The Vertical Illuminator, &c. By J. W. Stephenson. 267 



since been abundantly proved, and the present method affords an 

 ocular demonstration of the fact, most conclusive in its character 

 and fully supported by theory. 



It will be seen, on removing the eye-piece of the Microscope, 

 after having reflected a full beam of light through the objective, by 

 means of the Illuminator, and after having focussed the instrument 

 on any dry object adhering to the cover, that within the margin of 

 the lens there exists a brilliant annulus of light, and that the circum- 

 scribed internal space appears by comparison to be quite dark. 



This annulus rej)resents, and is produced by, the excess of 

 aperture beyond the equivalent angle of 180 , or what is called the 

 " plus 1(:>0^," of which it is also the measure. 



The internal dark space is of the exact diameter of that of a 

 dry objective of the same focus, and is in fact the maximum space 

 which it can itself utilize, on a dry object, by transmitted light. 



On looking down the tube of the Microscope on which is one of 

 Zeiss's homogeneous-immersion iths, with its numerical aperture of 

 1 • 25, it will be seen that the annulus has an apparent magnitude 

 corresponding with that attributed to it by theory, that is to say, a 

 width equal to one-fourth part of the radius of the dark central space. 



The explanation is. as it appears to me, simple enough : the 

 beam of light reflected by the parallel glass plate of the Illuminator, 

 is condensed by the objective, and brought to a focus on the under 

 side of the thin glass cover, the oil (or other homogeneous fluid) 

 having, thus far, allowed the light to be freely transmitted ; but, at 

 the focal point, having to pass from a denser to a rarer medium, 

 the passage of all rays which exceed the critical angle (in this case 

 41 ) is arrested, whilst those within that limit, or at all events the 

 greater part of them, pass through the glass and are lost. 



The bright image of the flame of the lamp, which is seen 

 crossing the field of view, is therefore almost exclusively formed by 

 the "j;/t<s" rays, which, being totally reflected as soon as they 

 impinge on the air surface of the cover-glass, are sent back by 

 the peripheral portion of the objective to the eye ; it is thus evident 

 that, unless the objective possessed the excess of aperture which we 

 have been considering, the image could not be formed by the totally 

 reflected rays, nor, if formed, could the reflected rays be taken up 

 by the objective and transmitted to the eye. 



These reflected rays, when seen without the eye-piece, form the 

 bright annulus of light, and constitute, as has been sljown, the 

 aperture in excess of the 180° limit, which limit is itself as clearly 

 indicated by the dark central area. 



That this is not a mere theoretical or nominal increase is 

 evident when we consider the areas of the transmitting portions of 

 the lens, which are proportional to the squares of their numerical 

 apertures or as 1 to 1 ' 5625, so that the Vertical Illuminator })icks 



