256 FRESNEL. ON DOUBLE REFRACTION. 



It would have been easy to arrive at the same consequence 

 without the aid of the general equation, by remarking that, since 

 in this particular case 



sin i =■ cos i and cos 2 7r it j = sin 2ir . t, 



the two coordinates 



cos i . cos 2-!r t and sin i . cos 2 7r li ) 



are always proportional to the sine and cosine of the same 

 variable angle 2 w . ^. 



Another remarkable peculiarity of the oscillatory motion in 

 the same case is, that the velocity of the molecule is uniform. 

 In fact, the formula (A), which expresses the square of this 

 velocity, becomes 



— sin^ 2n i + — cos^ 2^1, or — . 

 2 2 2 



This uniform cii'cular motion takes place in the same direction 

 for all the molecules situated along the ray projected in C ; but 

 they do not occupy at the same instant the corresponding points 

 of the circumferences which they describe ; that is to say, the 

 molecules, which in their state of rest were situated on the 

 straight line projected in C, instead of remaining on a straight 

 line parallel to this, and which would describe round it a cylinder 

 on a circular base, form a helix whose radius is that of the small 

 circles described by the vibrating molecules, and the distance 

 from thread to thread {" le pas") is equal to the length of an 

 undulation. If we turn this helix round its axis with a uniform 

 motion, so that it describes a circumference in the interval of 

 time during which a luminous undulation is performed, and if 

 we conceive, besides, that in each infinitely thin slice perpen- 

 dicular to the rays all the molecules perform the same move- 

 ments as the corresponding point of the helix and preserve the 

 same relative situations, we shall have a correct idea of the kind 

 of luminous vibration which I have proposed to call Circular 

 Polarization, giving the name of Rectilinear Polarization to that 

 which was observed first by Huygens in the double refraction 

 of Iceland spar, and which Malus has reproduced by simple 

 reflexion at the surface of transparent bodies. 



These circular vibrations are performed sometimes from right 

 to left and sometimes from left to right, according as the plane 

 of polarization of the system of waves preceding {en avant) is to 



