52 VISION WITH THE COMPOUND MICROSCOPE 



which the ray is sent out. The rays are more intense in proportion 

 as they are inclined to the surface which emits them, so that a pencil 

 varies in proportion as it is taken close to or is removed from the 

 perpendicular. A pencil is not, therefore, correctly represented by 

 fig. 33, but by fig. 34, the density of the rays decreasing continuously 

 from the vertical to the horizontal. 



Owing to the different emission in different directions, the quan- 

 tities of light emitted by an element in the same medium in cones of 

 different angle such as w and w', fig. 35, are not in the ratio of the 

 solid cones, as would be the case with equal emission, but in the 

 ratio of the squares of the sines of the semi-angles so that the squares 

 of the sines of the semi -angles constitute the true measure of the 

 quantity of light contained in any solid pencil. 



When, therefore, the medium is the same, it is seen that there 



FIG. 35. The unequal emission of rays. 



is no contradiction between the measure of the aperture of an ob- 

 jective (n sin u) and that of the quantity of light admitted by it 

 the latter being (n sin u) 2 . 



The simplest experimental proof of the unequal emission in 

 different directions will be found in the fact that the sun, the moon 

 the porcelain globe of a lamp or any other bright spherical object 

 with so-called uniform radiation in all directions, is seen projected 

 as a surface of equal brightness. If there were equal intensity of 

 emission in all directions, what would be the necessary result? 

 Compare two equal portions of the surface, one, a (fig. 36), perpen- 

 dicular to the line of vision, and the other, 6, greatly inclined. 

 Every infinitesimal surface-element of b sends to the pupil of the eye 

 a cone of the same angle u', as a similar point of a (the slight differ- 

 ence of the distance from the eye being disregarded). If the in- 

 tensity of the rays were equal as supposed, the whole area b would 

 send to the eye the same quantity of light as the equal area a, 

 since both areas contain exactly the same number of elements. But 

 the whole quantity of light from b would be projected upon a 

 smaller area of the retina than that from a (as b appears under a 

 smaller visual angle, being diminished according to the obliquity, or 



