the vibrations of the ether that are perpendicular to the plane of incidence will be retarded a quarter of a vibration, which causes the vibrating particles to describe a circular helix, or curve, like a corkscrew. However, that only happens when the plane of polarization is inclined at an angle of 45° to the plane of incidence. When these two planes form an angle, either greater or less, the vibrating particles move in an elliptical helix, which curve may be represented by twisting a thread in a spiral about an oval rod. These curves will turn to the right or left according to the position of the incident plane.

The motion of the ethereal medium in elliptical and circular polarization may be represented by the analogy of a stretched cord; for if the extremity of such a cord be agitated at equal and regular intervals by a vibratory motion entirely confined to one plane, the cord will be thrown into an undulating curve lying wholly in that plane. If to this motion there be superadded another, similar and equal, but perpendicular to the first, the cord will assume the form of an elliptical helix; its extremity will describe an ellipse, and every molecule throughout its length will successively do the same. But if the second system of vibrations commence exactly a quarter of an undulation later than the first, the cord will take the form of a circular helix, or corkscrew; the extremity of it will move uniformly in a circle, and every molecule throughout the cord will do the same in succession. It appears, therefore, that both circular and elliptical polarization may be produced by the composition of the motions of two rays in which the particles of ether vibrate in planes at right angles to one another.

Professor Airy, in a very profound and able paper lately

published in the Cambridge Transactions, has proved that all the different kinds of polarized light are obtained from rock crystal. When polarized light is transmitted through the axis of a crystal of quartz in the emergent ray, the particles of ether move in a circular helix; and when it is transmitted obliquely, so as to form an angle 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. 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 proved 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 phe nomena of the 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. MM. Fresnel and Arago proved by experiment 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 backwards and forwards 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 the 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 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 hap pen; but when two rays are transinitted 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 lays 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 centre.

A constellation of talent, almost unrivalled 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 accidentally viewing, with a doubly refracting prism, a brilliant sunset reflected from the windows of the Luxembourg palais 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.

SECTION XXIV.

The numerous phenomena of periodical colors arising from the interference of light, which do not admit of satis