understand the present state of our knowledge concerning them. I will only refer to two: one is an experimental fact, and the other is a theoretical speculation, and both are connected with the subject that I have been discussing.

It was discovered shortly before that time, and has been found by many experiments since, that there are certain substances which are in a real sense crystals, although they are liquid; that is to say, they affect light in its passage through them just as solid crystals do.

These extraordinary substances, which had been investigated by Professor Lehmann, were first shown in England by Mr. Bowman and Mr. Hartley, who were then working in my laboratory, at a conversazione at the Royal Society, not long after their discovery, and I can well remember the interest with which they were witnessed by Sir George Stokes and others. We can only picture these liquids as consisting of particles which, while they are free to move in all directions, always continue to face the same way, like a group of dancers who in all their evolutions continue to face the audience, instead of turning as they move. When the mechanism which renders possible this remarkable behaviour is better understood, we may be sure that it will bring about a better understanding of the manner in which a solid crystal is constructed. The interesting thing about it is that here at any rate the particles are in violent movement instead of being comparatively stationary, as they are in a solid crystal.

One is naturally led to imagine that before any solution begins to crystallize in the solid form it passes into this liquid state, and that the particles have begun to set themselves and all to face the same way before they begin to cohere and to build themselves into a solid. But so far as I know there is no evidence in favour of this suggestion—a solution before solid crystals begin to appear does not behave like a liquid crystal, but remains an ordinary solution up to the last moment when new crystals are born in it or are started by inoculation with a crystal germ.

The other discovery, which is in the nature of a speculation, is that of another person whom I am proud to reckon among my former pupils, namely, Professor Pope of Cambridge, working in conjunction with Mr. Barlow. Mr. Barlow had already been referred to by Lord Kelvin in his Boyle Lecture as the author of ingenious researches upon the various ways in which materials can be packed together, and the different arrangements and structures which result from this packing.

These two workers have now propounded a theory according to which, if the various atoms which constitute a substance are represented by spheres whose sizes represent the valency of the atoms, and if these spheres are packed together as closely as they will go, the resulting structure will represent very nearly the structure of the crystal; and so it may be possible for the first time from a knowledge of the chemical constitution of a substance to predict the structure of its crystals and therefore the form in which it will crystallize. You remember the bee’s cell arrangement and the similar arrangement of balls got by placing a ball in each cell and then removing the cells. Another way of getting the same arrangement is to place a number of equal balls on a table and to squeeze them together until they are packed as closely as possible. This arrangement of closest packing, the arrangement of a pyramid of cannon-balls, is precisely the same as before, the one in which each ball on the table is in contact with six others. According to Pope and Barlow the atoms in a crystal simply pack themselves together as closely as possible, but instead of being equal in size they have generally to be represented as of different sizes according to their valencies. If we imagine the coalescence of atoms to form a crystal to be due to their mutual attraction, it is very reasonable to suppose that they will get as close together as is possible, and therefore that the ways of close packing are the ways of crystal structure. The theory therefore suggests a reason for the growth as well as for the shape of a crystal. I may remind you that the bee’s cell itself, which is in the world of life the thing that most nearly resembles crystalline structure, is due to this same principle of close packing; for in their efforts to get as closely together as possible the bees are constrained to get into the hexagonal arrangement. The bees crowd their heads together and to each bee’s head corresponds one cell.

On the other hand, Professor Sollas has brought forward some most suggestive and convincing speculations concerning certain crystals which are based upon the principle of open, and not close, packing. His model of silver iodide, for example, is well known in Oxford.

I have mentioned these recent contributions to science, not only with the object of indicating that our knowledge of crystals is steadily increasing, but also in order to point out that little has yet been done to explain the mysteries of their growth. All that has been effected up to the present is an attempt to explain how they are constructed, not the process by which the construction takes place. It is as though we were to analyse the form and structure of animals and plants and never to watch them as they grow, but only to study them from fossils or from museum specimens. And I believe the reason to be this. All the speculations concerning crystals persist in regarding the particles of which they consist as fixed and immovable: the theories are all statical. And yet we know that the particles of matter, whatever they may be, are really in lively movement. Is it not possible that in order to get a correct understanding of the growth of a crystal we should take account not only of the positions, but of the movements, of its particles? Without some knowledge of these we are not able to approach the problem, or to ascertain how a crystal either of nitrate of soda or of Iceland spar draws the nitrate of soda out of the solution and makes it grow into a solid.

Remember that when we say we know how the particles of a crystal are arranged we really know nothing about their nature, and can only represent them by spheres, or solid figures, or cells, or even points, in order to get a representation of their arrangement. But we might arrange in the same way a number of bodies each of which is whirling in a fixed orbit, like a planet, about the corresponding point, or vibrating about it like the prong of a tuning-fork, or pulsating like a breathing animal; and so far from the arrangement being independent of the movements it may be due to them.

If I may seek another analogy, let me take a group of figure skaters; their centre remains fixed at the orange, maybe, about which their figures are executed, but the group of skaters is at one moment extended when they circle out to their furthest sweep, and at another moment concentrated when they converge to the centre; and this alternating expansion and compression occurs in a regular rhythm.

Imagine a pond covered by a number of such groups of skaters; the manner in which they will fit in, and have to arrange themselves, will depend both upon the dimensions and the rhythm of their curves, and they may even interlace and become part of one great figure system covering the whole pond. May not the growth of a crystal be something of this sort?

All the devices which I have quoted for picturing to ourselves the architecture of a crystal I would regard as merely models representing something that may be really quite different. But I venture to suggest that the