•G 



Mi 



F' 



FRESNEL ON DOUBLE REFRACTION. 259 



displacement parallel to the row of molecules A M B, these mole- 

 cules will become urged on to a similar motion. 



In fact, let us consider one of them in particular, the molecule 

 M for example, and examine what change has been operated in 

 the actions exerted upon 



it by the superior por- Fig. 2, 



tion of the medium. 



And, in the first place, ! 



I observe that these will i 



be the same as if it were , 



the molecule M which 

 had been displaced to « ? 



the same extent and in 



the same direction, the ^ — 



superior portion of 



the medium remaining « . 



E' 



fixed. I suppose then 

 M to be displaced in . » 4 • • 



the direction AB by a i 



small quantity, M m. 



The molecules E and F, for example, situated at equal distances 

 from M and from the perpendicular MG dropped upon AB, 

 acted equally on the molecule M in the direction MA and in 

 the direction M B before its displacement ; that is to say, the 

 component of their actions along AB mutually destroyed each 

 other, whilst the components perpendicular to AB were added 

 to each othei', but were counterbalanced by the opposite actions 

 of the molecules E' and F' situated below AB. When the ma- 

 terial point M is transported to m, the components parallel to 

 AB of the two actions exerted on it by the molecules E and F, 

 are no longer generally equal to each other, and the small 

 changes which they have undergone, or their differentials, act in 

 the same direction, and tend to bring back the point m to its 

 original position M, if this was one of stable equilibrium. 



In fact, represent by 4> (r) the action exerted by a molecule 

 situated at a distance (r), such as the molecules E and F. Take 

 M as the origin of coordinates, and the straight lines AB and 

 M G for the axes of x and y ; denote by x and y the coordi- 

 nates of the point F ; those of E will be y and <r. The distances 

 EM and FM or (r) are equal to Vx^ + y-, and therefore the 



