22 



Transactions of the Society. 



Thus it is certain from the simple notion of an aplanatic 

 system that pencils of different obliquities must yield identical 

 images of every plane object or of a single layer of a solid object. 

 However large an aperture may be, the resultant image of the 

 object cannot therefore be composed of dissimilar images, and the 

 wide aperture cannot be the cause of confusion, &c. 



We see also at the same time that the delineation of an 



object through the Microscope does not ex- 



FiG. 4. ^^'^It differences of perspective according to 



the obliquity of the delineating pencils to 



a the entire pencil starting from the axial point 

 A of an object, and collected to the axial point A* of 

 the image. 



i3 the entire pencil starting from an excentrical 

 point B collected to the excentrical point B* of the 

 image. 



a a and om an axial and a marginal elementary 

 pencil from A which are contained within the 

 pencil a. 



13 a and j3 m corresponding axial and marginal 

 elementary pencils of the whole pencil 13. 



The two axial pencils a a and )3 a pass through 

 the central part, a, of the clear opening : the marginal 

 pencils a m and j8 m touch the margin of the opening 

 at m. 



The limiting diaphragm of the clear opening is 

 assumed to be at the plane of the posterior principal 

 focus (as is always the case approximately with high 

 powers) in order to obtain the corresponding rays of 

 the two pencils a and parallel in front of the system, 

 or the same obliquity of a m and /3 m. 



the plane of the object, as is the assumption 

 of the all-round vision theory. The image 

 of any plane surface AB (e.g. the upper 

 surface of the minute die) is always the 

 same whether the rays are admitted to the Microscope in per- 

 pendicular or in any oblique direction. If that theory was right, 

 the image of A B, by the oblique pencils a m and /3 m ought 

 to be shorter (according to the perspective shortening of the 

 lines in oblique projection) than the image by the axial pencils 

 a a and /3 a, as we should of course have a shorter image of 

 A B if we observed it through a low-power Microscope with 

 inclined axis. 



This absence of perspective shortening of the lines according 

 to the obliquity of the rays exhibits therefore an essential geo- 

 metrical difference of microscopic vision, which renders it uncom- 

 parable to macroscopic observation. 



Secondly, consider the delineation of a solid object such as a 

 minute die. 



B A\ 



