WE shall now devote a few pages to the consideration of the nature of light, and the optical principles involved in the construction and use of the microscope. Two theories of light have been propounded. According to one, light consists of minute particles emanating from self-luminous bodies, as the sun, a candle, or a red-hot piece of iron; this is called the corpuscular theory. According to the other, light consists of waves or undulations like those of water or the ears of corn set in motion by the wind, of the molecules of an extremely subtle and rarified elastic matter, called ether, existing everywhere, and set in motion by the causes which produce light; this is called the undulatory theory. The consideration of the merits of these two theories would be foreign to our purpose: suffice it to say that the evidence in favour of the undulatory theory preponderates, so that the corpuscular theory is now laid aside.

It will often be requisite to make use of the term ray of light, by which must be understood the smallest bundle of luminous undulations which can be separated from a mass of light—as by passing light through a small hole in an opake body, or by any equivalent method.

The most casual observer must have noticed that the rays of light move in straight lines; as when the sun’s rays are seen entering a dark room through a small window or other aperture, their direction being then distinctly visible; the manner in which ordinary shadows are formed also illustrates the same fact.

Refraction.—But when the rays in their passage impinge or are incident upon and enter a transparent medium or material, of a different density from that which they were at first traversing, their course becomes altered, and the line of their direction broken, whence they are said to be refracted. If the medium upon which the rays impinge be denser than that through which they were at first passing, they will be refracted towards a line perpendicular to the surface, or they will be refracted towards the perpendicular, as it is expressed.

Thus, as shown in Pl. XII. fig. 1, the incident ray i, entering the plate of glass, will be refracted at its surface in the direction a r, towards the line p, which is perpendicular to the surface.

The extent to which the rays undergo refraction depends upon the degree of density of the medium, and varies in the case of each individual substance; but it follows a definite law. If, as in Pl. XII. fig. 2, a circle be drawn around the point b, at which the ray a is incident, b r representing the refracted ray, the lines s i and t r, drawn at right angles to the perpendicular p, will form respectively the sines, as they are called, of the angles s b i and t b r; s i being the sine of the angle of incidence s b i, or the angle formed by the incident ray with the perpendicular, and t r the sine of the angle of refraction t b r, or of that formed by the refracted ray with the perpendicular. These sines, for brevity, are called the sines of incidence and of refraction; and they bear a constant ratio or proportion to each other. Taking the sine of refraction as the unit, or as = 1, the value of the sine of incidence represents the refractive index or the refractive power of the medium for a ray entering the medium from a vacuum; or, the refractive power of air being extremely small, the value of the sine of incidence may be considered as representing the refractive power from air into the medium.

Although the ratio of the sines is constant, the refractive index varies in different media. Thus that of air is 1·0003; of water, 1·336; of Canada balsam, 1·549; of crown glass, from which window-panes are made, 1·535; of flint glass, from which bottles are made, 1·6; of Faraday’s heavy glass, composed of silicated borate of lead, 1·8; and of that consisting of borate of lead, 2·0.

A knowledge of this “law of the sines” is of practical importance in determining the direction which the rays will pursue when transmitted through glass lenses, &c. the refractive index of which is known; or in ascertaining the curve which should be given to their surfaces for producing a particular refraction and focal length. Thus, supposing the plate of glass in Pl. I. fig. 2 to consist of crown glass, the refractive index of which is 1·5, the length of the sine of refraction, t r, will be equal to one part or dimension, while the sine of incidence, s i, is equal to one part and a half.

It must be remarked that when light is incident at a right angle to the surface of the medium, no refraction takes place, the transmitted ray pursuing its original course.

When a ray of light leaves a denser medium, such as glass, to enter a rarer medium, such as air, it becomes refracted from the perpendicular. In such case, the angle of refraction being greater than the angle of incidence, its sine will also be greater than that of the latter; but the ratio is still preserved.

