other British marine invertebrata; the locality from whence they were obtained is not yet known, except that they were taken at a depth of 540 fathoms.

EXPLANATION OF PLATE LXVI.

FIG. 1.-Dorvillia agariciformis, viewed laterally, enlarged diameter.

2. The same, as seen from above, nat. size.

3.-Under surface of the upper portion or hood, showing where it becomes
continuous with the basal part, the netted structure of the sarcode × 3
linear.

4.-A fragment of this netted portion, highly magnified, and showing the
numerous minute irregularly stellate spicula interspersed through it.
5.-Three of the minute irregularly stellate spicula × 500 linear.
6.- One of the large bi-ternately terminating spicula, of which the greater
portion of the skeleton is constructed, x 20 linear.

7.-The same, viewed from above. 7a.-Portion of a simple porrecto-
ternate spiculum from the same region, equally magnified.
8.-One of the smooth anchorate spicula, abundant in the dependent root-
lets and on the superior surface of the sponge, x 40 linear.
9.-The anchorate termination of a variety of the same.

10.-Minute, rigid, delicately echinate hexradiate spicula, common in the
sarcode of the sponge, × 100 linear.

11.—An attenuate, flexuose, hexradiate spiculum, from the upper and superficial surface, × 50 linear.

12.

13.

The upper portion of an attenuate spinulate spiculum, from the same region, × 50 linear.

A simple attenuate, common on the superior and superficial layer, × 50 linear.

14.-Portion of an attenuate adpressly spined spiculum, similar to what obtains in the genus Pheronema.*

15.—An attenuate linear spiculum, showing its tendency to develop into an hexradiate form, × 50 linear.

16, 17.—Triradiate spicula, from the reticulated layer of sarcode shown at Fig. 3, × 100 linear.

18. A quadriradiate spiculum, from the same region, × 100 linear.

19. A minute clavate and profusely echinate spiculum, from the sarcode, × 100 linear. (This form is too scarce to be considered absolutely characteristic.)

*This spiculum is probably an interloper, as may also eventually prove to be the case with the form represented at Fig. 11. The great depth at which this sponge was taken, and the nature of the mud with which it is associated, makes it reasonable to anticipate that Pheronema flourished in its vicinity. The spined anchorate form of spiculum common to the last-named genus has also been detected.

II.-On Aplanatic Definition and Illumination with Optical
Illustrations. By G. ROYSTON-PIGOTT, M.D., M.A., &c.

(Read before the ROYAL MICROSCOPICAL SOCIETY, October 12, 1870.)
PLATE LXVII.

MR. PRESIDENT AND GENTLEMEN,

I have in the first place to express my regret that circumstances over which I had no control prevented me from accepting the invitation to be present at the discussion of the first paper T had the honour of sending for the consideration of the Council.

I have also to tender the Council my thanks for the present opportunity of explaining some views and methods applicable to Aplanatic Definition and Illumination. Important as is this subject, I fear that I shall fail to do justice to its merits to attention, though without doubt it forms the very pith and marrow of accurate instrumental vision.

At the outset I must ask your kind indulgence for the course I am about to pursue. There are many in this room who may perhaps think my conclusions turn upon points so elementary as to be unworthy of iteration; whilst many others may think the details, on the contrary, too technical or complex.

But, yet, I hope no apology is needed for appealing to fundamental truths. It is only by mastering the axioms of science that true progress can be made.

The man who starts on a voyage of discovery must provide himself not with instruments only, but with fundamental principles.

There are two fundamental cogent truths which have done more for exact science than any other par excellence.

Thus Astronomy, Navigation, Trigonometry, and Optics are built up upon that great property of right-angled triangles-that of the squares of their sides.

And Optics is especially dependent upon their relations to each other, or the rule-of-three proportion of their sides.

If it be desired to form a perfect square angle of 90°, we have only to form a ▲ whose sides are in the relation of 5, 4, and 3.*

Again, if a blue ray of light passes out of the spectrum, and is transmitted through two different media, as water and glass, a triangle constructed with its sides representing the refractive indices of the blue ray in each media, and one angle representing

*The square of 5 or 25 being equal to the sum of the squares of 4 and 3, or 25 = 16 +9.

the incidence, at the base, the angle of refraction will be represented by the other angle opposite the other side. I may mention one

tion.

Mr. Browning's very admirable spectroscope, exhibited at the Royal Society, depends upon this principle for its profound and truly astounding powers of spectroscopic analysis. And I do not hesitate to pronounce the opinion that through this subtle instrument alone his name will be handed down to posterity. It is one of the happiest ideas of the practical embodiment of principle.

