 309

Hindu, 292–295sample dates, 441

sunrise, 210, 210, 212, 355, 409Sunset, 4, 12, 73, 83, 84, 87, 89, 182,

207–213, 229, 233, 237, 441sample dates, 441

sunset, 210, 210–212, 234, 330, 355, 409sunset-in-haifa, 234, 234, 355, 415Surya-Siddhanta (present), 275, 276, 282,

284, 285, 293, 295, 298, 299,306, 312

Sweden, 44, 47, 79, 119Switzerland, 47

Tt (Lisp constant), 361Ta’anit Esther (Jewish fast), 103ta-anit-esther, 103, 103, 355, 382Taiwan, 16Talmud

Babylonian, 9, 163, 207Jerusalem, 101

Tamerlane (Mongol conqueror), 14tammuz, 90, 90, 98, 358, 378Táng (Chinese dynasty), 246tangent-degrees, 355, 395Tantzen, Robert G., 61Taqizdeh, Seyyid H., 218, 219, 227Tarvainen, Tapani, 47Tasmania, xxitehran, 219, 219, 358, 411Tehran (Iran), 192, 219, 233, 236tenth (Lisp function), 361Terce (Christian prayer time), 213Teresi, Dick, 46tevet, 91, 91, 98, 107, 110, 358, 379Thanksgiving Day

Korean holiday, 271U. S. holiday, xxi, 27

Thebes (Egypt), 72third (Lisp function), 361Thompson, J. Eric S., 136–138, 151Thompson, Sue E., 42thursday, 27, 27, 81, 104, 108, 110, 358, 362Tibetan calendar, 6, 10, 12, 315–322

animal totems, 314, 316epoch, 15, 316expunged day, 316holidays, 319–322karan. as, 319, 320leap day, 316leap month, 316Lisp code, 435–437months, 315naks.atras, 319, 320sample dates, 441weekdays, 316yogas, 319

tibetan-date, 355, 435tibetan-day, 355, 435tibetan-epoch, 316, 316–318, 358, 435tibetan-from-fixed, 318, 318, 321, 355, 436tibetan-leap-day, 355, 435tibetan-leap-month, 355, 435tibetan-leap-month?, 321, 321, 355, 437tibetan-month, 355, 435tibetan-moon-equation, 317, 317, 318, 355,

436tibetan-new-year, 321, 321, 355, 437tibetan-sun-equation, 317, 317, 318, 355,

435tibetan-year, 355, 435Tika (Balinese calendar), 157, 158







474 Index

Tikal (Guatemala), 144Time, 174–179

apparent, 184durations, 23–24Dynamical, 174, 177–179ephemeris, 174intervals, 22–23leap seconds, 175local mean, 175, 177, 184sidereal, 174, 185

actual, 187mean, 187

solar, 174–175, 177apparent, 182mean, 182

standard, 175, 177terrestrial, see Time, DynamicalUniversal, 174–175, 177zones, 175–177

time-from-clock, 23, 23, 355, 365time-from-moment, 18, 18, 23, 211, 355,

365time-of-day, 355, 365Tishah be-Av (Jewish fast), 92, 101, 103tishah-be-av, 103, 103, 355, 382tishri, 91, 91, 95, 97, 99, 101, 331, 358, 379Tishri (Hebrew month), 90–92, 95, 96,

98–103Tithi (Hindu calendar), 129, 278, 290, 292,

306, 312Titus Vespasianus, 92Toe-Wang-Yong-Sa (Korean calendar), 271Tokyo (Japan), 268Tonalpohualli (Aztec calendar), 145,

148–149Tondering, Claus, xxvtopocentric-lunar-altitude, 207, 207, 328,

355, 408Trajan (= Marcus Ulpius Traianus), 101Trần Đức Ngọc, xxvTrần Tiến Bình, 273Transfiguration (Orthodox holiday), 71Trepidation, 293Trinity Sunday (Christian holiday), 121Troesch, Albert, 42true, 66, 208, 359, 362Tseng, Karen, xxiiiTsuchihashi, Paul Y., 273Tsurphu calendar, 315Tsybulsky, Vladimir V., 87Tu-B’Shevat (Jewish holiday), 103, 110

tuesday, 27, 27, 59, 108, 110, 359, 361tumpek, 160, 160, 355, 394Tumpek (Balinese holiday), 155, 160Tumpek Kandang (Balinese holiday), 160Tumpek Krulut (Balinese holiday), 160Tumpek Kuningan (Balinese holiday), 160Tumpek Landep (Balinese holiday), 160Tumpek Ringgit (Balinese holiday), 160Tumpek Uduh (Balinese holiday), 160Tun, Li-Ch’en, 273Turkey, 47Turning of the Wheel of Dharma (Buddhist

holiday), 322Twilight, 212Tykocinski, Jehiel M., 212Type declarations, 337–359, 362Tzolkin (Mayan calendar), 30–31, 142–145,

148Tzom Gedaliah (Jewish fast), 103Tzom Tammuz (Jewish fast), 103Tzom Tevet (Jewish fast), 103, 104

UUayeb (Mayan calendar), 139, 140Uchida, Masao, 273ujjain, 292, 292, 295, 296, 308, 359, 429Ujjain (India), 292, 295, 300Ulisano, Benita, xxvUlugh Beg, 14, 85‘Umar, Caliph, 84Underhill, Muriel M., 313United States of America, see also Alaska,

Hawaii, New York, and Urbana,27, 47, 59, 121, 175, 328

Naval Observatory, xxiiUniversal House of Justice, 233universal-from-dynamical, 179, 179, 195,

