Part 1

_The Growth of a Crystal_

BEING THE

EIGHTEENTH ROBERT BOYLE LECTURE

DELIVERED BEFORE

_THE OXFORD UNIVERSITY JUNIOR SCIENTIFIC CLUB_

_On the 20th of May, 1911_

BY

HENRY A. MIERS, M.A., D.SC. (OXON.), F.R.S.

PRINCIPAL OF LONDON UNIVERSITY

LONDON: HENRY FROWDE, AMEN CORNER, E.C.

EDINBURGH: 12 FREDERICK STREET. GLASGOW: 104 WEST GEORGE STREET OXFORD: 116 HIGH STREET NEW YORK: 29-35 WEST 32ND STREET TORONTO: 25-27 RICHMOND STREET WEST MELBOURNE: CATHEDRAL BUILDINGS, 205 FLINDERS LANE

1911

OXFORD: HORACE HART PRINTER TO THE UNIVERSITY

THE GROWTH OF A CRYSTAL

When this date was fixed by your Secretary for the delivery of the BOYLE Lecture, I discovered that it happened to be the fifteenth anniversary of the very day on which I was first called upon to address a general audience in Oxford. On May 20, 1896, I delivered an inaugural lecture as Waynflete Professor of Mineralogy; when I look back upon the happy years spent here in teaching and studying a science which is dear to me, I feel that the present lecture should be an opportunity for expressing gratitude for those peaceful years, not unmingled with regret that they led to no such worthy achievement on my part as might have brought great credit to the University and so have repaid something of the debt which I owe to her.

Looking back from the busier world of London, it is easy to see how ideal are the conditions under which an Oxford Professor conducts his work; especially if his subject be one which does not overwhelm him with students who pursue it only for the purpose of passing an examination. Those who are attracted to his Laboratory probably come because they have some natural taste for the subject; he finds it a pleasure to devote his time to them; while his vacations and the conditions of Oxford life give him unique opportunities for his own researches.

It is true that those who have most leisure not infrequently waste most time. It is true also that the custom of Oxford is to burden her students and scholars in addition to their teaching, with the conduct of affairs which could be managed as well by persons specially appointed for the purpose. Still it is also certain that to those who enter into the genius of the place, and are animated by the spirit of Learning, Oxford is prodigal of opportunity, and enables them to live the Academic Life in a way which is scarcely possible elsewhere.

I know that the doors of the University are being opened to all the newer studies, and that many a student spends most of his time in acquiring the useful knowledge that is to equip him for his profession and for the direct purpose of that profession; knowledge which is to fit him to become lawyer, doctor, minister, engineer, or teacher; yet an Oxford Professor may always maintain the pursuit of Learning for its own sake and keep this purpose before his students even in their most technical work.

Now Mineralogy is one of those sciences whose practical applications are clear; it is necessary to the miner and the engineer; indeed, it sprang from their needs; even Crystallography (that is, the study of Crystals), which has always hitherto, though with little reason, been treated for University purposes as a branch of Mineralogy, has also become part of the necessary equipment of the practical chemist and geologist; but both Sciences are, in their general aspects, very far removed from the turmoil of practical life; it is with these aspects that I would fain deal, and especially in relation to the study of crystals.

In this connexion, a passage which I quoted from GOETHE fifteen years ago will bear repetition: ‘_There is a flavour_,’ he says, ‘_of the Monk or of the old Bachelor about Crystallography and therefore it is self-sufficient. Practical application in life it has none; its rarest objects, the crystallized precious stones, have to be cut and polished before we can adorn our ladies with them._’

In fact, this lecture, which I was constrained to prepare during a brief holiday in Italy, was written in the midst of surroundings where it was easier to think of Science as cultivated in the quiet of the Laboratory, rather than in the restless scenes of its practical applications, although I am familiar with both. Writing at a window overlooking the mediaeval town and ancient walls of Perugia, with the view of peaceful Assisi and the snowy cap of Monte Subasio across the plain, it was easier to recall the hours of quiet toil and reflection spent in one’s Laboratory at Oxford than visits to Mining Camp, or Metallurgical Works.

