264 FRESNEL ON DOUBLE REFRACTION. 



distant from ET to cause the molecular displacements occasioned 

 by these oscillations to diminish very slowly up to the points 

 which may be regarded as immovable ; so that the condensations 

 and dilatations of the consecutive strata will be almost insensible, 

 even if the equilibrium of pressure were not rapidly restored 

 from one stratum to another. 



Demonstration of two Statical Theorems, on which depends the 

 mechanical explanation of Double Refraction. 



After having deduced from facts the hypothesis which I have 

 adopted on the nature of luminous vibrations, and having proved 

 that it is not contrary to the principles of mechanics, I shall 

 now demonstrate two theorems belonging to general statics, on 

 which depends the theoretical explanation of the mathematical 

 laws of double refraction. 



First Theorem. 

 In any system of molecules in equilibrium, and whatever may 

 be the law of their reciprocal actions, the minute displacement 

 of a molecule, in any direction whatever, produces a repulsive 

 force equal in magnitude and direction to the resultant of three 

 repulsive forces which would be separately produced by three 

 rectangular displacements of this material point equal to the 

 statical components of the first displacement. 



Let M (fig. 4,) be one of the material points of the molecular 



■p. . system ; when the equilibi'ium comes to be dis- 



' turbed by the small displacement M C of the 



■ molecule M, the resultant of all the forces exerted 



i c upon it, which before was equal to zero, acquires 



-g a certain value : to calculate it, it is sufficient to 



determine the variations which these forces have 



undergone in magnitude and direction, and to 



find the resultant of all these differentials. In 



the next place, then, I consider the particular 



action of any other molecule N on the point 



M which has been displaced through M C, which I suppose 



very small relative to the distance M N which separates the two 



molecules. On M N I draw the perpendicular M S in the plane 



C M N ; if C N be joined, C P will be the small quantity by 



which the distance M N has increased, or the difFei'ential of the 



distance, and -ir^p^ will be the sine of the small angle by which 



