202 UNDULATOllY TIIEOEY OF LIGHT. 



It is difficult to conceive exactly tbc physical action by which rotatory polari- 

 zation is produced. But there is no diljliculty in imagining such a decomposition 

 of the molecular movements in a plane polarized ray, as shall represent the 

 relations which exist after the lotaiory polarization has been established. We 

 have seen that when a plane imdulation has been resolved into two equal rectan- 

 gular components, if the nodal ]om{?~ of these components become dislocated by 

 a quarter of an undulation, the resultant will be a movement in a circular orbit. 

 We have also seen that when the left-hand component is advanced by this 

 amount, the motion becomes dcxtrogyre ; and when the right hand component 

 is advanced, it becomes Irevogyre. In order, then, to explain the co-existence 

 of two opposite circular polarizations, we must suppose two sets of equal 

 rectangular components dislocated in these two opposite ways. This was the 

 hypothesis of Fresnel. 



In Older to facilitate the conception, suppose the arrow P to represent, in 

 quantity and direction, the molecular movement, at a given instant, in the origi- 



nal plane polarized wave. Imagine it to be 

 ''i^^Aa' /^ a resultant of two other waves, Q and 11, 



"' ' ■ //h f ^'^^ ^■'^ front of it, and the other behind it, 

 \J^^^r' each at the distance of one- eighth of an un- 

 dulation. Ihesc will then be a quarter ot 

 an undulation distant from each other. Let 

 Q and R be again resolved, each into two 

 equal rectangular components, in azimuths 

 -1-45° and — 45° ; Q, into q and r ; and 11 

 into q' and r'. Consider all these four component movements, at the instant 

 supposed, and in the positions represented, to be at their maximum of velocity, 

 in the direction of the several arrows denoting them. Then, if we consider the 

 relative stages of advancement, or phases of- movement, of the pair q and r, in 

 respect to q' and /', when both are referred to a common plane, it will be seen 

 that the latter, though most advanced in position, are least advanced in phase 

 For, if we conceive the curves of these waves to be drawn, the ascending node 

 of q' will be found in the plane of qr, and the descend if/g node of q in the plane 

 of q'r'. Hence, at the point where the wave q' begins, the wave q is one-quarter 

 advanced. 



W^e have, then, two pairs of plane undulations, q and ?•' and r and q^ , severally 

 normal to each other, and with nodes dislocated to the extent of one-quarter of 

 an undulation ; q and r being the members of the pairs Avhich are most advanced 

 in phase. In the case of the pair q and r\ the right-hand component being that 

 which is most advanced, the resultant movement is a revolution sinistrorsum 

 In the case of r and g-' the resultant will be a revolution dcxtrorsum. 



The values of these several components are determined from the general 

 equation following, which is simply equation [3,] with the symbols changed : 



p2=iQ2+R2+2QIlcos(7. 



P 

 By hypothesis R = Q, and tf = 90°. Hence P^ = 9Q2, and Q = --p=. 



Again. q:^ = q^ + ^ = 2q\ And ^ = -5| = ^|__ = ^R 



R P 



Also, R2 = 7'2+ r'2 = 2g '^ And c[ = -- = — — -^ = ^P. 

 ^ ^ ^/2 V2V2 



It appears, therefore, that the molecular velocity in each of the component 

 waves q, r, q', r', is equal to one-half that of P, as it should bo, in order that the 

 sum of their living forces may be equal to the living fn-ce of the primitive wave. 



Since the two circularly polarized rays in the axis of quartz have unequid 



