ILLUMINATION AND THEIR RELATION TO THE ABBE THEORY. 505 



this question more fully here, as it is a side issue which does not 

 affect the main points which I wished to bring out. 



We come now to Mr. Stokes's contention that his results are 

 not in accordance with the Abba Theory, that they show it to be 

 incorrect as regards dark-ground images, that dark-ground 

 illumination affords a crucial test between the Abbe and Airy 

 Theories, and justify us in turning to the latter. These proposi- 

 tions are one and all based upon misconceptions ; not one of them 

 will stand examination. 



The dark-ground effects as obtained in practice can be ex- 

 plained, dealt with and predicted readily enough by the Abbe 

 Theory, but I do not purpose wearying those present by entering 

 into any elaboration of this, as it would need a technical paper by 

 itself. For present purposes it suffices to point out once more what 

 I am sure will not be denied by Mr. Conrady, that his formula 

 Dark-Ground Resolving Power = | IST.A. of Objective -\- | N.A. 

 of Illuminator postulates that the direction of the main intensity 

 of the transmitted diffi-action fans suffers no change in its 

 passage through the object, and that if this and the change in 

 the light intensities in other directions which is consequent upon 

 this did take place, additional factors taking the intensity 

 changes into account would have to be dealt with. Or, stated 

 shortly, absence of refraction is assumed in the formula itself. 



Next, as regards object points illuminated by dark-ground 

 illumination not being in permanent phase relation, and there- 

 fore behaving as if self-luminous, surely Mr. Stokes will agree 

 that if under ordinary illumination the light focused on the 

 object points by the illuminator is such that contiguous detail 

 transmits light having a common origin and therefore in 

 permanent phase relation, that fact is not changed in any way 

 because dark-ground illumination is resorted to. All that is 

 changed is that in the latter case some other parts of the light 

 fans from these object points impinge on and are transmitted by 

 the objective, but that does not touch the question of perma- 

 nence of phase relation at all, even if there were any alteration 

 in the phase relations themselves. 



We see, then, that dark-ground illumination is far from 

 affording us the conditions of self-luminosity, and Airy's investi- 

 gations dealt only with self-luminous objects, and were, as was 

 pointed out by Mr. Conrady, and recognised by Mr. Stokes, 



