1898.J MICROSCOPICAL JOURNAL. 97 



The same conclusion follows from directions " how to 

 see the rulings." We first illuminate the object by a 

 near approximation to plane waves; and then behind the 

 lens further exclude everything but the narrowest pen- 

 cils of almost exclusively plaue waves. Thus we produce 

 a "ruling" extending far beyond the limits of a true 

 image, and which in other respects is as far as possible 

 from being any such. We are really producing, and do 

 produce, easily calculable results of interesting experi- 

 ments in the interferences of plane waves ; and though 

 these results are physically and directly related to the 

 periodic structure of the object, considered, as an inter- 

 ference-grating, they are no trustworthy representation 

 of it. This truth has always been recognized and insisted 

 upon by Prof. Abbe and his school, resulting in a sort of 

 " counsel of despair " as to any truth or certainty in 

 such microscopical images. 



8. This brings us back to the more concrete Abbe 

 " spectrum " theory, as already described. But Prof. 

 Abbe throughout, considers the object to be illuminated 

 by plane waves. In this limited case, what Dr. Stoney 

 advances is more or less true ; but Abbe differs from 

 the latter in constantly recognizing that condition and 

 its consequences. Thus, while Dr. Stoney states that a 

 cone of rays from the condenser, as wide as possible, 

 may be used (as in practice it may, for reasons to be seen), 

 Abbe again and again insists that such is not the case, 

 and this at great length. " Strictly similar images," 

 he says, "cannot be expected except with a central illu- 

 mination with a narrow incident pencil," This is the 

 condition for securing an approximation to plane-wave 

 illumination, with its diffraction phenomena. 



9. We may now consider how far the Abbe theory, 

 which possesses more or less undoubted truth, is an ade- 

 quate representation of microscopic vision ; and the most 

 satisfactory feature about the lengthy discussion from 



