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W A L 
WALLERSTEIN,a town of Bavarian Franconia; 4 miles 
north of Nordlingen. Population 1300. 
WALLERTH WAITE, a hamlet of England, in the parish 
of Rippon, Yorkshire. 
WA'LLET, s. [pealhan, to travel, Saxon.] A bag, in 
which the necessaries of a traveller are put; a knapsack.— 
Having entered into a long gallery, he laid down his wallet , 
and spread his carpet, in order to repose himself upon it. 
Addison. —Any thing protuberant and swagging. 
Who would believe, that there were mountaineers 
Dew-lapt like bulls, whose throats had hanging at them 
Wallets of flesh ? Shakspeare. 
WALLEY, a hamlet of England, in the parish of Cuck- 
ney, county of Nottingham. 
WA'LLEYE, s. [This word is written not wall but 
whall, in our old language: “ wholly eies, the signe of 
gelosy.” Spenser, F. Q. i. iv. 24. “ Whaule-eyed, glau- 
ciolus.” Huloet. ] A disease in the crystalline humour of 
the eye; the glaucoma.—A pair of wall-eyes in a face 
forced. B. Jonson. 
WA'LLEYED, adj. Having white eyes. 
Wall-eyed slave! whither wouldst thou convey 
This growing image of thy fiend-like face ? Shakspeare. 
WA'LLFLOWER, s. [ parietaria , Lat.] A species of 
stock-gilliflower. 
WA'LLFRUIT, s. Fruit, which to be ripened must be 
planted against a wall.—To wallfruit and garden-plants, 
there cannot be a worse enemy than snails. Mortimer. 
WALLHAUSEN, a town of Prussian Saxony, on the river 
Helm. Population 900. 
WALLI, a small kingdom of Western Africa, extending 
along the north bank of the Gambia, having Yani on the 
west, and Woolli on the east. 
WALLINGFORD, a borough and market town of Eng¬ 
land, in the county of Berks, situated on the river Thames, 
over which there is a stately stone bridge, above 300 yards 
long, with 19 arches, and four draw-bridges. This bridge, 
from its appearance, seems to be one of the oldest structures 
of the kind on the river, though the time of its erection is 
unknown. The pointed sterlings on the upper side are so 
well constructed, as to be capable of resisting the most vio¬ 
lent floods. The town has of late years been much increased, 
both in houses and inhabitants. It consists of two principal 
streets. Wallingford contains three churches, St- Mary’s, St. 
Leonard’s, and St. Peter’s. The latter was rebuilt about 50 
years ago, and was then ornamented with a spire of a sin¬ 
gular form. Here is a handsome market-house, and a town- 
hall, in which the assizes are sometimes held, and the 
quarter-sessions for the borough. Here are also six alms¬ 
houses and a free-school. Wallingford was a borough in the 
reign of Edward the Confessor, and has sent two members to 
parliament from the 23d year of Edward I. The right of 
election is in the corporation, and inhabitants paying scot 
and lot, and not receiving alms. The number of voters is 
about. 150. By the charter of James I. the corporation con¬ 
sists of a mayor, high steward, recorder, six aldermen, who 
act as justices within the borough, a town-clerk, a chamber- 
lain, and 18 burgesses. Markets on Tuesday and Friday, 
and four annual fairs; 14 miles north-north-west of Read¬ 
ing, and 46 west of London. Population 1901. 
WALLINGFORD, a post township of the United States, 
in Rutland county, Vermont; 32 miles west of Windsor.— 
2. A post township of New Haven county, Connecticut; 12 
miles north-north-east of New Haven. 
WALLINGTON, a parish of England, in Hertfordshire; 
3^ miles east-by-south of Baldock.—2.; A parish of England, 
county of Norfolk, near Market Downham.—3. A township 
of England, in Northumberland ; 14 miles west of Morpeth. 
—4. A hamlet of England, in the county of Surrey ; 3 miles 
west-south-west of Croydon. Population 804. 
