LIMITS OF OPTICAL CAPACITY OF THE illCROSCOPE. 425 



all this light and thus get the largest and clearest field of vision, 

 the pupil of the eye must be brought to this spot. The relation 

 between the area of the image and that of the pupil gives at once 

 the ratio by which the brightness of the image is less than that 

 of the object when looked at with the unarmed eye. The same 

 brightness of image as of object exists only when the size of the 

 image is equal to, or larger than that of the pupil. 



In the instance of the telescope, Lagrange had already stated that 

 the relation of size between the diameter of the objective and that 

 of the picture of the objective formed by the ocular, is directly as 

 the amplification, and he proposed to employ this ratio as a means 

 of determining the amplification. "With the telescope, however, 

 such a decrease of brightness is not a necessary accompaniment of 

 increased amplification, because the amount of incident light may 

 be augmented indefinitely by enlarging the object glass or reflector. 

 The aperture of the cone of light entering the microscope is, on the 

 contrary, definitely restricted by the limits of the angle measuring 

 that aperture. 



So far, our demonstration shows that the relation between bright- 

 ness of image and amplification is entirely independent of any 

 particular constraction of the instrument, provided only that it gives- 

 well defined images. An increase of amplification would only be 

 possible, therefore, when a more intense illumination, e.g., direct sun- 

 light "were employed, as indeed Listing had in view in the methods 

 proposed by him for obtaining enormous amplifications. But here 

 other difficulties present themselves, which arise from the very 

 slight divergence-angle of the emerging rays, as appears in al]^ 

 cases of high amplification from the conditions of the equation 

 representing the course of rays that enter an objective with wide 

 divergence-angle. 



The first difficulty is, that shadows of entoptic objects throng the 

 field more densely as the area of this field at the eye spot (ocular 

 image of the objective) becomes smaller. The retina is illuminated 

 from this area as if it were the source of light from which pro- 

 ceeded all the rays that enter the eye. Tliis area is at the same 



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