682 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
In criticising the Abbe spectrum theory the author observes that, 
although the image ultimately formed may be considered to be due to 
the spectra focused at S 0 , S x . . the degree of conformity of the 
image to tho object is another question. Consideration of the case of 
a very fine grating, which might afford no lateral spectra at all, shows 
the incorrectness of the usually accepted idea that if all the spectra are 
utilised the image will be complete. The author considers that the 
theory needs a good deal of supplementing. It is also inapjdicable 
when the incident light is not parallel and when the object is, for 
Fig. 103. 
example, a double point and not a grating. Even in the case of a 
grating, the spectrum theory is inapplicable if the grating is self- 
luminous ; for in this case no spectra can be formed since the radiations 
from the different elements of the grating have no permanent phase- 
relations. For theso reasons the author thinks it a desideratum that 
the matter should be reconsidered from the older point of view accord- 
ing to which the typical object is a point and not a grating. Such a 
treatment shows that the theory of resolving power is essentially the 
same for all instruments. The peculiarities of the Microscope, arising 
from the divergence-angles not being limited to be sm all, and from tho 
different character of the illumination, are theoretically only differences 
of detail. The investigation can be extended to gratings, and the results 
so obtained confirm for the most part the conclusions of the spectrum 
theory. 
The author commences the discussion by a simple investigation of 
the resolving power for a self-luminous double point. In fig. 104, as 
before, A B represents the axis, A being a point in the (bject and B a 
point in the image formed by the object-glass L L 1 . The limit to 
definition depends upon the fact that owing to diffraction the image 
thrown even by a perfect lens is not confined to a point, but distends 
itself over a disc of light, and that two points in the object can only 
appear fully separated when the representative discs are nearly clear of 
one another. 
In fig. 104, B is the centre of the diffraction disc representative of A. 
