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day-book, that eight houfes were demolifhed to make room 

 for this fortrefs. During the conteft between king Stephen 

 and the emprefs Maud, the latter refided in tiiis cattle, 

 which was ftrongly fortified in her behalf: Stephen befieged 

 it feveral times ; but all h:s alfauks were fruitlels ; the 

 ftrength of tlic place, and the bravery of the garrifon, effec- 

 tually refiiled his utmolt exertions. In the reigns of king 

 John and Henry III., this fortrefs was the fcene of nego- 

 ciation between the kings and the difcontented barons: it 

 alfo bore a confpicuous part in the civil war between 

 Edward II. and his nobles. When cardinal Wolfey was 

 about to found a college in Oxford, Henry VIII. gave him 

 this caftle as a part of the endowment of his intended col- 

 lege ; but on the cardinal's attainder, the grant appears to 

 have been refumed. Leland, who vifited Wallingford about 

 that time, fays, " the caftlc yoinith to the north gate of tlie 

 toune, and hath three dikis, large and deap, and welle 

 waterid. About ech of the two firft dikis rennith an em- 

 batehd waulle, now fore yn ruine, and for the molt part de- 

 faced. Al the goodly building, with the tourres and dim- 

 geon, be within the three dike." Camden, fpeaking of this 

 caftle, fays, " Its fize and magnificence ufed to llrike me 

 with aftonifhment when I came hither a lad : it is environed 

 with a double wall and double ditch, and in the middle, on a 

 high artificial hill, Hands the citadel, in the afcent to which 

 by fteps, I have feen a well of immenfe depth." At an 

 early period of the civil war between Charles I. and his par- 

 liament, Wallingford-caflle was put into a ftate of repair ; 

 and being well garrifoned, was efteemed one of the moll im- 

 portant fortrefles in the king's pofleffion. It efcaped a 

 fiege till nearly the termination of the war: in 1646 it 

 furrendered to the parliamentary forces ; and an order of 

 council for its demolition was iffued November 18, 1652. 

 So well was this order obeyed, that the greater part of it 

 was dcftroyed. Within the walls of the caille was an ancii-nt 

 college, founded and endowed by Edmund, earl of Corn- 

 wall, nephew to Henry III., for a dean, four prebendaries, 

 fix clerks, and four chorifters. Its revenues were further 

 augmented by Edward the Black Prince and king Henry VI. 

 Juil within the weft gate of the town was a convent of Be- 

 nediftine monks, founded in the reign of William the Con- 

 queror, by Paul, abbot of St. Alban's. The priory ellate 

 is now the property of William Hucks, ffq. who has a 

 farm-houfe on the fcite. Among the more dillinguifhed na- 

 tives of Wallingford, were Richard, abbot of St. Alban's, 

 and John, a monk of the fame place, who both derived a 

 furname from the place of their birth : the former was emi- 

 nent as a mathematician, the latter as an hiftorian. 



One mile fouth of Wallingford is Chofeley-farm, one of 

 the largeft and nioft compadl in England ; being let .'or 

 1000/. per annum : there is a barn on it lOO feet in length. 

 It was formerly in the pofrelTion of the earls of Warwick ; 

 but is now the properly of lord Kenfiiigton. — Beauties of 

 England and Wales, vol. i. BcrkHiire ; by J. Britton and 

 E.W. Brayley, 1801. Lyfons' Magna Britannia, vol. i. 

 Berkftiire, 410. 1806. 



Wallingfohd, a town of the (late of Vermont, in the 

 county of Rutland, containing 13^16 inhabitants ; 40 miles 

 N. of Bennington. — Alfo, a town of CouneAicut, in the 

 county of New Haven. This town, called by the Indians 

 Coginchauge, was fettled in 1671. It now contains 2320 

 inhabitants; 12 miles S.W. of Middleton. 



WALLIS, John, in Biogniphy,a well known mathemati- 

 cian, was born at Afhford, in Kent, in the year i6l6, and 

 after finifhing his fchool education, was admitted, in 1632, at 

 Emanuel college, Cambridge, witli a view to the church. 

