Roger, a celebrated English mathematician and philosopher, born at Burbach, Leicestershire, of which place his father was rector. Before his twelfth year he showed a decided predilection for mathematical study; and afterwards made such rapid progress in that science, that when only twenty-four years of age he was appointed Plumian professor of astronomy and experimental philosophy. He took orders in 1713; and that same year, at the request of Dr Bentley, he published the second edition of Newton's *Principia Mathematica*, enriched with an original preface. This, with an analytical memoir entitled *Logometria*, and a description of the great meteor which appeared in England on the 6th March 1716, inserted in the *Philosophical Transactions*, is all that Cotes lived to publish. He died June 5, 1716, at the age of thirty-three, and was buried in Trinity chapel, where a monument was raised to his memory, bearing a Latin inscription from the pen of Dr Bentley. He left unfinished a series of elaborate researches on optics, in reference to which Newton observed, "If Mr Cotes had lived, we should have known something." With regard to the pure mathematics, the principal discovery of Cotes consists in a theorem, which still bears his name, and which furnishes the means of integrating by logarithms and arcs of the circle the rational fractions whose denominator is a binomial. These expressions had already exercised the ingenuity of Leibnitz, and of John Bernouilli, and by their labours, in conjunction with those of Euler, this branch of the integral calculus soon assumed a more convenient and simple form. His papers were collected by his successor, Dr Robert Smith, and published under the title of *Harmonia Mensurarum, sive Analysis et Synthesis per Rationem et Angularem mensuras promota; accedant alia Opuscula Mathematica*, Cambridge, 1722, 4to. Of this work, the "Analyse des Mesures, des Rapports, et des Angles, ou Reduction des Integrations aux Logarithmes et aux Arcs de Cercle," published (Paris, 1747) by the English Benedictin Walmasley, is rather a paraphrase than a translation. Cotes left a valuable treatise on hydrostatics and pneumatics, which was also published by Smith, and afterwards appeared in a French translation, under the title of "Leçons de Physique Expérimentale sur l'Equilibre des Liqueurs," Paris, 1740, 4to.

CÔTES-DU-NORD, a maritime department in the N.W. of France, containing part of the old province of Brittany. It is bounded N. by the English Channel, W. by Finistère, S. by Morbihan, and E. by Ille-et-Vilaine. Area 2395 square miles. A chain of granitic mountains, of which the culminating point, Mount Menez, attains a height of about 1200 feet, runs through the department from E. to W., dividing it into two unequal parts, of which the southern is the smaller. Towards its western extremity this chain sends out two branches, the one extending westward and the other south-westward to the department of Finistère. Various smaller ramifications are sent off northward and southward from the main chain. The rivers are short and unimportant, the principal being the Rance, Arguenon, Guer, Trieux, Gouessant, and Gouet. The coast is generally steep and rocky. It is much indented by the mouths of numerous small rivers, and fringed, particularly towards its west end, by many small islands. The soil is mostly stony, primitive formations being everywhere found near the surface; and the plains on both sides of the mountain chain are often sandy and sterile. Agriculture is in a very backward state. Rye, oats, and wheat are the principal crops grown. Cattle, goats, and sheep are reared, but they are of inferior breeds. The draught horses, however, are much esteemed. The fisheries employ a great portion of its inhabitants, and constitute one of the most important resources of the department, which is thus an admirable nursery for the French navy. The forests are extensive, and abound with wolves, foxes, badgers, roe-bucks, and wild boars. Iron and lead-mines are worked, but otherwise this department is not rich in minerals. The linen manufacture, though still the staple of the department, has of late years much declined.

Côtes-du-Nord is divided into 5 arrondissements, which with their populations are as follows:

| Arrondissements | Cantons | Communes | Pop. in 1851 | |-----------------|---------|----------|-------------| | St Brieuc | | | | | Dinan | | | | | Loudéac | | | | | Lannion | | | | | Guingamp | | | |

Total: 47 379 632,613