PHYSICAL THEORY OF POLATJIZATIOX. 1C5 



tions is now generally admitted, though they are usually af^sumed to be incapable 

 of impressing the organs of vision. 



But while the molecular movements in luminous waves arc assumed to be at 

 right angles to the direction of progress, or of the ray, there exists no natural 

 necessity to determine them in azimuth toward one direction rather than toward 

 anothei-. It is accordingly capable of easy demonstration that ordinary light 

 has no determinate plane or azimuth of vibration, but that its successive undu- 

 lations assume every variety of azimuth. There is no proof, however, that 

 changes of azimuth are incessant ; in other words, that many undulations, in 

 fact, many thousands or perhaps millions, do not follow each other usually, in 

 the !;ame azimuth, between the changes. This, indeed, is probable, since the 

 ethereal vibrations take their character from those of the luminous body, and 

 these may reasonably be presumed to have a certain persistence in their modes 

 of vibration, or at least not to undergo incessant and abrupt changes. Beyond 

 a certain limit, however, this persistency could not continue; nor could there, 

 among the changes which occur, be a predominating disposition to return to one 

 azimuth oftener than to another, or to remain in it longer, without imparting to 

 the light, more or less decidedly, the character of polarization. If five hundred 

 millions of the mean undulations of white light were to follow each other in a 

 single azimuth, they would occupy less than the millionth part of a second ; 

 and, accordingly, if five hundred millions of such undulations should take place 

 in each of a million different azimuths successively, the whole would be per- 

 formed in one second, and no instrumental test could detect polarization in the 

 aggregate beam. 



The polarization of light consists, therefore, in the determination of all its 

 vibrations to a single plane. The effect of double refraction is to do this with 

 both the rays into which the incident common light is divided ; and the effect 

 of reflection at certain definite angles, from certain bodies, as heretofore ex- 

 plained, is to do the same with the reflected ray. 



Prof. Dove, of Berlin, has illustrated in a very ingenious manner the physical 

 relation of common to polarized light. A Nicol's prism having been mounted 

 in such a manner as to admit of being rapidly rotated about its axis, he trans- 

 mitted through it a ray of common light, which gave, of course, an emergent 

 polarized ray capable of traversing a crystal of Iceland spar (having its princi- 

 pal plane coincident with the plane of polarization) without double refraction. 

 On setting the prism into rotation double refraction instantly appeared, and the 

 ray was equally divided by the crystal in all azimuths. 



When two polarized rays follow each other in the same path or intersect un- 

 der a very acute angle, it is obvious that, if their planes of polarization agree 

 in azimuth, they are in condition to interfere. If in phase of undulation they 

 are perfectly accordant, the two waves will be superposed, and the molecular 

 velocity of the resultant wave will be equal to the sum of the velocities of the 

 two components; but if there is a difference of phase between them amounting 

 to exactly half an undulation, then the crest of one wave will fall on the hollow 

 of the other, and the resultant molecular velocity will be equal to the difference 

 of velocities of the components. If the difference of phase is any other frac- 

 tion of an undulation, the circumstances of the resultant are determined by 

 precisely the same equation as that which has been given for the resultant mo- 

 tion of a vibrating solid, (equation [3],) in the same case. If a vibrating solid 

 derive its motion from two impulses which are not synchronous, we have seen 

 that its phases of vibration will be somewhere between those which the im.- 

 pulses would have separately produced. Its actual vibration will therefore 

 produce an undulation or series of undulations, which will occupy the same 

 situation in space relatively to those which the separate impulses would have 

 produced, as the generating vibration occupies relatively to the component vi- 

 brations, in time. And it matters not to the result, whether we suppose two 



