Some Remarks on the Apertometer. By Prof. E. Abbe. 21 



This proposition is directly derived from the elementary notion 

 of conjugate points in optics : that all rays diverging in different 

 directions from one point are gathered in, or pass through, the 

 other conjugate point after their passage through the system, 

 Betting aside spherical aberration. 



Now let 0' be the clear opening of a diaphragm in any position 

 at the hack of an objective L, and the real or virtual image of 

 this opening as it is projected by the system to the other side. By 

 virtue of the proposition above, this diaphragm will exclude from 

 the passage through the system all rays which have not entered 

 through the area of its conjugate image in front, and will admit 

 all rays which have entered through this area. Therefore ani/ 

 diaphragm at the hach of an ohject-glass acts in every respect 

 exactly like a similar diaphragm at the conjugate focus in front, 

 the clear diameter of which is to the clear diameter of the former 

 one in the ratio of the linear amplification at the pair of conjugate 

 foci in question. 



In applying my apertometric method, there is in every case 

 such a diaphragm behind the objective limiting the pencils from 

 external objects (from the index-pointers, for instance, on the 

 glass disk) in their passage to the observer's eye. It may be 

 either an eye-hole at the end of the tube, or the pupil of the eye 

 itself; and when an auxiliary Microscope is used, this limiting 

 diaphragm may be either a stop belonging to its object-lens, or the 

 brasswork of the lens itself if there is no such stop. Therefore 

 all the pencils of light by which the telescopic image becomes 

 visible to the eye of the observer must in their entrance to the 

 objective have passed the area of the image conjugate to this 

 diaphragm in respect to the objective, or to the objective and 

 the auxiliary lens together. In consequence of this, the conjugate 

 focus, where the image of the said diaphragm would bo formed, ^^^ll 

 represent in every case the apex of the angle which is to be 

 measured as the angle of aperture ; this point therefore, and no 

 other, must be made to coincide with the focus of the objective 

 in its ordinary microscopic performance, and also with the centre 

 of the divided circle of the measuring apparatus. 



If an objective is focussed to the centre of the measuring circle 

 by means of an eye-piece and a long tube, or, as is recommended 

 by Professor H. L. Smitli,* without any eye-piece, a point very 

 near to the front princi[)al focus of the objective — in the latter case 

 even inside this focus — is made to coincide with the centre. If 

 now, as Professor Smith docs, the telescopic image is observed by 

 the naked eye through an eye-hole at the end of a tube of perhai)S 

 4 inches length, the conjugate imago of this eye-hole, i.e. the 

 apex of the angle-defining pencils, must obviously occur at a less 



* Tliia Journal, ii. (1870) p. 77tJ. 



