BRIGHTNESS OF THE FIELD OF THE MICROSCOPE. 85 



the aperture of the cones of light, while proceeding from the 

 single points, varies. The greater amount of light contained in 

 the larger pencils of rays is therefore always distributed over a 

 surface of the retina which is larger in the same proportion. 



It might be supposed that the same ratio would exist for 

 the eye in microscopic vision, and that hence the power of the 

 Microscope would vary in the same ratio with the angular aper- 

 ture of the incident rays. This brightness of the field would then 

 be equal to unity, i.e., we should see the objects equally bright 

 as with the naked eye. And if any combination of lenses were 

 able to receive and direct to the eye a cone of rays with an 

 aperture still greater than the above-mentioned ratio requires, 

 the field of view would naturally appear to be more brightly 

 illuminated, in proportion to the surplus, than when seen with the 

 naked eye. Such a case -can, however, never occur, as will be 

 shown, even with the lowest magnifications ; for the higher mag- 

 nifications it is primd facie an impossibility. The diameter of the 

 microscopic image (and therefore also the retinal image) increases 

 with higher magnifying power in a much more rapid proportion 

 than the angles of aperture of the incident cones of rays, which 

 reach the objective from the object-points, and thence the eye. 

 In vision with the naked eye this angle amounts to 28 34 

 minutes, that is, about half a degree, if we fix the diameter of 

 the pupil at 2 to 2J mm. and the distance of distinct vision at 

 about 250 mm. In microscopic vision, on the other hand, it 

 amounts to 100 and upwards in proportion to the power and 

 peculiarities of the objective. From every point in the plane of 

 adjustment, an amount of light, in this case, reaches the eye which 

 is greater than that received by the naked eye in the approximate 

 proportion of 100 2 : (i) 2 = 200 2 : 1. But this amount of light is 

 distributed over a surface of the retina mutinies greater, where m 

 is the coefficient of linear amplification. The brightness of the 

 field of view resulting from this, which we denote by v, is therefore 



200 2 

 expressed by v = -^^- ; or, in general, if we take the angle of 



Tflj 



aperture of the objective as equal to o>, and that of the naked eye 



equal to J, v = 4 ( \ . The luminous power is consequently 

 \ tn I 



equal to 1, if m = 2&> ; it is less than 1, if m > 2&>, which is 

 obviously the usual case. It is, of course, here assumed that the 