Reflexion.—When rays of light fall upon a plane surface, as the flat surface of the mirror, a greater or less number of them are reflected, and this according to a definite law, by which the angle of incidence, or that formed by the incident ray with the perpendicular, is equal to the angle of reflexion, or that formed by the reflected ray with the same. Thus, as shown in Pl. XII. fig. 3, the angle i b p, formed by the incident ray i b with the perpendicular p, is equal to the angle p b r, formed by the reflected ray b r with the perpendicular p b.

If the body upon the surface of which the rays are incident be transparent, some of the rays will be refracted and will pass through it, whilst others will be reflected. The proportion of those reflected is smallest when the rays are incident perpendicularly to the surface; but this increases as the incident rays become more oblique, i. e. as the angle of incidence becomes greater, although at no degree of obliquity are the whole of the rays reflected. The case is different, however, with those rays which enter the substance and impinge upon its inner or second surface; for these at a particular angle of incidence undergo total reflexion, so that none of the rays are transmitted at the second surface. The angle of total reflexion is constant for the same medium, but different for different media: thus in crown glass it is equal to about 40°, in flint-glass 38°, &c.; and this internal reflexion from the second surface of transparent media is more perfect than that occurring at the surface of opake reflecting surfaces or mirrors.

If the reflecting surface be concave, as in Pl. XII. fig. 4, parallel rays will be reflected to a focus a, nearer the mirror than the centre of its curvature b, and this focus is called the principal focus; while diverging rays are brought to a focus nearer the centre of curvature; and converging rays form a focus further from the centre of curvature.

Lenses.—In most instances, as far as the microscope is concerned, the surfaces of the glass through which the rays of light are transmitted are not plane or flat, but curved-being either convex or concave, and belonging to convex or concave lenses. In considering the course of rays through curved surfaces, the refraction may be viewed as taking place at a plane surface forming a tangent at the point of incidence of each ray; or each curved surface may be regarded as consisting of a number of minute plane surfaces placed at right angles to the perpendicular. Thus, in Pl. XII. fig. 5, the ray a, incident at the point b of the curved surface, is refracted towards the perpendicular p, as if it had fallen upon the plane surface represented by the tangent t. The forms of the most common lenses are represented in Pl. XII. figs. 6-10;—fig. 6 being doubly convex, or both surfaces being convex; fig. 7, plano-convex, or one surface plane, the other convex; fig. 8, doubly concave, or both surfaces being concave; fig. 9, plano-concave, one surface being plane, the other concave; and fig. 10 is a meniscus, in which one surface is convex and the other concave. The curved surfaces of lenses are usually portions of spheres.

The manner in which the course of a ray may be traced through a lens is illustrated by Pl. I. fig. 11, which requires no explanation after what has been already stated.

To facilitate the comprehension of the general action of lenses, they may be regarded as composed of two triangular prisms, with their bases in contact in a convex lens, as in fig. 12; their apices being opposed in a concave lens, as in fig. 13.

The point to which the rays converge after passing through a convex lens is called the focus (Pl. XII. fig. 14 f), the distance of which from the centre of the lens, called the focal length, obviously depends upon the direction of the incident rays. When these are parallel, which those coming from distant objects may be considered to be, the focus at which they meet is called the principal focus, or the focus for parallel rays: thus, in Pl. XII. fig. 14, the parallel rays meet at f, which is the principal focus.

If the incident rays are convergent, as in Pl. XII. fig. 15, the focus o will be situated nearer the lens than the principal focus, f. If, on the other hand, they are divergent, as in Pl. XII. fig. 16, the focus f will be situated further from the lens than the principal focus o. By concave lenses the incident rays are rendered divergent, as in Pl. XII. fig. 17, as if they emanated from a point f, situated on the same side of the lens as that upon which the rays are incident, and called the virtual focus.

Spherical aberration.—Although, as a general expression, we have stated that the rays of light meet at a focus on passing through a convex lens, this is not strictly correct. For, in ordinary convex lenses, the marginal rays are more refracted than the central ones, and meet at focal points nearer the lens than the latter, as shown in Pl. XII. fig. 18. This important defect is called spherical aberration, and arises from the lateral rays being incident upon more oblique portions of the curved surface of the lens than the central rays. Hence objects seen through such lenses appear misty and confused, the central and lateral parts of a flat object not being visible at the same time; and even when the marginal parts are visible, they appear distorted or deformed.

