ROGER

See also:

• ROGER COTES (1682-1716)

COTES (1682-1716)  , English mathematician and philosopher, was born on the loth of July 1682 at Burbage, Leicestershire, of which place his father, the Rev . Robert Cotes, was rector . He was educated at Leicester school, and afterward at St Paul's school, London . Proceeding to Trinity College, Cambridge, in 1699, he obtained a fellowship in 1705, and in the following year was appointed Plumian professor of astronomy and experimental philosophy in the university of Cambridge . He took orders in 1713; and the same year, at the request of Dr Richard Bentley, he published the second edition of Newton's Principia with an original preface . He died on the 5th of June 1716, leaving unfinished a series of elaborate researches on optics, and a large amount of unpublished manuscript . He contributed two memoirs to the Philosophical Transactions, one, " Logometria," which discusses the calculation of logarithms and certain applications of the infinitesimal calculus, the other, a " Description of the great fiery meteor seen on March 6th, 1716." After his death his papers were collected and published by his cousin and successor in the Plumian chair, Dr Robert Smith, under the title Harmonia Mensurarum (1722) . This work included the " Logometria," the trigonometrical theorem known as " Cotes' Theorem on the Circle " (see TRIGONOMETRY), his theorem on harmonic means, subsequently developed by Colin Maclaurin, and a discussion of the curves known as " Cotes' Spirals," which occur as the path of a particle described under the influence of a central force varying inversely as the cube of the distance . In 1738 Dr Robert Smith published Cotes' Hydro-statical and Pneumatical Lectures, a work which was held in great estimation . The exceptional genius of Cotes earned encomiums from both his contemporaries and successors; Sir Isaac Newton said, " If Mr Cotes had lived, we should have known something." COTES-DU-NORD, a maritime department of the north-west of France, formed in 1790 from the northern part of the province of Brittany, and bounded N. by the English Channel, E. by the department of Ille-et-Vilaine, S. by Morbihan, and W. by Finistere . Pop . (1906) 611,506 .

Area, 2786 sq. m . In general conformation, Cotes-du-Nord is an undulating plateau including in its more southerly portion three well-marked ranges of hills . A granitic chain, the Monts du Merle, starting in the south-east of the department runs in a north-westerly direction, forming the watershed between the rivers running respectively to the Channel and the Atlantic Ocean . Towards its western extremity this chain bifurcates to form the Montagnes Noires in the south-west and the Montagne d'Arree in the west of the department . The rivers of the Channel slope are the Rance, Arguenon, Gouessan, Gouet, Trieux, Treguier and Leguer, while the Blavet, Meu, Oust and Aulne belong to the southern slope . Off the coast, which is steep, rocky and much indented, are the Sept-Iles, Brehat and other small islands . The principal bays are those of St Maio and St Brieuc . The climate is mild and not subject to extremes; in the west it is especially humid . Agriculture is more successful on the coast, where seaweed can be used as a fertilizer, than in the interior . Cereals are largely grown, wheat, oats and buck-wheat being the chief crops . Potatoes, flax, mangels, apples, plums, cherries and honey are also produced . Pasture and various kinds of forage are abundant, and there is a large output of milk and butter .

The horses of the department are in repute . It produces

slate, building-stone, lime and china-clay . Flour-mills, saw-mills, sardine factories, tanneries, iron-works, manufactories of polish, boat-building yards, and rope-works employ many of the inhabitants, and cloth, agricultural implements and nails are manufactured . The chief imports are coal, wood and salt . Exports include agricultural products (eggs, butter, vegetables, &c.), horses, flax and fish . The chief commercial ports are Le Legue and Paimpol; and Paimpol also equips a large fleet for the Icelandic fisheries . The coast fishing is important and large quantities of sardines are preserved . The department is served by the Ouest-Etat railway; its chief waterway is the canal from Nantes to Brest which traverses it for 73 M . Cotes-du-Nord is divided into the five arrondissements of St Brieuc, Dinan, Guingamp, Lannion and Loudeac, which contain 48 cantons and 390 communes . Bas Breton is spoken in the arrondissements of Guingamp and Lannion, and in part of those of Loudeac and St Brieuc . The department belongs to the ecclesiastical province, the academic (educational division), and the appeal court of Rennes, and in the region of the X. army corps . St Brieuc, Dinan, Guingamp, Lamballe, Paimpol and Treguier, the more noteworthy towns, are separately treated .

Extensive remains of an

abbey of the Premonstratensian order, dating chiefly from the 13th century, exist at Kerity; and Lehon has remains of a priory, which dates from the same period . The department is rich in interesting churches, among which those of Ploubezre (12th, 14th and 16th centuries), Perros-Guirec (12th century), Plestin-les-Greves (16th century) and Lanleff (12th century) may be mentioned . The church of St Mathurin at Moncontour, which is a celebrated place of pilgrimage, contains fine stained glass of the 16th century, and the mural paintings of the chapel of Kermaria-an-Isquit near Plouha, which belongs to the 13th and 14th centuries, are celebrated . Near Lannion (pop . 5336), itself a picturesque old town, is the ruined castle of Tonquedec, built in the 14th century and sometimes known as "the Pierrefonds of Brittany," owing to its resemblance to the more famous castle . At Corseul are a temple and other Roman remains .