ILLUMINATION AND THEIR RELATION TO THE ABBE THEORY. 503 



Mr. Conrady's first demonstration, viz, that the full resolving 

 power of the objective is only obtainable with dark-ground 

 illumination when the illuminator has at least three times 

 the numerical aperture of the objective, is common ground 

 acknowledged by all. His second proposition, that in other cases 

 it is equal to one-fourth the N.A. of the objective plus one-fourth 

 the N.A. of the condenser, is a wonderfully simple and eleo^ant 

 deduction following from the laws of the Abbe Diffraction Theory ; 

 but it would seem that he has not made it sufficiently clear that it 

 applies solely to an ideal object, such as an homogeneous film of 

 alternate dark bars and clear spaces, which does not refract the 

 light transmitted through it. Refraction of Hght simply denotes 

 that the direction of main intensity of the light is shifted ; and 

 whilst it is perfectly true that such alterations of the passage of 

 light are fully covered by the Abbe Theory, which deals with the 

 subject on the broad principle of wave motions, Mr. Conrady's 

 limits postulate an absence of change in the direction of chief 

 intensity of the light, or, in common parlance, of refraction. It is 

 indeed one of the main features of interest of Mr. CWrady's 

 demonstration, that it brings out and draws attention to the fact 

 that even though there be an entire absence of refraction by an 

 object, it might nevertheless yield a well-defined image by dark- 

 ground illumination. As dark-ground images are popularly so 

 much associated with refraction phenomena, that fact will prob- 

 ably have been new to a good many microscopists. 



This said, it will be seen that we must agree with Mr. Stokes 

 that for practical purposes Mr. Conrady's limits do not hold good ; 

 indeed, the table of resolutions obtained with the Grayson ruling 

 is in itself conclusive evidence of this. I may say that I have 

 myself repeated the experiments with the Grayson ruling, and 

 obtained results in sufficiently close accordance with the table 

 given. The excess of resolution beyond Conrady's limits is too 

 great to be easily accounted for by errors in the ruling, and the 

 other matters he has adduced. The inference from the table of 

 resolutions is simply that refraction as such does play an impor- 

 tant role in dark-ground images, although it will not explain the 

 images by itself. This might indeed have been anticipated ; the 

 results afforded the experimental proof. 



It must not, however, be assumed from this that Mr. Conrady's 

 limits are of no value. On the contrary, they are of the greatest 