Spherical aberration is greatest in the most convex lenses; and, in a plano-convex lens, it is least when parallel rays enter at or emerge from its convex surface.

In certain lenses, the convex surface of which has the form of a parabola, a hyperbola, or an ellipse, the spherical aberration is absent; but it is impossible to grind microscopic lenses of these forms with absolute accuracy, so that the fact is of no practical value.

The form of simple convex lens most free from aberration is that in which the curves of the two surfaces form parts of a sphere, the radii of the curves being as 1 to 6; the focal length being rather less than twice the length of the radius of the most convex surface. This form of lens comes very near to a plano-convex lens, which is consequently the best form for a simple lens.

Dispersion, or Chromatic Aberration.—The rays of light have so far been considered as simple. They are, however, in reality compound, consisting of a number of primary-coloured rays, of which seven kinds are easily distinguishable, viz. red, orange, yellow, green, blue, indigo, and violet. The coloured rays of the sun are, as is well known, often seen separated by the action of the triangular glass bars or prisms forming the lustres of a chandelier; the separation arising from the different refrangibility of the coloured rays, by which each is refracted to a different degree from that of the others. This is shown in Pl. XII. fig. 19, representing a ray of white light entering a triangular prism, at the surface of which the paths of the rays become different according to the degree of their refrangibility, whence they emerge separately, forming a spectrum at v r; the most refrangible violet rays (v) being most refracted, the less refrangible red (r) least so, the intermediate rays being refracted to intermediate degrees according to their respective refrangibilities. This separation of the coloured rays is called dispersion; and as different substances or media disperse the coloured rays over a larger or smaller space, so as to produce spectra of different lengths, they are said to possess different dispersive powers. Thus the dispersive power of flint glass and balsam are about equal, while that of crown glass is considerably less.

The extent to which dispersion is produced by the same medium also depends upon the angle of the prism, being greater as the angle is larger; increased obliquity of the incident light also increases the dispersion, so that the spectrum produced by a small prism may be equal to that produced by a larger one upon which the light is less obliquely incident.

In consequence of the dispersion of light, rays passing through a convex lens do not meet at a single point or focus (Pl. XII. fig. 20), but form as many foci as there are coloured rays.

When the spectrum is received upon a convex lens, the coloured rays are brought to a focus, and the light appears again white; for it is only when the primary-coloured rays are parallel, and seen close together, that they produce the impression of white or colourless light. The spectra produced by different dispersive media not only differ in length, but also in the breadth of the coloured spaces not being in the same ratio to each other; hence the spectra are said to be irrational, or the dispersion is said to be irrational.

Vision.—The visibility of an object depends upon the rays of light which emanate from each point of its surface presented to the eye being brought to a focus upon the ret´ina or expansion of the nerve of sight lining the inside of the back of the eye; so that, an image of each point being impressed upon the retina, the sum of the images forms the compound image of the entire object.

The manner in which the image is formed is shown in Pl. XII. fig. 21, in which, to prevent confusion, the rays coming from three points of the arrow only have been represented. The rays diverging from these three points, a b c, form cones in contact by their bases; the apex of each cone outside the eye being situated at the points a b c, the common base of each being situated at the crystalline lens x, immediately behind the pupil or rounded aperture in the coloured curtain of the eye, called the iris, i i, and which limits the base of the cones. The apices of the cones within the eye, a´b´c´, are formed by the rays brought to foci upon the retina by the crystalline lens. The marginal cones of rays coming from the object cross within the eye, so that the uppermost rays from the object become lowermost upon the retina, and thus an inverted image of the object is formed. This appears to the eye to be erect, because the eye or rather the mind judges the parts of an object to be situated in that direction in which the rays coming from them are impressed upon it. Hence, as in fig. 21, the rays impressed upon the retina at the lower part a´, appear to come from the upper part of the cross, although they are lowermost in the image, and so on for the other rays. For distinct vision the rays of each cone must be parallel, or nearly so.

