PRINCIPLES OF MATHEMATICAL PHYSICS 607 



there are others from which we are able to draw the same advantage. 

 These are: 



The principle of Carnot, or the principle of the degradation of 

 energy. 



The principle of Newton, or the principle of the equality of action 

 and reaction. 



The principle of relativity, according to which the laws of phys- 

 ical phenomena should be the same, whether for an observer 

 fixed, or for an observer carried along in a uniform move- 

 ment of translation; so that we have not and could not 

 have any means of discerning whether or not we are carried 

 along in such a motion. 



The principle of the conservation of mass, or principle of 



Lavoisier. 

 I would add the principle of least action. 



The application of these five or six general principles to the differ- 

 ent physical phenomena is sufficient for our learning of them what 

 we could reasonably hope to know of them. 



The most remarkable example of this new mathematical physics 

 is, beyond contradiction, Maxwell's electro-magnetic theory of light. 



We know nothing of the ether, how its molecules are disposed, 

 whether they attract or repel each other; but we know that this 

 medium transmits at the same time the optical perturbations and 

 the electrical perturbations; we know that this transmission should 

 be made conformably to the general principles of mechanics, and 

 that suffices us for the establishment of the equations of the electro- 

 magnetic field. 



These principles are results of experiments boldly generalized; 

 but they seem to derive from their generality itself an eminent 

 degree of certitude. 



In fact the more general they are, the more frequently one has 

 the occasion to check them, and the verifications, in multiplying 

 themselves, in taking forms the most varied and the most unex- 

 pected, finish by no longer leaving place for doubt. 



Such is the second phase of the history of mathematical physics, 

 and we have not yet emerged from it. 



Do we say that the first has been useless? that during fifty years 

 science went the wrong way, and that there is nothing left but to 

 forget so many accumulated efforts as vicious conceptions condemned 

 in advance to non-success? 



Not the least in the world ; the second phase could not have come 

 into existence without the first? 



The hypothesis of central forces contained all the principles; it 

 involved them as necessary consequences; it involved both the con- 



