ON THE THEORY OP THE MICBOSCOPE, 211 



throughout the whole theory of the microscope and which maj^ be 

 thus formularised. 



When an oljective is perfectly aplanatic for one of its focal planes j 

 everij ray proceeding from this focus strikes the plane of the conjugate 

 focus at a point, whose lineal distance from the axis is equal to the 

 sum of the equivalent focal length of the objective x the sum of the 

 angle which that ray forms with the axis. 



Now as this condition must be fulfilled in every correct 

 instrument, both for the objective and for the whole optical part 

 of the microscope, the formula above given establishes a relation 

 of quantity between the angle of aperture of the microscope and 

 the lineal diameter of the aperture images above the objective and 

 ocular. Moreover, it is thus possible to determine, by micrometric 

 measurement of the position in the upper focal plane of the 

 objective which the track of any ray occupies, the direction which 

 it took before entering the microscope. Consequently the aperture 

 images formed above the objective, when examined with a suitable 

 micrometer eyepiece, can be used for measurement of the diver- 

 gence which the rays coming from the object undergo. 



V. In the next place, we need a more characteristic exposi- 

 tion (than is afforded by the ordinary schematic diagram) of the 

 essential optical functions which, in the case of images formed 

 under larger angles, by rays having a great inclination to the axis 

 fi.e., wide angles of aperture), differ greatly from the abstraction 

 by which theory represents the action of a set of lenses in forming 

 an image. And such an exposition offers itself when we can 

 define by axioms of general validity the mode in which an image 

 is focussed and spread out on the focal plane of an optical system, 

 and distinguish the focussing function and the extension of image 

 over a surface as the two principal factors of the image-forming 

 process, alike independent in their abstract idea, and distinct in 

 actual specific function. Apart from the fact that no exhaustive 

 analysis of a faulty image, nor any means of perfect correction are 

 possible until such characteristic distinction can be laid down, we 

 have no other means of determining the part taken by each con- 



