with the axis of the prism, the particles of ether move in an elliptical helix, the ellipticity increasing with the obliquity of the incident ray; so that, when the incident ray falls perpendicularly to the axis, the particles of ether move in a straight line. Thus quartz exhibits every variety of elliptical polarization, even including the extreme cases where the eccentricity is zero, or equal to the greater axis of the ellipse (N. 210). In many crystals the two rays are so little separated, that it is only from the nature of the transmitted light that they are known to have the property of double refraction. M. Fresnel discovered by experiments on the properties of light passing through the axis of quartz, that it consists of two superposed rays, moving with different velocities; and Professor Airy has shown, that in these two rays, the molecules of ether vibrate in similar ellipses at right angles to each other, but in different directions; that their ellipticity varies with the angle which the incident ray makes with the axis; and that, by the composition of their motions, they produce all the phenomena of polarized light observed in quartz.

It appears from what has been said, that the molecules of ether always perform their vibrations at right angles to the direction of the ray, but very differently in the various kinds of light. In natural light the vibrations are rectilinear, and in every plane. In ordinary polarized light they are rectilinear, but confined to one plane; in circular polarization the vibrations are circular; and in elliptical polarization the molecules vibrate in ellipses. These vibrations are communicated from molecule to molecule, in straight lines when they are rectilinear, in a circular helix when they are circular, and in an oval or elliptical helix when elliptical.

Some fluids possess the property of circular polarization, as oil of turpentine; and elliptical polarization, or something similar, seems to be produced by reflection from metallic surfaces.

The colored images from polarized light arise from the interference of the rays (N. 211). MM. Fresnel and Arago found that two rays of polarized light interfere and produce colored fringes if they be polarized in the same plane, but that they do not interfere when

polarized in different planes. In all intermediate positions, fringes of intermediate brightness are produced. The analogy of a stretched cord will show how this happens. Suppose the cord to be moved backward and forward horizontally at equal intervals; it will be thrown into an undulating curve lying all in one plane. If to this motion there be superadded another similar and equal, commencing exactly half an undulation later than the first, it is evident that the direct motion every molecule will assume, in consequence of the first system of waves, will at every instant be exactly neutralized by the retrograde motion it would take in virtue of the second; and the cord itself will be quiescent in consequence of the interference. But if the second system of waves be in a plane perpendicular to the first, the effect would only be to twist the rope, so that no interference would take place. Rays polarized at right angles to each other may subsequently be brought into the same plane without acquiring the property of producing colored fringes; but if they belong to a pencil the whole of which was originally polarized in the same plane, they will interfere.

The manner in which the colored images are formed may be conceived, by considering that when polarized light passes through the optic axis of a doubly refracting substance,—as mica, for example,—it is divided into two pencils by the analyzing tourmaline; and as one ray is absorbed there can be no interference. But when polarized light passes through the mica in any other direction, it is separated into two white rays, and these are again divided into four pencils by the tourmaline, which absorbs two of them; and the other two, being transmitted in the same plane with different velocities, interfere and produce the colored phenomena. If the analysis be made with Iceland spar, the single ray passing through the optic axis of the mica will be refracted into two rays polarized in different planes, and no interference will happen. But when two rays are transmitted by the mica, they will be separated into four by the spar, two of which will interfere to form one image, and the other two, by their interference, will produce the complementary colors of the other image, when the

spar has revolved through 90°; because, in such positions of the spar as produce the colored images, only two rays are visible at a time, the other two being reflected. When the analysis is accomplished by reflection, if two rays are transmitted by the mica, they are polarized in planes at right angles to each other. And if the plane of reflection of either of these rays be at right angles to the plane of polarization, only one of them will be reflected, and therefore no interference can take place; but in all other positions of the analyzing plate both rays will be reflected in the same plane, and consequently will produce colored rings by their interference.

It is evident that a great deal of the light we see must be polarized, since most bodies which have the power of reflecting or refracting light also have the power of polarizing it. The blue light of the sky is completely polarized at an angle of 74° from the sun in a plane passing through his center.

