230 Scientific Proceedings, Royal Dublin Society. 
and at this distance the interval between adjoining cones subtends 
an angle of nearly 1’. Hence, in order that the images of two 
points of light may fall on the corresponding parts of different 
cones, their distance asunder must subtend an angle of, or exceed- 
ing, 1’ at the optical centre of the eye; in other words, the 
interval between the objects in external nature that are being 
examined, must subtend this angle at the eye. ‘Thus we fail to 
see with the unassisted eye much detail which is revealed to us by 
the microscope. This happens if ata distance of ten inches, the 
distance of most distinct vision, the intervals at which these 
objects are spaced subtend an angle of less than 1’. Such objects 
may, however, be seen with optical aid, provided it is such that the 
little interval subtends an angle exceeding 1’ at the optical centret 
of the object-lens used in the microscope, a point which, with the — 
higher powers of the instrument, lies close to the object on the 
stage. But beyond this limit, and therefore beyond the reach of 
the microscope, there are still worlds of events in nature which we 
can never see, although we may infer the existence of some of 
them in other ways. 
We have found that the spacing of the cones in the fovea 
lutea is competent to put a limit to the minuteness of the 
detail that can be seen with the naked eye. Now, the small 
size of the pupil of the eye also, and independently, determines 
such a limit. Astronomers are familiar with the fact that the 
image of a star (which is virtually the image of a point of light, 
since no telescope is competent to show the true disk of a star) 
consists of a small round central patch called the spurious disk, 
surrounded by coloured rings which very rapidly fall off in 
brightness. This phenomenon is due to the interference of the 
light coming from the two halves of the object-lens, and is 
susceptible of mathematical treatment. It thus appears that the 
angular radius of the first dark ring, estimated from the middle of 
the object-lens, is 
r 
A 
where A is the wave-length of the light, and A the aperture, ‘.e. 
6 = (1:22) 
1 The optical centre of the object-lens of a microscope is the point where the “un- | 
deviated rays’’ cross (see last footnote). In compound microscopes this point lies 
some distance in front of the object-lens, and with high powers is close to the object. 