Accordingly when, under these circumstances, I set about choosing a subject for the present occasion, it occurred to me that I might be allowed to take up my discourse where I laid it down in 1896 and in some sense to continue and conclude the remarks which I then made to the University; and, considering how recently I have left you, I might regard this as my farewell address corresponding to the opening lecture which I then delivered.

In that address, I recollect, I began with an inquiry into the resemblances and differences between minerals and other objects of nature in respect of their beauty, especially as regards the beauty of form which is so specially characteristic of minerals. Some minerals, indeed, are found in delicate fronds and leaflets, and in mossy tufts, which, in their form and texture, in their sheen and lustre, so closely resemble plants that they are often mistaken for them. [Those who heard RUSKIN’S lectures will remember the delight with which he described these beauties of the mineral kingdom and the affection which he felt for them.] I pointed out, I remember, that these delicate forms are, like the frost patterns on a window-pane, really expressions of the crystalline shape and symmetry of the mineral; each mineral consists of crystals, and therefore has its own peculiar crystalline shape which is one of its inherent properties; moreover, this persists unchanging through the ages, and under all conditions, and is in no way dependent upon the environment in which the mineral is situated.

The shape of a crystal does not depend like that of the animal or the plant upon the life which its forefathers have led or the conditions under which they have grown.

There are indeed other features in which a mineral or any crystal may resemble a living thing in a way even more surprising than in its form. Two of the most remarkable are these: it grows out of a solution as though it were alive; and, if it is wounded or broken, it heals itself and replaces the missing part just as a living organism may do. But, as I pointed out, there is this radical difference. The crystal is not responsive to the change of its surroundings; its form is not the result of external forces; it does not adapt itself to its environment; it is not undergoing any progressive evolution; but remains fixed and unchanging. Its form is the expression of its permanent composition, and so far as we know has always been the same. Indeed, until it has been converted into its constituent elements and destroyed, it is in a sense not only unchanging, but imperishable. For, take a crystal and break or dissolve it away until only the tiniest fragment remains; that fragment (e. g. sugar), though it may be only an invisible speck, will, if immersed in the appropriate solution, continue to grow again and will once more assume the form of a perfect crystal. Neither does it make any difference if the crystal fragment has been kept for years or even centuries; it will, when supplied with nourishment from the appropriate solution, heal itself and continue to grow as though the process had never been suspended. In a sense it is immortal, for, if not destroyed, it never loses the mysterious power of growth, and is therefore more imperishable than any seed or germ of life.

The main conclusion of my lecture was that, having been led by analogy to compare the growing crystal with the growing plant, one finds the growth and life of the crystal to be totally unlike the growth and life of any organism. Its life is only an unchanging persistence without the display of any struggle for existence, any movement, any adaptation, or response to environment; its growth is only the addition of new material on the surface of the old, without assimilation, so that the crystal remains uniform and increases in size; there is no distinction of any one part from any other; the crystal grows, therefore, without the development of any organs.

One appears to be left with the conclusion that the crystal should be regarded rather as a type of death than of immortality.

SCHOPENHAUER expressed this idea when he said: ‘_The crystal has only one manifestation of life, crystallization, which afterwards has its fully adequate and exhaustive expression in the rigid form—the corpse of that momentary life._’

This, however, is not the conclusion which I would have you draw from the facts; and I shall ask you on the present occasion to accompany me in pursuing a little further the inquiry into what we may call the vitality of a crystal and the manner in which it is displayed; although this vitality is not to be confounded in any way with that of a living plant or creature.

It is, I hope, not unfitting that the subject of crystal growth should be dealt with in a BOYLE Lecture, for ROBERT BOYLE was himself one of the first to treat it in a scientific spirit. He was the exact contemporary of NICOLAS STENO, the famous Danish physician who laid the foundation of modern crystallography; and BOYLE, in his treatise on the origin and virtues of gems, was the first to express the conviction which was almost simultaneously expressed by STENO—that gems must have solidified from the liquid state. One of his reasons for thinking so was their crystalline form, which resembles that of salts which crystallize from solutions. Let me quote his exact words: ‘_The origin assigned to gems may be countenanced by the external figuration of divers of them. For we plainly see that the corpuscles of nitre, alum, vitriol, and even common salt, being suffered to coagulate in the liquors they swam in before, will convene into crystals of curious and determinate shapes._’ And then he points out that when a salt such as nitre crystallizes in a vessel it is only where it is free to grow in the liquid, and away from contact with the sides of the vessel, that it can acquire this shape. These crystals (he says), ‘_having a fluid ambient to shoot in, will have those parts of their bodies that are contiguous to the liquor curiously formed into such prismatical shapes as are proper to nitre._’

When BOYLE wrote these words he had not seen the work of STENO, which had just been published.

