Two points are to be constantly borne in mind in connection with this system of representation. First, all lenses of the same aperture (as so represented) give the same illumination of the plate (except for differences due to loss of light by absorption and reflection in the lens system). This follows simply from the fact that the illumination of the plate is directly proportional to the square of the lens diameter, and inversely as the square of the focal length. Secondly, the illumination of the plate is inversely as the square of the numerical part of the expression for aperture. That is, lenses of aperture F/4.5 and F/6 give images of relative brightness (6/4.5)^2 = 1.78. What lens aperture, and therefore what image brightness, is feasible, is determined chiefly by the angular field that must be covered with any given excellence of definition. The largest aperture ordinarily used for work requiring good definition and flat field free from distortion is F/4.5. Anastigmatic lenses of this aperture cover an angle of 16° to 18° from the axis satisfactorily, which corresponds to an 18 × 24 centimeter plate with a lens of 50 centimeters focus. Lenses with aperture as large as F/3.5 were used to some extent in German hand cameras of 25 centimeters focal length, with plates of 9 × 12 centimeters. English and American lenses of this latter focal length were commonly of aperture F/4.5, designed to cover a 4 × 5 inch plate. As a general rule the greater the focal length the smaller the aperture—a relationship primarily due to the difficulty of securing optical glass in large pieces. Thus while 50 centimeter lenses of aperture F/4.5 are reasonably easy to manufacture, the practicable aperture for quantity production is F/6, and for 120 centimeter lenses, F/10. This means that a very great sacrifice of illumination must be faced to secure these greater focal lengths. As is to be expected from the state of the optical glass industry, the German lenses were of generally larger aperture for the same focal lengths than were those of the Allies. Besides the F/3.5 lenses already mentioned, their 50 centimeter lenses were commonly of aperture F/4.8, their 120 centimeter lenses of aperture F/7, or of about double the illuminating power of the French lenses of the same size. Demands for large covering power also result in smaller aperture. The 26 centimeter lenses used on French hand cameras utilizing 13 × 18 centimeter plates were commonly of aperture F/6 or F/5.6. The lens of largest covering power decided on for use in the American service was of 12 inch focus, to be used with an 18 × 24 centimeter plate (extreme angle 26°); the largest satisfactory aperture for this lens is F/5.6.