DARK-GROUND ILLUMINATION. 479 



together, with the result that whilst c would fall well within the 

 aperture of the objective, b would fall outside it ; there would be 

 only one spectrum within the aperture, hence no resolution. It 

 is not difficult to follow this up and to see that no structure 

 coarser than the limit would be resolvable until we came to one 

 having 2/3rds of the limiting number of lines, which would be 

 resolved by the simultaneous entry of the second and third 

 spectra. This leads to my third point a new one, I believe : 



(3) With dark-ground illumination it is important that the 

 " wheel-diaphragm " should be only just large enough to secure 

 a dark background, otherwise there may be certain ranges of 

 structure which cannot be resolved, although both finer and 

 coarser ones are visible. 



I was led to the above investigation by a short paper by 

 Mr. E. M. Nelson in J.R.M.S. 1908, pp. 671 and 672, dealing 

 with the observational fact that "structures resolved (with a 

 given objective) on a bright field may become invisible with 

 dark-ground illumination," and which contained the statement 

 a challenge it appeared to me that " the Abbe theory may be 

 wrung up to its breaking-point, but not a drop of enlightenment 

 can be squeezed out of it." Evidently Mr. Nelson did not squeeze 

 it very hard. His paper, however, supplies a remarkable and 

 welcome experimental confirmation of my theoretical results in 

 the form of his first thesis : 



"When periodic structures are examined with object-glasses 

 having a N.A. of 0*35 and upwards, they should be placed upon 

 a bright ground." 



On the reasonable assumption that the underlying observations 

 were made chiefly with dry condensers, it will be seen that this 

 agrees marvellously with my first result, for theoretically 0*33 

 N.A. would be the highest with which full resolving power could 

 be obtained over a dry condenser. With higher numerical 

 apertures the bright ground would have the advantage. 



Lest it should be thought that the little investigation dealt 