I may, therefore, claim that he was the first person to deal in a scientific spirit with the subject which I have chosen for this lecture, the ‘Growth of a Crystal.’

Three years before I came back to Oxford—on May 16th, 1893, the subject of crystal structure had been treated in the second BOYLE Lecture in a most original and masterly manner by no less a person than LORD KELVIN. I well remember that Lecture, at which I had the good fortune to be present; and to one who was already interested in crystals it was a wonderfully illuminating and inspiring address.

On that occasion my venerable predecessor and teacher, Professor STORY MASKELYNE, conducted LORD KELVIN to the lecture table.[1]

[Footnote 1: It is with the deepest regret that I add that my old friend and revered teacher died on the very day on which these words were spoken.—H. A. M.]

At that time, however, there was no laboratory in Oxford for mineralogical and crystallographical research; the Professor only had a lecture-room, he did not reside in Oxford, and his scientific work was necessarily carried on elsewhere. To-day I am more fortunate in being able to draw upon the resources of the well-equipped laboratory of my successor, and former pupil, Professor BOWMAN, and upon his still more valuable personal assistance and that of Mr. BARKER; so that, though I only have to deal with ideas that are simple compared with those which issued with fiery vigour from the fertile brain of the BOYLE Lecturer of 1893, I have a better opportunity of showing to an Oxford audience to-day the actual things of which I am speaking, and may help to make my meaning clear to those who cannot know much from personal experience concerning the growth of crystals.[2] When I delivered my own inaugural lecture I had no means of making visible to an audience the astonishing features of crystal growth. Beautiful effects may easily be witnessed by anyone with a few drops of common solution and a magnifying glass, yet I believe that they are witnessed by comparatively few persons.

[Footnote 2: This lecture was beautifully illustrated by excellent slides showing the actual _growth_ of crystals.—ED.]

I have alluded to laws of crystalline structure, to which LORD KELVIN had directed attention: these are the laws of geometrical arrangement which prove crystals to be constructed in an entirely different manner from the living plants which they may so closely resemble; these laws, however, were not established by observations or experiments upon the growth of crystals. They were the result of a century of patient measurements of the external shape of countless crystals; more than a century of accurate determinations of what happens when heat and light are transmitted through them and of numberless other experiments made by physicists; and, added to this, the labours of mathematicians who studied the manner in which solid particles could be arranged so as to correspond to the geometrical and physical proportions thus determined by experiment.

But all these were experiments and reasoning upon matter which appears to be as nearly as possible inert; they entirely ignore the power of growth possessed by crystals; indeed, no such power is contemplated by the ordinary theories of crystal structure or could be predicted from them.

So far, then, we may regard the comparison of crystals with plants and all the fanciful ideas concerning their connexion with the origin of life which were suggested by that comparison as only one more example of the dangers of reasoning from analogy. The recollections that I retain of the allusions to that process—in text-books of logic and treatises on Science alike—give me the impression that examples of reasoning from analogy are generally quoted only as instances of its danger and futility. That, indeed, might seem to be the conclusion of my own inaugural lecture; for, when we come to examine the growth and structure of crystals, so far from finding that there is any real likeness to the life and structure of the plants which they resemble, we find nothing but a profound difference.

That, however, is not my real opinion, and was not my opinion fifteen years ago. On the contrary, I have the greatest belief in analogy as one of the most useful guides to discovery, and as the means by which in practice new lines of investigation are most frequently opened and new hypotheses suggested. In fact, I think that most of the advances which are made in science, and especially in scientific theory, have been made with the help of analogies.