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Having taken orders, he commenced the duties 0/ \m mi- 

 nifterial office in 1641, as chaplain to fir William Darnley, 

 in Yorkfliire ; and whilft he occupied the fame Ration in the 

 family of lady Vere, he had an opportunity of exhibiting 

 his extraordinary talent in the art of decypheruig. Id 

 1643 ^^'^ parliament, to which he was then attiiched, con- 

 ferred upon him the fecjueftrated living of St. Gabriel, ia 

 Fenchurch-ftreet, London ; and in this y-ar he publiftied a 

 quarto volume, entitled " Truth tried, or .-^niinadverfions 

 on Lord Brookes's Treatife of the Nature of Truth." At 

 this time he became pofleflcd of a handfome patrimony by 

 the death of his mother j and in 1644 he was appointed one 

 of the fecretaries of the alTembly of divines. In the fol- 

 lowing year he concurred with thofe perfons who laid the 

 foundation of the Royal Society, and communicated fpeci- 

 mens of his Ikill in mathematics; and in 1647 he difco- 

 vered a new method of folving cubic equations. When the 

 independents acquired an afcendancy* over the covenanters, 

 Wallis united with other minifters, who alTembled at Sion 

 college, in fubfcribing a paper, entitled " A Teftimony 

 to the Truth of Jefus Chriil, and to the Solemn League 

 and Covenant, as alfo againll the Errors, Herefies, and Blaf- 

 phcmies of thofe Times, and the Toleration of them." Ill 

 1648 lie fubfcribed a rcmonllrance againll putting the king 

 to death, and another paper, denominated " A ferious and 

 faithful Reprefentation of the Judgrn'Mit of Minifters of the 

 Gofpcl, within the Province of London, in a Letter from 

 them to the General and his Council of War." In the 

 next year he was appointed by the parliamentary vifitor Sa- 

 vilian profefliDr of geometry, and quitting his church in Lon- 

 don, entered himfelf of Exeter college, Oxford, where he 

 became mafter of arts, and foduloufly difcharged the duties 

 of his office, connecting himfelf with thofe wlio formed the 

 Philofophical Society in that city. Towards the end of 

 this year he became acquainted with Cavalleri's method of 

 indivifibles, which he thought applicable to the quadrature 

 of the circle ; but after beftowing confidcrable attention 

 upon it, it failed in completely anfwering his expectations. 

 In 1653 he publiftied, in oftavo, his " Grammar of the 

 Englifti Tongue, in Latin," with an " Introduftory Trea- 

 ti(e on Speech," containing a philofophical inquiry into the 

 formation of articulate founds. MS. copies of letters which 

 he had decyphcred were this year depofited in the Bodleian 

 library, together with an " Account of the Origin and Pro- 

 grefs of Cryptography, or Secret Writing." In the fol- 

 lowing year he was admitted to the degree of doiElor in divi- 

 nity. In ifijj he printed the propofitiou in his " Arith- 

 metica Infniitorum," relating to the quadrature of the circle, 

 which he fent to Oughtred, and he afterwards publiftied the 

 whole work in quarto, with an introduftory treatife on the 

 conic fedlions, the principal properties of which he demon- 

 (Irated, independently of the cone, by his method of infi- 

 nites. At this time he publiftied his " Elenehus Geometriae 

 Hobbianx," containing a confutation of Hobbes's meihod 

 of quadrating the circle, which was followed by an angry 

 controveriy of fomc continuance. In 1656 he brought out 

 his trad " On the Angle of Contaift," in which he con- 

 tradifted the opinion of Peletarius, who had maint.iined 

 that tins angle had no magnitude. In the following year he 

 pubhihed his " Mathefis Univerfalis, &c." and carried on a 

 controveriy with M. Fermat and M. Freniele, in letters, 

 which ai)prared in the" Commercium Epillolieum," in 1658. 

 About this tune he was chofen " cullos archivorum" to the 

 univerfity ; and he folved fome prize queftions propofcd by 

 Pafcal, that related to the cycloid. His letter to Huygena, 

 " De Conoide et Corporibus inde genitis," and alfo " Dc 



Cycloide, 



