ge ten Royal Microscopical Society. 301 
If the decussating cones of rays be received upon ground glass 
or oiled paper, as originating from a distant brilliant point, each 
position of the screen displays its own peculiarities, which I must 
not stop to describe, except to notice that the decussation is very 
intense just beyond the least circle of aberration Yat X a. 
This may possibly account for the black specific border seen in 
the fine definition of a brilliant disk. 
I wish next to draw the attention of the Society to a greatly 
magnified representation of a pair of spurious disks formed at the 
least circle of aberration, corresponding to the arrows in the last 
diagram. As in telescopes, the disks are smaller as the corrections 
are more and more refined. The small disk above is the natural 
size. One diffraction pmk annulus, and a black border, compietes 
the picture. (Twelve diagrams were exhibited to the meeting.) 
I believe that I have not exhibited these disks to any one of 
the Fellows, except our Secretary, Mr. Slack (through the micro- 
scope). The delicacy required for their exhibition, opposing an im- 
mersion 7/gth to an immersion ith, so that their foci coincide, a 
water-film intervening, prevents my showing them with safety on 
an occasion like the present, as I did at home to Mr. Slack. 
I then found, upon viewing these disks, they could be selected 
in pairs, either overlapping or just enlarged into contact. The 
diameter being known, and their distance apart from centre to 
centre, the actual expansion of the disk could thus be very conve- 
niently estimated. In this way residuary aberration was abundantly 
exhibited in the best glasses ; 1-16000th became 1—40000th inch. 
If now we apply these principles to definition, we see that each 
bright point has a halo of aberration ; if two points be near enough, 
overlapping images are produced. 
Since a line is an assemblage of points, the edge of a fine object, 
as a scale or diatom, appears sharper, freer from overlapping, as the 
definition is exalted. If we attempt to define the finest gull of a 
scale, the secondary image or burr universally obscures a pure 
definition. Whether the straggling rays be represented white, or 
whether they be coloured, stil/ the same want of perfect decisive 
sharpness, when using high power and large aperture, is more or 
less to be lamented. Hence astronomers prefer the lowest power 
practicable to resolve the required details.* 
Perfect aplanatism, or perfect freedom from aberration, can only 
be obtaimed when all the rays from a point intersect and form 
* Mr. Slack has particularly drawn my attention to the appearance of the cracks 
in fine thin plates of deposited silica. Not knowing the object, I at first imagined 
from improper focussing that these cracks were cylindrical bodies. But as each 
crack formed two edges, it had apparently caused two filaments. There appeared, 
however, two such delusive forms equidistant above and below the best focus. 
This proved their delusive character. 
