hemispherical, the axis of the illuminating ethereal ray incident impinging on the centre of the hemisphere. Were the rectilineal progression of this ray not interrupted, the length of the pulsation to which the ray would give rise, in any one movement, reckoned from the point O, would be the same whatever was the direction of the ray, and in the course of incidence. Nor will the case be different on entering another medium, provided, like the radiant, that medium have an uniform structure; therefore, the pulses propagated by the incident ray, in the dense medium, in the course of incidence, will be represented by the radii of a circle, when the incident ray is moved upwards and downwards in the same plane. But, while a pulse is propagated by the incident ray through the radius, with more or less directive force, another is simultaneously propagated from the surface, through the sine corresponding to that radius. The polarity of the pulses being developed only at the moment when the movement is at zero, the pulse, in the course of incidence, will pass through the larger sines without interference. But, at the point i, two polarities are simultaneously generated, whose force and direction, supposing the directive force of both equal, are represented by oi and si. The ray which is to be continued through the medium, then, will be the resultant of these, or that in which an ivory ball would run, if struck simultaneously by two coming in the directions of oi and s i, and with forces proportional to these lines. Let O R' be drawn parallel to Ri, and let & r, the sine of its inclination to P P', be drawn. It is evident that & r always varies in the same ratio as s s", or its half si. But &r is the sine of inclination of the refracted ray, and si that of the same ray incident; or they are the cosines of the angles of incidence and refraction, and these being in a constant ratio, so also must be their sines, as commonly stated. To account for different refractive powers in different media at the same incidence, we have only to suppose, that the illuminated hemispheres, in different substances, according to their intensity, diminish more or less the directive energy of the ray propagated in the course of incidence, which has to penetrate them, while the directive energy of their own ver

H

dense lamina of the same substance, provided some singled light be reflected at the first, the pencil ultimately emergent, will be completely singled also, the plane of its edges being of course transverse to that which is obtained by reflection of the same pencil. Thus, when receiving a pencil of common light upon a number of parallel plates of glass at the singling angle, by reflection from the first surface, a considerable pencil may be obtained completely singled in one plane; and, by transmission through a greater or less number, a considerable pencil may be obtained, completely singled in a transverse plane. Let R (Fig. 28) be a perfect pencil, incident at the singling angle upon the surface of the photomotive pile A B, a part of the excitement rises up in the direction of R', singled with the edges of the molecules transverse to the plane of incidence and reflection, or parallel to the reflecting surface. A singling action goes on at the illuminated surfaces of the successive plates, and the pencil R" is completely singled, the edges being in the plane of incidence and reflection, or transverse to those of R'. These two singled pencils correspond to the two wires of an electro-motive pile.

OF DOUBLE REFRACTION.

SUCH are some of the most obvious phenomena produced by lumeniferous excitement, when propagated, transmitted, or conducted through media, which have not a specific polarity of their own, and which, during transmission, act equally upon both the parts of which a pencil of common light consists. The transmitted pencil may simply be regarded as the prolongation of the incident pencil, refracted and mutilated at the surface of the dense medium, according to circumstances. But when the refracting medium consists of molecules symmetrically disposed in it, cach having a specific polarity of its own, it will readily be inferred, that the different parts of a ray of light will be differently affected, when they come in contact with the polarized molecules. To give rise to a molecule possessed of free polarity, it is only necessary that its form de

viate from the spheroidal or polygonal tessular (17). If there be an excess either of equatorial or polar parts, it becomes possessed of an excess either of negative or positive polarity, and such a state being in different degrees of intensity in different regions of the molecule, the lumeniferous excitement will be constituted in the medium in two directions, which must, of course, be possessed of consecutive polarities. A polarized medium cannot admit a body, neutral by consisting of two polarized parts neutralizing each other, to pass through it, or exist in it. As between the voltaic poles, potash is separated into oxygen and potassium, or water into oxygen and hydrogen, so, by a symmetrical pile of polarized molecules, a ray of light is separated into two, and made to conform in the state of its polarity, and, consequently its position, to the demands of the pile. The action of a doubly refracted crystal cannot be regarded as a mechanical splitting or diffracting into parts an incident ray. It is a new organization of the lumeniferous excitement, conformable to the medium in which it must exist. Instead of attempting any thing like a delineation of the movements of the subtile matter, by which this new distribution of lumeniferous excitement is effected, which may be done once for all, when the molecules of some doubly refractive crystals shall have been constructed, or imagining geometrical constructions to explain the phenomena, which has been well enough done already, it may only be remarked, in general, that, when a perfect ray of light is incident upon a polarized pile of molecules, except in the direction of the axes of no polarization of the molecules, two rays are instituted instead of one, as obtains in the radiant and other tessular media, consecutive to each other, and, consequently, at their emerging into the radiant medium again, two ethereal rays are developed, the edges of the molecules being in transverse planes. One of these rays may be regarded as the atomic or ordinary, and the other the molecular, unusual, or extraordinary. The direction of the atomic ray is always determined by the direction of the original ray, and the action of the illuminated atomic hemisphere, which has been already conceived

