colours most brilliantly. When this kind of sugar is subjected to heat, especially in contact with acids, it loses its crystallizability, and then acquires left-handed polarization. In the manufacture

of barley-sugar, hard bake, &c., the makers of these kinds of hard confectionary use a little cream of tartar to destroy the crystallizability of sugar. Soubeiran found that a syrup of cane-sugar heated by a salt-water bath, the air being excluded, underwent a series of remarkable changes in respect of its rotative power.

its rotative power 0°, and became. The precise nature of the latter kind of sugar is not known.

In sugar-refining the object is never to let the syrup get beyond the first zero; that is, not to convert crystallizable unto uncrystallizable sugar. Raw sugar contains, however, both crystallizable and uncrystallizable sugar: the latter alone should constitute treacle. But, from Soubeiran's optical examination, it appears that treacle contains a portion of crystallizable sugar.

The optical characters of sugar have been made use of to detect fraud in Pharmacy. In 1842, more than a ton of a substance purporting to be manna was offered for sale in Paris at less than fivepence per pound, the excuse given for the unusually low price was, that cash was immediately required. Suspicion was raised, and the substance was submitted to careful examination, the result of which was the establishment of the fact, that it was not manna, but potato-sugar. Its aspect, taste, fermentibility (mannite not being fermentible), and the presence of sulphate of lime proved this. Biot submitted it to a very careful optical examination, and found its characters to be those of a starch-sugar. Manna contains two kinds of saccharine matter, one called mannite, and the other a fermentable sugar. Now mannite, when pure, has no rotative power on polarized

But the two rays thus obtained differ in their properties from those produced by Iceland spar and other doubly refracting crystals, for while the latter are rectilinearly polarized, those of quartz are circularly polarized. Now every circularly polarized ray is equal to two rectilinearly polarized waves, differing in their progress an odd number of undulations. It follows therefore, that the two circularly polarized waves are equal to four rectilinearly polarized waves. Hence then to explain the phenomena, we must assume that the rectilinearly polarized ray (which I shall call R) incident on the quartz, is resolved into two others (A and B) of equal intensity, the one (A) polarized in a plane 45° inclined to the right, the other (B) 45° inclined to the left of the plane of polarization of the primitive ray (R). Let us further conceive that each of the two rays (A and B) is resolved into two other rays, namely A into Aa and Ab, and B into Ba and Bb. Aa and Ab are polarized in one plane, viz., +45°, while Ba and Bb are polarized in another plane, viz.,-45°. Aa and Ba have each their phases advanced, or + undulation, while Ab and Bb have each their phases retarded, or undulation *. Now if we suppose these four rays to be combined two and two in a cross order, we shall have resulting two circularly polarized rays, one right-handed, the other left-handed. Thus Aa and Bb combine to form a left-handed ray, while Ab and Ba form a right-handed one. For when the advanced system of waves has its plane of polarization to the right of that of the retarded system, the ethereal molecules rotate from right to left; whereas they rotate from left to right when the first plane is to the left of the second.

These two circularly polarized rays are propagated along the axis of quartz with unequal velocities. In right-handed quartz, the right-handed ray is transmitted with greater velocity, in lefthanded quartz with lesser velocity than the left-handed ray; and thus at their emergence one is in advance of the other. If the surface of egress or ingress be oblique to the axis, the two circularly polarized rays will emerge in different directions; but if it be perpendicular (as in the experiment under examination) they will emerge superposed, and will compound a single ray polarized

.

"It results from the laws of interference," says Fresnel, "that a system of waves, polarized rectilinearly, may be replaced by two others, polarized at right angles to each other, and coinciding in their route; and that for each of these we may substitute two other systems of waves having the same plane of polarization, but the one advanced, the other retarded 4th of an undulation; and thus separated 4th of an undulation. In this way are obtained four systems of waves of equal intensity, of which two, polarized at right angles to each other, are th of an undulation behind the two others polarized in the same planes."

in a single plane. Now this plane is removed from the plane of primitive polarization by an angle proportional to the interval of retardation (therefore, proportional to the thickness of the crystal) and to the refrangibility of the ray.

Thus then the differently coloured rays emerge from the quartz plate polarized in different planes; hence, by rotating the analyzer, they are successively transmitted and brought into view.

The following diagram may, perhaps, serve to render more intelligible the explanations of the action of a plate of quartz, of one millimetre (0.03937 of an English inch) in thickness, on the incident rectilinearly polarized red light.

A succession of quartz prisms does not give a further multiplication of images-a circumstance which distinguishes the double refraction of quartz from that of Iceland spar and other crystals.

