IMAGE

(Lat. imago.) In Rhetoric, a term somewhnt loosely used; but which appears generally to denote a metaphor dilated, and rendered a more complete picture by the a emblage of various ideas through which the same meta an allegory.phor continues to run, yet not sufficiently expanded to form I'mage. A representation of the Deity in stone, wood, or metal. (See art. Idol.) The custom of representing Christ, the Virgin, and the Saints by images in the churches, which forms a principal feature of Roman Catholic worship, is an ancient but not a primitive practice. For the principal events in the history of Christian image worship, see art. Iconoclasts. I'mage, in Optics, is the spectrum or appearance of an object made by reflection or refraction; or the image of an object may be more correctly defined as the locus of all the pencils of converging or diverging rays emanating from every point of the object, and received on a surface. It is by means of optical images that vision is effected. The eye is an a emblage of lenses which concentrate the rays emanating from each point of the object on a ti ue of very delicate nerves called the retina, where an exact image or representation of the object is formed; and it is this image which is perceived or felt by the retina. The brightne of an imnge depends evidently on the quantity of light concentrated in each point. Setting aside the effects of aberration, the brightne must therefore be proportional to the apparent mngnitude (as seen from the object) of the mirror or lens by which the rays are reflected or refracted, multiplied by the area of the object and divided by the area of the image. But the apparent mngnitude of the lens, as seen from the object, is proportional to the square of the diameter of the lens divided by the square of the distance of the object; and the area of the object divided by the area of the image is equal to the squnre of the distance of the object divided by the square of the distance of the image from the lens: therefore the brightne of the image is proportional to the square of the diameter of the lens divided by the square of the distance of the image from the lens; that is to say, the brightne or degree of illumination of the image depends only on the apparent magnitude of the lens as seen from the image, and not in any way on the distance of the object. When the object and its image are only physical points, and have no apparent magnitude,as stars for example, the brightne of the image is simply proportional to the magnitude of the lens, or to the square of the diameter of the aperture of the telescope; and for this reason certain stars are rendered visible by large telescopes, while their light is too feeble to be perceived by smaller ones. The images of external objects are painted on the retina in a reversed position, and from the retina the impre ions are transmitted to the sensorium by the optical nerves. See Eye, Optics. IMAGERY may be defined as the generic term for jimiles, allegories, and metaphors, or such rhetorical figures as denote similitude or comparison. IMAGINARY QUANTITIES, or IMPOSSIBLE QUANTITIES, in Algebra, are the even roots of negative quantities, or the imaginary results of some impo ible operation. The square root of any positive number may be affected indifferently with the positive or negative sign; thus, v^a'2 = — 3a; because +3a or —3a, raised to the square, equally produce 9a2. But if the number or quantity is negative, the extraction of its square root is impo ible, because the square of any quantity, whether positive or negative, is e entially positive; that is to say, a negative quantity cannot be the square of any real quantity whatever. The symbolical expre ions y/— 9, y/— 4a*, v/— 5, indicate operations which are im|X) ible; and hence they are designated imaginary impre ions. But, though the quan tities denoted by these symbols have no real values, the symbols themselves may have all the algebraic operations performed on them which can be performed on real quantities. Thus, v/=9 = v/9" V~1 = V— i; and^^: Via2 • y/— 1 = 2aV— L Such expre ions are of very frequent occurrence in the higher analysis, and sometimes lead to results of the greatest importance, which it would be dif ficult, if, indeed, po ible, to obtain in another way. (Se« Peacock's Algebra.) IMAGINARY ROOTS OF EQUATIONS are roots which can only be indicated by imaginary expre ions. DAlembert first demonstrated that every imaginary root of an equation can be reduced to the form a-\-by/— 1, wh«re « [s. 604]