142 



SUMMAEY or CURRENT RESEARCHES RELATING TO 



Fig. 26. 



displayed on this diatom, according as we admit or exclude particular 

 sets of spectra. The results obtained from this manipulation may be 

 summarized in three propositions : — 



(1) The same structure will give different images when the 

 diffraction-beams are made different. 



(2) Different structures will give the same image when the diffrac- 

 tion-beams are made similar in each case. 



(3) (the proposition which is most pertinent to our present subject). 

 The microscopic image of a structure is never in perfect accordance 

 with its actual composition, or true structure, unless tlie whole of tlie 

 diffraction-pencil is admitted to the Microscope ; or, in other words, the 

 image is always more and more dissimilar from the true structure in 

 proportion to the greater number of diffraction-pencils which are 

 excluded from the Microscope. 



The diagram will serve to illustrate the practical application of 

 the last proposition to the examination of diatoms. If the structure 



is ' coarse,' the diffraction- 

 beams will all be included 

 within a small space around 

 the central pencil (the inner 

 circle of the figure), and in 

 this case an objective, even of 

 limited aperture, will receive 

 them all, and we shall have 

 an image of the true structure. 

 If the object is finer, the 

 limited aperture will not be 

 sufficient to take up all the dif- 

 fraction-pencils, but a larger 

 aperture (the middle circle of 

 the figure) will. Still more 

 minute structure will require 

 a still larger aperture, as is 

 shown by the outer circle. 

 Now the elements of S. 

 gemma are of such fineness that they far surpass the limits of any 

 aperture that we are able to obtain at the present day. Aperture is 

 limited by the refractive index of the glass of which the objectives 

 are made, and that of the immersion fluid, cover- glass, and slide, and 

 hitherto we have not been able to obtain more than 1 • 47 N. A. out of 

 a possible 1 • 52. An aperture even of 1 ' 52 would take up but a part 

 of the diffraction-beams to which the structure of S. gemma gives 

 rise, and, therefore, with our widest apertures it is impossible for us 

 to see its true structure. I need not give the figures of the calcula- 

 tion here ; but the fact is that to see the true structure in reality, we 

 should require objectives, slides, and immersion fluids far surpassing 

 in refractive index any substance hitherto known to exist in nature. 



To quote Prof. Abbe : ' All speculations as to the true structure 

 of even P. angulatum, so far as they depend on microscopic vision, 

 are mere phantoms, castles-in-the-air. No human eye has ever seen. 



