ON THE THEOEY OF THE MICEOSCOPE . 205 



previously obtained from trial-prisms by means of the spectro- 

 meter, in order to compensate any accidental variation of material 

 by suitable alteration of the construction. Each constituent lens 

 is ground as nearly as possible to its prescribed dimensions and 

 accurately htted. In the highest-power objectives only is 

 there a single element of the construction (a lens distance) 

 left variable, in order that unavoidable slight deviations 

 from accuracy of the work may be adjusted. And thus it 

 has been shewn beyond dispute that a well-grounded theory, 

 combined with rational technical processes, which utilise all 

 the means that physical science can offer to practical optics, 

 may be successfully substituted for empiiical practice, even 

 in the construction of the microscope. 



II. In the course of the studies which led to the results above 

 stated, it became apparent that the theory of the microscope as 

 hitherto propounded fails in several important points. In the 

 first place, the manner in which the conditions of perfect projec- 

 tion of an image and the causes of its imperfect projection have 

 been discussed, proved altogether inadequate to the real facts of 

 the case as they occur in the microscope. The circumstance that 

 an amount of angular aperture, which is unknown in any other 

 instrument, comes here into question, renders the accepted ideas 

 of ''aberration" entirely useless, even for a moderately critical 

 estimation of any given microscope already constructed, to say 

 nothing of any attempt to determine beforehand the effect of 

 combinations not yet executed. 



To obtain the data needful for a trial of this last kind, a 

 theoretical analysis of the action of a system of lenses constructed 

 with large angular aperture, had to be carried out on a far wider 

 mathematical basis and in much more precise detail than has 

 been hitherto done. And in doing this it became manifest that 

 the correct performance of any combination of lenses for the 

 microscope which should meet all demands satisfactorily, depends 

 upon an unexpected number of conditions, each independent of 

 of the other, a proper estimation of which would not be possible 



