the astronomical tables of william rede

The Astronomical Tables of William RedeAuthor(s): Richard HarperSource: Isis, Vol. 66, No. 3 (Sep., 1975), pp. 369-378Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/228843 .

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The Astronomical Tables of

William Rede

By Richard Harper*

ILLIAM REDE WAS A NATIVE of Exeter diocese, although the exact date of his birth is not known.' His father died when Rede was still

a young man, and he became the protege of Nicholas of Sandwich, Lord of Bilsington and Folkstone, who was a graduate of Oxford himself 2 and undoubtedly encouraged the young Rede to seek a university education as the first step necessary to a civil career or ecclesiastical preferment. At any rate, William Rede went to Oxford and appeared on the rolls of Merton College as a Fellow in 1344.3 He remained there for several years and served as second bursar in 1352-1353. The neatly written accounts of his year as a College officer are still preserved in the Merton College Records.4 The next year he held the office of subwarden, and the last year in which his name appears in the Records is 1357.5

During the years while he was still at the university, William Rede's name was included along with several others in a petition for ecclesiastical benefices that was sent by the chancellor and convocation of Oxford to Pope Clement VI. The Pope awarded him the reservation of a benefice in the gift of the Bishop of Bath and Wells. In the award Rede was referred to as "clerk of the diocese of Exeter, M.A."6 In addition to this grant, he received several others during the years 1354-1359. He was first granted a dimissory letter

Received October 1973: revised/accepted March 1974. *Department of History, University of Wyoming, Laramie, Wyoming 82070. I would like to thank the National Endowment for the Humanities for the Fellowship that

made the research for this article possible. 'There are many variant spellings of his name, among them Read, Reade, Rede, and Reede.

I have followed A. B. Emden and C. L. Kingsford in using Rede. The most extensive biographic account of him is found in A. B. Emden, A Biographical Register of the University of Oxford to A.D. 1500 (Oxford: Clarendon Press, 1959), Vol. III, p. 1556. I have added nothing new to this account and have only attempted to place before the reader the major events of his life and career. See also C. L. Kingsford, Dictionary of National Biography (London, 1896), Vol. XLVII, pp. 374-376; George C. Broderick, Memorials of Merton College with Biographical Notices of Wardens and Fellows (Oxford: Clarendon Press, 1885; Oxford Historical Society, No. 4), p. 211 and R. T. Gunther, Early Science in Oxford (Oxford: Clarendon Press, 1922; Oxford Historical Society, Nos. 77, 78), Vol. II, pp. 56-59.

2F. M. Powicke, The Mediaeval Books of Merton College (Oxford: Clarendon Press, 1931), p. 28. Emden, A Biographical Register, Vol. III, p. 1639. Nicholas is described as "M.A. by 1305."

3Merton College Records, Nos. 3676, 3678. Emden, A Biographical Register, Vol. III, p. 1556. 4Merton College Records, No. 3787. 5Ibid., No. 4148; Nos. 3690, 3691. Emden, loc. cit. 6Mar. 1349. W. H. Bliss, ed., Calendar of . . . Petitions to the Pope, Vol. 1 (1342-1419), p. 149.

369



370 RICHARD HARPER

as acolyte with title to a fellowship at Merton by John de Grandisson, Bishop of Exeter, in August 1354.7 In the next several years he also enjoyed the benefactions of John de Trillek, Bishop of Hereford, who named him subdeacon in March 1355 and subsequently in 1358 and 1359 deacon and presbyter with title to a fellowship at Dore Abbey in Herefordshire.8

In the meantime, during 1356, he had been named successively subdeacon, deacon, and presbyter with title of fellowship by Bishop Shepey of Rochester; and in 1359 he was named archdeacon of Rochester by the Bishop.9 Three years later his name once again appeared in a university petition to Pope Urban V. He was granted on this occasion a benefice valued at twenty marks in the gift of the archbishop of Canterbury, even although he already possessed the archdeaconry of Rochester. In the petition Rede was described as M.A. and S.T.P., or doctor of theology.'0 The following year, the Pope confirmed his "collation by ordinary" to the provostship of Wingham College, an appoint- ment valued at sixty marks.'1

