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CISSOID—CISTERCIANS

he was in consequence relieved from duty. An inquiry subsequently held resulted in de Cissey’s favour (1881). He died on the 15th of June 1882 at Paris.

CISSOID (from the Gr. κισσός, ivy, and εἶδος, form), a curve invented by the Greek mathematician Diocles about 180 b.c., for the purpose of constructing two mean proportionals between two given lines; and in order to solve the problem of duplicating the cube. It was further investigated by John Wallis, Christiaan Huygens (who determined the length of any arc in 1657), and Pierre de Fermat (who evaluated the area between the curve and its asymptote in 1661). It is constructed in the following manner. Let APB be a semicircle, ВТ the tangent at B, and APT a line cutting the circle in P and ВТ at T; take a point Q on AT so that AQ always equals PT; then the locus of Q is the cissoid. Sir Isaac Newton devised the following mechanical construction. Take a rod LMN bent at right angles at M, such that MN = AB; let the leg LM always pass through a fixed point О on AB produced such that OA=CA, where С is the middle point of AB, and cause N to travel along the line perpendicular to AB at C; then the midpoint of MN traces the cissoid. The curve is symmetrical about the axis of x, and consists of two infinite branches asymptotic to the line ВТ and forming a cusp at the origin. The cartesian equation, when A is the origin and AB = 2a, is y2(2ax) = x3; the polar equation is r = 2a sin θ tan θ. The cissoid is the first positive pedal of the parabola y2+8ax = 0 for the vertex, and the inverse of the parabola y2=8ax, the vertex being the centre of inversion, and the semi-latus rectum the constant of inversion. The area between the curve and its asymptote is 3πa2, i.e. three times the area of the generating circle.

The term cissoid has been given in modern times to curves generated in similar manner from other figures than the circle, and the form described above is distinguished as the cissoid of Diocles.

A cissoid angle is the angle included between the concave sides of two intersecting curves; the convex sides include the sistroid angle.

See John Wallis, Collected Works, vol. i.; T. H. Eagles, Plane Curves (1885).

CIS-SUTLEJ STATES, the southern portion of the Punjab, India. The name, now obsolete, came into use in 1809, when the Sikh chiefs south of the Sutlej passed under British protection, and was generally applied to the country south of the Sutlej and north of the Delhi territory, bounded on the E. by the Himalayas, and on the W. by Sirsa district. Before 1846 the greater part of this territory as independent, the chiefs being subject merely to control from a political officer stationed at Umballa, and styled the agent of the governor-general for the Cis-Sutlej states. After the first Sikh War the full administration of the territory became vested in this officer. In 1849 occurred the annexation of the Punjab, when the Cis-Sutlej states commissioner ship, comprising the districts of Umballa, Ferozepore, Ludhiana, Thanesar and Simla, was incorporated with the new province. The name continued to be applied to this division until 1862, when, owing to Ferozepore having been transferred to the Lahore, and a part of Thanesar to the Delhi division, it ceased to be appropriate. Since then, the tract remaining has been known as the Umballa division. Patiala, Jind and Nabha were appointed a separate political agency in 1901. Excluding Bahawalpur, for which there is no political agent, and Chamba, the other states are grouped under the commissioners of Jullunder and Delhi, and the superintendent of the Simla hill states.

CIST (Gr. κίστη, Lat. cisfa, a box; cf. Ger. Kiste, Welsh kistvaen, stone-coffin, and also the other Eng. form “chest”), in Greek archaeology, a wicker-work receptacle used in the Eleusinian and other mysteries to carry the sacred vessels; also, in the archaeology of prehistoric man, a coffin formed of flat stones placed edgeways with another flat stone for a cover. The word is also used for a sepulchral chamber cut in the rock (see Coffin).

“Cistern,” the common term for a water-tank, is a derivation of the same word (Lat. cisterna; cf. “cave” and “cavern”).

CISTERCIANS, otherwise Grey or White Monks (from the colour of the habit, over which is worn a black scapular or apron). In 1098 St Robert, born of a noble family in Champagne, at first a Benedictine monk, and then abbot of certain hermits settled at Molesme near Châtillon, being dissatisfied with the manner of life and observance there, migrated with twenty of the monks to a swampy place called Cîteaux in the diocese of Châlons, not far from Dijon. Count Odo of Burgundy here built them a monastery, and they began to live a life of strict observance according to the letter of St Benedict’s rule. In the following year Robert was compelled by papal authority to return to Molesme, and Alberic succeeded him as abbot of Cîteaux and held the office till his death in 1109, when the Englishman St Stephen Harding became abbot, until 1134. For some years the new institute seemed little likely to prosper; few novices came, and in the first years of Stephen’s abbacy it seemed doomed to failure. In 1112, however, St Bernard and thirty others offered themselves to the monastery, and a rapid and wonderful development at once set in. The next three years witnessed the foundation of the four great “daughter-houses of Cîteaux”—La Ferté, Pontigny, Clairvaux and Morimond. At Stephen’s death there were over 30 Cistercian houses; at Bernard’s (1154) over 280; and by the end of the century over 500; and the Cistercian influence in the Church more than kept pace with this material expansion, so that St Bernard saw one of his monks ascend the papal chair as Eugenius III.

The keynote of Cistercian life was a return to a literal observance of St Benedict’s rule-how literal may be seen from the controversy between St Bernard and Peter the Venerable, abbot of Cluny (see Maitland, Dark Ages, § xxii.). The Cistercians rejected alike all mitigations and all developments, and tried to reproduce the life exactly as it had been in St Benedict’s time, indeed in various points they went beyond it in austerity. The most striking feature in the reform was the return to manual labour, and especially to field-work, which became a special characteristic of Cistercian life. In order to make time for this work they cut away the accretions to the divine office which had been steadily growing during three centuries, and in Cluny and the other Black Monk monasteries had come to exceed greatly in length the regular canonical office: one only of these accretions did they retain, the daily recitation of the Office of the Dead (Edm. Bishop, Origin of the Primer, Early English Text Society, original series, 109, p. xxx.).

It was as agriculturists and horse and cattle breeders that, after the first blush of their success and before a century had passed, the Cistercians exercised their chief influence on the progress of civilization in the later middle ages: they were the great farmers of those days, and many of the improvements in the various farming operations were introduced and propagated by them; it is from this point of view that the importance of their extension in northern Europe is to be estimated. The Cistercians at the beginning renounced all sources of income arising from benefices, tithes, tolls and rents, and depended for their income wholly on the land. This developed an organized system for selling their farm produce, cattle and horses, and notably contributed to the commercial progress of the countries of western Europe. Thus by the middle of the 13th century the export of wool by the English Cistercians had become a feature in the commerce of the country. Farming operations on so extensive a scale could not be carried out by the monks alone, whose choir and religious duties took up a considerable portion of their time; and so from the beginning the system of lay brothers was introduced on a large scale. The lay brothers were recruited from the peasantry and were simple uneducated men, whose function consisted in carrying out the various field-works and plying all sorts of useful trades; they formed a body