CHAPTER III

LIFE AS THE DIRECTOR OF LABORATORY WORK IN THE SCHOOL OF PHYSICS AND CHEMISTRY. GENERALIZATION OF THE PRINCIPLE OF SYMMETRY. INVESTIGATIONS OF MAGNETISM

It was in the School of Physics, in the old buildings of the Collège Rollin, that Pierre Curie was destined to work, first as Director of Laboratory Work, then as Professor, for twenty-two years, a period covering practically the whole of his scientific life. His memory seemed to cling to these old buildings, now destroyed, in which he had passed all his days, returning only in the evening to his parents in the country. He counted himself fortunate since he enjoyed the favor of the Founder-Director Schützenberger, and the esteem and good will of his students, many of whom became his disciples and friends. In alluding to this experience, at the close of an address delivered at the Sorbonne near the end of his life, he said:

"I desire to recall here that we have made all our investigations in the School of Physics and Chemistry of the city of Paris. In all creative scientific work the influence of the surroundings in which one works is of great importance, and a part of the result is due to that influence. For more than twenty years I have worked in the School of Physics and Chemistry. Schützenberger, the first director of the School, was an eminent scientist. I remember with gratitude that he procured for me opportunities for my own investigations when I was yet but an assistant. Later, he permitted Madame Curie to work beside me, an authorization which was at that time far from an ordinary innovation.

"Schützenberger allowed us all great liberty; his direction made itself felt chiefly through his inspiring love of science. The professors of the School of Physics and Chemistry, and the students who have gone from it, have created a kindly and stimulating atmosphere that has been extremely helpful to me. It is among the old students of the school that we have found our collaborators and our friends. I am happy to be able, here, to thank them all."

The newly appointed director of the laboratory was, when he first assumed his duties, scarcely older than his students, who loved him because of his extreme simplicity of manner, which was much more that of a comrade than of a master. Some of these students recall with emotion their work carried on with him and his discussion at the blackboard, where he readily allowed himself to be led to debate scientific matters to their great profit both in information and in kindled enthusiasm. At a dinner given in 1903 by the Association of Former Students of the School, which he attended, he laughingly recalled an incident of this period. One day after lingering late with several students in the laboratory, he found the door locked, and they all had to climb down from the first floor single file, along a pipe that ran near one of the windows.

Because of his reserve and shyness he did not make acquaintances easily, but those whose work brought them near him loved him because of his kindliness. This was true of his subordinates during his entire life. In the school his laboratory helper, whom he had aided under trying circumstances, thought of him with the greatest gratitude, in fact, with veritable adoration.

Although separated from his brother, he remained bound to him by their former bond of love and confidence. During vacations, Jacques Curie would come to him that they might renew again that valuable collaboration to which both willingly sacrificed their periods of liberty. At times it was Pierre who joined Jacques, who was engaged in making a geological chart of the Auvergne country, and there they covered together the daily distances necessary to the tracing of such a map.

Here are a few memories of these long walks, extracts from a letter written to me shortly before our marriage:

"I have been very happy to pass a little time with my brother. We have been far from all immediate care, and so isolated by our manner of living that we have not even been able to receive a letter, never knowing one night where we would sleep the next. At times it seemed to me that we had gone back to the days when we lived entirely together. Then we always arrived at the same opinions about all things, with the result that it was no longer necessary for us to speak in order to understand each other. This was all the more astonishing because we differed so entirely in character."

From the point of view of scientific investigation, one must recognize that the nomination of Pierre Curie to the School of Physics and Chemistry retarded from the very first his experimental research. Indeed, at the time of his appointment nothing yet existed in that establishment; everything had to be created. Even the walls and the

## partitions were hardly yet in place. He had, therefore, to organize

completely the laboratory and its work, and he acquitted himself of this task in a remarkable manner, injecting into it the spirit of precision and originality so characteristic of him.

The direction of the laboratory work of the large number of students (thirty by promotion) was alone a strain on a young man, assisted as he was only by one laboratory helper. The first years were, therefore, hard years of assiduous work, of benefit chiefly to the students trained and developed by the young laboratory director.

He himself profited by this enforced interruption of his experimental research by trying to complete his scientific studies and, in

## particular, his knowledge of mathematics. At the same time he became

engrossed in considerations of a theoretical nature on the relations between crystallography and physics.