The above explanation is applicable only when the direction of the rays coincides with the principal axis of the crystal. When it is inclined to this axis, Mr. Airy has shown that the two resulting rays are elliptically polarized, the elliptical vibrations. in the two rays being in opposite directions (that is, one righthanded, the other left-handed), and the greater axis of the ellipse is for the extraordinary ray, in the principal plane of the crystal, and, for the ordinary ray, in a plane perpendicular to the principal one. The ratio of the axes in these ellipses, varies with the inclination of the ray to the principal axis of the crystal. When the direction of the ray coincides with this axis, the ratio is one of equality, and the ellipses become circles. But when the ray is inclined to the axis, the ratio increases indefinitely with the inclination. "It is also necessary to suppose that the axis of revolution of the spheroid (prolate for quartz) in which the extraordinary ray is supposed to diverge, is less than the radius of the sphere into which the ordinary wave diverges."

Hitherto we have had no satisfactory theory of the cause of the unequal velocities with which the two rays are transmitted along the principal axis of quartz. We conceive that it must depend either on some peculiarity in the molecules themselves,

or in their mode of arrangement. "The crystal," says Fresnel, "cannot be constituted from right to left as it is from left to right, either in virtue of the arrangement of its particles, or of their individual constitution." If it be a molecular property, it must be acquired in the act of crystallization, by the mutual action of the molecules on each other, for other forms of silica, as well as melted quartz, are devoid of it. An helicoidal arrangement (right or left-handed, as the case may be) of the molecules furnishes a physical explanation of the fact above referred to. It has been objected to this hypothesis, that it is not applicable to the case of circularly polarizing liquids. But as the circular polarization of quartz is dependent on direction, while that of liquids is independent of it, it is tolerably clear that the cause must be different in the two cases. In the first, it may depend on the arrangement of the molecules; in the second, on some peculiarity in the molecules themselves.

If two plates of quartz, cut obliquely to the principal axis of the crystal (fig. 49, bb, bb), be superposed crosswise and examined in the polariscope, they present a series of parallel coloured bands or stripes, with a central black or white stripe. When the tourmaline plates are crossed, the central stripe is black, when they coincide, it is white. The lateral coloured stripes seen in the one case, are complementary to those seen in the other. Amethyst is a mixture of right and left-handed quartz, and will be hereafter noticed among tesselated crystals.

5. Circular Polarization by Fluids.- Some liquids possess the remarkable property of circularly polarizing light. The following are the most important:

Volatile oils (those of mustard and bitter almonds excepted). Naphtha.

Aqueous solutions of several kinds of sugar, dextrine, tartaric acid, and tartrates (tartrate of alumina excepted).

Diabetic urine.

Albuminous urine.

Alcoholic solutions of camphor and artificial camphor.

Most vegetable juices.

Biot found that vaporization did not destroy the circular polarization of oil of turpentine.

The following liquids have been found devoid of this property:

Water.
Alcohol.

Pyroxilic spirit.
Pyroacetic spirit.
Olive oil.

The apparatus necessary for observing this property of fluids consists essentially of three parts; viz., a polarizer, a tube to contain the fluid, and an analyzer.

The polarizer is an unsilvered glass mirror, a bundle of parallel glass plates, or a Nichol's prism. Both Biot and Professor

Powell use the first, while Ventzke employs the last. A plate of glass, blackened at the posterior surface, answers very well. Sometimes a second mirror (of silvered glass) is used to throw the light on the polarizing plate.

The tube, to hold the liquid, should be from six to twenty-four inches long. In general, it is to be filled with the fluid under examination, and to be closed at each end by a flat glass plate. Professor Powell, however, employs a common test-tube, open at the top, and having the usual hemispherical bottom. In some cases it is desirable to have two or three perforated diaphragms of sheet silver or platinum, placed at intervals in the tube, to exclude the light reflected from the sides of the tube, but to admit those rays which traverse the axis of the tube.

The analyzer should be either an achromatic, doubly refracting prism, or a Nichol's prism. Biot uses a doubly refracting prism of calc spar, made of a rhombohedron of this substance, rendered achromatic by replacing a portion of the crystal by a glass prism. Achromatic quartz prisms are objectionable, since they are never so accurately prepared as to yield two images only, but always four; of which two, however, are very faint. Professor Powell employs a rhombohedron of calc spar, in its natural state, as his analyzer, and a lens to magnify the separation of the images. Ventzke uses a Nichol's prism as the analyzer.

The amount of rotation which a ray of light suffers during its passage through the liquid, is measured by an index attached to the analyzer, and moving on a graduated circular metallic plate. Before the tube containing the liquid is introduced, we must fix the zero, or O°. If a doubly refracting prism be the analyzer, the index is made to point to zero, or Ŏ°, when the ordinary image alone is seen. If, however, a Nichol's prism be used as ana

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