FRESNEL'S THEORY OF DOUBLE REFRACTION. 207 



It has been already shown (104^ that when light, diverg- 

 ing from a luminous origin, passes through two near aper- 

 tures in a screen, the two pencils into which it is thus divided 

 will interfere, and produce fringes, the central fringe being 

 the locus of those points at which the two rays have tra- 

 versed equal paths. Now, if two plates of glass, cut from the 

 same plate, and of exactly the same thickness, be placed per- 

 pendicularly, one in the path of each ray, the two rays will be 

 equally retarded, and the central fringe will remain undis- 

 placed. But if, instead of glass plates, we employ plates cut 

 in different directions from the same biaxal crystal, the plates 

 being of exactly the same thickness, the fringes produced by 

 the interference of the two rays in question will remain still 

 undisplaced, if the velocity of these rays is the same in the 

 two plates ; while, on the other hand, if the velocities be dif- 

 ferent, the fringes will be shifted from their original position. 

 On trial, the result was found to be as Fresnel had antici- 

 pated: the fringes were displaced; and the amount of that 

 displacement agreed with the calculated difference of velocity, 

 which had been previously deduced from theory. 



(219) There are two remarkable cases of Fresnel's theory, 

 which have since furnished a very striking confirmation of 

 its truth. 



If we make y = 0, in the equation of the- wave-surface, so 

 as to obtain its intersection with the plane of xz, the result- 

 ing equation is reducible to the form 



# 2 -t s 2 - t> z 3 x 7 - + c*z*- a 2 c 8 = 0. 



This equation is manifestly resolvable into the two follow- 

 ing : 



x 2 + 2 = b*, a 2 x" + c 2 s 2 = a* c z ; 

 so that the surface intersects the plane of xz in a circle and 



