certainly administered the coup de grâce to all researches in this direction by the following final verdict:-"It is most easy to produce the beading (as described post facto in July) with the worst of three th objectives in his possession, by means of a deep eyepiece and long draw-tube." Mr. Wenham also produces his September knotted cord beading (described by the President and now disclaimed) by his th.

These few spherules, such as can be described with the th can readily be shown with a fine half-inch and a power of 800, by spoiling the definition of the crowd of beading I have described, i.e. by totally disarranging the corrections.

The effect as thus produced may be explained roughly as follows:-When a brilliantly refracting bead is seen in the "clearing" peeping through the single structure, it swells out as all bright points do, as an effect of the error of the glasses, and the false appearance is produced as figured. Shillalahs are then rendered instead of spines equally false.

The optical difficulties of defining rouleaus of transparent beading, arranged in close parallel lines and crossed by similar rouleaus at a small inclination, cannot be overrated; the free beads at the intersections of the lattice-work are of course most readily developed.

In the Degeeria kindly presented to me by Mr. MacIntire, the rouleaus cross at a greater angle than those in Test-Podura curvicollis. The upper set may be plainly made out in the smallest and most transparent rounded scales, lying like straightened necklaces of beads or strings of pearls, of a faintly tinted rose colour.

When the adjustments are made for the plane of vision intervening between the two sets, on the large scales both sets may be seen at once. But in all similar cases the beading next the source of light is of a brighter and paler colour than the second set nearer the eye, just as described in D note, December 1869, and as is seen in Lepisma, note C.

Where Mr. Reade and Mr. Wenham have described beads isolated and separated by at least six diameters, the beads I have discovered and described a month before these papers appeared, lie in close contact, and are at least six times more numerous.

It is to be regretted that large coarse Podura scales of the best sort are exceedingly scarce. It is earnestly to be hoped some enterprising entomologist will rediscover a colony of these interesting insects, which doubtless still exist in abundance.

Mr. Slack, F.G.S., gives another instance of advancing power in the beading into which he has lately resolved the costa of Pinnularia major by means of Powell and Lealand's new immersion 4th, which he eulogizes as a triumph of optical art.

I lately communicated to this gentleman an interesting observation made upon the P. Formosum. Each spherule appeared

surrounded with six black round dots; the power was about 4000 diameters, and a similar objective was employed.

In my hands the immersionth has displayed the beading of

appear to be composed. Very curiously the diameter of these beads bore a different proportion to the general beading in each case, as above indicated; a confirmatory fact for the truth of their existence, and negativing the supposition of their being spurious, and guaranteeing their integrity.

THE NEW DOUBLE-STAR AND IMAGE TESTS.

Before describing these tests, it will be convenient to lay down an optical principle upon which they entirely depend.

The smallest section of any converging pencil of rays is called its circle of least aberration.

If a brilliant point of the utmost minuteness be examined with a high-power microscope, it will always present a spurious disk more or less surrounded with coloured rings and diffraction rings. This disk, the best image of a minute point, is always larger than a perfect image. It is this effect which enlarges and confuses minute refracting molecules, which gives a blur to a sharp terminal boundary of a scale, and which renders individual spherules so difficult of perfect definition. It is only with the very finest glasses that these common effects are diminished. A BURR envelops the point of light. And lastly, the spurious disk is even in good glasses more than double the true size of a perfect aplanatic image.

*

The next point to be stated is that an image is an assemblage of circles of least confusion corresponding to every point in the object.

It follows from these principles that the slightest deviation from aplanatism or perfect focalization produces an enlarged spurious disk instead of a perfect image of any, the minutest point of light, considered as an object: the object and image being of course placed at what are termed the conjugate foci.

THE NEW DOUBLE-STAR TEST.

Taking Mr. Wenham's further objection as a text :"In this inquiry it is remarkable how the use of the mercury globule is

* I once heard an optician declare that aplanatic meant a flat field! The perfect meeting of all the converging rays in an absolute mathematical point is of course the proper meaning.

ignored; yet I have no hesitation in saying that without this test it would be impossible to construct perfect objectives." "This test discovers the least fault"-we all admit that a minute globule of mercury, say the roboth or even the th of an inch diameter, displays a beautiful little image. Its size is easily calculated, which is done at Mr. Wenham's request.

