FRESXEL ON DOUBLE REFKACTIOX. 249 



c' will be nothing ; or if it is the component (c) which is nothing 

 in the former, {b') in the second will equal zero. Thus we must 

 conclude, from the two preceding equations, 



6 = and c' = 0, or c = and b' = 0; 

 that is to say, that in each of the two beams there are only vibra- 

 tions parallel or perpendicular to its plane of polarization. 



When we have explained the mechanical causes of double 

 refraction, we shall show that these vibrations are perpendicular 

 to the principal section in the ordinary ray, that is to say, to the 

 plane which it has been agreed to call the j^/awe 0/ polarization. 



Having demonstrated that in polai'ized light the aetherial mo- 

 lecules cannot have any vibration normal to the waves, we must 

 suppose that neither does this mode of vibration exist in ordi- 

 nary light. In fact, w4ien a beam of ordinary light, falling per- 

 pendicularly on a doubly-refracting crystal, is divided into two 

 polarized beams, they no longer contain vibrations normal to 

 the waves. If then there were any such in the incident light, 

 they must have been destroyed ; whence there must have been 

 a diminution of vis viva, and therefore a weakening of the light, 

 which would be contrary to observation ; for, when the crystal 

 is perfectly transparent, the two emergent beams, when reunited, 

 reproduce a light equal to that of the incident beam, if there be 

 added to them the small quantity of light reflected at the faces 

 of the crystal. Now, we cannot suppose that it is into this small 

 quantity of light that the vibrations normal to the waves have 

 betaken themselves, since on causing it to traverse the crystal it 

 could also be transformed almost entirely into two polarized 

 beams, where we are certain that this kind of vibration does 

 not exist. It is therefore natural to suppose that ordinary light 

 also contains only vibrations parallel to the waves, and to con- 

 sider it as the assemblage and rapid succession of a multitude of 

 systems of waves polarized in all azimuths. According to this 

 theory, the act of polarization does not consist in the creation of 

 transversal vibrations, but in the decomposition of these vibra- 

 tions into two fixed rectangular directions, and in the separation 

 of the rays resulting from this decomposition. 



Theoretical Explanation of the Laws of Interference of 

 Polarized Rays. 



According to what we have just said concerning the nature of 

 the vibrations of polarized rays, it is clear that they cannot pre- 



s 2 



