ON THE THEORY OF THE MICROSCOPE. 245 



angular aperture cannot, by any possible means, be increased 

 beyond the degree which would correspond, in effect, to 180*^ in 

 air, it follows that whatever improvement may be effected in 

 regard to serviceable magnifying power, the limit of resolving 

 power cannot be stretched sensibly beyond the figure denoting 

 the wave length of violet rays when direct illumination is used, 

 nor beyond half that amount when extreme oblique illumination 

 is used. The last limit is, in point of fact, already reached by 

 the finest lines of the Robert plate and the finest known markings 

 on Diatom valves, as far as seeing is concerned. Only in the 

 photographic copy of microscope images can resolution of detail 

 be carried any further. Here, in consequence of the considerably 

 shorter wave length of chemically acting rays, the conditions for 

 photographic reception of the microscopic image are much easier 

 for every objective, inasmuch, namely, as they present a picture 

 which would be in the proportion of 3 : 2 larger in its details 

 than is seen by the eye. For this reason alone, apart from all 

 others, the performance of an objective in photography does does 

 not express the real measure of its performance in the ordinary 

 use of the microscope. 



Section IY. — The optical power of the microscope. 



XX. The foregoing researches afford a sound basis for an 

 accurate determination of the nature of those functions which 

 constitute the real optical power of the microscope, and, at the 

 same time, for arriving at some rational definition of the perform- 

 ance which may be expected from our present optical combina- 

 tions. 



The distinction so long recognised between ''defining" and 

 ^' resolving " powers receives, through the facts and proofs here 

 brought forward, a far wider significance than could fairly be 

 attributed to them upon any previously known grounds. From 

 these facts it appears that the microscope image — excluding 

 two cases of a similar and exceptional kind — consists, 

 as a general rule, of two superimposed images, each 



