Examination of Photographic Lenses at Keiv. 433 



small. In fig. 10 is shown the effect of bringing two bright surfaces 

 near together ; that is to say, of a dark line as seen against a bright 

 background ; /, g, f will represent a section through the image of 

 the line, gx being equal to xc. If this curve is turned upside down, 

 as in fig. 9, it can be shown that it represents the image of a bright 

 line on a dark ground. 



In this latter case that of the bright line on the dark ground it 

 can be readily seen that the effect of narrowing the slit of light will 

 be to decrease the illumination gd at the centre of the line until it 

 becomes zero as the slit closes. The worse the definition of the lens, 

 the sooner will the centre of the line reach the limit of visibility ; but 

 by ascertaining what is the width of the finest bright line just 

 visible, a good test for defining power will not be obtained for the 

 following reasons ; in the first place, the illumination of the image 

 will be feeble, which has already been shown to be objectionable, 

 and in the second place, since with feeble illuminations the ocular 

 sensation varies as -a first approximation as the intensity of the 

 illumination, considerable errors would arise through the difficulty of 

 obtaining a constant illumination through lenses of different types. 



These objections do not apply, however, to testing definition by 

 finding the width of the finest dark line that can be seen against a 

 bright background. In this case as the line becomes thinner, the 

 illumination at its centre increases until it reaches that intensity of 

 illumination which can no longer be distinguished by the eye from 

 the illumination of the field. If the illumination eg in fig. 10 can be 

 distinguished from cd by the eye, it is evident that a blurred image 

 of the dark line is visible, and if any illumination greater than eg is 

 indistinguishable from cd by the eye, it is evident that the figure repre- 

 sents the image of the thinnest black line which is visible. Fig. 11 

 represents generally the same condition of things as that shown in 

 fig. 10, except that the defining power of lens is much better ; and it 

 will be seen how much finer the line must be in this case to produce 

 the same proportional illumination at its centre ; that is to say, 

 before the limit of visibility is reached. Now there is a certain 

 intensity of illumination at which and about which the eye is at its 

 maximum of sensitiveness to differences of shade, and this is when 

 the object is what would be described as not bright and not 

 dark; between these wide limits the minimum difference of shade 

 visible is a fixed proportional part of the total illumination. This 

 proportion differs with different observers, but not to a very great 

 extent. Hence if a plan is adopted by which a dark line 011 a 

 bright ground can be made to vary in thickness, and if the illumina- 

 tion is arranged so that the eye is at its maximum sensitiveness (that 

 is therefore so that the line remains longest visible as it diminishes in 

 width), then the moment at which it disappears will occur when the 



