oblique solar rays from a plane mirror. Having arranged a diatom (the Pleurosigma Formosum was the one selected) with its axis towards the oblique source of light, and having developed the lines with a good objective, so as to show the structure, cut off the excentrical rays by means of the Aberrameter.

Immediately a gorgeous coloured disk can be seen-perhaps four times as large as the individual beading. Now traverse the diatom slowly across the field, lengthways; immediately the brilliant disk appears to roll in a contrary direction, each bead appears in succession (telling a wondrous tale of internal action). With intense vividness of colouring, the rolling disk resembles a setting sun, travelling on the horizon with the motion of the observer in a rapid train; whilst its splendour glows rapidly through all the prismatic colours. Only one disk is visible at once; a new one, with a new colour, starts forth in place of the old at the slightest movement of the object across the microscopic field.

Without commenting upon this magnificent and lovely phenomenon further, than to say that it is evident each bead acts as a refracting sphere, or lens, forming in its focus an image of the sun spuriously enlarged, I pass forward to Diagram III.

arrows

Parallel solar rays converge to a focus at F. Opposite the the rays, in their decussation, pass through the smallest ring. Each ray has here been carefully laid down from the Deviation Tables, refractive index being

3
2

In Diagram III. the caustic curve formed by the intersection of the refracted rays, and to which curve they are successively tangents, is shown on an enlarged scale. A spherule 40000th of an inch in diameter, being represented by a segmentary portion, the sphere being delineated 5 feet in diameter. The short arrows denote the position of the least circle of aberration.

The central rays cut the axis at F, the ultimate, or solar focus -distant 4th of the diameter from the surface of the sphere. Some of the rays are lost by internal reflexion.

It will be seen by examining the diagram that as the aperture is cut off, the smallest ring is found constantly nearer the final focus F. The smallest ring through which pencils from a given aperture can pass is the least circle of aberration; and here it only is reduced to a point where the aperture is exceedingly diminished.

The diameter of the spurious disk of aberration is here about a small fraction of the diameter of the refracting spherule. But in the prismatic effects just described, the spurious disk of an image of the sun was at least four times the size of the bead or lens producing it: producing the very remarkable phenomena already alluded to.

* In the diagram exhibited at the meeting.

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 at X x.

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

One diffraction pink annulus, and a black border, completes 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 microscope). The delicacy required for their exhibition, opposing an immersionth to an immersion 1th, 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 conveniently 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 quill 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, still 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 obtained 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.

another point: so that the least circle of aberration is reduced to a point. 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, centrally, when thoroughly recognized, gives the finest possible proof of the existence of spherules, except the brilliant spurious disks already described.

or

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 in 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 refraction).

I 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 innumerable primary and secondary foci, causing so complex a decussation 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 LXVII.—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, instead of clear spurious round disks sharply defined. (Diagram III.)

Practically, in illumination, these are got rid of to some extent