and explained. The direction of the molecular ray is determined, not by its relation to the surface on which it happens to be incident (which is the equator of the atomic refracting movement,) but to the equator of the molecule.

Both the rays, like those in a perfect ray of radiant matter, are equal in quantity; and like them, also, they are of consecutive polarity, and must therefore develope rays in the radiant medium, singled in opposite planes. The atomic or ordinary ray (though it is to be remembered, that it is ordinary only in as far as its refractions obey the ordinary law of the sines) gives rise to a ray in the radiant medium on the emergent side, having its edges in the same direction as if it had been singled by reflection. The molecular, or extraordinary ray, gives rise to an ethereal ray, having its edges singled as if by transmission through a singling pile; and this ray found upon either side of the other, in the plane of the axes of the crystalline molecules, according as the external current in these is from the equator to the poles, or from the poles to the equator (figs. 19 and 20). The plane of the edges of one of the rays is always parallel to the equator of the crystalline molecules; of the other, to the axis. The bifurcation, consequently, always takes place in the plane of the axis, which is named the principal section of the pile or crystal.

is

All crystalline bodies which are destitute of tessular forms, present in a greater or less degree the phenomena which have now been noticed: and on tessular crystals, and transparent masses not possessing individuality of form, they may be induced by changing the condition of the matter in different parts, as by temperature or compression. In no body, however, are they exhibited so eminently as in calcareous spar or the carbonate of lime. This beautiful mineral occurs crystallized in hundreds of different forms; but all the forms, when broken down, yield fragments which are all similar, being rhomboids with angles of 105° 5' and 74° 55", the exact dimensions depending on the temperature in which they are examined. As the heat is raised, they approximate the tessular form, in consequence of the diminution of the cohesion

(which caused a deviation from the tessular), and an exhilaration of electricity, which tends to develope the tessular series. The axis of such a rhomboidal fragment is the line joining the symmetrical angles. When a pencil of common light is incident in any manner upon the natural face of such a rhomboid, it is remarked, that two immediately make their appearance in the crystalline medium, both of which always traverse the axis; so that, in whatever way the crystal is turned about, they sympathise with the motion, and are always constituted in a plane which contains the axis and the short diagonals of the opposite faces, that is, in the principal section. Even when the ray is incident vertically on any of the natural faces of the rhomboid, two make their appearance in the crystal, one of which, the atomic, ordinary, or normal, is not solicited from the vertical by any force, and proceeds without refraction; the other is drawn away from the axis, as if by a current sweeping it towards that pole to which it is already most contiguous. If any number of rays be incident, however much scattered and confused, those developed in the spar are all reduced to parallel planes, which are so many principal sections of rhomboids smaller than the mass, in a parallel position, and involved as parts of the whole. On whatever side of the rhomboid the incident light is applied, the success is the same. As rays of light can only be constituted in particular ways in the radiant medium, which depend on its structure and polarity, so, in this crystal they are developed according to its specific structure. When the incident ray is vertical, the two constituted in the crystal contain an angle of 6° 12′; so that, even in a small mass, the remarkable phenomenon is very obvious. If, however, the symmetrical or obtuse angles be polished away, or other means taken for constituting a pencil parallel to the axis, a vertical ray gives no double refraction; and the same happens if a vertical ray be sent upon a plane, found by cutting away two opposite lateral edges, and replacing them by transparent surfaces parallel to the axis. But in these directions, in which the axis and the equator of the molecule are discovered, when the incident ray is not perpendicular to the