Rede vacated both the archdeaconship and provostship, however, when he was named Bishop of Chichester by papal provision October 11, 1368.12 Edward III restored the temporalities of the see June 9, 1369, and Rede was consecrated at Avignon September 2 of the same year.'3 The registers of his tenure as Bishop of Chichester have not survived,'4 but the records of the diocese that do remain show that he was a careful administrator, conscious of the spiritual as well as the temporal duties of episcopal office.'5 His zeal in safeguarding the rights of his diocese brought him into negotiations with other lords both lay and ecclesiastical. He satisfactorily concluded business with Richard, Earl of Arundel, concerning the rents and services due from that nobleman, and with Sir Henry Percy to regain the amercement of his tenants.'6 John of Gaunt also recognized the episcopal rights to "tithe of pannage of Asschesdon when there [was] any in the chace." 17

7F. C. Hingeston-Randolph, ed., The Register of John de Grandisson, Bishop of Exeter (1327-1369) (London/Exeter, 1897), Vol. II, p. 1130.

8 Joseph Henry Parry, ed., RegistrumJohannis de Trillek. Episcopi Herefordensis (1344-1360) (London, 1912), pp. 401, 616, 617, 619, 624, 627.

9Reg. Shepey, dioc. Rochester, Vol. I, fols. 285v-286 and fol. 295v (as cited in Emden, A Biographical Register, Vol. III, p. 1556).

1?Bliss, Petitions to the Pope, Vol. I, p. 390. " Ibid., p. 503; London, Lambeth Palace, Reg. Islip. fol. 302r. John Peckham, Archbishop of

Canterbury in the years 1279-1292, founded the College of St. Mary, Wingham, having made statutes for it in 1287. The college consisted of a provost and six canons: two priests, two deacons, and two subdeacons. See William Page, ed., The Victoria History of the County of Kent, Vol. II, p. 233.

'2C. Eubel, Hierarchia Cath. Medii Aevi, Vol. I, p. 193. 13Calendar. . . Close Rolls, Edward III, Vol. XIII (1369-1374), p. 122; William Stubbs, Reg.

Sacr. Anglic., p. 79. 14 The Survey of the Ecclesiastical Archives of the Diocese of Chichester (London: Church of England;

Pilgrim Trustees Report; Survey of Ecclesiastical Archives, 1952). There are eleven volumes of registers listed for the years 1397-1596.

'5These records are preserved in W. D. Peckham, ed., The Cartulary of the High Church of Chichester (Sussex Record Society, 1942-1943), Vol. XLVI.

"Ibid., Nos. 879 and 881. 7Ibid., Nos. 883, 884, 885.



THE ASTRONOMICAL TABLES OF WILLIAM REDE 371

A somewhat humorous episode involving a porpoise indicated that Rede was no less zealous in maintaining the rights of his see against usurpations by his ecclesiastical superior, the Archbishop of Canterbury:

In the time of Sir Simon Sudbury, Archbishop of Canterbury (1357-1381), and Sir William Reede, Bishop of Chichester, a porpoise cast up by the sea into Wydering harbour floated upstream to Selsey ferry and there stranded on the land of one Matthew the clerk, a tenant of the Bishop's. Walter Parker, parker, and John Geffroy, reeve, of the Bishop's manor of Selsey, came and took the fish as a royal fish belonging to the Bishop's liberty, and carted it to the Bishop's house at Duryngewyke. Thereupon Richard Tangemere, steward of the archbishop's lordship of Pageham, sent in haste to the Archbishop for an order to Mr. Peter, rector of Selsey, and Sir John Adam, vicar of Sidlesham, to cite the Bishop's servants for removing the fish. They came to Duryngewyke and showed the Archbishop's order to the Bishop; he saw it and, after summoning his clerks and notaries, appealed to the Roman Curia, determined to fight the case while he had a penny to spend. So the Archbishop left him in peace.'8

During the remainder of his life, Rede continued to play an active role in the affairs of the nation as well as his university. He was a trier of petitions in various parliaments between the years 1369 and 1380,19 and he was one of the commissioners appointed to settle a dispute between the Faculties of Arts and Theology and the Faculty of Civil and Canon Law in June 1376.20 He was also interested in building and received a license from Richard II to crenellate Amberley Castle in Sussex.2' In addition, he left one hundred pounds in his will for reparation of the library of Merton College.22

