PRINCIPLES OF MATHEMATICAL PHYSICS 605 



vals enormous in relation to their dimensions, and describing orbits 

 following regular laws. 



These infinitesimal stars are the atoms. Like the stars properly 

 so called, they attract or repel each other, and this attraction or this 

 repulsion directed following the straight line which joins them, de- 

 pends only on the distance. The law according to which this force 

 varies as function of the distance is perhaps not the law of Newton, 

 but it is an analogous law; in place of the exponent --2, we have 

 probably a different exponent, and it is from this change of exponent 

 that springs all the diversity of physical phenomena, the variety of 

 qualities and of sensations, all the world colored and sonorous which 

 surrounds us, in a word, all nature. 



Such is the primitive conception in all its purity. It only remains 

 to seek in the different cases what value should be given to this 

 exponent in order to explain all the facts. It is on this model that 

 Laplace, for example, constructed his beautiful theory of capillarity; 

 he regards it only as a particular case of attraction, or as he says 

 of universal gravitation, and no one is astonished to find it in the 

 middle of one of the five volumes of the Mecanique celeste. 



More recently Briot believed he had penetrated the final secret 

 of optics in demonstrating that the atoms of ether attract each other 

 in the inverse ratio of the sixth power of the distance; and does not 

 Maxwell himself say somewhere that the atoms of gases repel each 

 other in the inverse ratio of the fifth power of the distance? We have 

 the exponent --6, or --5 in place of the exponent --2, but it is 

 always an exponent. 



Among the theories of this period, one alone is an exception, that 

 of Fourier; in it are indeed atoms, acting at a distance one upon the 

 other; they mutually transmit heat, but they do not attract, they 

 never budge. From this point of view, the theory of Fourier must 

 have appeared to the eyes of his contemporaries, even to Fourier 

 himself, as imperfect and provisional. 



This conception was not without grandeur; it was seductive, and 

 many among us have not finally renounced it; we know that we 

 shall attain the ultimate elements of things only by patiently disen- 

 tangling the complicated skein that our senses give us; that it is 

 necessary to advance step by step, neglecting no intermediary; that 

 our fathers were wrong in wishing to skip stations; but we believe 

 that when we shall have arrived at these ultimate elements, there 

 again will be found the majestic simplicity of celestial mechanics. 



Neither has this conception been useless; it has rendered us an 

 inestimable service, since it has contributed to make precise in us 

 the fundamental notion of the physical law. 



I will explain myself; how did the ancients understand law? It 

 was for them an internal harmony, static, so to say, and immutable; 



