Page:The New International Encyclopædia 1st ed. v. 14.djvu/383

NEF. 333 NEGATIVE QUANTITY. was professor of chemistry in Purdue University (].;ifayctte. Ind.). lu 1,SS!)-!I2 lie was assistant professor of chemistry and actiiij,' director of the clicmical lalioratory in Clark L'niversity (Worces- ter, ilass.), in 18!l2-l»li was professor of elicm- islry in the I'niversity of Cliicago. and in ISHO hci-ame head of tlic department of cliemistry in that institution. NEGAPATAM, npg'rt-po-liim'. A seaport city on the Coromandel coast., in the district of Tanjore, Madras. British India, and the ter- minus of a branch line from Tanjore, 48 miles tu the west (Map: India, D 0). It has regular steamer communication with Ceylon, Burma, and the Straits Settlements, and carries (m an active trade exporting rice and paddy, and imjiorting cotton goods and betel nuts. The extraction of oil from cocoanuts and oil seeds is an important industry. The extensive buihling and repairing plant of the Great Southern Railway of India is located here. Negapatam was one of the earliest Portuguese settlements on the Coroman- del coast; it was tal<en by the Dutch in KiOO, and was the capital of their Indian possessions until captured bv the English in 1781. Population, in 1891, 59,221 ; in 1901, 57,190. NEGATIVE (from Lat. ncgaliciis, negative, from IK (Idle, to deny, from ncc, not + aicrc, Skt. ah, to say, Gk. r/fu, imi, I say). A photo- grajihic ])icture in which the lights and shades of tile object are reversed. A negative is usually produced in a camera by the action of light upon the sensitized surface of a glass plate, celluloid film, or paper. (See Photograph v, I When the plate is developed, the portions most ali'ected by the light receive the densest deposits, and are rendered nearly if not quite opaque, while the portions corresponding to the shadows appear transparent. A good negative should show the gradations of light and shade, and should be distinct in all its detail. The presence of as many tones, or values of light and shade, as pos- sible, is desired, while at the same time the high lights and shadows must be marked. The pro- duction of a good negative, outside of ipiestionsof the preparation of the i)late or film, depends chiefly upon a proper length of ex])Osure and suc- cessful development. A negative is used for making positives by contact printing or with an enlarging or copying camera. ¥m- contact print- ing the negative is placed film side upward in a printing frame, and on it is laid a sheet of sensi- tized ])aper with its coating next to the film. The printing frame is then exposed to the light I and the rays passing through the clear or trans- Iparent portions of the negative afl'ect the paper Ibeneath, while those portions beneath the dark [or opaque parts of the negative are protected and [remain white. In this way a large niimbcr of [positives or correct reproductions can be ob- Itained from one negative. NEGATIVE QUANTITY. The inverse op- erations of niafheniatir.-.. such as subtraction, division, and evolution, often lead to results which cannot be expressed in terms of the same unit as the numbers entering the operation. The intcrjiretation of these results leads to the so- called artificial numbers, and in the particular case of subtraction to the notion of negative num- ber. For example. .$2 — .$3 is impossible if the result is to be expressed in terms of the positive unit $1, but, since the result of subtraction is the number which added to the subtrahend will produce the minuend, it is ea.sy to see that the number which added to $3 will make $2 must be ecpiivalent to the number which subtracted from .$3 will make $2. In other words, instead of subtracting $1 from $3 to reduce it to $2, a number mu>.t be 'added which will produce the same result. Such a number is called a negative number and is desig- nated by the sign — placed before it. ' Hence $2 — -$3 = — $1. This notion of negative num- ber as the opposite of ])ositive number, and ap- parently growing out of an arbitrary interpre- tation of a mathematical process, has its counter- part in concrete magnitudes opj)Osed in function or extent. For example, in the above case, if a man's assets are .$2 and his debts .$3, the number expressing his financial status is .$1 of indebted- ness, which may be expressed by — $1. Similarly, time A.D. is often expressed by positive numbers, and time B.C. by negative numbers. In astronomy north latitude is expres.sed by positive numbers and south latitude by negative numbers; west longitude is designated as positive and east longi- tude as negative. Such extensions of the mean- ing of signs and modes of operation are the nat- ural outgrowths of a constantly iirogressive science. The introduction of the negative num- ber doubles the number space of arithmetic by adding an infinite series of numbers opposite in meaning and having a 1 to 1 correspondence (see C0RKE.SPONDENCE) with the series of positive numbers. The negative quantity enters geometry through the phases of motion and direction. For ex- ample, the segments AB. BC, and CD, of a hori- zontal straight line AD thought of as extending to the right ai'e considered positive, but the seg- ments DC, CB, and BA thought of as extending to the left are considered negative. Similarly, many writers regard all angles generated by a line revolving counter-clockwise about a point as positive and those generated by a clockwise mo- tion as negative. The introduction of negative quantities into geometry, especially in connection with the theory of continuity (see Contixvity) , has greath' increased the ])ower and scope of the subject. The meaning of negative quantities as em- ployed in the physical sciences may be illustrated from elementary mechanics. A material point confined to a horizontal straight line may move to the right, remain stationary, or move to the left. The first condition may be expressed by a positive velocity toward the right, the second by a zero velocity, and the tliird by a negative velocity. By analog}" to inathematical usage, the positive and negative notation is sometimes apidied to quantities measured by scales like those of the ordinary thermometers, on which an arbitrary point is denoted as the zero-point and all degrees below zero are denoted by negative numbers. Such conventional notations are convenient, but not always well founded. Thus, the temperature — 1° C. is not the physical opposite of +1° C. ; the two temperatures would be the physical oppo- sites of each other only if 0° C. represented a state in which bodies would have no heat at all, and if it were possible that a body shoiild have less than no heat. (In the other band, in the case of physical magnitudes whose character, like that of electricity, may be dual, the positive and