156 MICROSCOPIC VISION. 



gratins:, sia u must also == „-^. therefore -=-— - and 8 = 



= — inch. The scale actually had 64 lines per inch. 



2. The converse problem may be treated in a similar 

 manner. Looking through a hole in a diaphragm, placed 

 close to the eye, a scale of 50 lines to the inch can be just 

 perceived at a distance of 9 inches. What is the diameter ^ 



of the hole ? The hole subtends an angle of - at the scale ; 



this angle must be equal to sin ?t, if the grating is just 



resolved. Therefore, sin u^ ^ = ~-', a= ~ = -0\ inch. The 



actual size of the hole by micrometric measurement was 

 •Oil inch. 



Prof. Abbe summed up the results of his experiments on 

 the diffraction image in these words : ^ — 



" Everything visible in the microscopic picture which is 

 not accounted for by the simple absorption image, but for 

 which the co-operation of groups of diffracted rays is needed 

 — in fact, all minute structural detail — is, as a rale, not 

 imaged geometrically, that is conformably with the actual 

 constituent detail of the object itself. However constant, 

 strongly marked, and, so to speak, materially visible, such 

 indications of structure may appear, they cannot be inter- 

 preted as morphological, but only as physical characters ; 

 not as inages of material forms, but as signs of certain 

 material differences of composition of the particles compos- 

 ing the object. And nothing more can be safely inferred 

 from the microscope revelation than the presence in the 

 object of such structural peculiarities as are necessary and 

 adequate to the production of the diffraction phenomena on 



Monthly Microscopical Journal, vol. xiv. (1875), p. 219. 



