the formuliB o/Cauchy /or the Motion of Light, 29,9 

 plane P^ the following relations subsist : ■ -■^r-Trwin^'- 



{f A^^ (f)l IT 



M= analogon mut. mut.^ N= analogon mut. mut. 

 P = 2mS -?3 . A?/ A^ sin ^ { M A^ + 1? A?/ + ^^ A^ } ^. 



Q= anal. mut. mut., R= anal. mut. mut., 



where the symbols denote as follows : 



1. m the mass of a particle of sether. 



2. Ar the distance of any sether particle whatever from the 

 origin of coordinates ; the projections of the said distance upon 

 the three axes, that is to say, the coordinates of the particle, 

 being denoted by A^, Ay, ^z. 



3. / and (\> certain functions of Ar not to be further charac- 

 terized here. 



4. Uj V and w, the cosines of the angles which the normal to 

 the plane of undulation encloses with the three axes. The 

 summation expressed by the sign S is, strictly speaking, to be 

 extended to all the aether particles. 



As the motion of the light is due to the play of molecular 

 forces, by far the greater portion of the accelerating force of any 

 particle is derived from the action of those particles which lie 

 near it ; so that in our formulae those members only are to be 

 retained in which A^, Ay, Az refer to those particles which im- 

 mediately surround the origin of coordinates. And further, 

 since the proximity of the particles is very great, in a case where 

 an approximate result only is required, the members may be 

 neglected in which any one of the quantities Ao? . . . appears in- 

 volved higher than the first power. True, the constants which 

 enter into the resulting laws will be thus rendered independent 

 of the wave length X, and hence we must give up the expression 

 of the dispersion ; we obtain only an approximation to the phse- 

 nomena displayed by homogeneous light. In order, then, to 

 bring the analysis into harmony with the results of experience, 

 let us express the constants which enter into the formulae ; that 

 is to say, the principal indices of refraction for a certain colour, 

 by the values obtained from measurement. With this procedure 

 we must rest satisfied ; the results, indeed, almost completely cor- 

 respond to the exactitude of our observations. 



We develope, therefore, in the expressions for the coefficients 

 of the ellipsoid of polarization, the sinus function in its equiva- 

 lent series ; and neglecting the members which, in respect to 

 A^ . . . &c., are of a higher order than the first, we obtaiu^>:i --mi 