William Rede was a typical example of the educated man of affairs of his day. He held an important ecclesiastical office, was a benefactor and friend to his own and other Oxford colleges as well as the university.23 He also instigated the collection of a volume of provincial constitutions and another volume of ecclesiastical documents relating to his see. Unfortunately, only the former

24 of these two survives. H wacredited with the authorship of a series of

'8Ibid., No. 897. "9Kingsford, DNB, Vol. XLVII, p. 375. 20Emden, A Biographical Register, Vol. III, p. 1556. 21 Calendar. . . Patent Rolls (1377-138 1), p. 76; W. D. Peckham, "Architectural History of Amberley

Castle," Sussex Archaeological Collections, 62:27-36 and 79:226-227. 22Powicke, The Mediaeval Books of Merton College, p. 87. Rede's will is printed on pp. 87-91. 23 In addition to the 100 pounds that Bishop Rede bequeathed to Merton College for the reparation

of the library, he also left 100 books on various subjects to Merton and another 100 pounds to be deposited in the college chest for the use of its scholars. He left 50 books of theology to St. Mary's, Wynton (New College); 20 books and 20 pounds to Exeter; 10 books and 10 pounds to Queen's; 10 books and 100 s to Oriel; to Balliol, 10 books and 100 s; 13 books and 20 marks to the College of the Earl of Arundel in Arundel as well as other monetary bequests to a number of priories.

24Emden, A Biographical Register, Vol. III, p. 1556. The collection of constitutions, Liber cicestrensis, survives in Oxford, Bodley, MS Ashmole 1146. I have examined this manuscript and it seems originally to have consisted of four parts with the following titles: (1) De generalibus constitutionibus legatorum sedis apostolice et archiepiscoporum; (2) De statutis seu constitutionibus scriptis et non scriptis in curia Cantuariensi; (3) De cartis, statutis regum Anglie de libertatibus liberis consuetudinibus ecdesie Anglie concessis; (4) De constitutionibus . . . ecdesie Cicestrensi. The volume ends, however, after section (2) and contains none of the material specific to Chichester.



372 RICHARD HARPER

biographies of the popes and the archbishops of Canterbury, but James Tait has shown that this attribution is incorrect.25 He was, nonetheless, the author of an adaptation of the Alphonsine Tables for the meridian of Oxford with a canon on their use, and a solar almanac for 1341-1344 was also attributed to him.

The Alphonsine Tables were created under the aegis of King Alfonso X of Castile in 1272 by Jehuda ben Moses and Isaac ibn Sid, but the most widely used version in the Latin West was that of John of Lignieres with the canon on their use that was written by his student John of Saxony.26 This popular version of the tables was a radical modification of the original in format and organization: it was based upon a sexagesimal reckoning system that required both chronology and motion to be expressed in base-60 units. Although the original tables are lost, the Castilian canon to them survives and is evidence that the original version followed the usual medieval practice of using days, months, and years and the signum = 300 rather than signum = 600 of the Lignieres-Saxony tables.27

Several years ago, Dr. J. L. E. Dreyer demonstrated that the version of the tables made by William Rede followed the original Castilian source much more closely than the Lignieres-Saxony one.28 The bishop's canon, however, is much briefer than the original and is indicative of the practical character of English astronomy of the fourteenth century. The original canon has several initial chapters dealing with chronology reckoning and conversion from one chronological schema to another-for example, from Arabic to Christian or Christian to Persian years and months.29 Rede eliminates these considerations and commences with an explanation of his purpose in making a version of the tables:

For those wishing to forecast the effects of the planets on earthly affairs, it is necessary to calculate the diversities of their motions in order that there may be a natural progression from the speculative to the practical. Among the tables presently available, those that are most precise and best suited to daily use are the tables of the illustrious King Alfonso of Castile, which are composed for the meridian of Toledo. Yet the use of those tables is time consuming and so tedious that scarcely anyone fully understands their usage. Therefore, I have constructed a series of tables designed to lighten the chore and I have based them on the radices

25The manuscripts of the historical work are London, British Museum, Cotton Julius B iii and Lambeth Palace, 99. The attribution was based upon a note on the flyleaf (fol. 3) of the Cotton MS that was then copied into the Lambeth Palace MS (fol. 112v). James Tait has shown, however, in his edition of the Chronica Johannis de Reading et anonymi Cantuariensis (Manchester, 1914) from the internal evidence that the work should be attributed to a monk of Christ Church, Canterbury.