356, 399universal-from-local, 175, 175, 177, 184,

209, 300, 356, 398universal-from-standard, 177, 177, 213,

219, 234, 241, 248, 250, 251, 326,330, 356, 398

Unix, xxiiunlucky-fridays-in-range, 60, 60, 356, 372urbana, 172, 172, 191, 211Urbana (Illinois), 0, 170, 172, 174, 191, 211,

448urbana-sunset, 211, 211urbana-winter, 191, 191Urip (Balinese calendar), 157







Index 475

Uspensky, James V., 61, 121Uttar Pradesh (India), 277

VVah. id (Bahá’í calendar), 230Vaikunta Ekadashi (Hindu holiday), 306Vaisakha (Hindu month), 278, 306, 321van Dalen, Benno, 87, 227van der Waerden, Bartel L., 42van Flandern, Thomas C., 60van Gent, Robert H., xxv, 119, 180, 181, 188,

194van Vlijmen, Oscar, xxvvan Wijk, Walther E., 124, 126, 128, 135,

275, 292, 299, 313Varalakshmi Vratam (Hindu holiday), 306Varanasi (= Banaras) (India), 303Varro (= Marcus Terentius Varro), 46Vatican Council, Second, 121V.E. (= Vikrama Era), 290Vedic months, 239Vega (star), 186Venus, 5, 124, 199, 282Verne, Jules, 172Vesper (Christian prayer time), 213Victorian cycle, 115Vietnamese calendar, 271–272

celestial stem names, 272Lisp code, 423months, 272terrestrial branch names, 272

vietnamese-location, 271, 271, 356, 423Vikrama Era (Hindu calendar), 289Vilhjálmsson, Porsteinn, 80Vilna Gaon, see Eliyahu ben Shlomo ZalmanVishnu (Hindu deity), 306visible-crescent, 326, 326, 327, 356, 438Vollers, Karl, 326Voltaire, see Arouet, Francois Marievon Dechend, Hertha, 258von Lieven, Carl Christoph, 52von Linne, Carl, 239

WWustenfeld, Ferdinand, 87Wada, Eiiti, xxvWallis, Faith, 46Wallis, John, 116Warnings, 39–41Wassef, Cérès W., 77Wauchope, Robert, 150

Waupotitsch, Roman, xxvwednesday, 27, 27, 104, 109, 110, 312, 359,

362Week, 4–5

Hebrew, 89Islamic, 83–84Persian, 218

WeekdaysArmenian, 5Bahá’í, 229Coptic, 74Ethiopic, 75Hebrew, 89Hindu, 124Islamic, 83, 84Persian, 218sample dates, 441Tibetan, 316

Welch, Windon C., 273Whitmundy (Christian holiday), 119Whitney, William D., 312Whitsunday (Christian holiday), 119Widiarki, Ni Made, 152Wiesenberg, Ephraim J., 111, 331Wildmann, Helmut, xxvWilhelm, Robert, 479Willey, Gordon R., 150winter, 191, 191, 251, 359, 400Woodworth, Joyce, xxvWoolhouse, Wesley S. B., 41, 87World Council of Churches, 119, 121, 325,

331World Wide Web, xxiv, 2, 361Wynn, Peter, 42

XXıan (China), 246Xihuitl (Aztec calendar), 145–147Xiuhmolpilli (Aztec calendar), 149Xú Xıqí, 247, 273

YY10K problem, 39Y2K problem, xxYadav, Bhuri S., 312yahrzeit, 107, 107, 108, 356, 383Yahrzeit (Jewish event), 105–108yahrzeit-in-gregorian, 108, 108, 356, 384Yallop, Bernard D., 215Yáng Guangxian, 248Yaqob, Daniel, xxv







476 Index

Yarshater, Ehsan, 227Year, 4, 6–9, 185–236

A.U.C., 69–70embolismic (Hebrew calendar), 90equinoctial, 222, 226gravid (Hebrew calendar), 90Gregorian calendar, 47–48Hebrew sabbatical, 91leap, 7, 32–39, 45, 49, 63, 64, 73, 74,

90–94, 97, 100, 103, 105–107,109, 218, 223, 240, 243, 275

negative, 12–14Roman, 69–70sıvıs (Ottoman Empire), 83sabbatical (Hebrew calendar), 91sidereal, 125, 187, 276, 284solar, 7, 146, 195, 241tropical, 46, 105, 140, 187, 195, 247

Year bearer (Mayan calendar), 144, 149year-rome-founded, 69, 69, 70, 359, 373Yoga

Hindu, 311–312Tibetan, 319

yoga, 311, 311, 356, 435

Yoh.anan ben Zakkai, 70Yom ha-Shoah (Holocaust Memorial Day),

104Yom ha-Zikkaron (Israel Memorial Day),

104Yom Kippur (Jewish holiday), 92, 101, 103yom-ha-zikkaron, 104, 104, 356, 383yom-kippur, 101, 101, 356, 382Yucatan (Mexico), 137, 140

ZZarineba, Fariba, xxvZeller’s congruence, 53, 56–57Zeller, J. Christian J., 56–57, 61Zhongqì (Chinese calendar), 248, 249Zodiac, 6, 88, 123, 126, 127, 130, 186, 195,

248, 274, 276–278, 280, 286, 287,305

Zomorodian, Afra, xxvzone, 356, 396zone-from-longitude, 175, 175, 295, 356,

398Zoroastrian calendar, 26, 217

epoch, 15

The covers of this book are too far apart.—Attributed to Ambrose Bierce







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