The question now is, Why is the microscope incapable of defining the shape of this reflected image? Two reasons may be assigned either it is imperfectly defined or formed in the focus of the objective, or else it is too diminutive to be distinguished. The latter can be obviated by using a larger globule; the former arises either from the errors of reflexion from the surface of the mercury, or from errors in the microscope itself.

As for the size, it will be shown further on that for minute globules the image is within a thousand millionth of an inch, the twentieth part of the globular diameter, provided the object is 15 inches from it, and 3 inches in diameter.

Now for the other causes. The image formed by the globule is sufficiently clear of aberration to be distinguished by a perfect glass. The aberration is much more easily calculated than even for a refracting lens, and diminishes as the diameter lessens.

In order to introduce the subject in a clearer manner, I beg to describe an experiment exhibited at the soirée of the Royal Society.

Having observed that plate glass contains air or other gas bubbles of many different sizes and degrees of perfection, and that these lenses possess an aperture of close upon 180°, I found that they form brilliant minute pictures as in a jet-black frame. You can with a Coddington see a whole prospect portrayed within their tiny black rings; the image being formed nearly at the back surface of the bubble.

Placing one of these minute negative lenses on the stage, and reflecting the light directly, the flame, brass rim of the mirror, and other details, may be charmingly seen within it, with a lowpower objective and a deep eye-piece. But a large-aperture objective and a low-power eye-piece, giving similar power on the whole, fails to give the same picture in its beautiful precision of definition. The instant the aperture is reduced by means of the aberrameter, the picture regains its beauty and decision.

This happens with the smallest bubbles, with minute solid fused glass spheres, and with minute plano-convex lenses. The effects of this kind of aberration are instantly displayed. If a brilliant flame be imaged in one of these very minute lenses, the shape of the flame is lost; it becomes a round disk, but much larger than it ought to be. Detached single spherules from scales and diatoms show the same thing-spurious disks of refracted points of light.

Precisely in the same way, the image of a flame reflected by the test globule is a round disk, much larger than it ought to be, as seen in all isolated brilliant points in the microscopical field.

It is interesting then to inquire at what size of image its shape can be discerned. And if such small globules be used that the shape is gone, and if the real diameter of the spurious disk is a test of the correction of the glasses, what becomes of the boasted accuracy of the globule test, in which the size of the spurious disk is totally neglected? No one ever thinks, in testing microscopes, at all about this spurious appearance, or takes any thought about its size, arising from bull's-eye illumination.

In telescopic testing the most essential part of the ordeal is the diameter of the spurious disk. In a case of optical correction the microscope cannot be exempted from the same experimentum crucis. In the diameter of the spurious disk compared with the true image really lies the whole pith of the objective corrections.

But nothing can exceed the coarseness with which the experiment is usually conducted. Thus a bull's-eye condenser, which is known to be one of the worst form for spherical aberration, is placed before a lamp, and discharges a confused pencil of rays upon the test globule, forming a nondescript image upon its surface.

In cases where errors are reckoned by the 100,000ths of an inch a more perfect system is necessary.

I therefore propose the use of Double Stars imaged upon the mercury globule from two brilliant paraffin flames placed edgeways towards the quicksilver for a position of maximum brilliance.

The resolution of the double star must not be considered fair (when the disks are merely ovalized or elongated) except they are really divorced or sharply divided. The size of the globule, the distance of the flames and interval separating them being measured, data are at once given for finding the size and separation of the minute disks in the double-star test.

Let G be the globule 50th of an inch in diameter and Tobooth radius; then if the distance of the flames from the globule be fifteen inches, and the interval separating their flames be three inches,

then the space separating the image flames is almost exactly one hundred thousandth of an inch.

If a number of globules be selected of various diameters from theth to 3000th of an inch in diameter, the miniature intervals of the same flames undisturbed in position may thus be tabulated :—

These results are obtained in the following manner; the flames, 3 inches apart, being 15 inches from the globule,

Let a be the distance between the minute images.

▲ the diameter of the globule (r its radius).

q the distance of the images from its centre.

i.e. a =

20

as the other terms are so exceedingly small as to be neglected.

The interval between the images is th of the diameter of the globule,* within the three thousand millionth of an inch when the diameter is 3000.

If therefore microscopists will take the trouble to measure the diameter of the smallest globule which just divides or fairly divorces

the three thousand millionth of an inch. The other terms are smaller still.