26Incipit: Tempus est mensura motus. 27The canon has been printed from a seemingly unique manuscript (Madrid, National Library,

L. 97) by Don Manuel Rico y Sinobas, Libros del saber de astronomia de rey D. Alfonso X de Castile (Madrid: Tipocrafia de Don Eusebio Aguado, 1886), in 5 vols. of which Vol. IV contains the canon, Libros de las taulas Alfonsies.

28J. L. E. Dreyer, "On the Original Form of the Alfonsine Tables," Monthly Notices, Royal Astronomical Society, 1920, 80(No. 3):243-262.

29Chapters 1 through 13 deal with this sort of thing.




and motions of the tables of Alfonso. Moreover, I have modified them for the meridian of Oxford, which is 150 longitude and 510 50' latitude. This meridian precedes the meridian of Toledo by 4? and corresponds to 16 minutes of an hour.30

The assertion that he had lessened the labor involved in using the tables is somewhat exaggerated, for Rede outlines the same operations as the Castilian version, albeit somewhat more tersely. His claim to having simplified the operations may, however, refer to initial data gathering rather than to computation. The tables of medii motus of the various planets follow the familiar format of organization and presentation. The medii motus are recorded for anni collecti, anni expansi, menses, dies, etc. But because the anni collecti commence with the year 1340,3' Rede may have made a modification that would have rendered the tables more convenient for contemporary use. The original version took as its starting date the year of Alfonso's coronation, 1252. And although the canon explains that the anni collecti are recorded at twenty-year intervals just as they are in Rede's tables, this would have produced anni collecti 1252, 1272,

.1312,1332,1352. . ., which would have been somewhat more inconvenient. Moreover, if the base date is taken as 1252 = 0, then another step of addition or subtraction would be required.32 The anni expansi, in both Rede's version and the original, are obviously from one year to twenty years, and therefore he would have been required to make no change in that table or in the tables of monthly, daily, or hourly medii motus.

The first chapter in Rede's canon explains the method of calculating the medii motus and mean arguments of the various planets, while the second section deals with the auges (apogees) and mean centers. In these two chapters he has combined material that is found in Chapter 1533 with information

30London, British Museum, MS Harley 1009, fol. 3r: Volentibus prenosticare futuros effectus planetarum in inferioribus primo secundum opus tabularum oportet calculare ipsarum motuum diversitates ut a speculativa ad practicam fiat progressio naturalis. Set inter tabulas nunc inventas precisiores et cottidiano experimento propinquiores sunt tabule quas Alfonsus illustris rex Castellie super meridiem civitatis Tholeti composuit. Sed istarum tabularum operatio est ita prolixa et tediosa quod vix aliqui perveniunt ad completam cognitionem planetarum. Ideo quasdam tabulas compendiosas super annos incarnationis Christi et super radices et motus tabularum Alfonsi fundatas ad levitatem operis ordinavi et ad meridiem civitatis Oxonie reduxi que distat ab occidente per 15 gradus et ab equinoctiali per 51 gradus et 50 minutas nam meridies precedit meridiem Tholeti per 4 gradus equinoctialis circuli quibus minute 16 hore correspondent. I have used the following British Museum manuscript versions of Rede's tables in this study:

Egerton 847, fols. 122-142; Egerton 889, fols. 111-119; Harley 1009, fols. 3-11; Royal 12 D vi, fols, 85-90; Sloane 407, fols. 39-56 (tables only).

"A few MSS commence with 1320. 32The Ligni'eres tables contain a number of different radix dates with their conversions into

sexagesimal reckoning. Among these is both radix ere incarnationis and radix ere Alfonsii. This might be interpreted as evidence that the original tables were predicated on radix 1252 = 0, as the Toledan Tables of Arzachel were based on radix 622 A.H. = 0. Further the canon confirms this possibility: "Et possiemos el comencio deste anno sobredicho [i.e., 1252] por comiencio desta era. et possiemosle nombre la era Alfonsi"

33 Rico y Sinobas, Las taulas, pp. 133-134. Although it is rather nitpicking to point it out, in the edition of Las taulas the title of Ch. 14 describes the contents of Ch. 15, and vice versa, so that the correct title to Ch. 15 should be "Para saber sacar los medios cursos de los planetas et de los otros movimientos depues del tiempo de la era Alfonsi."