A constellation of talent almost unrivaled at any period in the history of science, has contributed to the theory of polarization, though the original discovery of that property of light was accidental, and arose from an occurrence which like thousands of others would have passed unnoticed, had it not happened to one of those rare minds capable of drawing the most important inferences from circumstances apparently trifling. In 1808, while M. Malus was accidently viewing with a doubly-refracting prism a brilliant sunset reflected from the windows of the Luxembourg palace in Paris, on turning the prism slowly round, he was surprised to see a very great difference in the intensity of the two images, the most refracted alternately changing from brightness to obscurity at each quadrant of revolution. A phenomenon so unlooked for induced him to investigate its cause, whence sprung one of the most elegant and refined branches of physical optics.

X

SECTION XXIII.

Objections to the Undulatory Theory, from a Difference in the Action of Sound and Light under the same circumstances, removed-The Dispersion of Light according to the Undulatory Theory.

THE numerous phenomena of periodical colors arising from the interference of light, which do not admit of satisfactory explanation on any other principle than the undulatory theory, are the strongest arguments in favor of that hypothesis; and even cases which at one time seemed unfavorable to that doctrine have proved upon investigation to proceed from it alone. Such is the erroneous objection which has been made, in consequence of a difference in the mode of action of light and sound, under the same circumstances, in one particular instance. When a ray of light from a luminous point, and a diverging sound, are both transmitted through a very small hole into a dark room, the light goes straight forward and illuminates a small spot on the opposite wall, leaving the rest in darkness; whereas the sound on entering diverges in all directions, and is heard in every part of the room. These phenomena, however, instead of being at variance with the undulatory theory, are direct consequences of it, arising from the very great difference between the magnitude of the undulations of sound and those of light. The undulations of light are incomparably less than the minute aperture, while those of sound are much greater. Therefore when light diverging from a luminous point enters the hole, the rays round its edges are oblique, and consequently of different lengths, while those in the center are direct, and nearly or altogether of the same lengths. So that the small undulations between the center and the edges are in different phases, that is, in different states of undulation. Therefore the greater number of them interfere, and by destroying one another produce darkness all around the edges of the aperture; whereas the central rays having the same phases, combine, and produce a spot of bright light on a wall or screen directly opposite the hole. The waves of air producing sound, on the

contrary, being very large compared with the hole, do not sensibly diverge in passing through it, and are therefore all so nearly of the same length, and consequently in the same phase, or state of undulation, that none of them interfere sufficiently to destroy one another. Hence all the particles of air in the room are set into a state of vibration, so that the intensity of the sound is very nearly everywhere the same. Strong as the preceding cases may be, the following experiment made by M. Arago about twenty years ago seems to be decisive in favor of the undulatory doctrine. Suppose a planoconvex lens of very great radius to be placed upon a plate of very highly polished metal. When a ray of polarized light falls upon this apparatus at a very great angle of incidence, Newton's rings are seen at the point of contact. But as the polarizing angle of glass differs from that of metal, when the light falls on the lens at the polarizing angle of glass, the black spot and the system of rings vanish. For although light in abundance continues to be reflected from the surface of the metal, not a ray is reflected from the surface of the glass that is in contact with it, consequently no interference can take place; which proves, beyond a doubt, that Newton's rings result from the interference of the light reflected from both the surfaces apparently in contact (N. 194).

Notwithstanding the successful adaptation of the undulatory system to phenomena, the dispersion of light for a long time offered a formidable objection to that theory, which has only been removed during the present year by Professor Powell of Oxford.

A sunbeam falling on a prism, instead of being refracted to a single point of white light, is separated into its component colors, which are dispersed or scattered unequally over a considerable space, of which the portion occupied by the red rays is the least, and that over which the violet rays are dispersed is the greatest. Thus the rays of the colored spectrum whose waves are of different lengths, have different degrees of refrangibility, and consequently move with different velocities, either in the medium which conveys the light from the sun, or in the refracting medium, or in both; whereas rays of all colors