study what is happening on the surface of the growing crystal where the advancing solid is in actual contact with the solidifying liquid. If you wish to understand a plant or an animal it is not enough to study dried specimens or specimens in spirits, but to watch the living organisms growing under natural conditions; and in the same way it is surely worth while to study the growing crystal surrounded by the solution which feeds it, and even to make under these conditions the measurements and observations which are usually made upon crystals only after they have been taken out of the solution and have ceased to grow.

In the case of living things, we know that growth takes place by internal processes and not only by new material added on the surface. How much easier, then, should it be to study the growth of a crystal when we have found that it is only a surface activity, and does not involve internal changes?

As I have already said, when I came to Oxford there was no laboratory of Mineralogy nor any apparatus for research, but I brought with me a piece of apparatus which I had constructed a few years previously for this exact purpose; to measure the angles of crystals while they are growing in the solution and to ascertain whether any changes take place in those angles, in the hope of getting some insight into the nature of the surface and what I have called the frontier problem. Many days and also nights had I spent with this apparatus in the absorbing pursuit of measuring growing crystals, watching the curious changes that take place in the position of their facets, excited by the knowledge that I was looking at things that had certainly not been seen before, and by the expectation of what they might disclose.

I need not weary this audience with any description of these experiments, which doubtless seem more interesting and important to their author than to anyone else. But I wish to draw your attention to the result that came out of them. I found that it was possible with the same apparatus to measure the refractive power of the liquid in absolute contact with the growing crystal and from this to calculate the exact strength of the solution at that spot. It was thus possible to prove that the solution in contact with the crystal is rather stronger than at a very short distance from it, and to know exactly how much stronger. In other words, while a crystal of, say, alum is growing, the liquid in contact with it contains more particles of alum and less particles of water, or is richer in alum, than the liquid at a short distance from it. I will ask you to bear this in mind in what follows. There is another curious fact connected with this subject. Crystals of nitrate of soda have almost exactly the same shape and almost the same physical properties as crystals of the common mineral calcite, which, in its purest and most perfect form of transparent glassy crystals, is known as Iceland spar. Now, when a perfectly clean crystal of Iceland spar is immersed in a strong solution of nitrate of soda, although it is not dissolved by the liquid itself and therefore cannot crystallize out of it, the Iceland spar actually continues to grow, and becomes enveloped by the nitrate of soda so as to form what is apparently a single crystal.

It appears, therefore, highly probable that a crystal of nitrate of soda and a crystal of Iceland spar behave alike in this respect when placed in a strong solution of the nitrate; each draws to itself the liquid nitrate in the solution, then draws it out of the solution in the solid state, and further arranges the particles upon its own surface in a perfectly regular manner, so that the arrangement of the particles in the shell of nitrate is the same as the arrangement of the particles in the spar which it surrounds; just as a bricklayer sets upon the rising wall new bricks arranged in the same way as those which he has already laid. I remember that on Lord Kelvin’s last visit to Oxford, shortly before his death, mindful of his Boyle Lecture, I showed him, in company with my pupil, Mr. Barker, this beautiful experiment, with which he was at that time not familiar, and I shall never forget the interest and enthusiasm with which he witnessed the beautifully regular and instantaneous growth of the nitrate crystals. He always was as enthusiastic and inquiring as a boy, and these characteristics were exhibited on that occasion in his old age. It is an experiment which sets one thinking, and I have no doubt that, if Lord Kelvin, even at that advanced age, had set his mind to consider it, he would have been able to deduce far more than it has yet suggested to those who have witnessed it.^[3]

Some two years or so before the time of which I am speaking, Mr. Barker had at my suggestion made an exhaustive study of a great number of different substances in order to ascertain which of them behave towards one another like nitrate of soda and calcite, and why they do so, and he has really discovered the secret. When two substances like nitrate of soda and calcite have nearly the same shape and resemble one another closely in their physical properties, the geometrical laws of crystalline structure of which I have already spoken make it certain that they consist of particles arranged in the same way. We do not know what these particles are or what is their shape or size, but we may be sure that they are arranged in the same way. I am perhaps using the word particles in a loose sense, for they might be hollow cells or they might be the space occupied by moving particles, or anything else, but whatever they may be it is pretty certain that they are arranged in the same way.

Well, Mr. Barker has proved that, if two crystals grow together like nitrate of soda and calcite, their particles are not only arranged in the same way, but they must be of the same size, or at any rate occupy the same space. In more scientific language, the two crystals not only have the same molecular structure, but the same molecular volume. It is, therefore, mainly a question of fitting together, and, if the two structures do not fit, they cannot grow together, like nitrate of soda and Iceland spar, as a continuous crystal.

Let me illustrate by a suggestive comparison. The bee’s cell is one of the most remarkable and symmetrical structures in nature. Its regularity is probably due to the fact that bees of the same size are, in making it, so closely crowded together; there is one bee’s head in each cell, and therefore you may say that the arrangement of the bees is the same as that of the cells. For example, if you place in each cell a ball which exactly fits it and then take away the cells, you have an arrangement of balls which is the same as that of the cells, each being in contact with six neighbours. It may be called a hexagonal arrangement. You have only to push together a number of balls on a table, and they will fall into this arrangement. It was a contemporary and associate of Boyle, and an Oxford man, Dr. Robert Hooke, who pointed out that with balls piled together in this way you can build up the shapes of crystals, and that, for example, a pyramid of cannon-balls stacked together in the manner that I have just shown, has the shape and angles of an alum crystal. Now, if two such