Cooper Union

COOPER UNION, a unique educational and charitable in stitution "for the advancement of science and art" in New York city. It is housed in a brownstone building in Astor Place, be tween 3rd and 4th avenues immediately N. of the Bowery, and was founded in 1857-1859 by Peter Cooper, and chartered in 18S9. In a letter to the trustees accompanying the trust-deed to the property, Cooper said that he wished the endowment to be "for ever devoted to the advancement of science and art, in their application to the varied and useful purposes of life" ; provided for a reading room, a school of art for women, and an office in the Union, "where persons may apply . . . for the services of young men and women of known character and qualifications to fill the various situations"; expressed the desire that students have monthly meetings held in due form, "as I believe it to be a very important part of the education of an American citizen to know how to preside with propriety over a deliberative assembly"; urged lectures and debates exclusive of theological and party questions; and required that no religious test should ever be made for admission to the Union. Cooper's most efficient assistants in establishing and developing the Union were his son, Edward Cooper, and his son-in-law, Abram S. Hewitt. In 19oo Andrew Carnegie increased the financial resources of the Union by gifts aggregating $600,000. In i9o8 the City of New York leased to the Cooper Union at a nominal rental f or ioo years the site formerly occupied by the 69th Regiment Armory, opposite the Cooper Union building on Third Avenue. On this site the Cooper Union has erected a building which has been called Hewitt Annex. This building has substantially enlarged the educational capacity of the institution, enabling it to provide physical laboratories of the most advanced type. For the year 1927 its revenue was $304,655; its expenditures $282,91 o; at the same time its assets were $5,250,733, of which $3,539,147 was general and permanent endowment, plant investment $1,422,275 ($205,000 being various endowments by Peter Cooper; $34o,000, the William Cooper Foundation; $600,000, the Cooper Hewitt Foundation ; $391,656, the John Halstead Bequest; $217,820, the Hewitt Memorial Endowment), and $243,908 was special endowments.

The educational work of the Union has been very successful, the instruction is adequate, and the interest of the pupils notably eager. All courses are free. The reading-room and library con tain full files of current journals and magazines; the library has the rare complete old and new series of patent office reports, and in 1927 had 58,028 volumes; in the same year there were 206,246 readers. There is an excellent museum for the arts of decoration. Apart from lecture courses, the principal departments of the Union with their attendance in 1927, were: a night school of engineering, comprising five-year courses in civil, electrical, me chanical and chemical engineering, 849; a night school in art comprising courses in freehand drawing, decorative arts, modelling and architectural drawing, 1,389; a school of technical science —a four-year course in civil, mechanical, chemical and electrical engineering, 210; a woman's art school comprising courses in freehand drawing, decorative design, costume design, illustration, still life and life painting, interior decoration, mural painting and sculpture, 319, a class in elocution, 48; and classes in oratory and debate, 8o, making a total enrollment of 2,895. In the great hall of the Union free lectures for the public are given throughout the winter under the auspices of the Peoples Institute.

CO-OPTATION,

the election to vacancies on a legislative, administrative or other body by the votes of the existing mem bers of the body instead of by an outside constituency (Lat. co-optare). Such bodies may be purely co-optative like the Royal Academy, or elective with power to add to the numbers by co-optation. An example of the latter are the municipal corpo rations in England.

CO-ORDINATES

in the widest sense are class character istics (in mathematics, primarily magnitudes) that serve to distinguish and arrange the elements or units of an assemblage, specifically of a continuum. More particularly, in geometry they determine the position of each point, line, plane or other extent in a total of such. Co-ordinates of the simplest and principal type are called Cartesian from Rene Descartes in whose Geometrie (1637) they first made a somewhat disguised and in formal appearance, though vague hints may be found much earlier, as in Nicole Oresme's Latin Treatise on the Latitudes of Forms (c. 1361). Perhaps with exacter justice they might be named "Fermatian," as invented by Pierre de Fermat (1601-65) in his study of maxima and minima (1629), who communicated his idea to M. Despagnet of Bordeaux, according to Fermat's letter to Roberval (Sept. 22, 1636). Immediately following the appearance of the Geometrie, Fermat wrote to Descartes (Jan. io, 1638) setting forth his own conceptions, first published, how ever, in his V aria Opera in i679—ideas and methods far in ad vance of Descartes' and nearer to the modern form, range and system. Indeed, it may be said that they almost distinguish him as the "sole founder of analytic geometry" (H. Wieleitner, 1927), if not of modern mathematics.

Parallel Co-ordinates.

The Cartesians are the two distances (x, y) of a point P (x, y) from two axes (OX, OY) in its plane, that meet (commonly at right angles) in the origin O. A fitting name is parallel co-ordinates (fig. 1). Suppose the plane filled completely with each of two systems of parallel lines, the two intersecting at any angle. Suppose also that the lines are all numbered, from a base line in each system, along the base line in the other (OX, 0 Y) ; then through each point of the plane passes one and only one line of each system, and each line bears a number representing the length it cuts off from 0 on the other axis, and is given by an equation as x=3, Y=4; these lengths, numbers and equations are called co-ordinates of the point of intersection P(x, y), rectangu lar or oblique according to angle