IQg UNDULATORY THEORY OF LIGHT. 



^•■yrations, being in opposite directions, Avould produce a rectilinear resultant. I« 

 this case, suppose the molecule, M, to be in any part of tho 

 circumference in which either of the gyrations would cause 

 it to revolve ; it will be subject to the action of three forces : 

 one, MC, directed toward the centre of its orbit, and the 

 other two, represented by P and Q, equal and opposite. The; 

 two latter neutralize each other, and the molecule pursues tho 

 path MC. When the molecule is at M', the tangential forces 

 JP and Q, which will then have the directions P' and Q'. will 

 not directly balance .each other, but will have a resultant in 

 the direction RG. And for all other points in the path of 

 the molecule, as M'', M'", &c., the resultant of the tan- 

 ii'^ gential forces will always be in the diameter, MN, of the 



Fig. 4:'J orbit. 



In Fi"". 48 we have supposed the arrows PP'and P''P'" to represent not only 

 tlie iwsUions of the planes of molecular vibration, but the direction of the move- 

 ments. Their resultant plane is accordingly QQ'. If the direction of one of 

 them, as of P"P'", had been opposite, the resultant would be RR. If the two 

 were in any equal positive and negative azimuths, greater or less than 45'-^, their 

 resultant gyrations would be elliptic ; but the ellipses, being equal and similar, 

 and similarly situated to the plane..of reflection, whilt they are opposite in move- 

 ment, would still produce the vibration QQ . And two movements in azimuths 

 equally above and below 90°, either positive or negative, would in like manner 

 produce the plane vibration RR . iSiow the condition of natural light is such 

 that, for every azimuth of its successive plane vibrations, as PP , producing, by 

 total reflection, a gyratory molecular movement, whether circuldr or elliptic, 

 there wdl always be found another which will produce an equal and opposite 

 gyration. And, although these gyrations are successive and not simultaneous, 

 ihough, therefore, there is never, in this case, any real composition, like that 

 illustrated in Fig. 49, neutralizing, in Jact, the gyratory movements, yet the 

 compensatory effects follow each other with such rapidity that, to our instru 

 ments and our powers of vision, they are as if they did not exist. Commori 

 light cannot, therefore, be polarized by total reflection. Moreover, common 

 lio-ht need not, in any case, be supposed to be made up strictly of plane vibra- 

 tions. It is only necessary to suppose its gyratory movements to be as impar- 

 tially distributed as we have heretofore presumed its plane vibrations to be. 



If, however, we suppose a surface which is not a surface of total reflection to 

 possess the power of accelerating or retarding one of the rectangular components 

 of the incident molecular velocity over the other, then the reflected light will, 

 in general, be (dliptically polarized. For the two components are never equally 

 reflected except in total reflection. Now there are very few substances capable 

 of reflecting light Avhich do not possess this power, and, accordingly, elliptical 

 polarization is the effect most usually attending reflection. As has been else- 

 where stated, it is only those substances whose indexes of refraction are very 

 near to 1.414 that produce a kind of polarization that is sensibly plane. 



This subject has been very thoroughly investigated, theoretically, by Mr. 

 Caucby, and experimentally by Mr. Jamin, -wifh results mutually corroborative 

 of each other. In order to clearly understand the experimental methods 

 cmployc^d, lot us observe that, if a plane polarized wave be supposed to be 

 decomposed into two rectangular component undulations, the cui-ves represent- 

 ing these components will cross the common intersection of their planes in the 

 same points. These crossing points may be called nodes. In the case sup- 

 posed, the nodes of the two components are coincident. The effect of reflection 

 is, in o-eneral, {i. c., in all cases except those which have the index of i-efraction 

 just now mentioned,) to throw the nodi'S of the components out of coincidence. 

 And the original plane polarization will be restored by br'niging hack the nodes 



