110 Transactions of the Boijal Microscopical Society. 



An examination of the table will clearly show the value of a 

 large aperture in defining lines at very small intervals on flat objects 

 like Diatomacese, though in practice this advantage may be entirely 

 counterbalanced by other disadvantages in the case of a different 

 class of objects. The largest possible aperture would define lines 

 at half the distance apart that could be defined with an aperture of 

 only 60°, It follows from the law of the sine that there would be 

 a rapid increase in defining power on increasing the aperture when 

 small, but when large a similar increase would have no such corre- 

 sponding advantage. Mr. Jabez Hogg informs me that by a com- 

 parison of diff'erent object-glasses he has been led to conclude that 

 the defining power varies as the chord of the aperture, which of 

 course is in absolute agreement with this theory of Helmholtz, It 

 is the same, only expressed in diff'erent words. Of course the 

 defining power of different object-glasses depends on several other 

 circumstances ; but since we find that many of the facts may be 

 explained by the action of the interference fringes, depending on 

 the essential characters of light itself, no matter how perfect the 

 manufacture of the instrument or the capabilities of the eye, it 

 appears to me that they deserve far more consideration than has 

 been given to them. Their influence has been entirely over- 

 looked by many who have treated on this question. At all events, 

 since they are altogether independent of the mechanical construction 

 of the instrument, it appears to me tLat we cannot do better than 

 adopt these principles in forming some conclusion as to the size of 

 the smallest object that could be distinctly seen with a theoreticalh/ 

 perfect microscope. Looked at from this point of view alone, ivith 

 a dry lens this could not be less than -g^^ir of an inch. Even 

 when TT^oT the fringes due to the extreme red rays would begin 

 to produce partial obscurity, and at tts^otj the brightest part of the 

 spectrum would make the obscurity more or less complete. If it 

 were possible to make use of the blue end alone, lines of ttoVoo 

 could still be seen, since their shorter waves would not produce 

 obscurity until the size was reduced to ysoV o o of an inch. The 

 size of the smallest bright point that could be seen depends on 

 entirely different considerations, and might be considerably less, as 

 far as the physical constitution of light is concerned. 



The question now arises, Are these general conclusions borne 

 out by actual observation ? As fiir as I am able to judge from 

 such evidence as I have been able to collect, they are very strongly 

 confirmed, if not actually established. Thus, according to Helmholtz, 

 Dippel* found that the limit of the true resolution of Nobert's lines 

 was about ^-ooo^ of an inch, which is just within the limit for the 

 mean rays, with a very wide aperture. By theory this limit might 

 be considerably exceeded by the use of blue light ; and, since the 

 * 'Das Mikroscop uud seine Anwenduug,' 1867. 