A prism like a lens forms two foci, primary and secondary ; and for the purposes of the most subtle analysis which has ever engaged the human intellect, it is evident the most subtle and perfect powers of differentiation and resolution were absolutely necessary. By a series of prisms automatically arranged so as in each case to obtain the finest definition by means of preserving a minimum aberration, very extraordinary results are now obtained.

The Huyghenian eye-piece was invented on the principle of the angles of immergence and emergence being nearly equal, as in the case of the prismatic minimum deviation; and by good luck (most of the best inventions are lucky thoughts) the same principle rendered the eye-piece achromatic.

Now the microscope is really an instrument formed of innumerable prisms. The action of any and every lens can be traced on the prism principle.

There seems, then, good ground for concluding that in all cases the conditions of least aberration should be applied.

A ray of light may be of any colour, and obeys exactly the same laws as every other. Spherical aberration is equally true of coloured rays as of light, considered theoretically homogeneous. A violet or a red ray obeys the law of the triangle.

Regard now this rough sketch of gold leaf viewed under a high power by transmitted solar rays. The thing itself is full of mystery and beauty. Why are here red spots, bright spots, and blackinky black-edgings? The wave theory of light may give us a clue. Whence comes the rich, translucent, malachite green of the gold? Whence the red and whence the black? Science shakes her head, and says the answer is long and deep. Ask the rainbow and the dewdrop whence come its colours, or the rose-leaf. Absorption, reflexion, refraction, undulation, vibration of the ether and rays of interference. Such are the hard dry answers to these simple questions.

But here all definition gets its programme of sharpness and decision.

What is this black edging? It is almost specific of a fine definition.

What the red spots? The gold is thicker there, perhaps, but I am not sure of that. The best leaf is only 1500ooth thick.

Again, view these coarse disks. The same black rings; the light is dead, producing darkness; wave collisions wave.

Sir John Herschel describes some of the effects of interference and diffraction, as producing some of the most gorgeous phenomena in the range of physical science.

But definition is supremely dependent upon the extent, nature, and direction of these collisions and decussations.

It may now be stated in general terms that:

If an object composed of minute bodies be placed in a blaze of confused decussation, fine definition is impossible.

If there be any confused decussation in the focal rays of the object, as a brilliant point of light, however small, it acquires a spurious exaggerated disk, more or less coloured.

These cardinal facts appear to sum up the whole theory of illumination and definition.

An image of an object is an assemblage of the images of every point in the object.*

If every point produces a spurious disk, the final image is simply an agglomeration of spurious disks: and the definition is better or worse, according as these disks are smaller or larger.

* See Parkinson's 'Optics.'

Dec. 1, 1870.

The spurious disk is that identically the same with the smallest circle of greatest condensation of converging rays.

Here the subjects of illumination and definition obtain a common base of operation. Indeed, the same diagrams and facts which illustrate the one apply equally to the other. (Diagram I., Plate LXVII.)

If conical pencils proceed from Q, and are reflected by a concave mirror obliquely, a series of foci are formed. Confused images are produced of great complexity: and that space or section through which all the reflected pencils pass is a locus of the greatest confusion and decussation.

Each cone of light produces two foci--long and short-primary and secondary. The art of microscopy often consists entirely in selecting the most favourable points of the confused decussation to produce the desired effect. I say desired, because the microscopist more than any other observer is under temptation to produce special effects, dealing as he often does with the really unknown.

An oblique illumination with a concave mirror is the worst possible source of illumination imaginable from a brilliant point or definite origin of light. Hence the value of the white cloud.

Aplanatic illumination is impossible from an oblique spherical mirror. Indeed, even with the parabolic form of Browning's silver glass mirror the slightest obliquity gives a strong wing or flare to an observed star or coma-a sufficient proof of the well-known destruction of aplanatism. The image is no longer clear of aberration or wandering rays. But if we turn to the property of the ellipse the lines QP, F P, drawn from the foci, are equally inclined to the tangent at P, P R.* Every ray shot from Q against the internal curvature will accurately cross the axis at one and the same point, F, and the two foci are absolutely aplanatic to one another.

In Diagram III. an image is formed by an infinite number of spurious disks corresponding to each point of the object. If a plate stencilled with small apertures in outline be employed, the spurious disk of each will appear expanded, and coalesce into one continuous image, which is very imperfectly defined by a plano-convex lens, when the convex side is turned towards the image. Reversing the lens, the image is improved; if a double convex lens be used, and the image be formed of the same size as the object, by arranging each equidistant from its centre the spurious disks will more nearly equal

the true.

I now turn to a novel experiment (at which I feel sure every one that performs it for the first time will be greatly surprised), by which spurious disks of rare and brilliant beauty and significance are developed with the most gorgeous hues. The experiment requires * Q and F are the foci, and P a point in the curvature.