An important point to notice is that these data are uniformly plotted in terms of a lens of 100 millimeters focal length irrespective of the actual focal length of the lens measured. Thus this particular chart is for a 50 centimeter lens but would be plotted on the same scale for a 25 or a 100 centimeter lens. Underlying this practice is the assumption that all the characteristics of lenses of the same design and aperture are directly proportional to their focal length. If this were so, then a 50 centimeter lens would give double the size of image that a 25 centimeter does, and so on. As a matter of fact, test shows that the size of the image does not increase so rapidly as the focal length; so that while the image size for a 25 centimeter lens would be, say, .05 millimeters per 100 millimeters focal length, it will be only .03 or .04 millimeters per 100 millimeters focal length for a 50 centimeter lens. The actual size of a point image will therefore be greater, though not proportionately greater. [Illustration: FIG. 16.—Chart recording measurements of lens characteristics.] The chart presents tests on a good quality lens, and so gives a good idea of the permissible magnitude of the various errors. In many ways the most important figure is that for image size, including as it does the result of all the aberrations. In the example given, this varies from .075 to .15 mm. actual size. For the same type of lens of 25 centimeters focus this range will be from .05 to .10 mm. Since these are commonly used focal lengths, a good average figure for image size, commonly used in aerial photographic calculations, is ⅒ mm. In regard to astigmatic tolerances, the two astigmatic foci should not be separated at any point by more than 6 to 7 millimeters, and the mean of these should not deviate from the true flat field by more than ½ millimeter, in each case the figures being based on the conventional 100 millimeters focal length. Distortion should not be over .08 millimeter at 18° or .20 millimeter at 24° from the axis (per 100 millimeters focal length). =Lens Aperture.=—In the simple lens the aperture is merely the diameter. In compound lenses the aperture is not the linear opening but the effective opening of an internal diafram. Photographically, however, aperture has come to have a more extensive meaning. While in the telescope the actual diameter of an objective is perhaps the most important figure, and in the microscope the focal length, in photography the really important feature is the amount of light or illumination. This is determined by lens opening and focal length together; specifically, by the ratio of the lens area to the focal length. The common system of representing photographic lens aperture is by the ratio of focal length to lens diameter, the lens being assumed to be circular. Thus F/5 (often written F.5) indicates that the diameter is one-fifth the focal length.