lens. This mode of conducting the experiments presents the most decided manifestation of the whole phenomenon. But it must be remarked, that if the image is received on a transparent paper instead of ground glass, it does not in any case present the least illusion of relief. The surface of the paper has the property of preserving to both eyes the same intensity of image from whatever direction the rays are refracted on that surface, and at whatever angle the eyes recede from the centre to examine the image. In fact, all the various images refracted through every part of the lens and coinciding on the surface of the paper, are visible at whatever angle they are examined. The reason of this difference between the effect of the ground glass and that of the paper is, that through the surface of the ground glass, composed of innumerable molecules of the greatest transparency, only deprived of their original parallelism by the operation of grinding, but acting as lenses or prisms disposed at all kinds of angles, the rays refracted by the various parts of the lens continue their course in straight lines in passing through these transparent molecules, and are visible only when they coincide with the optic axes, being invisible in all other directions; that, in short, they are not stopped by the surface of the ground glass; while the paper being perfectly opaque, stops all the rays on their passage, by which the image of the object remains fixed on the surface. Each molecule of the paper becoming luminous, sends new rays in all directions; and from whatever direction we look on the paper, we always perceive at once all the images superposed, so that each eye seeing the two perspectives mingled, the process of convergence according to the horizontal distances of the same points of the various planes, cannot have its play, and no stereoscopic effect can take place, as it is the case with the ground glass, which presents to each eye an image of a different perspective. The author explains that he has ascertained these facts by several experiments, the most decisive of which consists in placing before one of the marginal openings of the lens a blue glass, and a yellow glass before the other. The object of these coloured glasses is to give on the ground glass two images, each of the colour of the glass through which it is refracted. The result is two images, superposed on the ground glass, one VOL. VIII. 2 T yellow and the other blue, forming only one image of a grey tint, being the mixture of yellow and blue, when we look with the two eyes at an equal distance from the centre. But when shutting alternately, now the right eye and then the left eye, in the first case the image appears yellow, and in the second it appears blue. If while looking with the two eyes (the opening on the right of the lens being covered with the yellow glass, and the opening on the left with the blue glass) we move the head on the right of about 6o, the mixture of the two colours disappears, and the image retains only the blue colour; on the other hand, if after having resumed the middle position, which shows again the mixture of the two colours, we move the head on the left of 6°, the mixture disappears again, and the image retains only the yellow colour. This proves evidently that each eye sees only the rays which, when after having been refracted by any part of the lens, and continuing their course in a direct line through the ground glass, coincide with the optic axes, while all the other rays are invisible. The consideration of these singular facts has led the author to think that it would be possible to construct a new stereoscope, in which the two eyes looking at a single image could see it in perfect relief, such a single image being composed of two images, of different perspectives superposed, one visible only to the right eye and the other to the left. This would be easily done by refracting a stereoscopic slide on a ground glass, through two semi-lenses separated enough to make the right picture of the slide coincide with the left picture at the focus of the semi-lenses. The whole arrangement may be easily understood; we have only to suppose that we look through a ground glass placed before an ordinary stereoscope at the distance of the focus of its semi-lenses, the slide being strongly lighted, and the eye seeing no other light than that of the picture on the ground glass. The whole being nothing more than a camera having had its lens cut in two parts, and the two halves sufficiently separated to produce at the focus the coincidence of the two opposite sides of the stereoscopic slide placed before the camera. Received XXIV. "Supplementary Researches on the Partition of Numbers." By ARTHUR CAYLEY, Esq., F.R.S. March 19, 1857. (Abstract.) The paper is supplementary to the author's memoir, "Researches on the Partition of Numbers," which comprises the two papers abstracts of which appear in the 'Proceedings' of the Meeting of the 3rd of May, 1855. It contains some additional developments in relation to the theorem referred to at the conclusion of the former memoir, and an application to the determination of the expression for P (1, 2, 3, 4, 5, 6,) 9. XXV. "On the