Lith. pilnas, OChurch Slav. plǔnǔ, OIr. lōn, full. Goth. fulls, OHG. fol, foll, Ger. voll, AS., Eng. full). In mathematics, that which completes a given magnitude or increases it to the value of al fixed magnitude. In angular measure it signifies the angle which, added to a given angle, produces 90°; e.g. 30° is the complement of 60°, 1° is the complement of 89°, 45° is the complement of 45°, 100° of -10°, and 0° of 90°. Such pairs are called complementary angles. The arithmetic complement of an integer is the difference between the integer and the next higher power of 10; e.g. 40 is the arithmetic complement of 60, 1 is the arithmetic complement of 99, 375 of 625, and 7 of 3. The complement logarithm, or 'cologarithm. of a number, is the logarithm of the reciprocal of the number, or the complement of the logarithm (of the given number) less 10. See LOGARIHM.
If through any point on the diagonal of a parallelogram lines are drawn parallel to the sides, four parallelograms are formed. The two of these that are not bisected by the given diagonal are called complements of the given parallelogram.
COMPLEMENT. In music, the interval which must be added to any given interval to complete the octave: for example, a fourth is the complement of a fifth, a third is that of a sixth, etc.
COMPLEMENT. In nautical language, all persons designed to be on board a ship for the purposes of navigating or fighting her. or to enable her to carry on the service for which she is intended. The complement includes the officers and crew; but the latter terms apply to the persons actually on board, while the former applies to all who should be on board if there are no vacancies.
COMPLEMENTARY COLORS. Colors which. when combined. produce white light. Examples of pairs of such colors are given in the following table:
| Red | Green-blue |
| Orange | Cyan blue |
| Yellow | Ultramarine blue |
| Greenish-yellow | Violet |
| Green | Purple |
These colors may be observed readily with a simple polariscope, where polarized light from a Nicol's prism (q.v.) falls upon a prism of calespar and glass, in which by virtue of the doubly refracting power of the calc-spar (see LIGHT, paragraph Double Refraction) there is furnished a double image of the aperture through which the polarized light from the Nicol passes. strip of selenite be interposed between the polarizing prism and the crystal, the two images referred to will be different in color, one shade being complementary to the other. These strips of selenite may be of various thicknesses, and will thus produce various colors. This follows from the well-known principle that, when plane-polarized light is transmitted through a thin plate of a doubly refracting medium, the ordinary and extraordinary rays when examined with a doubly refracting analyzer will give images brightly colored, which where they overlap are white, showing that the two colors are complementary. If two complementary colors are combined and it must be remembered that the colors themselves, not the pigments, are here meant― then white light is produced. This can be accomplished best, perhaps, with the Maxwell color disk where a disk of cardboard composed of segments of complementary colors is rapidly rotated. The impressions of the two colors follow each other so rapidly that the sensations are blended, and if the colors are used in the right proportions we have a gray tint produced, as the luminosity of the two colors either singly or jointly is not so great as that of a white surface with which it would be compared. Complementary colors vary with the light by which they are viewed, and are different when seen by gaslight from what they are in the daytime. The explanation is to be found in Young's theory, where the color-sensation is considered to be furnished by three groups of nerves corresponding to the red. green, and violet-blue waves. If all of these nerves are stimulated together, the sensation produced is that of white light. Consequently, a certain red acts on the red nerves while its corresponding complementary color, green-blue. would stimulate the other sets of nerves, and the result of all acting together would be the sensation of white light. For a thorough discussion of this subject. which may be appreciated by the general reader as well as the student of physics. consult Rood. Modern Chromaties, a new edition of which was published (New York, 1899) under the title of A Text-Book of Color. See VISUAL SENSATION.
COMPLEXION (OF., Fr. complexio, from Lat. complexio, combination, from complecti, to entwine, from com-, together + plectere, to weave). The color of the skin, existing in the epidermis and dependent upon certain pigment-cells. Those persons most exposed to the weather and least under the influence of civilization are usually of the darkest color. Light hair is the usual accompaniment of white and thin skin: while dark hair and dark complexions commonly go together. There does not appear to be any anatomical difference in the skins of persons of light and dark complexions; the differences are the result of temperature, climate. and exposure. The more decided differences in skin-color which may be called racial-the white of the Caucasian, the brown or olive of the Mongolian, the yellow or tawny of the Malayan, the red of the Amerind, and the black of the African and Australian-are apparently connected with deep-scated physiologic processes as well as hereditary causes: they are discussed elsewhere. See SOMATOLOGY.
COMPLEX NUMBER. The steps in the growth of the number system of algebra may easily be illustrated by the roots of equations, thus: The solution of the equation - x-3=0 is 3. a positive integer which may be represented graphically on a straight line. The solution of the equation 3x-2=0 is ⅔a fraction which may also be represented graphically on a straight line. The solution of is , a surd which may be represented by the diagonal of a square whose side is 1. The solution of is 2, a negative number, which may be rep- resented on a straight line in the opposite direc- tion from that of the positive number. But the solution of is or called an imaginary number. The symbol
