294 FRESXEI^ ON DOUBLli: REFRACTION. 



the formulsB uhich I have given in my memoir on Diffraction. 

 But, without recurring to these formulae, it is evident belbrehand 

 that if the intensity of the incident wave A B is the same in all 

 its parts, the elements of the integration will be the same for the 

 different points A', H, h, &c. of the emergent wave situated at a 

 sufficient distance from the surface C A, whatever in other re- 

 spects may be the form of the integral ; and that consequently 

 the intensity and the position of the resultant wave will be the 

 same in each of these points ; it will therefore be parallel to C E, 

 the geometrical locus of the primitive disturbances ; the formulae 

 of integration place it at a quarter of an undulation behind this 

 plane ; but this does not alter its direction, which alone deter- 

 mines that of the visual ray, or of the axis of the telescope by 

 which is observed the line of sight*. 



Thus the sines of the angles BAG and C A E, made by the 

 refracting surface with the incident and refracted waves, are to 

 each other as the lengths C B and A E, that is to say, as the ve- 

 locities of propagation of light in the two contiguous media. 



We see, then, that in order to calculate the prismatic effects 

 of doubly-refracting media, when the point of sight is at an infi- 

 nite distance, and the incident wave consequently plane, it is 

 sufficient to know the velocity of propagation of the ordinary and 

 extraordinary waves in the interior of the crystal for each direc- 

 tion of the plane of the wave, this velocity being measured per- 

 pendicularly to this plane. Now these things are given by the 

 greatest and smallest radius vector of the diametral section made 

 in the surface of elasticity by the plane of the wave. But when 

 the point of sight is very near the refracting medium, and w-e 

 employ a crystal whose double refraction is very strong, such as 

 calcai'eous spar, in which the curvature of the waves differs 

 greatly from that of a sphere, it becomes necessary to know the 

 form of these waves. 



Principle which determines the direction of the refracted rays^ 

 when the point of sight is not sufficiently distant to allow of the 

 curvature of the luminous vmves being neglected. 



In order that I may be more easily comprehended, 1 shall 

 take a very simple case, that in which the point of sight {point 



* I have thought it advisable to repeat here, in an abridged form, the expla- 

 nation which I have given of the law of Descartes for ordinary refraction, in 

 the last note of my memoir on Diffraction, in order to save the reader the 

 trouble of referring to it. 



