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The mechanical properties of the curves are treated in the article Mechanics, where various forms are illustrated. The simple catenary is shown in the figure. The cartesian equation referred to the axis and directrix is y = c cosh (x/c) or y = ½c(ex/c + ex/c); other forms are s = c sinh (x/c) and y2 = c2 + s2, s being the arc measured from the vertex; the intrinsic equation is s = c tan ψ. The radius of curvature and normal are each equal to c sec2 ψ.

The surface formed by revolving the catenary about its directrix is named the alysseide. It is a minimal surface, i.e. the catenary solves the problem: to find a curve joining two given points, which when revolved about a line co-planar with the points traces a surface of minimum area (see Variations, Calculus of).

The involute of the catenary is called the tractory, tractrix or antifriction curve; it has a cusp at the vertex of the catenary, and is asymptotic to the directrix. The cartesian equation is

x = √ (c2y2) + ½c log [{c − √ (c2y2)} / {c + √ (c2 + y2)}],

and the curve has the geometrical property that the length of its tangent is constant. It is named the tractory, since a weight placed on the ground and drawn along by means of a flexible string by a person travelling in a straight line, the weight not being in this line, describes the curve in question. It is named the antifriction curve, since a pivot and step having the form of the surface generated by revolving the curve about its vertical axis wear away equally (see Mechanics: Applied).

CATERAN (from the Gaelic ceathairne, a collective word meaning “peasantry”), the band of fighting men of a Highland clan; hence the term is applied to the Highland, and later to any, marauders or cattle-lifters.

CATERHAM, an urban district in the Wimbledon parliamentary division of Surrey, England, 20 m. S. of London by the South-Eastern & Chatham railway. Pop. (1901) 9486. It lies in a healthy, hilly district, and has grown in modern times from a village into a large residential town. There are large barracks in the neighbourhood, and the Metropolitan lunatic asylum is close to the town.

CATERPILLAR, the popular name of the larva of various insects, particularly of butterflies and moths (see Lepidoptera, Hexapoda, Metamorphosis). The word appears first in the form caterpyl (Promptorium Parvulorum, about the middle of the 15th century). This may be the original form, with the addition of -ar or -er; if so, it represents the O. Fr. chatepelose or chatepeleuse, i.e. “hairy-cat” (chat, cat, and pelouse, hairy, Lat. pilosus), a name applied to the hairy caterpillar, and also according to Cotgrave to a weevil. The use of “cat” in this connexion is paralleled by the Swiss name for a caterpillar; teufelskatz, and the popular English name for the blossom of the willow, “catkin,” somewhat resembling a caterpillar (cf. “palmer”); the modern French is chenille, Latin canicula, a little dog. The termination of the word seems to have been early connected with “piller,” a robber, plunderer from the destructive habits of the larva, cf. Joel i. 4—“That which the palmer-worm hath left, hath the locust eaten.” The spelling “caterpillar,” a 17th century corruption, has been the usual form since Johnson.

CATESBY, ROBERT (1573–1605), English conspirator, son of Sir William Catesby of Lapworth in Warwickshire, a prominent recusant who was a descendant of Sir William Catesby, speaker of the House of Commons in 1484, executed by Henry VII. after the battle of Bosworth, was born in 1573, and entered Gloucester Hall (now Worcester College), Oxford, in 1586. He possessed a considerable estate, and was said to be wild and extravagant in his youth. In 1596 he was one of those arrested on suspicion during an illness of Queen Elizabeth. In 1601 he took part in the rebellion of Essex, was wounded in the fight and imprisoned, but finally pardoned on the payment of an enormous fine, to obtain which he was forced to sell a portion of his property. In 1602 he despatched Thomas Winter and the Jesuit Tesimond alias Greenway to Spain to induce Philip III. to organize an invasion of England, and in 1603, after James’s accession, he was named as an accomplice in the “Bye Plot.” Catesby was a man of great beauty of person, “above 2 yards high,” says Father Gerard, “ and though slender, yet as well-proportioned to his height as any man one should see.” He possessed a clear head and unflinching courage, and with a strong determination and fascinating manner mastered the minds of his associates and overpowered all opposition. He was, however, headstrong, wilful and imprudent, fit for action, but incapable of due deliberation, and entirely wanting in foresight. Exasperated by his personal misfortunes and at the repressive measures under which his co-religionists were suffering, and blinded by a religious zeal which amounted to fanaticism, he was now to be the chief instigator of the famous Gunpowder Plot, which must in any event have brought disaster upon the Roman Catholic cause. The idea of some great stroke seems to have first entered his mind in May 1603. About the middle of January 1604 he imparted his scheme of blowing up the Parliament House to his cousin Thomas Winter, subsequently taking in Guy Fawkes and several other conspirators and overcoming all fears and scruples. But it was his determination, from which he would not be shaken, not to allow warning to be given to the Roman Catholic peers that was the actual cause of the failure of the plot. A fatal mistake had been made in imparting the secret to Francis Tresham (q.v.), in order to secure his financial assistance; and there is scarcely any doubt that he was the author of the celebrated letter to his brother-in-law, Lord Monteagle, which betrayed the conspiracy to the government, on the 26th of October. On receiving the news of the letter on the 28th, Catesby exhibited extraordinary coolness and fortitude, and refused to abandon the attempt, hoping that the government might despise the warning and still neglect precautions; and his confidence, was strengthened by Fawkes’s report that nothing in the cellar had been touched or tampered with. On the 2nd of November his resolution was shaken by Tresham’s renewed entreaties that he would flee, and his positive assurance that Salisbury knew everything. On the evening of the 3rd, however, he was again, through Percy’s insistence, persuaded to stand firm and hazard the great stroke. The rest of the story is told in the article Gunpowder Plot. Here it need only be said that Catesby, after the discovery of the conspiracy, fled with his fellow-plotters, taking refuge ultimately at Holbeche in Staffordshire, where on the night of the 8th of November he was overtaken and killed. He had married Catherine, daughter of Thomas Leigh of Stoneleigh, Warwickshire, and left one son, Robert, who inherited that part of the family estate which had been settled on Catesby’s mother and was untouched by the attainder, and who is said to have married a daughter of Thomas Percy.

CAT-FISH, the name usually applied to the fishes of the family Siluridae, in allusion to the long barbels or feelers about the mouth, which have been compared to the whiskers of a cat. The Siluridae are a large and varied group, mostly inhabitants of fresh waters; some of them by their singular form and armature are suggestive of the Devonian mailed fishes, and were placed at one time in their vicinity by L. Agassiz. Even such authorities as T. H. Huxley and E. D. Cope were inclined to ascribe ganoid affinities to the Siluridae; but this view has gradually lost ground, and most modern ichthyologists, if not all, have adopted the conclusions of M. Sagemehl, who has placed the Siluridae near the carps and Characinids in the group Ostariophysi. The Silurids and Cyprinids may be regarded as two parallel series derived from some common stock which cannot have been very different from the existing Characinids. In spite of the archaic appearance of some of its members, the family Siluridae does not appear to extend far back in time, its oldest known representative being the Bucklandium diluvii of the Lower Eocene (London Clay) of Sheppey. A great number of forms were placed by Cuvier and his successors in the family Siluridae, which has since been broken up by T. Gill and other American authors into several families, united under the name of Nematognathi. A middle course appears the more reasonable to the