54 VISION WITH THE COMPOUND MICROSCOPE 



In 1864 R. Clausius established, by distinguished research, the propo- 

 sition l that the power of emission of a body in regard to heat as well 

 as light is not the same in different media, but varies in the ratio 

 of the squares of the refractive indices, so that the whole emitted 

 light from any surface-element of a self-luminous body is increased 

 in the proportion of 1 : n 2 when this body is brought from air into a 

 denser medium of refractive index n. If a glowing body at a con- 

 stant temperature, such as a bar of iron, could be immersed in a 

 medium of 1'5 refractive index in such a way that the surface were 

 in optical contact with the medium, and the eye of the observer im- 

 mersed likewise in suitable conditions, the body would be seen brighter 

 in all directions in the proportion of 9 : 4 than it appeared in air. 



The whole hemisphere of radiation in air is indeed less than the 

 whole hemisphere of radiation in water or oil, as the squares of the 

 refractive indices of the media, viz. as I'O, 1'77, and 2*25. 



Thus it is seen that the quantity of light emitted from an object 

 under a given illumination is not measured by the angle of the 

 emitted cone at the radiant, nor can it be measured in any way by 

 means of the angle alone. The quantity depends under all circum- 

 stances on the product of the sine of the semi-angle and the refractive 

 index of the medium in which the object is luminous, and is expressed 

 by the square of this product, or by the square of the ' numerical 

 aperture ' of the pencil. 



It thus follows that the estimation of the quantity of light is 

 found to be in complete accordance with the expression of aperture? 

 We are now prepared to advance to another point. It was a 

 view very commonly held until recently, that the superiority of im- 

 mersion objectives over dry ones was confined to the case of the 

 former being used with balsam-mounted objects. 



If w T e have a pencil in air, say 170, as shown in fig. 37, a dry 

 objective of large aperture will be able to admit it. If, however, the 

 object is in balsam, as in fig. 38, it is no longer possible for so large 

 a pencil to emerge from the balsam. The rays shown by the dotted 



FIG. 37. 



lines in fig. 38 will be totally reflected by the cover-glass, and only 

 those within a smaller angle of 82 will pass out. Although these 

 are expanded into 180 on emerging into air, of which the objective 

 takes up 170, yet this 170 contains, it is supposed, less light than 

 the 170 in fig. 37, as it has been 'diluted' by the refraction. 



1 ' Ueber die Concentration von Wa'rme- und Lichtstrahlen &c.' Fogg. Annalen 

 d. Physik, cxxi. 1864. 



2 Fig. A 2 gives a good, practical illustration of the relative illuminating power of 

 objectives of varying apertures, and at the same time affords a simple explanation 

 of the reason why (n sin u} 2 is a measure of this illuminating power. Let the circles 

 A and B represent the backs of two objectives of the same power but of different 

 apertures ; then the radii C D and E F will represent the angle n sin u (or fj. sin (/>) 

 in fig. Al (p. 48, note). Now because the areas of circles are to one another in the 



