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.