li:mits of optical ca-pacity of the microscope. 415 



If, perhaps, occasional allusion has been made to diffraction as a 

 cause of deterioration of the microscopic image, I have yet no- 

 where found any methodical investigation into the nature and 

 amount of its influence, but such an investigation shews, as will 

 here appear, that diffraction necessarily and inevitably increases 

 with the increase of magnifying power, and at length presents an 

 impassable limit to the further extension of microscopic vision 

 which limit, moreover, has been already closely approached in our 

 newest and best instruments. 



That diffraction and consequent obscurity of microscopic image 

 must necessarily increase with increasing amplifications of the image, 

 and this quite independently of any particular construction of the 

 instrument, rests as a fact upon a general law which applies to all 

 optical apparatus, and which was first formularised by La Grange * 

 for combinations of any kind of "infinitely thin" lenses. This 

 law has apparently remained almost unknown, perhaps because 

 La Grange enunciated it in equations whose co-ef&cients have not 

 characters which readily present clear ideas to the mind. In my 

 treatise on physiological optics, I have given expression to this law 

 in a somewhat more general form, namely, for centred systems of 

 refracting curved surfaces with any singly refracting medium 

 between them, and have endeavoured to formularise it in readily 

 intelligible physical characters. I shall therefore recapitulate as 

 briefly as possible this theorem and its demonstration. It holds 

 good for every centred system of spherical refracting or reflecting 

 surfaces through which rays pass with angles of incidence so fine 

 as to form punctiform images of punctiform objects ; that is to say 

 refracts homocentric rays, homocentrically. 



By the term, centred system, I designate one in which the 

 centres of the curves of each refracting or reflecting spherical 

 surface lie in the same straight line, the "axis" of the system. 

 In front of such a system, and situate in its axis, let us suppose a 

 luminous point belonging to some object lying in a plane at right 



* Sur une Loi general d'Optique — Memoires de rAcademie de Berlin 1803, 