In 1884 he published a memoir on questions of the order and repetition that are at the base of the study of the symmetry of crystals. This was followed in the same year by a more general treatment of the same subject. Another article on symmetry and its repetitions appeared in 1885. In that year he published, too, a very important theoretical work[3] on the formation of crystals, and the capillary constants of the different faces.

This rapid succession of investigations shows how completely engrossed Pierre Curie was in the subject of the physics of crystals. Both his theoretical and his experimental research in this domain grouped itself around a very general principle, the principle of symmetry, that he had arrived at step by step, and which he only definitely enunciated in memoirs published between the years 1893 and 1895.

The following is the form, already classic, in which he made his announcement:

"When certain causes produce certain effects, the elements of symmetry in the causes ought to reappear in the effects produced.

"When certain effects reveal a certain dissymmetry, this dissymmetry should be apparent in the causes which have given them birth.

"The converse of these two statements does not hold, at least practically; that is to say, the effects produced can be more symmetrical than their causes."

The capital importance of this statement, perfect in its simplicity, lies in the fact that the elements of symmetry which it introduces are related to all the phenomena of physics without exception.

Guided by an exhaustive study of the groups of symmetry which might exist in nature, Pierre Curie showed how one should use this revelation in character at once geometric and physical, in order to foresee whether a particular phenomenon can reproduce itself, or whether its reproduction is impossible under the given conditions. At the beginning of a certain memoir, he insists in these terms:

"I think it is necessary to introduce into physics the ideas of symmetry familiar to crystallographers."

His work in this field is fundamental, and even though he was led away from it later by other investigations, he always retained a passionate interest in the physics of crystals, as well as in projects of further research in this domain.

The principle of symmetry to which Pierre Curie had so eagerly devoted himself is one of the small number of great principles which dominate the study of the phenomena of physics, and which, having their root in ideas derived by experiment, yet little by little detach themselves and assume a form more and more general and more and more perfect. It is in this way that the idea of the equivalence of heat and of work, added to the earlier notion of the equivalence of kinetic and potential energies, brought about the establishment of the principle of the conservation of energy whose application is entirely general. In the same way the law of the conservation of mass grew out of the experiments of Lavoisier, which belong to the foundations of chemistry. Recently an admirable synthesis has made it possible for us to attain a still higher degree of generalization through the union of these two principles, for it has been proved that the mass of a body is proportional to its internal energy. The study of electrical phenomena led Lippmann to announce the general law of the conservation of electricity. The principle of Carnot, born of considerations on the functioning of thermal machines, has acquired also so general a significance, that it made possible the foreseeing of the most probable character of spontaneous evolution for all material systems.

The principle of symmetry furnishes an example of an analogous evolution. To begin with, observation of Nature was able to suggest the idea of symmetry; though such observations reveal only imperfectly any regular dispositions in the aspects of animals and plants. The regularity becomes very much more perfect in the case of crystallized minerals. We may consider that Nature furnishes us the idea of a plane of symmetry and of an axis of symmetry. An object possesses a plane of symmetry, or a plane of reflection, if this plane divides the object into two parts, of which each one may be thought of as the image of the other reflected in the plane as in a mirror. It is this, approximately, that occurs in the external appearance of man and of numerous animals. An object possesses an axis of symmetry of the order _n_, if it preserves the same appearance after a rotation on this axis of the nth part of a revolution. Thus a regular flower of four petals has an axis of symmetry of the order four, or a quarternary axis. Crystals like those of rock salt or of alum possess many planes of symmetry and many axes of symmetry of different orders.

Geometry teaches us to study the elements of symmetry of a limited figure such, for instance, as a polyhedron; and to discover the relations between its parts which permit us to reunite different symmetries in groups. The knowledge of these groups is of the greatest usefulness in establishing a rational classification of crystal forms in a small number of systems each of which is derived from a simple geometric form. Thus the regular octahedron belongs to the same system as the cube, for in the case of each the group formed by the axes and the planes of symmetry is the same.

In the study of the physical properties of crystalline matter it is necessary to take account of the symmetry of such matter. This is, in general, _anisotropic_; that is to say, it has not the same properties in all directions. On the other hand, media such as glass or water are isotropic, having equivalent properties in all directions. It was the study of optics which first showed that the propagation of light in a crystal is dependent upon the elements of symmetry in that crystal. The same thing is true for the conduction of heat or electricity, for magnetization, for polarization, etc.

