Experiments on a Fundamental Question in Electro-Optics: Reduction of Relative Retardations to Absolute. By John Kerr, LL.D., F.R.S. 252 On the Liquation of Silver Copper Alloys. By Edward Matthey, A Contribution to the Study of Descending Degenerations in the Brain and Spinal Cord, and of the Seat of Origin and Paths of Conduction of the Fits in Absinthe Epilepsy. By Rubert Boyce, M.B., Assistant Professor of Pathology, University College, London............. 269 A Research into the Elasticity of the Living Brain, and the Conditions governing the Recovery of the Brain after Compression for Short Periods. By A. G. Levy, M.B. (London).......... On the Effects produced on the Circulation and Respiration by Gun- shot Injuries of the Cerebral Hemispheres. By S. P. Kramer, M.D., and Victor Horsley, M.B., F.R.C.S., F.R.S., Professor of Pathology On the Influence of Carbonic Acid and Oxygen upon the Coagulability of the Blood in Vivo. By A. E. Wright, M.D. (Dubl.), Professor of On the Disappearance of the Leucocytes from the Blood, after Injection Account of the appropriation of the sum of £4,000 (the Government Grant) annually voted by Parliament to the Royal Society, to be em- ployed in aiding the Advancement of Science (continued from vol. liii, p. 321). April 1, 1893, to March 31, 1894........ Report of the Incorporated Kew Committee for the Year ending On Variations observed in the Spectra of Carbon Electrodes, and on the Influence of one Substance on the Spectrum of another. By W. N. Hartley, F.R.S., Royal College of Science, Dublin................................... Electrical Interference Phenomena somewhat analogous to Newton's Rings, but exhibited by Waves along Wires. By Edwin H. Barton, On Rocks and Minerals collected by Mr. W. M. Conway in the Kara- koram Himalayas. By Professor T. G. Bonney, D.Sc., F.R.S., and On the Specific Heats of Gases at Constant Volume. Part II. Carbon Dioxide. By J. Joly, M.A., Sc.D., F.R.S............... On the Specific Heats of Gases at Constant Volume. Part III. The Specific Heat of Carbon Dioxide as a Function of Temperature. By A Contribution to the Study of the Yellow Colouring Matter of the Urine. By Archibald E. Garrod, M.A., M.D. Oxon, F.R.C.P............. Some Points in the Histology of the Nervous System of the Embryonic The Refractive Character of the Eyes of Horses. By Veterinary Captain F. Smith, F.R.C.V.S., F.I.C., Army Veterinary Department. 414 Correction of an Error of Observation in Part XIX of the Author's Memoirs on the Organisation of the Fossil Plants of the Coal Report on some of the Changes produced on Liver Cells by the Action of some Organic and Inorganic Compounds. By Dr. Lauder Brunton, Note on the Production of Sounds by the Air-bladder of certain Siluroid Fishes. By Professors T. W. Bridge and A. C. Haddon CROONIAN LECTURE.-La fine Structure des Centres Nerveux. By Santiago Ramón y Cajal, Professor of Histology, University of No. 335. On Rocks and Minerals collected by W. M. Conway in the Karakoram Himalayas. By Professor T. G. Bonney, D.Sc., F.R.S., and Miss C. PROCEEDINGS OF THE ROYAL SOCIETY January 18, 1894. The LORD KELVIN, D.C.L., LL.D., President, followed by Sir JOHN EVANS, K.C.B., D.C.L., LL.D., Vice-President and Treasurer, in the Chair. The Right Hon. James Bryce was admitted into the Society. A List of the Presents received was laid on the table, and thanks ordered for them. The following Papers were read: I. "On Homogeneous Division of Space." By LORD KELVIN, P.R.S. Received January 17, 1894. § 1. The homogeneous division of any volume of space means the dividing of it into equal and similar parts, or cells, as I shall call them, all sameways oriented. If we take any point in the interior of one cell or on its boundary, and corresponding points of all the other cells, these points form a homogeneous assemblage of single points, according to Bravais' admirable and important definition.* The general problem of the homogeneous partition of space may be stated thus:Given a homogeneous assemblage of single points, it is required to find every possible form of cell enclosing each of them subject to the condition that it is of the same shape and same ways oriented for all. An interesting application of this problem is to find for a crystal (that is to say, a homogeneous assemblage of groups of chemical atoms) a homogeneous arrangement of partitional interfaces such that each cell contains all the atoms of one molecule. Unless we 'Journal de l'École Polytechnique,' tome. 19, cahier 33, pp. 1-128 (Paris, 1850), quoted and used in my 'Mathematical and Physical Papers,' vol. 3, art. 97, P. 400. VOL. LV. B knew the exact geometrical configuration of the constituent parts of the group of atoms in the crystal, or crystalline molecule as we shall call it, we could not describe the partitional interfaces between one molecule and its neighbour. Knowing as we do know for many crystals the exact geometrical character of the Bravais assemblage of corresponding points of its molecules, we could not be sure that any solution of the partitional problem we might choose to take would give a cell containing only the constituent parts of one molecule. For instance, in the case of quartz, of which the crystalline molecule is probably 3(SiO2), a form of cell chosen at random might be such that it would enclose the silicon of one molecule with only some part of the oxygen belonging to it, and some of the oxygen belonging to a neighbouring molecule, leaving out some of its own oxygen, which would be enclosed in the cell of either that neighbour or of another neighbour or other neighbours. § 2. This will be better understood if we consider another illustration—a homogeneous assemblage of equal and similar trees planted close together in any regular geometrical order on a plane field either inclined or horizontal, so close together that roots of different trees interpenetrate in the ground, and branches and leaves in the air. To be perfectly homogeneous, every root, every twig, and every leaf of any one tree must have equal and similar counterparts in every other tree. So far everything is natural, except, of course, the absolute homogeneousness that our problem assumes; but now, to make a homogeneous assemblage of molecules in space, we must suppose plane above plane each homogeneously planted with trees at equal successive intervals of height. The interval between two planes may be so large as to allow a clear space above the highest plane of leaves of one plantation and below the lowest plane of the ends of roots in the plantation above. We shall not, however, limit ourselves to this case, and we shall suppose generally that leaves of one plantation intermingle with roots of the plantation above, always, however, subject to the condition of perfect homogeneousness. Here, then, we have a truly wonderful problem of geometry-to enclose ideally each tree within a closed surface containing every twig, leaf, and rootlet belonging to it, and nothing belonging to any other tree, and to shape this surface so that it will coincide all round with portions of similar surfaces around neighbouring trees. Wonderful as it is, this is a perfectly easy problem if the trees are given, and if they fulfil the condition of being perfectly homogeneous. In fact we may begin with the actual bounding surface of leaves, bark, and roots of each tree. Wherever there is a contact, whether with leaves, bark, or roots of neighbouring trees, the areas of contact form part of the required cell-surface. To complete the cell-surface we |