374 RICHARD HARPER

from a number of subsequent chapters of the original version. The medius motus is discussed in Chapter 15, but the arguments and centers are explained in connection with each individual planet. In his first chapter, on the other hand, Bishop Rede explains in simple style that the medius motus of any planet is found by adding up the appropriate values found in the several tables; for example, the medius motus of the sun for the date March 1, 1342, is the following:34

1340 = 9s 180 11' 3"

1 year = 11 29 45 39

Feb.= 1 28 9 11

I day= 59 8

lis 170 5' 1"

He then explains that the medii motus of the sun, Venus, and Mercury are the same, and for that reason the mean arguments of Venus and Mercury as well as of the moon are found by a process of addition identical to that of the medius motus, using of course tables of the mean argument of the specific planets. The argument of any one of the other planets, on the other hand, is found by subtracting its medius motus from the medius motus of the sun.

The apogees and mean centers are dealt with in the second chapter. The table of the values of the apogee for the anni collecti is included along with tables giving the modification or change for each twenty-year period, as well as each year within a particular two-decade epoch. The mean center of all planets except the moon is found by subtracting its apogee from its medius motus. (In the case of the sun, this difference is called the mean argument rather than the mean center.) For the moon, the mean center is twice the difference of its medius motus less the medius motus of the sun.

Chapters 4 and 5 of Rede's canon deal with the procedure for calculating the true place of a planet.35 He combines into two chapters the material covered in Chapters 16, 17, and 18 of the original version, where one chapter each is given to the sun, the moon, and the five planets.36

In the case of the sun and the five planets, there are no substantive differences between William Rede's procedures and those outlined in the Castilian version,37 but there is a peculiarity with regard to the calculation of the true place of the moon. In the canon on reckoning the position of the moon, Rede provides

34The quantities used are always perfecti, or completed, so that to find a medius motus in 1342 the values for 1340 and one year are added together.

35There is some confusion among the various manuscripts with respect to the order of the chapters. In some, the chapter on mean conjunctions and oppositions comes before the chapters on determining the true place. The internal evidence, however, proves the order that Rede intended.

36Rico y Sinobas, Las taulas, pp. 134-136. 37There is one startling difference that must be a scribal error. As outlined above, the mean

argument of the sun is found by subtracting the apogee (aux) from the medius motus. In the original version, however, this is reversed: "Saca el medio curso del sol al tiempo que tfu quieres. et lo que fuer mingualo del so auxe. et lo que fincar. esso es el argumento."




the usual methodology, which is also found in the canons on the Toledan Tables of Arzachel, as well as the canons of John of Saxony on the Lignieres version of the Alphonsine Tables. The center of the moon is computed as twice the difference of the medius motus of the moon less the medius motus of the sun. In the instructions of Jehuda ben Moses and Isaac ibn Sid, however, there is added a novel refinement. One finds the medii motus of the sun and moon in the usual way; then one subtracts the apogee of the sun from the medius motus of the moon and multiples the signa of the difference that results by 5 2 seconds. If the moon was between the apogee of the sun and its perigee,38 the product is subtracted from the medius motus of the moon. On the other hand, if the moon was located between the perigee and the apogee, the product is added to the medius motus. This adjusted medius motus is then used to find the mean center of the moon by the regular method.39

The remaining chapters of Rede's canon deal with orthodox matters such as the determination of mean and true conjunctions and oppositions, whether a planet is direct, retrograde, or stationary, and the calculation of the time at which the sun shall enter Aries. In all these processes he follows and epitomizes the original canon of the Alphonsine Tables.

