Page:The New International Encyclopædia 1st ed. v. 05.djvu/518

CORRENTI. 444 CORRIGAN. collaborator, have ailvaiK-ed statistical science in Italy. CORRESPONDENCE (Lat. co»i-, together + rrsiiundcrc, to answer, Iruni re-, back -{- spondere, to promise). A term used in mathematics to express certain reciprocal relations. If each in- dividual of one ■;roiip of objects bears a certain relation to a detiiiite number of individuals of another groi]), and a definite number of individu- als of the first group bears the same relation to each individual of the second group, there is said to be a corresi)ondence between the objects of the groups. If 1 of tlie first group corresponds to B of the 2d, and 1 of the second group corre- sponds to A of the 1st, the relation is called an A to B correspondence. If A = B = 1, it is called a 1 to 1 ( = 1 ) correspondence ; e.g. two numbers are said to be equal when there exists a 1 to I correspondence between their units. In geometry the simplest cases of 1 to I cor- respondence, or 'conformal representations,' are furnished by two planes superposed one upon the other. Here to ever.y point of tlie first figure there corresponds one and only one point of the second figure, and to every point of the second figure there corresponds one and only one point of the first. The simplest case of Chasles's (q.v.) corre- spondence formula may be stated thus: If two ranges of points R, and R, lie upon a straight line so that to every point x of Rj there corre- spond in general o points^ of Rj, and again to every point ;/ of R™ there always correspond ^ points X ot' R„ the configuration formed from R, and Rj has (a -- p) coincidences, or there are (a -r ;3) times in which a point x corresponds with a point x. I'^rom these linear transforma- tions Poncelet, PlUcker, JIagnns, Steiner, passed to the quadratic where they first investigated 1 to 1 correspondence between tw'O separate planes. The 'Steiner projection' (1832) em- ployed two planes Ei and E, together with two straight lines Pi and .(/_. not coplanar. If we draw through a point P, or P, of Ei or E, the straight line x^ or ,r, which cuts fl, as well as g^, and determines the intersection X, or Xj, with E™ or E,. then are Pj and X; and P; and Xi corre- sponding points. In this manner to every straight line of the one plane corresponds a conic section in the other. In 1847 Pliicker had deter- mined a point upon the hyperboloid of one sheet, like fixing a point in the plane, by the segments cut off by two fixed generators upon the two generators passing through the point. This was an example of a imiform representation of a sur- face of the second order upon the plane. Corre- spondence relative to surfaces has been studied by Chasles, Clebsch, Cremona, Cayley, and others. In space of three dimensions, only a beginning has been made in the development of this theorj'. Consult: Schubert, Kalkiil der AhziiMenden Geo- metrie (Leipzig, 1879) ; Klein, Terffleichende BetrachtutHjen. iiber neuere geoinetrische Forsch- ungen (Erlangen, 1872) ; Mijbius, Der barycen- triscke Calctil (Leipzig, 1827), CORRESPONDENCE CLASSES. See Chau- tauqua. CORREZE, ko'rez'. A south central depart- ment of France (q.v.), formerly part of the Prov- ince of Limousin, taking its name from an affluent of the Vez6re, the C'orr^ze, which traverses the department Troni northeast to southwest (Map: Trance, H 6). Area, 22G5 square miles; popula- tion, in 1800, SlOMi; in 1901, 318,422. The sur- face of the ilepartment is mountainous, especially in (he north and east, where it is broken in upon by offsets from the Auvergne Mountains, which range from 2500 to 3320 feet (Mont Besson) above the sea. In the south and southwest the .■roil yields wheat, oats, barley, rye, maize, etc. Wine is also produced, but of poor quality. Coal, iron, and lead are found in considerable quanti- ties. Capital, Tulle. COR'RIB, LouGii. A lake in the north of Galway, in the western part of Ireland, with an area of G8 square miles (Map: Ireland, B 3). From its southern end, fdur miles north of Gal- way, it discharges its surplus waters by Galway River into Galway Bay. It receives the waters of the Clare and smaller rivers, and those of Lough Mask, through the Pigeon Hole and other caves at its northern end. On its sides are metamor- phic rock, carboniferous limestone, and marble. Near it are many monumental heaps and mega- lithic circles. It contains many islets, and to the west arc mountains 3000 feet high. CORRIENTES, kOr-ryan'tas. A city of Ar- gentina and capital of the province of that name, situated on the Parana, just above the mouth of the Paraguay (Map: Argentina, F 9). It has several plazas, hospitals for men and women, a jioorliouse and a national college, a normal school and a library. The natural history museum was at one time managed by the naturalist Bonpland. The citj' is the centre of a fertile district, and has considerable trade in lumber and oranges. Its chief industry is shipbuilding, but there are also meat-curing establishments and a foundry. Poptilation, in 1901, 17,000. Corrientes w'as founded in 1588. It occupied a place of considei-- able prominence in the revolutionary movements during the latter half of the nineteenth centtiry. COR'RIGAN, Michael Augustine (1839- 1902). An American Roman Catholic prelate, born at Newark, N. J. He graduated in 1859 at Mount Saint Mary's College (Emmitsburg, Md.), pursued a theological course at the American Col- lege of Rome as one of the twelve students with wiiom that institution was begun, was ordained priest in 1863, and from 1864 to 1868 was pro- fessor of dogmatic "theology and sacred Scriptures in the Diocesan Seminary of Seton Hall College (South Orange, N. J.). From 1868 to 1873 he was president of the college, and in 1873 was ajipointed Bishop of Newark. During his admin- istration of the diocese he greatly increased the number of churches, introduced religious commu- nities, and fotmded charitable institutions. In 1880 he became coadjutor (with right of succes- sion and the title of Archbishop of Petra) to Cardinal McCloskey, Archbishop of New York, and from that time directed the larger part of the work of the archdiocese. He entered into the office of Archbishop of New York in 1885, and received the pallium in 1886, His administration was marked by the prolonged controversy between Dr. Edward McGlynn (q.v.) and the Roman Catholic Church. He efi'ectively developed the archdiocese, which at the time of his death was one of the largest and most important in the world. Although personally retiring and un- obtrusive, he became known, through his many activities, as one of the most prominent Roman Catholics in the United States. He was a scholar of high attainments.