200 



UNDULATORY THEORY OP^ LIGHT. 



1.414. They unite, for substances whose index has that exact value. Mr. 

 Jamin found but two substances in which this condition is fulfilled. They were 

 a specimen of menilite, and a crystal of alum cut perpendicularly to the axis of 

 ihe octahedron. Water and glass, which under ordinary liglit appear to polarize 

 |:eifcctly, are easily seen not to do so under the strong light of the sun. 



In the cases in which the index has the particular value just mentioned, the 

 advance of phase at the polarizing angle is "brusque" from ^A to X. This is 

 \cry nearly the case with water and glass. 



lleflection from the surface of metals always produces elliptical polarization. 

 The advance of phase is progressive from incidence 0° to incidence 90°. There 

 are, however, very large differences between metals in this respect. 



§ IX. ROTATORY POLARIZATION. 



We are now perhaps prepared to understand the reason of the rotation of the 

 plane of polarization of a ray transmitted along the axis of a crystal of quartz. 

 We have seen that Fresnel, by an ingenious combination of prisms, succeeded in 

 demonstrating the existence within the crystal of two circularly polarized rays, 

 gyrating in opposite directions. And we have seen that the resultant effect of 

 two opposite gyrations is to produce a movement in a plane. The gyratory 

 movements within the crystal are then not actual but virtual — in other words 

 there are forces constantly tending to produce these gyrations, which hold each 

 other in equilibrio or at least nearly so. We must consider these forces as suc- 

 cessively traversing all azimuths Avitliin the length of each undulation. If the 

 wave were of the same length for both gyrations, the forces being presumed 

 equal, the molecular movement would be constantly rectilinear, and the plane 

 of polarization would not change. But, as the plane does in fact change, we are 

 led to infer that the undulation lengths for the two rays are not equal. The 

 annexed figure may serve to illustrate the mutual action of 

 these rays. Suppose 3IADB to be the orbit in which a 

 force P tends to urge a molecule, M, to revolve around the 

 centre, C, to which it is drawn by the force MC. Suppose 

 the equal force Q to urge the same molecule to describe the 

 same orbit in the opposite direction. These forces holding 

 each other in equilibrio, the molecule will follow the direc- 

 tion of the third force, MC. 



Now suppose the force Q suspended, the molecule will 

 take the direction of the circle ADB, and will continue to 

 revolve in it so long as the force P (supposed always tan- 

 gential) continues to act. But its movement Avill impart to 

 the molecule next below it a similar motion, and that to the 

 next, and so on ; so that, as these successive molecules take 

 up their movement later and later, there will be a series in 

 different degrees of advancement in their several circles, 

 forming a sjiiral ; and when the molecule M shall have 

 returned to its original position, the series will occupy a position like the curve 

 MFLN'OR. If now P be supposed to be in turn suspended, while the force Q 

 continues to act, the effect of Q will be to produce a contrary spiral, Avhich may 

 be represented by MSKTV. If MD be a diameter of the circle MADB, drawn 

 i'rom M, and DNHN' be a line parallel to the axis CG of the cylindrical surface 

 which is the locus of tlie spirals, then, if the undidation lengths are the same 

 for both movements, the two spirals will intersect DH in the same point, the 

 intersections markiug the completion of a half undidation for each. But if these 

 lengths be unequal, the intersections with DH will take place at different points, 

 as N and N'. 



Let now a plane intersect the cylinder at any distance below MADB, as at 



