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FIG. 44.

Oblique Rectangular Prism, Oblique Rhombic Prism, Oblique Rectangular Octokedron, and Oblique Rhombic Octohedron.

a a. Principal axis. bb, c c. Secondary axes.

Crystals. To this system belong the crystals of sulphur, when obtained by slow cooling; realgar (red sulphuret of arsenic), and red antimony (native Kermes).

A considerable number of salts belong here also: as the sulphates of soda, lime (selenite), and iron; carbonate and sesquicarbonate (trona) of soda, bicarbonate of potash, chlorate of potash, phosphate of soda, borax (tincal), the acetates of soda, copper, zinc, and lead, binacetate of copper, binoxalate of potash, glauberite (sulphate of lime and soda), and chromate of lead.

To this system are also referred oblique prismatic mica (one of the kinds of diaxial mica described by Count de Bournon), tartaric and oxalic acids, sugar candy, and the crystals from oil of cubebs.

Properties.-The forms of this system have three axes, all of which are unequal. Two of them cut one another obliquely, and are perpendicular to the third. From the forms of the preceding system they are distinguished by this obliquity of two of their axes. As the three axes are unequal, it is indifferent which we take for the principal axis; but one of the inclined axes is usually selected, because, in general, the crystals are extended in the direction of one of these, so that in most cases the faces which are parallel to this axis greatly predominate. This axis, therefore, corresponds with that which Mr. Brooke calls the prismatic axis. The other two axes are called secondary axes. the one which is oblique being termed the first secondary axis ; the other, which is perpendicular to it, being denominated the second secondary axis.

The crystals of this system are doubly refracting with two optic axes. They are tri-unequiexpanding, and tri-unequiaxed. On the ellipsoidal hypothesis their atoms are assumed to be ellipsoids with three unequal axes.

In the opticians' shops, plates, cut from several crystals of the this system, are sold for showing, in the polariscope, the systems of lemniscates. They are usually cut perpendicularly to one of the optic axes; and, therefore, show but one system of rings traversed by a bar. Of these I shall notice three.

Borax deserves especial notice on account of its optic axes for the different homogeneous colours lying in different planes, a fact for the knowledge of which we are indebted to Sir John Herschel. As in other biaxial crystals it will be observed that the rings, or lemniscates, are traversed by only one bar or arm of the cross. In the next place it will be perceived, that the axes for red light make a greater angle with each other than the axes for blue or purple; hence, unlike nitre and carbonate of lead, the red ends of the rings are outwards, while the blue ends are inwards. This fact, however, only proves that the axes for different colours do not coincide: it does not show that they lie in different planes. But if, the tourmaline plates being crossed, the plate of borax be placed at such an azimuth that the bar or arm of the black cross distinctly traverses the centre of the system of lemniscates and leaves an interval perfectly obscure, we shall then see that the arm of the cross is not straight, as in nitre (fig. 40), but has a hyperbolic form. The reason of this difference is obvious: in nitre all the axes lie in the same straight line or plane, while in borax they are disposed obliquely, or in different planes.

Selenite is sometimes cut to show one of its two systems of rings. I have already described this crystal, and demonstrated the uniform tints produced by films of selenite of equal thickness. To show the rings the crystal must be cut at right angles to one of its optic axes.

This

Sugar Candy makes an interesting polariscope object. crystal is also cut perpendicular to one of its optic axes, and, therefore, shows only one of its two systems of rings.

Exceptions. Owing to irregularities of crystallization, the rings of some of the crystals of this system are often seen more or less distorted. Macled selenite is very common, as I have before mentioned. Sir John Herschel states, that idiocyclophonous crystals of bicarbonate of potash are frequent. I shall hereafter notice them.

SYSTEM VI.

DOUBLY OBLIQUE PRISMATIC SYSTEM.

Synonymes.-The one- and one-membered, the anorthotype, the triklinohedric, or the tetartohedric-rhombic system. Forms.-To this system belong the doubly oblique octohedron

and the doubly oblique prism. Rose makes no distinction of homohedral and hemihedral forms; but arranges the forms of this system as follows:

1. Forms whose faces are inclined to all the three axes. (Octohedra.) 2. Forms whose faces are inclined to two axes, and are parallel to the third. (Prisms.)

3. Forms which have their faces inclined towards one axis only. These forms are the faces of truncation of the three kinds of angles of the octohedron.

FIG. 45.

Two Doubly Oblique Prisms, and two Doubly Oblique Octohedra.
a a. The Principal Axis. bb, c c. The Secondary axes.

Crystals -The most important substances, whose crystalline forms are referable to this system, are boracic acid, sulphate of copper*, nitrate of bismuth, sulphate of cinchonia, quadroxalate of potash, and gallic acid.

Properties.-The forms belonging to this system have three axes all unequal and oblique-angular to one another; they are doubly refracting, with two optic axes; and they are tri-unequiexpanding. Consequently they have three unequal elasticities.

