EINGS SEEN IN CIRCULARLY POLARIZED LIGHT. 



211 



tions, or values of h, equal to \l., |A, &c., will be seen, with the crossed analyzer, 

 other bright rings; while at the intermediate couvergencies, corresponding to 

 value.^ of h=-K 2/, oX, &c., will be seen dividing rings, intens<'ly dark. When 

 white light is used, the dark rings will be mainly occupied by the smaller rings 

 of the colors whose undulations are shorter than the mean, or the larger rings 

 of those which are longer. Since the retardation depends directly upon the 

 convergency, and the place of a ring of any color depends on the equality of 

 the retardation with the length of a half undulation of that color, it will be 

 evident without further demonstration, that the longer the undulation the larger 

 the ring, and vice versa. 



Rotating the crystalline plate in azimuth will produce no change in the phe- 

 nomena. For in all positions of the plate there will always be one principal 

 plane in azimuth 0"^, and another in azimuth 90^. 



Rotating the analyzer will cause the rings to pass by progressive changes 

 into the complementary tints. In this rotation ;? becomes :='/ and >a succes- 

 sively for every one of the radiating principal planes which it passes, up to 

 ^:=90^. The sign of the chromatic term changes, therefore, in every such case. 

 And, as the sign changes also for /S=:a±90', yS=::a±iSO\ or /?=:a±270^, the color 

 in all the quadrants will undergo similar changes simultaneously. Thus, in an 

 entire revolution of the analyzer, the colors will be four times successively 

 reversed ; and for every position in which /33r45'^ or any of its odd multiples 

 they will disappear. 



The remarkable dislocation of the rings seen in crystals cut across the axis, 

 when examined in circularly polarized light, has been mentioned. By applying 

 the principles we have been considering we shall be able now to account for this 

 singular cifect. Suppose the crystal under examination to be a positive one, in 

 which the ordinary ray has a higher velocity than the extraordinary. When a 

 circularly polarized ray falls upon such a crystal, its component undulations, 

 which, as we have seen, are at right angles to each other, Avith nodes dislocated 

 by a quarter of an undulation, will advance with unequal velocities, and the 

 amount of their nodal discrepancy will be changed. This would not disturb 

 the symmetry of the rings, if the change were similar in all the quadrants. By 

 attending to the following analysis, we shall see that such is not the case. 



pV 



Let RR' represent the direction of progress of a circularly polarized wave, 

 of which the component molecular movements are represented by PP' and QQ-'. 

 The positions of these arrows are those in which the molecular movements of 

 their respective undulations are assumed to be at tlieir maximum of velocity, 

 and the distance between them, upon the line RR', is to be taken as represent- 

 ing a quarter of an undulation. If Ave consider the effect of this composition of 

 forces upon a molecule in the plane of movement of QQ', we shall perceive that 