WALLIS (John), a well known mathematician, was born 
at Ashford, in Kent, in the year 1616, and after finishing his 
school education, was admitted, in 1632, at Emanuel col¬ 
lege, Cambridge, with a view to the church. Having taken 
LIS. 
orders, he commenced the duties of his ministerial office in 
1641, as chaplain to Sir William Darnley, in Yorkshire- 
and whilst he occupied the same station in the family of 
Lady Vere, he had an opportunity of exhibiting his extra¬ 
ordinary talent in the art of decyphering. In 1643 the par¬ 
liament, to which he was then attached, conferred upon him 
the sequestrated living of St. Gabriel, in Fenchurch-slreet,- 
London; and in this year he published a quarto volume, 
entitled “ Truth tried, or Animadversions on Lord Brookes’s 
Treatise of the Nature of Truth.” At this time he became 
possessed of a handsome patrimony by the death of his 
mother; and in 1644 he was appointed one of the secreta¬ 
ries of the assembly of divines. In the following year he 
concurred with those persons who laid the foundation of the 
Royal Society, and communicated specimens of his skill in 
mathematics; and in 1647 he discovered a new method of 
solving cubic equations. When the independents acquired 
an ascendancy over the covenanters, Wallis united with other 
ministers, who assembled at Sion college, in subscribing a 
paper, entitled “ A Testimony to the Truth of Jesus Christ, 
and to the Solemn League and Covenant, as also against the 
Errors, Heresies, and Blasphemies of those Times, and the 
Toleration of them.” In 1648 he subscribed a remonstrance" 
against putting the king to death, and another paper, deno¬ 
minated “ A serious and faithful Representation of the Judg¬ 
ment of Ministers of the Gospel, 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 visitor Savilian professor of geometry, and 
quitting his church in London, entered himself of Exeter 
college, Oxford, where he became master of arts, and sedu¬ 
lously discharged the duties of his office, connecting himself 
with those who formed the Philosophical Society in that 
city. Towards the end of this year he became acquainted 
with Cavalleri’s method of indivisibles, which he thought 
applicable to the quadrature of the circle; but after bestow¬ 
ing considerable attention upon it, it failed in completely an¬ 
swering his expectations. In 1653 he published, in octavo, 
his “ Grammar of the English Tongue in Latin,” with an 
“ Introductory Treatise on Speech,” containing a philoso¬ 
phical inquiry into the formation of articulate sounds. MS. 
copies of letters which he had decyphered were this year 
deposited in the Bodleian library, together with an “ Ac¬ 
count of the Origin and Progress of Cryptography, or Secret 
Writing." In the following year he was admitted to the 
degree of doctor in divinity. In 1655 he printed the pro¬ 
position in his “ Arithmetica Infinitorum,” relating to the 
quadrature of the circle, which he sent to Oughtred, and he 
afterwards published the whole work in quarto, with an in¬ 
troductory treatise on the conic sections, the principal pro¬ 
perties of which he demonstrated, independently of the cone, 
by his method of infinites. At this time he published his 
“ Elenchus Geometrise Hobbianre,” containing a confutation 
of Hobbes’s method of quadrating the circle, which was fol¬ 
lowed by an angry controversy of some continuance. In 
1656 he brought out his tract “ On the Angle of Contact,” 
in which he contradicted the opinion of Peletarius, who had 
maintained that this angle had no magnitude. In the fol¬ 
lowing year he published his “ Mathesis Universalis, &c." 
and carried on a controversy with M. Fermat and M. Fre- 
nicle, in letters, which appeared in the “ Commercium Epis- 
tolicum,” in 1658. About this time he was chosen “ custos 
archivorum” to the university; and he solved some prize 
questions proposed by Pascal, that related to the cycloid. 
His letter to Huygens, “ De Conoide et Corporibus inde 
genitis,” and also “ De Cycloide, &c.” was published in 
1659. His talent for decyphering recommended him to 
Charles II., by whom he was graciously received after his 
restoration ; and who, besides continuing him in his offices 
at the university, made him one of his chaplains in ordinary. 
In 1660 he was concerned with those who were employed in 
reviewing the book of common prayer; and having com¬ 
plied with the requisitions of the act of uniformity, he re¬ 
tained his connection with the church till his death. Having- 
suggested that it was possible to teach a deaf man to speak, 
