FRESXEL ON DOUBLE REFRACTION. 295 



de mire) is situated in the interior of the ci7Stal, or else against 

 its lower sui-face. Let M (fig. 8) be the luminous point, E C 

 the upper surface of the plate by 

 which the rays emerge ; let M a, 

 MA, M «' be rays starting from 

 the luminous point, and following 

 such a course as to strike against 

 the opening b b' of the eye or of 

 the object-glass of the telescope. 

 I suppose that the curve bB b' re- 

 presents the geometrical locus of 



the disturbances which arrive first, starting from the refracting 

 surface E C ; it will be parallel, as we have seen, to the resultant 

 wave of all the elementary disturbances. Now it is on the direction 

 of the element of the emergent wave which falls on the opening of 

 the pupil that the position of the image of the luminous point on 

 the retina depends, and consequently that on which depends the 

 direction of the visual ray which is perpendicular to the element 

 of the wave. It is therefore the direction of this element, or of 

 its normal, that we have to determine. This normal is the ray 

 A B of swiftest arrival at the middle B of the element, since this 

 element is the tangent to the sphere described from A as centre. 

 We have then only to seek amongst all the broken rays M a B, 

 M A B, M a' B, for that which will bring the first disturbance to 

 B, and its direction outside the crystal will be that along which 

 will be seen the object. 



But the section made in the surface of elasticity does not fur- 

 nish immediately the quantities necessary for determining the 

 inter\'als of time comprised between the arrivals of the disturb- 

 ance from M at the points a, A, a' ; for it does not give the ve- 

 locity of propagation except the direction of the cutting plane, 

 or of the element of the wave to which it is parallel, be known ; 

 and it is to be remarked, moreover, that the velocity of propa- 

 gation has always in this construction been supposed to be 

 reckoned on the perpendicular to the plane of the wave, whilst 

 here it would be necessary to have it on the direction of the ray, 

 for, as we have just said, the problem consists in finding the ray 

 of first arrival. It is therefore necessary to calculate, in the first 

 place, the velocities of propagation of the wave, whose centre is 

 in M, along the different rays M «, MA, M a', that is to say, the 

 lengths of these rays comprised between the centre M and the 



VOL. V. PART XV 11 1. X 



