306 FRESNEL OX DOUBLE REFRACTION. 



" ordinary ray" although in ideality iu this general case neither 

 of the two beams of light follows the laws of " ordinary" refrac- 

 tion, as we conclude from the equation. 



The position of the straight line through which the tangent 

 plane must be drawn is determined here, as in the construction of 

 Huygens, that is to say, we must take on a direction R'T (fig. 10.), 

 parallel to the incident rays, a quantity B T equal to the space 

 described by the light outside the crystal during the unit of time ; 

 then through the point B draw perpendicularly to these rays the 

 plane A B, which will represent an element of the incident wave 

 at the commencement of the unit of time, supposing A B very 

 small relatively to the distance of the luminous point. 



Now if through the point T a straight line be drawn parallel 



to the intersection of this plane with the face of the crystal, this 



-p. line projected in T (the plane of the 



^* ' figure being supposed perpendicu- 



, R lar to the intersection of the plane 



i \^ x^ B with the surface A T of the 



■? I y<f crystal) will be the intersection of 



\^ ; / \. the surface with the element A B 



-^^^ \ ^^ ' of the wave at the end of the unit 



\ Vj^bi<;f^^ of time ; it is therefore through this 



^--♦^j;^ straight line that a tangent plane 



! must be drawn to the waves formed 



i in the crystal at the end of the same 



interval of time, and whose centres 



are situated on the first intersection A. The points of contact 



M and N with the two sheets of the surface of these waves, will 



determine the two directions A N and A M of the two refracted 



rays, which in general will not coincide with the plane of the 



figure. 



The same construction will be applicable to waves of any form 

 whatever ; and the general principle of the path of swiftest arrival 

 reduces all problems on the determination of refracted rays to 

 the calculation of the surface which the wave assumes in the 

 refracting medium. 



Determination of the axes of elasticity, and of the three con- 

 stants a, b and c in the equation to the wave. 



For the case which forms the object of this memoir, the sur- 

 face of the wave is represented by the equation (D.) ; the direc- 



