with Special Reference to the Microscope. 171 



While it is certain that the image ultimately formed may 

 be considered to be due to the spectra focussed at S , S x . . ., 

 the degree of conformity of the image to the original object 

 is another question. From some of the expositions that have 

 been given it might be inferred that if all the spectra emitted 

 from the grating were utilized, the image would be a complete 

 representation of the original. By considering the case of a 

 very fine grating, which might afford no lateral spectra at all, 

 it is easy to see that this conclusion is incorrect, but the 

 matter stands in need of further elucidation. Again, it is not 

 quite clear at what point the utilization of a spectrum really 

 begins. All the spectra which the grating is competent to 

 furnish are focussed in the plane 8 E^; and some of them 

 might be supposed to operate partially even although the part 

 of the image under examination is outside the geometrical 

 cone defined by the aperture of the object-glass. For these 

 and other reasons it will be seen that the spectrum theory *, 

 valuable as it is, needs a good deal of supplementing, even 

 when the representation of a grating under parallel light 

 is in question. 



When the object under examination is not a grating or a 

 structure in which the pattern is repeated an indefinite number 

 of times, but for example a double point, or when the incident 

 light is not parallel, the spectrum theory, as hitherto developed, 

 is inapplicable. As an extreme example of the latter case we 

 may imagine the grating to be self-luminous. It is obvious 

 that the problem thus presented niust be within the scope of 

 any complete theory, and equally so that here there are no 

 spectra formed, as these require the radiations from the different 



with, bitumen, was substituted for it, very different effects ensued. The 

 structure could be seen even although the object-glass were drawn back 

 through 1| inch from its focussed position ; and the visible lines were 

 twice as close, as if at the rate of 12,000 to the inch The difference 

 between the two cases is easily explained upon Abbe's theory. A soda 

 flame viewed through the original showed a strong central image 

 (spectrum of zero order) and comparatively faint spectra of the first and 

 higher orders. A similar examination of the copy revealed very brilliant 

 spectra of the first order on both sides, and a relatively feeble central 

 image. The case is thus approximately the same as when in Abbe's 

 experiment all spectra except the first (on the two sides) are blocked out. 

 * The special theory initiated by Prof. Abbe is usually called the 

 " diffraction theory," a nomenclature against which it is necessary to 

 protest. Whatever may be the view taken, any theory of resolving 

 power of optical instruments must be a diffraction theory in a certain 

 sense, so that the name is not distinctive. Diffraction is more naturally 

 regarded as the obstacle to fine definition, and not, as with some expo- 

 nents of Prof. Abbe's theory, the machinery by which good definition is 

 brought about. 