Anatomy and Physiology of the Spongiada." By J. S. BOWERBANK, F.R.S., F.L.S., &c. Received June 17, 1857. (Abstract.) The arrangement of the Spongiada by Lamarck, based entirely on external form, is wholly inadequate for the discrimination of species. The classification adopted by Drs. Fleming, Grant, and Johnston, dependent more especially on the chemical constituents of those bodies, is far too limited to be applied in generic characters. The author has, therefore, for this purpose rejected both systems, and has retained the latter one for forming primary divisions only, and he purposes founding the generic characters principally on the organic structure and mode of arrangement of the skeleton, in accordance with the practice so generally adopted by naturalists with regard to many of the higher classes of animals. Tethea, Geodia, Dysidea and a few others are the only well-defined genera that have yet been established; while others, such as Halichondria, even in the narrow circle of the list of British species, contain at least ten distinct modes of arrangement of the skeleton, each of which is constant and well-defined in its character. It is not intended to propose the rejection of any of the well-established genera of preceding authorities, but to confine each genus strictly within the bounds indicated by the peculiar mode of structure of the skeleton which exists in that species of sponge which is the oldest-established and best-known type of the genus, and to refer all others that may distinctly differ from that type to new genera founded on structural principles. It is proposed to characterize the elementary tissues in the following order : 1. Spicula. 2. Keratode or horny substance. 3. Membranous tissues. 4. Fibrous tissues. 5. Cellular tissues. 6. Sarcode. And, in the second place, to treat of the organization and physiology in the following order : 1. The skeleton. 2. The sarcodous system. 5. The dermal membrane. 6. The pores. 7. The oscula. 8. Inhalation and exhalation. 9. Nutrition. 10. Cilia and ciliary action. 11. Reproduction, gemmules, &c. And to conclude with observations on the generic characters. The author then proceeds to describe the spicula, which he states are essentially different in character from the fibres of the sponge; although the latter may be equally siliceous with the former. However closely the spicula may be brought into contact with each other, or with siliceous fibre, they appear never to unite or anastomose ; while the fibre, whether siliceous or keratose, always anastomoses when it comes in contact with other parts of its own body or with those of its own species. A detailed description is given of the origin and progressive development of these organs, from which it is inferred that they are the homologues of the bones in the higher classes of animals, and that the forms they assume are always of an organic type, never crystalline or angular; and the same forms of spicula are found composed of either silex or carbonate of lime, demonstrating the fact that the deposits of earthy matter are influenced by the laws of animal organization only, and never oy those of inorganic or crystalline arrangement. Each species of sponge has, not one form of spiculum only, equally dispersed throughout its whole substance; but, on the contrary, separate parts have their appropriate forms; and thus we find that there are often three, four, or even more forms of spicula in the same individual. The author therefore, in describing them, proposes to treat of these organs in the following order : 1. Spicula of the skeleton. 2. Connecting spicula. 3. Defensive spicula. 4. Spicula of the membranes. 5. Spicula of the sarcode. 6. Spicula of the gemmules. : 1st. The spicula of the skeleton in the siliceous sponges are usually simple, elongate in form, slightly curved, and are occasionally more or less furnished with spines. They are either irregularly matted together, collected in fasciculi, or dispersed within or upon the keratose fibres of which the skeleton is to a great extent composed. All these elongate forms of spicula are subject to extreme variety of length. In some species they maintain a great degree of uniformity, while in others they vary to a very considerable extent, according to the necessities arising from the mode of the construction of the skeleton. 2nd. The connecting spicula are not necessarily a part of the skeleton; they are a subsidiary portion of it under especial circumstances, in a few genera only, as Geodia, Pachymatisma, and other sponges which have a thick crustaceous surface, which the spicula serve to support and retain in due connexion with the mass of the animal beneath. The normal form of these spicula is very different from that of the general mass of those of the skeleton, and they are much more complex and varied in their structure. They usually have a long, stout, cylindrical or attenuating shaft terminating either acutely or hemispherically at the base, while the apex is divided into three equi-angular radii, which assume in different species a considerable amount of variety as regards form and direction. The triradiate apices are usually cemented firmly to the inner surface of the |