_Illumination._—The amount of light concentrated by the lens on each elementary area of the image determines its brightness or illumination. The ideal image would, of course, be equally bright over its whole area of good definition, and for lenses of narrow angle this is approximately true. But when it is desired to cover a wide angle the question of illumination becomes serious. The relationship between angle from the axis and illumination is that illumination is proportional to the fourth power of the cosine of the angle. This relationship is shown in the following table: Angle Image brightness 0° 100 per cent. 10° 94.1 per cent. 20° 78.0 per cent. 30° 56.2 per cent. 40° 34.4 per cent. 50° 17.1 per cent. If the field of view is 60°, which corresponds to an 18 × 24 centimeter plate with a lens of 25 centimeter focus, the brightness is only 56 per cent., and the necessary exposure at the edge approximately 1.8 times that at the center. This effect is shown in Fig. 15. It is very noticeable if the exposure is so short as to place the outlying areas in the under-exposure period. [Illustration: FIG. 13.—Barrel and pin-cushion distortion.] _Distortion._—Sometimes a lens is relatively free from all the aberrations, mentioned above, so that it gives sharp, clear images on the plate, yet these images may not be exactly similar to the objects themselves as regards their geometrical proportions; in other words, the image will show distortion. Lens distortion assumes two typical forms, illustrated in Fig. 13, which shows the result of photographing a square net-work with lenses suffering in the one case from “barrel” distortion and in the other from “pin-cushion” distortion. In the first the corners are drawn in relative to the sides; in the latter case the sides are drawn in with respect to the corners. Either sort is a serious matter in precision photography, such as aerial photographic mapping aspires to become. It must be reduced to a minimum and its amount must be accurately known if negatives are to be measured for the precise location of photographed objects. In general symmetrical lenses give less distortion than the unsymmetrical (Fig. 14). [Illustration: FIG. 14.—Arrangement of elements in two lenses suitable for aerial work: _a_, Zeiss Tessar; two simple and one cemented components (unsymmetrical); _b_, Hawkeye Aerial; two positive elements of heavy barium crown, two negative of barium flint, uncemented (symmetrical).]