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."]