106 »OUBLE BEFRACTIOif Of CRVSTALJ. 



ceptible curve it describes in its passage from a vacuum into a 

 transparent medium, and consider its velocity as constant^ 

 when it has entered into it by a perceptible quantity. The 

 principle of a minimum of action then is reduced to this, that 

 the light arrives from a point without the crystal to a point 

 within it, in such a manner, that, if we add the product of the 

 right line it describes Without multiplied by its primitive velo- 

 city, to the product of the right line it describes within 

 multiplied by its corresponding velocity, the sum will 

 be a minimum. This principle always gives the velocity 

 of light in a transparent medium, when the law of refrac- 

 tion is known : and reciprocally it gives this law^, when the 

 Case of extra- ^'^locity is known. But a condition to be fulfilled in the case 

 ordinary re- of extraordinary refraction is, that the velocity of the luminous 

 ray in the crystal shall be independent of the manner in which 

 it entered, and depend only on its position with respect to the 

 axis of the crystal, that is, on the angle which it forms with a 

 line parallel to the axis. In fact, if we imagine an artificial 

 face perpendicular to the axis, all the interior extraordinary 

 rays, that are equally inclined to this axis, will be so likewise 

 to the face, and will evidently be subjected to the same laws at 

 issuing from the crystal: all v/ill resume their primitive velo- 

 * city in the vacuum ; the velocity in the interior therefore is the 



Law of H same for all. I have found, that the law of extraordinary re- 

 gens, fraction given by Huygens fulfils this condition, as well as it 

 does that of the principle of a minimum of action ) which 

 leaves no room to doubt, that it is owing to attractive and 

 repulsive forces, the action of which is sensible only at imper- 

 ceptible distances. Hitherto it could only be considered as 

 approaching it within limits less than the inevitable errours of 

 experiment : now it may be taken as a precise law. 



A valuable datum -for the discovery of the nature of the 

 « . - forces that produce it is the expression of the velocity, to which 

 the velocity, analysis has conducted me ; and which I find equal to a frac- 

 tion, the numerator of which is unity, and the denominator of 

 which is the radius of the preceding ellipsoid, according to 

 which the light is directed, the velocity in vacuo being taken as 

 unity. I show, that the velocity of the ordinary ray is unity 

 divided by the scmiaxis of revolution of the ellipsoid j and by 



thes« 



