302 Transactions of the [Sours Dec ame 
another point: so that the least circle of aberration is reduced to a 
oint. Considering, therefore, the principles already laid down,— 
First, that the cause of inferior definition is oblique spherical 
illumination, abounding with double aberration in its worst form, 
it is plain the more perfect we can illuminate by rays free from 
aberration or decussation, or the more perfect the aplanatism of the 
illuminator, the more effectively do we destroy the false shadows of 
decussation. 
Again, by aplanatic illumination the light is intensified in the 
proportion that wandering, decussating rays are concentrated upon 
the point required, instead of being wastefully dispersed. 
If we also wish to develop sharp shadows, the rays spoiling the 
shadow must be cut off. And when dealing with spherules and 
molecules, a knowledge of shadow peculiar to them is of the highest 
importance. According to the form of the illuminating aplanatic 
pencil, beads can be made to appear shaded into black strokes, 
crescentic shadows, half shadows, or destitute of shadow. And the 
optical play of shadow, to the right, the left, above or below, or 
centrally, when thoroughly recognized, gives the finest possible 
proof of the existence of spherules, except the brilliant spurious 
disks already described. 
The subject of definition is so inextricably mixed up with the 
illuminating and image rays, spherical and chromatic aplanatism, 
or freedom from wandering rays, either white, red, or blue, or any 
other colour, that the diagrams I now venture to bring before the 
notice of the Society may be said to illustrate both subjects at once. 
-Reflexion perhaps is more simple than refraction im a diagram, 
and therefore let us consider this :— 
The points I wish particularly to draw attention to are the 
primary and secondary focal lines of oblique reflexion (or refrac- 
tion). 
‘ may state here that even the passage of pencils of rays 
through the glass cover produces primary and secondary foci. But 
in achromatic condensers, as usually employed, there are mnu- 
merable primary and secondary foci, causing so complex a decussa- 
tion as to defy all lineal representation. And as in principle they 
are the same as in reflexion, the same diagram will illustrate it. 
In Diagram II., Plate LX VII.—Over-corrected pencils. Central 
pencils focalize nearer the surface, whilst the excentrical cross the 
axis farther from it. The red rays in a vertical plane cut each 
other or focalize farther from the surface than the rays in a plane 
at right angles to it. In consequence of these elaborate longer and 
shorter foci of given oblique pencils, a figure of 8 is formed at 
their common intersections; and indeed a variety of figures, in- 
stead of clear spurious round disks sharply defined. (Diagram IIT.) 
Practically, in illumination, these are got rid of to some extent 