If an explanation of any fact in Nature consists in correlating it with some apparently distinct fact, and showing that the two have a common cause, or are connected in a definite manner, how often has the explanation of a new occurrence been suggested by the analogy of some other known occurrence which is brought to mind by the memory; not by a conscious effort of the reason, but by the recollection of a resemblance. Do not some of the standard methods which are familiar in the descriptions or criticisms of scientific discovery, such as ‘_reasoning from the known to the unknown_’, ‘_the adoption of a working hypothesis_’, ‘_the scientific use of the imagination_’, often resolve themselves on analysis into the simple process of being struck by an analogy and being led by it to adopt an explanation or to try an experiment suggested by it?

I daresay that scientific discoverers are ashamed to confess that they may have been led to a theory by a superficial analogy just as they are ashamed to confess that they have hit upon a discovery or an invention by chance, and have found one thing when they were looking for another. But there is no need to be ashamed, for the discoveries only come to those who have the eyes to see, or the knowledge which enables them to remember a resemblance, and who have further the intellectual power to make use of it. Science grows on the acquisition of new knowledge and we must not hesitate to grasp it where we can. There is a danger lest the formulation of the methods of science may deter the inquisitive student from seeking knowledge wherever it is to be found, and make him believe that it is only by the orthodox processes of reasoning based upon a lifetime of training that he is to discover anything new. Rather let him be encouraged to seek any resemblance or analogy that may point a way in the gloom.

It is true that in the past the argument from analogy has often proved dangerous when, because the things possess certain attributes in common, it was inferred that they are alike in other respects. Yet even here it may prove useful. NEWTON only asserted that the diamond is inflammable because it resembles other inflammable substances in possessing a high refractive power; and yet he turned out to be right, although his analogy was wrong. Moreover, it was the analogy which prompted the experiment. To detect an analogy, to test it, and to find that it cannot be maintained, may be as useful an addition to knowledge as the establishment of a real causal relationship: it has had the effect of setting the worker on to new experiments or observations, and every such step is necessarily an advance. The conscientious search for one thing almost invariably leads to the discovery of another; and, even if it does not, who shall say that it may not be as important and useful, say, to establish a difference as to prove the resemblance which has been suspected?

If, however, reasoning from an analogy may be fallacious when inferences are drawn from the fact that two things possess the same attributes in common, it is, I think, a safer guide when it is used to suggest a new hypothesis; a corpuscular theory of light may be suggested by the analogy between the reflexion of light and the rebounding of elastic bodies; an undulatory theory by the analogy of a wave propagated along a string or on the surface of water. The one theory may be found to fit the facts and the other may be condemned; but without some analogy as a guide how are such theories to be devised? What we require in science are continual stimuli to start us on new experiments, new observations, and new ideas, and prevent us, especially those who are teachers, from constantly repeating the old ones.

I shall be satisfied if the present lecture is regarded as a plea for the use of reasoning from analogy, and as an illustration of its value.

Let me, then, after this exhortation, return to my problem of the growth of crystals, and show how I still think that we may be guided by analogy in seeking to understand it.

So far from regarding the growth of a crystal as of no further importance after it has been proved to be quite different from the growth of a plant, we must still think of it as one of the most interesting and mysterious events, and the one through which we may hope to get the clearest insight into the nature of the crystal itself.

For, after all, when after making physical experiments upon the solid crystal and studying its action upon heat and light we are led to speculate upon the manner in which it is constructed, we must not forget that it grew, and that the material was laid down under conditions which we can only understand by studying what happens on the surface as it grows.

LORD CURZON devoted his ROMANES Lecture to the consideration of Frontiers, and explained their interest and importance in the growth of nations. In the study of Science also nothing is more interesting and important than frontier problems. In two senses is this true. The problems which lie on the borderland between two sciences are the most fruitful of all, because they throw light upon each science, and, by bringing into harmony things that were previously distinct and separate, lead to an immediate extension of knowledge.

And also in a more restricted sense. You will find, I think, that the scenes of the most interesting events in Nature are generally those places where different things come into contact and where there is consequently stir and action; where two substances meet to form a new chemical compound; where two bodies touch and react upon each other; at the surface of a solid or a liquid; these are the regions in which events are taking place that we can study and measure with the prospect of discovery.

Impressed by the analogy between the growth of crystals and of living things, I have always felt that, for a proper understanding of the things themselves, the study of their growth is as important for the one as for the other; that to obtain this understanding it is necessary to 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.