It was in reflecting upon the relations between cause and effect that govern these phenomena that Pierre Curie was led to complete and extend the idea of symmetry, by considering it as a condition of space characteristic of the medium in which a given phenomenon occurs. To define this condition it is necessary to consider not only the constitution of the medium but also its condition of movement and the physical agents to which it is subordinated. Thus a right circular cylinder possesses a plane of symmetry perpendicular to its axis in its position, and an infinity of planes of symmetry pass through its axis. If the same cylinder is in rotation on its axis, the first plane of symmetry persists, but all the others are suppressed. Furthermore, if an electric current traverses the cylinder lengthwise, no plane of symmetry remains.

In every phenomenon the elements of symmetry compatible with its existence may be determined. Certain elements can coexist with certain phenomena, but they are not necessary to them. That which is necessary is that certain ones among these elements shall not exist. It is _dissymmetry_ that creates the phenomenon. When several phenomena are superposed in the same system, the dissymmetries are added together. "Works of Pierre Curie," page 127.

It was from the above considerations that Pierre Curie announced the general law whose text, already cited, attains the highest degree of generalization. The synthesis thus obtained seems complete, and all that was further needed was to deduce from it all the developments of which it admits.

For this it is convenient to define the particular symmetry of each phenomenon and to introduce a classification which makes clear the principal groups of symmetry. Mass, electric charge, temperature, have the same symmetry, of a type called _scalar_, that of the sphere. A current of water and a rectilineal electric current have the symmetry of an arrow, of the type _polar vector_. The symmetry of an upright circular cylinder is of the type _tensor_. All of the physics of crystals can be expressed in a form in which the particular phenomena in question are not specified, but in which are examined only the geometrical and analytical relations between the types of quantities where certain ones are considered as causes and the other as effects.

Thus, the study of electrical polarization by the application of an electric field becomes the examination of the relation between two systems of vectors, and the writing out of a system of linear equations having 9 coefficients. The same system of equations holds for the relation between an electric field and an electric current in crystalline conductors; or for that between the temperature gradient and the heat current, except that the meaning of the coefficients must be changed. Similarly, a study of the general relations between a vector and a system of tensors can reveal all the characteristics of piezo-electric phenomena. And all the rich variety of the phenomena of elasticity depends on the relation between two sets of tensors which require, in principle, 36 coefficients.

The foregoing brief exposition reveals the high philosophic import of these conceptions of symmetry which touch all natural phenomena, and whose profound significance Pierre Curie so clearly set forth. It is interesting in this connection to recall the relation which Pasteur saw between these same conceptions and the manifestations of life. "The universe," he said, "is a dissymmetric whole. I am led to believe that life, as it is revealed to us, must be a function of the dissymmetry of the universe, or of the consequences that it involves."

As his organization of his work in the School progressed, Pierre Curie could begin to dream of going forward again with his experimental research. He could do so, however, only under most precarious conditions, for he had not even a laboratory for his personal work, nor a room of any kind entirely at his disposition. Besides, he possessed no funds to support his investigations. It was only after he had been several years at the School that he obtained, thanks to the influence of Schützenberger, a small annual subvention for his work. Up to that time the materials necessary for him were provided, thanks to the kindness of his superiors, to the extent possible, by drawing upon a very limited general fund of the teaching laboratory. As for a place to work in, he had to content himself with very little. He set up certain of his experiments in the rooms of his pupils when these were not in use. But more frequently he worked in an outside corridor running between a stairway and a laboratory. It was there that he conducted, in

## particular, his long research on magnetism.

This abnormal state of affairs was manifestly prejudicial to his work, but it had, nevertheless, the happy result of bringing his students closer to him, for it allowed them, at times, to share in his personal scientific interests.

His return to experimental research is marked by a profound study of the "direct reading periodic precision balance for least weights." (1889, 1890, 1891.) In this balance, the use of small weights is suppressed by the employment of a microscope by means of which one reads a micrometer attached to the extremity of one of the arms of the balance. The reading is made when the oscillation of the balance is arrested, which can occur very rapidly, thanks to the use of pneumatic dampeners conveniently constructed. This balance marks a considerable advance over old systems. It has shown itself particularly valuable in laboratories for chemical analysis, where the rapidity of the weighings is frequently a test of precision. We can say that the introduction of the Curie balances marks an epoch in the construction of these instruments. The work done in this field was far from empirical; it comprised a study of the theory of damped movements and the construction of numerous curves established with the aid of some of his students.