Of the three axes just referred to, one is taken for the principal axis, the other two for the secondary axes; but geometrically considered the selection is altogether arbitrary. The principal axis coincides with Mr. Brooke's prismatic axis. "The forms of this system," says G. Rose," have not symmetrical faces. All the faces are unique, so that this system is the one which differs the most from the regular or cubic system, in which we find the greatest symmetry on account of the equality and perpendicularity of the axes.' It is sometimes exceedingly difficult to distinguish the forms of this system. "The doubly oblique prism," observes Mr. Brooke," will be found the most

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* Mr. Brooke (art. Mineralogy, in the Encyclopædia Metropolitana), says, that the primary form of Sulphate of Copper is an oblique rhombic prism, and Mr. R. Phillips (Translation of the Pharmacopoeia, p. 237, 4th edit., 1841) has adopted Mr. Brooke's statement. If this be correct, sulphate of copper of course belongs to the oblique prismatic system, and not to the doubly oblique prismatic system. I have, however, referred it to the latter system on the authority of Gustav Rose, and most of the other eminent German crystallographers.

difficult of all the primary forms to determine from its secondary crystals. It is distinguishable from all other forms, when its crystals are single, by the absence of symmetrical planes analogous to those of other prisms; but it very frequently occurs in hemitrope or twin crystals, which must resemble some of the forms of the oblique rhombic prism, and can then be distinguished only by some re-entering angle or other character on the surface of the crystal."

Sulphate of Copper (Cu O. SO,. 5 Aq.) is sometimes cut to show the two sets of rings or lemniscates of this system; but the blue colour of the crystal destroys their brilliancy.

LECTURE IV.

4 CIRCULAR POLARIZATION.

The name of circular or rotatory polarization has been applied to a peculiar modification of light, first observed by Arago in the mineral called Quartz, and whose characteristic and distinctive properties I shall presently point out.

On the wave hypothesis, the term circular or rotatory is peculiarly appropriate, since it is assumed that the ethereal molecules describe circles, in other words that they vibrate or revolve uniformly in circles, and the form of the ethereal wave thereby produced, is that of a spiral or circular helix (that is, to a helix traced round a circular cylinder), of which a corkscrew and a bell-spring are familiar illustrations.

But apart from all hypothetical considerations, the name is an appropriate one. For unlike the rays of common polarized (that is, plane or rectilinearly-polarized) light, those of circularly polarized light have no distinction of sides, or, in other words, they have "no particular relations to certain regions of space," but present similar properties on all sides, and the angles of reflection at which they are restored to plane polarized light, in different azimuths, are all equal, like the radii of a circle described round the ray.

There are two varieties or kinds of circularly polarized light which have been respectively distinguished by the names of dextrogyrate or right-handed, and lavogyrate or left-handed.

In one of these the vibrations are formed in an opposite direction to those in the other. Unfortunately, however, writers are not agreed on the application of these terms; and thus the polarization, called, by Biot, right-handed, is termed, by Herschel, left-handed, and vice versa. There is, however, no difference as to the facts, but merely as to their designation. If, on turning the analyzing prism or tourmaline from left to right, the colours descend in Newton's scale, that is, succeed each other in this order-red, orange, yellow, green, blue, indigo, and violet, Biot designates

the polarization as right-handed, or +, or

; whereas

if they descend in the scale by turning the analyzer from right

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Herschel, on the other hand, supposes the observer to look in the direction of the ray's motion. Let the reader, he observes, "take a common corkscrew, and holding it with the head towards him, let him use it in the usual manner, as if to penetrate a cork. The head will then turn the same way with the plane of polarization as a ray in its progress from the spectator through a right-handed crystal may be conceived to do. If the thread of the corkscrew were reversed, or what is termed a left-handed thread, then the motion of the head, as the instrument advanced, would represent that of the plane of polarization in a left-handed specimen of rock crystal.'

I shall adopt Biot's nomenclature, and designate the polarization right-handed or left-handed, according as we have to turn the analyzing prism to the right or to the left to obtain the colours in the descending order.

In a former lecture I endeavoured to explain the nature of circularly polarized light, according to the wave hypothesis. Powell's machine (see p. 27) gives a very clear notion of the difference between a circular and a plane wave. You may, perhaps, remember that I stated, that a circular wave is composed of two plane waves of equal intensity, polarized at right angles, and differing in their progress one quarter of an undulation. I endeavoured to demonstrate this fact by a machine invented, I believe, by Mr. Wheatstone (see p. 33).

Now, in order that you may comprehend how we effect the circular polarization of light, I must beg of you to keep in mind these statements. Remember, that to convert plane-polarized into circularly-polarized light, two conditions are necessary, namely, 1st, the existence of two systems of luminous waves, of equal intensity, polarized perpendicularly to each other; and, 2dly, a difference in the paths of these two systems of an odd or uneven number of quarter undulations. Now, whenever these two conditions are satisfied, circularly polarized light results. But how are we to satisfy them? By so doubly refracting plane polarized light, that the two resulting waves shall differ in their path an odd quarter undulation,

There are five modes of effecting the circular polarization of light, that is of satisfying the conditions above mentioned; but they all agree in acting on the principle now laid down, namely, that by them plane polarized light is doubly refracted, and two rectangularly polarized waves produced, which differ in their path an odd quarter undulation.

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