218 ON THE THEOET OP THE MICEOSCOPE. 



Mathematical analysis further shews us in what form spherical 

 aberration will lAanifest itself when from faulty construction a 

 noticeable residual error appears. However irregular the actual 

 course of the rays may be in any particular case in the neigh- 

 bourhood of the plane where they should coincide, (according 

 to construction) this course may be always so altered by mere 

 change of a lens-distance in the system (as is affected for 

 example by correcting for glass cover) that the central and peri- 

 pheral zones of the objective may work together correctly while the 

 intermediate zone remains for the time more or less over corrected. 

 At the same time, it is evident that so typical a difference of cor- 

 rection, where it once exists, cannot be removed, or even 

 diminished, by any external means ; for since it lies in the 

 relations of curvature and refractive power of the front lenses of 

 the objective, every appliance by which the amending of such 

 aberration has been attempted — whether by correcting lenses 

 placed above the objective or by particular construction of ocular 

 — wiU produce, under the most favourable circumstances, no 

 better result than what is already effected by changing the 

 distance of the front lens of the objective from those behind it. 

 They simply permit the existing residual aberration to be trans- 

 ferred — shifted backwards or forward between the centre and 

 outside border of the aperture — and by this means to keep, for a 

 time, some particular zone of the objective more or less free from 

 aberration, at the cost of the rest I Arrangements like the 

 "aplanatic searcher," invented by Dr. R. Pigott, originate in a 

 misconception of the true state of the matter. They rest upon a 

 conception of spherical aberration, which, as it leaves place only 

 for a single alternative, over or wider corrected^ is, together with 

 the whole theory of aplanatic foci built upon it, utterly without 

 meaning or object, in the case of the powerful microscopes of 

 the present day. 



YIII. An analysis of the conditions which belong to a perfect 

 construction finds its fit conclusion in applying it to investigate the 

 influences severally exercised by the different parts on the general 