It was toward 1891 that Pierre Curie began a long series of investigations on the magnetic properties of bodies at divers temperatures, from the normal up to 1400° C. These investigations, covering years, were presented as a Doctor's thesis before the Faculty of Sciences of the University of Paris in 1895. In it he stated precisely in the following few words the object and results of his work:

"From the point of view of their magnetic properties, bodies may be divided into two groups: _diamagnetic_ bodies, bodies only feebly magnetic, and _paramagnetic_ bodies.[4] At first sight the two groups seem entirely separate. The principal aim of this research has been to discover if there exist transitions between these two states of matter, and if it is possible to make a given body pass progressively through them. To determine this I have examined the properties of a great number of bodies at temperatures differing as much as possible, in magnetic fields of varying intensities.

"My experiments failed to prove any relation between the properties of _diamagnetic_ and those of _paramagnetic_ bodies. _And the results support the theories which attribute magnetism and diamagnetism to causes of a different nature_. On the contrary, the properties of _ferro-magnetic_ bodies and of bodies _feebly magnetic_ are intimately united."

This experimental work presented many difficulties, for it necessitated the measuring of very minute forces (of the order of ¹⁄₁₀₀ of a milligramme weight) within a container where the temperature could attain 400° C.

As Pierre Curie well understood, the results he obtained are, from a theoretic point of view, of fundamental importance. The Curie law, according to which the coefficient of magnetization of a body feebly magnetized varies in inverse ratio to the absolute temperature, is a remarkably simple law. It is quite comparable to the Gay-Lussac law relating to the variation of the density of a perfect gas with the temperature. In his well known theory of magnetism P. Langevin, in 1905, took into account the Curie law and arrived again, theoretically, at the difference between the origins of diamagnetism and paramagnetism. His work, as well as the important investigations of P. Weiss, demonstrated the accuracy of Pierre Curie's conclusions, as well as the importance of the analogy that he perceived between the intensity of magnetization and the density of a fluid--the paramagnetic state being comparable to a gaseous state, and the ferro-magnetic state to the state of condensation.

In connection with this work, Pierre Curie spent some time in the search for unknown phenomena whose existence did not seem, _a priori_, impossible to him. He sought for bodies strongly diamagnetic, but found none. He tried to discover, too, if there were bodies that acted as conductors of magnetism, and if magnetism can exist in a "free state," like electricity. Here also the result was negative. He never published any of these investigations, for he had the habit of thus engaging in the pursuit of phenomena, often with little hope of success, solely for the love of the unforeseen, and without ever thinking of publication.

Because of this entirely disinterested passion for scientific research the presentation of a doctor's thesis which would give an account of these early investigations had never appealed to him. He was already thirty-five years old when he decided to gather together, in such a thesis, the results of his beautiful work on magnetism.

I have a very vivid memory of how he sustained his thesis before the examiners, for he had invited me, because of the friendship that already existed between us, to be present on the occasion. The jury was composed of Professors Bonty, Lippmann, and Hautefeuille. In the audience were some of his friends, among them his aged father, extremely happy in his son's success. I remember the simplicity and the clarity of the exposition, the esteem indicated by the attitude of the professors, and the conversation between them and the candidate which reminded one of a meeting of the Physics Society. I was greatly impressed; it seemed to me that the little room that day sheltered the exaltation of human thought.

In recalling this period in the life of Pierre Curie, between 1883 and 1895, we can appreciate the great progress the young physicist had made while acting as Chief of Laboratory. He had succeeded during this time in organizing an entirely new teaching service; he had published an important series of theoretical memoirs, as well as the results of experimental research of the first order. In addition, he had constructed new apparatus of great perfection--and all this in spite of very insufficient accommodations and resources. This achievement suggests the distance he had traveled since the doubts and hesitations of his early youth in learning to discipline his methods of work, and to derive from them the full advantage of his exceptional capacities.

He enjoyed a growing esteem in France, and in foreign countries. He was listened to with interest at the meetings of the learned societies (Society of Physics, Society of Mineralogy, Society of Electricians), where he was in the habit of presenting his communications and where he joined readily in the discussion of various scientific questions.