It is obvious from this outline of the contents of Bishop Rede's canon that his work was not very original nor did it add anything new to the theories of medieval astronomy. It was primarily designed to simplify the calculation of planetary ephemerides and to provide a handy and concise manual or textbook explaining the use of the tables. Its value to his contemporaries as well as its contribution to the history of astronomy therefore depend on the care and accuracy with which he modified the tables. Although no direct comparison can be made between Rede's tables and the original ones of Jehuda ben Moses and Isaac ibn Sid because the latter are lost, it is possible to compare the Rede tables and those of Jean of Lignieres. Admittedly, all that can be judged in a comparison of this sort is Rede's accuracy with respect to Lignieres. But after their creation, the Lignieres tables enjoyed great vogue and could not have been very inaccurate.

I have used the Lignieres tables to calculate the medius motus of the sun and the five planets for annus collectus 1340, adjusting them for the meridian of Oxford. Further, I have computed the mean motion in twenty years for each of them. From the data of Table 1 it is obvious that there is a very close agreement between Rede's tables and those of the French astronomer.40

388*. oPPosito dell auxe = 3600 - auxe. 39"Saca el medio curso de la luna. et su argumento. et otrossi cl medio curso del sol a la

ora que tiu quieres. et depues mingua ell auxe del sol del medio curso de la luna. et lo que fincar toma su signo. et multiplicalo en .V. segundos et medio. et guarda lo que se ayuntar. Et depues cata la luna. et depues. si fuer entrell auxe del sol et entre su opposito. mingua lo que tui guardeste del medio curso de la luna. et si fuer la luna entrell opposito dell auxe del sol et entre su auxe. annade lo que tiu guardeste sobrel medio curso de la luna. et depues lo que fuer el medio curso de la luna depues del minguamiento dell. o depues dell annadimeinto sobrell. esso sera' el medio curso eguado de la luna. et guardalo. Et depues mingua dell el medio curso del sol. et lo que fincar doblalo...."

401 have adopted the values of Rede's tables in this and the following table to modern notation: 11 s 290 = 3590, etc.



376 RICHARD HARPER

Table 1. A comparison of the medii motus of the Rede and Lignieres tables

Medius motus in annis collectis Medius motus in 20 anni Medius motus in 16 min. hore

Sun Rede Lignieres Rede Lignieres Year 1340 2880 11' 3" 2880 11' 41" 36"' 00 8' 49" 00 8' 49" 0' 39" 0"' 0"" 1360 288 19 52 1380 288 28 41 1400 288 37 30 1420 288 46 19 1440 288 55 8 1460 289 3 57 1480 289 12 46 1500 289 21 35 Saturn

1340 2680 33' 45" 2680 33' 46" 31"' 2440 41' 37" 2440 41' 37" 1" 20"' 23""n 1360 153 15 22 1380 37 56 59 1400 282 38 37 1420 167 20 14 1440 52 1 51 1460 296 43 28 1480 181 25 5 1500 66 6 42 Jupiter

1340 1850 55' 49" 1850 55' 52" 0"' 2470 14' 36" 2470 14' 36" 3" 19"' 30"" 1360 73 10 25 1380 320 25 1 1400 207 39 38 1420 94 54 14 1440 342 8 50 1460 229 23 26 1480 116 34 3 1500 3 52 40 Mars

1340 2180 35' 44" 2180 36' 4 43 2280 18' 58" 2280 18' 58" 20" 57"' 45"". 1360 86 54 42 1380 315 13 19 1400 183 32 37 1420 51 51 35 1440 280 10 33 1460 148 29 31 1480 16 48 29 1500 245 7 26 Venus*

1340 1930 44' 31" 1930 44' 55" 29"' 1830 38' 51" 1830 38' 51" 24" 39"' 28"" 1360 17 23 22 1380 201 2 13 1400 24 41 4 1420 208 19 55 1440 31 58 45 1460 215 37 36 1480 39 16 27 1500 222 55 18 Mercury*

1340 2940 14' 13" 2940 16' 17" 25"' 140 27' 39" 140 27' 39" 2' 4" 16"' 1360 308 41 52




Table 1 (continued)

Medius motus in annis collectis Medius motus in 20 anni Medius motus in 16 mins hore

Mercury* Rede Lignieres Rede Lignieres Year 1380 323 9 31 1400 337 37 10 1420 352 4 49 1440 6 32 27 1460 35 27 45 1480 49 55 24 1500 64 23 3 *medium argumentum

The additional tables of medii motus for months, days, and hours show a comparable similarity.

