DUALISM. 483 DUANE. is regarded that tlic iiiaiiitenniuo of fundamental unity is compatible with that of fundamental duality of distinetions within that unity, and that fundamental duality of distinctions is com- patible with fundamental multiplicity of more specilic distinctions. The question as to the form in which the fundamental tuiity of the universe must be conceived is treated elsewhere. See -MoxisM. But one further question remains to be dis- cussed here, in what way must the correlation of the physical and the psychical be conceived? Are they merely parallel distinctions within experience, or do they interact? This again de- pends upon the meaning of terms. If by inter- action is meant mechanical interaction or the transfer of energy- in aooordance with the law of the transformation of energy (see Energetics), then interaction is impossible unless it can be made out that psychical activity is a mode of spe- cial motion (materialism). This cannot be done. All that can be made out empirically is that certain changes in the psychical are accom- panied and followed by certain clianges in a cer- tain portion of the physical phenomena, viz. the body, and vice versa. This may be expressed by saying that there is merely a parallelism. But if by interaction is meant that there is causal connection in the sense in which causality (q.v.) is now used by the best modern logicians, there is interaction. That is, certain psychic events are invariably sequent upon certain physical events, and vice versa. See Knowl- edge, TlIEOKY OF. DUALITY (Lat. diialitas, state of being two- fold, from duaUs, relating to two). A principle of geometry by which one proposition is trans- formed into another through the interchange of a pair of elements; e.g. the proposition. If two triangles have two sides and the included anqle of the one respectively equal to two sides and the included aitf/Ie of the other, the triangles are congruent, may be transformed by the inter- change of the words sides and (Dir/lcs into an- other familiar proposition: If two triangles have two angles and the included side of the one respectively equal to two aiif/les and the included side of the other, the triangles are concrruent. This principle is often called the principle of reciprocity, and is extensively used in geometri". Although the reciprocal of a valid proposition is not of itself necessarily valid, it often siiggests new possible theorems for in- vestigation. In plane geometry the dual ele- ments most commonly interchanged are: point — line: line — point; angles of a triangle — • (opposite) .sides of the triangle; sides of a triangle — (opposite) sides of the triangle ; pencil of lines — range of points; range of points — pencil of lines. Similarly there are dual propositions of solid geometry, as those formed by interchanging the words siraiftlit line and plane; e.g. two inter- secting slraipht lines determine a plane; two intersecting planes determine a straif/hf line. Such propositions also exist, one in plane geome- try and the other in solid geometry, as when the terms triangle and trihedral anr/le are inter- changed : e.g. one side of a triangle is less than the sum of the other two; one faee angle of a trihedral angle is less than the stun of the other two. The term duality appears in the projective geometry of Ciergonnc (1S13), and tiie develop- ment of the 'princii)le of duality' in another work by the samonautlior (182(i). This prin- ciple is a powerful agent of modern geometry, and it has been applied to various properties of curves. DUANE, dii-.nn', J.vmes (1733-97). An American lawyer and jurist. He married into the Livingston family, studied law, and attained great prominence in his profession, before the Kevolution. In the heated political discussions preceding the war, he opposed all radical meas- ures, being ready to sacritice nuich for the sake of peace. He was chosen a delegate to the first Continental Congress in 1774, and aroused vio- lent opposition by his proposal for a recognition of the validity of the British Navigation Acts and his advocacy of Galloway's scheme for a union of all the colonies under a chief magis- trate appointed by the King. His distrust of a republican form of government led him vigorous- ly to oppose the adoption of the Declaration of Independence. He continued to hope for paci- fication until the last, but when the break came he tlirew in his lot with the Patriot party. He continued a member of the Continental Congress throughout the entire Revolutionary period, tak- ing an active part in the debates. He was one of the atithors of the first N'ew York State Con- stitution, was a member of the Committee of Safety in Xew York City in 1776-77, and after the evacuation of the city by the British in 1783 he was chosen the first Mayor under the new charter, serving until 1789. In that year he was appointed by Washington to the office of United States District .Judge for Xew York, which he held until 1794, rendering many de- cisions which were of considerable importance in the formative period of the country's exist- ence. _ DUANE, James CH.vrH.M (1824-97). An American military engineer, born in Schenec- tady, X. Y. He graduated at Union College in 1844 and at West Point in 1848; commanded the engineer company in the Utah expedition of 1858, and was instructor at West Point from that year until 1801. In the Civil War he served with distinction as captain of engineers in the Peninsular Campaign of 1862; was chief engineer of the .rniy of the Potomac in the battles of South Mountain and Antietam: was chief engineer of the Department of the South for a time in 1803; and from July, 1803, until the close of the war again served in the Army of the Potomac. He was brevetted brigadier- general in 180.5; had charge of the construction of the fort at Willets Point, X. Y.. from 1805 to 1868; served as superintendent of fortifica- tions on the JIaine and New Hampshire <oasts, and in 1880 became chief of engineers with the reunilar rank of brigadier-general. He published a Manual for Engineer Troops (1862). DUANE, William (ITOO-lS.'iS). An Ameri- can politician and journalist, born in northern Xew York near the banks of Lake Champlain. He was sent to Ireland in 1771 to be educated, learned the printer's trade, and in 1784 went to British India, where he made a fortune, and established a newspaper called The World at
