74 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
tion of tlie image F. At x is formed the image which can be seen on 
removing the eye-piece. 
As regards the illumination of the object, the light from the iris- 
diaphragm and stops should be such as would be emitted in the reverse 
direction downwards from a perfectly featureless self-luminous plane 
occupying the position of the objective field. The ideal position for 
the iris-diaphragm and stops would be a position z (corresponding to 
x and y ) where beams of uniform plane waves emitted downwards from 
the supposed luminous plane would be brought to a focus by the con- 
denser. This position is very close to the condenser, and the author 
suggests that it would be a marked improvement in Microscopes if the 
iris-diaphragm and stops were brought nearer to this ideal position than 
is usually the case. 
A consideration of the composition and resolution of undulations 
leads to the following modification of Proposition 1 : — The whole of the 
light emitted from the objective field may be resolved into beams of uniform 
plane leaves; these beams may be divided into smaller groups , each an 
elementary sheaf of beams, and each elementary sheaf of beams may have 
a single beam substituted for it . 
According to the author, the great advantage of this Abbe method of 
resolution into plane waves is that it substitutes uniformity for that want 
of uniformity which exists in all other methods of resolution in just those 
places where we are unable to assign the law of this want of uniformity. 
Part III. of the memoir commences with a discussion of the Numerical 
Aperture, or, as the author prefers to call it, Grasp. Let c denote the 
medium between the cover-glass and the objective. Everything below 
the objective, except medium c which is to be extended downwards, 
may be supposed to be removed and replaced by image C (i.e. standard 
image No. 2, formed in medium c by two reversals of the light.) The 
Fir*. 3. 
light from C is resolvable into beims of uniform plane waves, each with 
its axial ray. If a and /3 (see fig. 3) are the angles which one of these 
rays makes with the optic axis at o and s, then by Lagrange’s theorem 
n sin a = M sin /3 , 
where M denotes the magnification, and n sin a is the aperture or grasp 
of the beam. The author represents the grasp by G (instead of the 
usual N.A.) in the case of the most inclined beam, whose axial ray can 
be caught by the objective, and by g in the case of any less inclined 
beam. 
