Richard of Wallingford

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(b. Wallingford, Berkshire, England, ca. 1292; d. St. Albans, Hertfordshire, England, 23 May 1336) mathematics, astronomy, horology.

Since Richard of Wallingford was for nine years abbot of St. Albans, the best chronicled monastery in England, much more is known about his personal life than about most medieval writers. From the Gesta abbatum Monasterii Sancti Albani (H. T. Riley, ed., Rolls Series, II [London, 1867], (181–183), we learn that he was the son of William, a blacksmith, and his wife, Isabella; the family was moderately prosperous. When his father died, Richard was adopted by the prior of Wallingford, William of Kirkeby, who in due course sent him to oxford (ca. 1308).

Having determined in arts before he was twenty- three years of age, Richard left for St. Albans, where he assumed the monastic habit. He was ordained deacon (18 December 1316) and then priest (28 May 1317). His abbot sent him back to Oxford—probably to Gloucester College, a Benedictine establishment— where he studied philosophy and theology for nine years. Having determined as B.Th. in 1327, he returned once again to St. Albans to ask for the festive expenses of his graduation. While he was there the abbot died, and Richard was elected in his place. He visited Avignon for the papal confirmation, which was at length obtained, despite some legal difficulties.

Once back at St. Albans Richard found himself oppressed by three great burdens: the abbey was deeply in debt; the townsmen of St. Albans were in revolt, objecting to the abbot’s feudal privileges; and he himself had contracted leprosy. Before he died of this disease, in 1336, he had cleared most of the debts and put down the revolt in the town. He had also kept control of a difficult internal situation, several of his monks having objected to his holding office, and one having gone so far as to instigate a papal inquisition. He skillfully negotiated these difficulties; and when he died in office, he left a reputation not only for moral firmness, but for intellectual and practical genius. He was especially remembered at St. Albans for the vast and intricate astronomical clock that he designed, and which in its final form was completed after his death.

Richard’s first essay in mathematical or astronomical writing seems to have been a product of the early years in his second period at Oxford and was a set of instructions (canons) for the use of the tables that had been drawn up by John Maudith, the Merton College astronomer, in the approximate period 1310-1316. Richard followed this easy with Quadripartitum, a work on such of the fundamentals of trigonometry as were required for the solution of problems of spherical astronomy. The first part of this work has the appearance of a theory of trigonometrical identities, but at the time it was written it was regarded as a basis for the calculation of sines and cosines, and chords and versed chords. The next two parts of the Quadripartitum deal with a systematic and rigorous exposition of Menelaus’ theorem, in the so-called “eighteen modes” of Thãbit ibn Qurra. Finally, the work ends with an application of the foregoing principles to astronomy. The main sources of the work were Ptolemy’s Almagest, the canons to the Toledan tables, and a short treatise that was possibly by Campanus of Novara. The Quadripartitum may reasonably be claimed as the first comprehensive medieval treatise on trigonometry to have been written in Europe, at least outside Spain and Islam. When Richard was abbot of St. Albans, he revised the work, taking into account the Flores of Jãbir ibn Aflạ, but only one copy of the later recension is known.

Before finally leaving Oxford in 1327, Richard wrote three other works. The Exafrenon pronosticacionum temporis was a treatise on astrological meteorology. There is no good reason to doubt that it was his. Richard’s most important finished treatise, Tractatus albionis, dealt with the theory, construction, and use of his instrument, the “Albion” (“all by one”), which was a highly original equatorium to assist in calculating planetary positions, together with ancillary instruments concerned with eclipse calculation, ordinary astrolabe practice, and a saphea Arzachelis. The Albion earned considerable renown in England, where Simon Tunsted produced a new version differing slightly from the original. John of Gmunden’s recension included some new parameters, drawn from the Alphonsine tables, in place of the Toledan parameters. His version was much copied in southern Europe, and the instrument continued in vogue until the sixteenth century, influencing Schöner and Apian. The original treatise provides very few clues as to its sources, and many of its best parts are undoubtedly original. Regiomontanus drafted a much debased version.

While writing Albion (1326–1327) Richard composed a treatise on another new instrument he had designed, the “rectangulus.” This instrument was meant as a substitute for the armillary sphere and was intended for observation and calculation. The chief advantage it was supposed to have was simplicity of construction: it was made from seven straight pivoted rods. Nevertheless, there were certain inherent disadvantages in its design. In connection with the treatise on the rectangulus, we note a table of an inverse trigonometrical function.

At St. Albans, where he was able to direct relatively large sums of money, Richard embarked on the task of building his astronomical clock. It seems that a sound mechanical escapement had been known for more than forty years when he began his work, but his clock is the first entirely mechanical clock of which we have detailed knowledge. It had a mechanism for hour-striking and an escapement older than (and in some ways superior to) the better-known verge and foliot as used with a contrate wheel. But the true originality of the design relates to its astronomical trains, with, for example, an oval wheel to give a variable velocity for the solar motion, correcting trains for the moon (leading to a theoretical error of only 7 parts in 106), and a lunar phase and eclipse mechanism. No mechanism of comparable complexity is known from any earlier time. The clock was lost to history after the dissolution of the monasteries in the sixteenth century. John Leland reported that it included planetary trains and a tidal dial. It had, of course, an astrolabe face, which, like the works, was probably ten feet across. The solitary treatise from which the details of the mechanism are known is now bound out of sequence, added to which it seems to have been copied from a pile of disordered drafts, with duplication of subject matter. It originally belonged to the subsacristan of the abbey.


I. Original Works. Transcripts of parts of Albion, Rectangulus, and Quadripartitum have appeared in print. See R. T. Gunther, Early Science in Oxford, II (Oxford, 1926), 337–370, for parts of the first two works by H. H. Salter. J. D. Bond printed the first book only of Quadripartitum, from an inferior MS, in Isis, 5 (1923), 99–115, with English trans. (ibid., 339–363). The bulk of Richard’s writings are available only in MSS, but J. D. North has in the press a complete ed. of all the known writings, including translations and commentaries, and a discussion of conjectured and spurious works not mentioned above.

II. Secondary Literature. For the best bibliographical guide before the work by J. D. North, see Thomas Tanner, Bibliotheca Britannico-Hibernica (London, 1748), 628–629. Bishop Tanner drew heavily on the sixteenth-century antiquary John Leland. The most fundamental biographical source is Gesta abbatum, referred to in the text above.

John D. North