The number of manuscripts of the canon and tables indicates that they enjoyed a limited popularity during the fourteenth century, although there are many more exempla of the Lignieres version of the Alphonsine Tables. Indeed, Chaucer in his Equatorie of the Planetis seems to have been more familiar with the work of the French astronomer than with the treatise of his country- man.41

In connection with their practical use, there is an interesting Almanach solis super meridiem Oxonie that may be based on the tables of Rede.42 The work is frequently ascribed to Rede, although Lynn Thorndike suggested that it might be better assigned to Simon Bredon, an older fellow Mertonian.43 The best argument in favor of Bredon's authorship is the date of the work; it covers the years 1341-1344, when Rede was probably too young and Bredon was already an established scholar.' On the other hand, solar almanacs of this sort were designed for four-year periods, because whether a year is bissextile, or the first, second, or third year after the bissextile year determines the solar longitude rather than the actual calendar year. The solar tables of the Almanach perpetuum of Prophatius Judaeus follow this same arrangement.45 Therefore the calculator of the Almanach for 1341-1344 may simply have taken advantage of the convenient starting date of Rede's tables (1340) in the computation of the solar positions. Table 2 compares the solar ephemerides of the Almanach

41 D. J. de Solla Price, ed., The Equatorie of the Planetis (Cambridge: Cambridge University Press, 1955), pp. 125-127 and passim.

42Oxford, Bodley Library, Digby 178, fols. 11-13. 43Lynn Thorndike, History of Magic and Experimental Science (New York: Columbia University

Press, 1934), Vol. III, p. 523. 44For Simon Bredon see Emden, A Biographical Register, Vol. I, p. 257; Gunther, Early Science

in Oxford, Vol. II, pp. 52-54; and George Sarton, Introduction to the History of Science (Baltimore: Williams and Wilkins, 1931), Vol. III, Pt. 1, pp. 673-674.

45G. Boffito, and C. Melzi d'Eril, Almanach Dantis Aligherii sive Profacii judaei Montispessulani (Florence: Olschki, 1908).



378 RICHARD HARPER

Table 2. A comparison of the Almanach solis, the ephemerides of Rede's tables, and the ephemerides of John of Lignieres' tables

Year Alrnanach Rede Lignieres Almanach Rede Lignieres

1341 349? 27' 21" 349? 27' 21" 3490 27' 20" 1360 32' 50" 1360 32' 50" 1360 32' 51' 1342 349 12 55 349 12 54 349 12 57 136 18 45 136 18 46 136 18 48 1343 348 58 27 348 58 0 348 58 5 136 4 53 136 4 55 136 4 59 1344 349 43 34 349 43 32 349 43 40 136 48 36 136 48 32 136 48 34

with those calculated by means of Rede's tables, as well as the Lignieres tables adjusted for the meridian of Oxford.46

The comparison among the three sets of ephemerides is too close to assign the Almanach solis definitely to William Rede or to his tables. It is clear, however, that the Alphonsine Tables are the ultimate basis for its creation. Because Simon Bredon was a fellow of Merton during these years, and because one of the manuscripts of the Almanach solis is in his own handwriting,47 it is much more likely that the Almanach is Bredon's rather than Rede's. But of perhaps greater importance, the existence of such a work demonstrates that the Alphonsine Tables were in use in England at that time.

Astronomy was an extremely popular science in England during the fourteenth century, and William Rede is a typical example of the sort of individual who advanced the science. Despite his public duties and the burdens of ecclesiastical office, he nonetheless found time for scholarship and research. Although his work was not of a speculative or theoretical nature that proferred modifications or improvements of contemporary theory, his astronomical tables did provide a simple and accessible introduction to observation and calculation. It was the sort of work necessary for the gradual accumulation of data that over a period of years results in modifications in theory or the advancement of new ideas, and it was a characteristic example of the sort of quantification done by men such as Simon Bredon and later John Chilmark, John Killingworth, and John Holbrook.48

46The Almanach gives the solar positions every day for each of the four years of the cycle. 47Oxford, Bodley, MS Digby 176, fol. 7 1r. See Thorndike, History of Magic, loc. cit. 481 am presently investigating the treatises and tables of these English astronomers.



the astronomical tables of william rede

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