Among foreign scholars who already at this time appreciated him highly, I can name, in the first place, the illustrious English physicist, Lord Kelvin, who joined with him in a certain scientific discussion, and who often expressed for him, from that time on, both esteem and sympathy. During one of his visits to Paris, Lord Kelvin was present at a meeting of the Society of Physics when Pierre Curie made a statement regarding the construction and the use of standard condensers with guard ring. In this statement he recommended the use of an apparatus which involved the charging of the central part of the guard ring plate by a galvanic cell and in uniting the guard ring with the earth. One uses then, as a measure, the charge induced on the second plate. Even though the resulting disposition of lines of the field be complex, the charge induced can be calculated by a theorem of electrostatics, with the same simple formula as is used for an ordinary apparatus in a uniform field, and one has the benefit of a better isolation. Lord Kelvin believed at first that this reasoning was inexact. Despite his great repute and his advanced age, he went the following day to the laboratory to find the young Director. Here he discussed the matter with him before the blackboard. He was completely convinced, and seemed even delighted to concede the point to his companion.[5]

It may seem astonishing that Pierre Curie, in spite of his merits, continued during twelve years in the small position of Chief of Laboratory. Without doubt this was largely due to the fact that it is easy to overlook those who have not the active support of influential persons. It was due also to the fact that it was impossible for him to take the many steps that the pushing of any candidature involves. Then, too, his independence of character ill fitted him to ask for an advance, and this notwithstanding the fact that his position was very modest. Indeed his salary, then comparable to that of a day laborer (about 300 francs a month), was scarcely sufficient to enable him to lead the simple life that would yet permit him to carry on his work.

He expressed his feelings on this subject in the following words:

"I have heard that perhaps one of the professors will resign, and that I might, in that case, make application to succeed him. What an ugly necessity is this of seeking any position whatsoever; I am not accustomed to this form of activity, demoralizing to the highest degree. I am sorry that I spoke to you about it. I think that nothing is more unhealthy to the spirit than to allow oneself to be occupied by things of this character and to listen to the petty gossip that people come to report to you."

If he disliked soliciting an advancement in position, he was even less inclined to hope for honors. He had, in fact, a very decided opinion on the subject of honorary distinctions. Not only did he believe that they were not helpful, but he considered them frankly harmful. He felt that the desire to obtain them is a cause of trouble, and that it can degrade the worthiest aim of man, which is, work for the pure love of it.

Since he possessed great moral probity, he did not hesitate to make his acts conform to his opinions. When Schützenberger, in order to offer him a mark of esteem, wished to propose him for the _Palmes académiques_ he refused this distinction, despite the advantages which, according to general belief, it would confer. And he wrote to his director:

"I have been informed that you intend to propose me again to the _prefet_ for the decoration. I pray you do not do so. If you procure for me this honor, you will place me under the necessity of refusing it, for I have firmly decided not to accept a decoration of any kind. I hope that you will be good enough to avoid taking a step that will make me appear a little ridiculous in the eyes of many people. If your aim is to offer me a testimony of your interest, you have already done that, and in a very much more effective manner which touched me greatly, for you have made it possible for me to work without worry."

Faithful to this firm opinion, he later declined the decoration of the Légion d'Honneur, which was offered him in 1903.

But even though Pierre Curie refused to take steps to change his situation it was at last improved. In 1895 the well-known physicist, Mascart, professor in the Collège de France, impressed with his ability, and with Lord Kelvin's opinion of him, insisted that Schützenberger create a new Chair of Physics at the School of Physics and Chemistry. Pierre Curie was then named professor under conditions in which his talents were duly recognized. However, nothing was done at this time to ameliorate the inadequate material conditions under which, as we have already seen, he was carrying on his personal investigations.

[Footnote 3: In this very brief memoir is presented, for the first time, a theory which explains why crystals develop certain faces simultaneously, in a particular direction, and consequently why crystals possess a determined form.]

[Footnote 4: _Paramagnetic_ bodies are those which are magnetized in the same manner as iron, either strongly (_ferro-magnetic_) or feebly. _Diamagnetic_ bodies are those whose very feeble magnetization is opposed to that which iron takes in the same magnetic field.]

[Footnote 5: The following is the text of a letter from this distinguished savant to Pierre Curie, written during one of his visits to Paris:

October, 1893.

"DEAR MR. CURIE:

"I am much obliged to you for your letter of Saturday and the information contained in it, which is exceedingly interesting to me.

"If I call at your laboratory between 10 and 11 tomorrow morning should I find you there? There are two or three things I would like to speak to you about; and I would like also to see more of your curves representing the magnetization of iron at different temperatures.

"Yours truly,

"KELVIN."]

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