G18 APPLIED MATHEMATICS 



elusions; and between the two an abyss. Statistic considerations, 

 the law of great numbers, do they suffice to fill it? Many points 

 still remain obscure to which it is necessary to return, and doubtless 

 many times. In clearing them up, we shall understand better the 

 sense of the principle of Carnot and its place in the ensemble of 

 dynamics, and we shall be better armed to interpret properly the 

 curious experiment of Gouy, of which I spoke above. 



Should we not also endeavor to obtain a more satisfactory theory 

 of the electro-dynamics of bodies in motion? It is there especially, 

 as I have sufficiently shown above, that difficulties accumulate. 

 Evidently we must heap up hypotheses, we cannot satisfy all the 

 principles at once; heretofore, one has succeeded in safeguarding 

 some only on condition of sacrificing the others; but all hope of 

 obtaining better results is not yet lost. Let us take, therefore, the 

 theory of Lorentz, turn it in all senses, modify it little by little, and 

 perhaps everything will arrange itself. 



Thus in place of supposing that bodies in motion undergo a con- 

 traction in the sense of the motion, and that this contraction is the 

 same whatever be the nature of these bodies and the forces to which 

 they are otherwise submitted, could we not make an hypothesis 

 more simple and more natural? 



We might imagine, for example, that it is the ether which is 

 modified when it is in relative motion in reference to the material 

 medium which it penetrates, that when it is thus modified, it no 

 longer transmits perturbations with the same velocity in every direc- 

 tion. It might transmit more rapidly those which are propagated 

 parallel to the medium, whether in the same sense or in the opposite 

 sense, and less rapidly those which are propagated perpendicularly. 

 The wave surfaces would no longer be spheres, but ellipsoids, and we 

 could dispense with that extraordinary contraction of all bodies. 



I cite that only as an example, since the modifications one might 

 essay would be evidently susceptible of infinite variation. 



It is possible also that the astronomer may some day furnish us data 

 on this point; he it was in the main who raised the question in 

 making us acquainted with the phenomenon of the aberration of light. 

 If we make crudely the theory of aberration, we reach a very curious 

 result. The apparent positions of the stars differ from their real 

 positions because of the motion of the earth, and as this motion is 

 variable, these apparent positions vary. The real position we cannot 

 know, but we can observe the variations of the apparent position. 

 The observations of the aberration show us, therefore, not the 

 movement of the earth, but the variations of this movement; they 

 cannot, therefore, give us information about the absolute motion 

 of the earth. At least this is true in first approximation, but it 

 would be no longer the same if we could appreciate the thousandths 



