In 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 . In that year he published, too, a very important theoretical work on theformation 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 and .
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.
