On the Estimation of Aperture. By Prof. E. Able. 403 



There are various direct proofs that the angular distribution 

 of the radiating light is changed whenever the medium of the 

 radiant is changed. The rays which emanate from a given object 

 in different media are not, it is true, numbered like the sheep of 

 a flock, and it is impossible therefore to show the identity or non- 

 identity of certain rays under different circumstances without 

 having first established an express principle of identification. 

 This wiU be required for the view above expressed just as well as it 

 would be required if any one should try to prove the (assumed) indif- 

 ference of the medium in regard to radiation. There is one particular 

 case, which however is of considerable importance for the Microscope, 

 in regard to which such a principle may be readily established. 



When a preparation contains transparent (perfectly pellucid) 

 portions, the depiction of which yields the outlines of the non- 

 transparent elements in the microscopic field, the rays emitted 

 from such portions are purely transmitted rays. Every ray 

 emanating from a transparent element of the object is the direct 

 continuation of one distinct ray which is thrown upon that element 

 by the illuminating apparatus. Suppose now an object of this 

 kind, having a perfectly flat upper surface, and connected to the 

 slide, in the one case uncovered, in the other case mounted in 

 water or balsam under a cover-glass, and illuminated by means 

 of an immersion condenser which collects a pencil of not less 

 than 82° (measured within the slide) upon every point of the 

 microscope-field. In both these cases one and the same trans- 

 parent element will send into the objective, by virtue of transmission, 

 the same incident rays ; but when the object is in air, these same 

 rays are distributed above the object in a different manner to that 

 which obtains when the object is in water or balsam. In the former 

 case all rays which are embraced by an incident cone of 82° within 

 the glass slide make up the whole hemisphere ; whilst with water 

 above, the same rays are contained within an emergent cone of 96°, 

 and with balsam within 82°. 



Under the circumstances in question, those rays transmitted 

 through the object are of course identical rays — notwithstanding 

 their different directions in air, water, or balsam — which are the 

 continuation of identical incident rays. In regard to that kind of 

 radiation, therefore, on which the delineation of the outlines of non- 

 transparent or semi-transparent objects is based, a pencil of '62^ in 

 balsam or of 96° in water, conveys the same rays to the Microscope 

 as the whole hemisphere in air, and there is a different angular dis- 

 tribution of the radiating light in different media. In this case 

 the causa efficiens of the pl^enomenon is, of course, the different 

 refraction with which the transmission is connected. A dioptrical 

 explanation of the varying distribution does not, however, change 

 the fact that there is such distribution. 