Angle of Vision.—The marginal rays coming from the object cross at a point corresponding to the centre of the pupil, and thus form an angle, as seen in fig. 22, where the cones are omitted, to avoid confusion; this angle is the angle of vision. Now the size which objects appear to possess is measured by this angle, or by the linear magnitude of their images (i. e. their size estimated in one direction, as of length or breadth) upon the retina. When the object is distant, the angle and its linear magnitude are small, and it appears small and distant; whilst if it be large, or if small and brought near the eye, the reverse will be the case.

Magnification.—Hence an object may be made to appear larger, or may be magnified, by increasing the linear magnitude of its image upon the retina, which can be done by bringing it nearer the eye, as shown in fig. 22, where the image of b formed at b´ is larger than the image of a formed at a´. But when an object is brought nearer the eye than about 8 or 10 inches (for the distance varies with different persons), its image becomes indistinct and misty; and this because the rays composing the cones are too divergent to meet at a focus upon the retina, as shown in fig. 23. By interposing a convex lens, however, between the eye and the object, the too divergent rays may be made to meet at a focus upon the retina, as in fig. 24, the object at the same time being rendered apparently larger or magnified, from the refracting action of the lens upon the cones.

Aplan´atism (a, not, p?a???, to wander).—The effect of spherical aberration in rendering the image of an object seen through a lens indistinct and misty may now be intelligible. In order that such image may be distinct, the rays emanating from each point of the object must converge at one spot upon the retina. But since, when spherical aberration exists, the marginal rays are more refracted than the central ones, they will meet at foci before those formed by the latter; and when the foci of one set are coincident with the retina, so that the image would otherwise be distinct, the latter is rendered confused and indistinct by the rays of the other set.

In this consideration, we imply that there are only two sets of rays, the central and the marginal; but the central and marginal rays are not separate, for the rays possess every intermediate degree of obliquity, hence the foci and images are really innumerable.

Now there are evidently two methods of destroying or correcting spherical aberration, viz. by excluding the marginal rays, or by altering their direction.

The exclusion of the marginal rays is often adopted; and is effected by means of a diaphragm, or stop as it is called. This consists of a plate of metal, with a round aperture in the middle, and it is placed behind the lens; but it has the serious defect of diminishing considerably the amount of light transmitted.

The alteration of the direction of the marginal rays is produced by refraction, a thin plano-concave lens being placed in front of the convex one (Pl. XII. fig. 25). The doubly convex lens is composed of crown glass, and the concave lens of flint glass, which has a higher refractive and dispersive power than crown glass. In this way we get a compound lens, which, if the two lenses had the same refractive power, would simply amount to a plano-concave lens with the marginal portions removed. But as the concave lens consists of more highly refracting material than the convex, if the curve and thickness of the two lenses be properly adapted, the marginal portions of the concave correct the too great convergence of the marginal rays produced by the convex lens, and so the rays are brought to nearly the same focus. An idea of this action may be obtained from fig. 25, the dotted lines indicating the direction which the rays would take, if passing through the convex lens only.

A lens in which the spherical aberration is corrected is said to be aplanatic.

AchrÓmatism.—Supposing the spherical aberration of a lens to be corrected, there still remains the chromatic aberration (p. 173); for although the central or mean coloured rays may meet at a focus, the other coloured rays belonging to the same compound or ordinary ray will meet at different foci, so that a series of coloured images of the object will be formed at different distances from the lens; hence, at whichever focus the object is viewed, it will appear coloured.

Now the coloured primary rays can only be made to coincide in direction, so that the light parts of an object may appear white, by refraction. And the correction is produced by the same plano-concave lens as that which corrects the spherical aberration. But in this case the relative dispersive powers of the media composing the convex and the concave lenses form the point to be considered. If the dispersive power of the media of which the convex and concave lenses are composed were the same, the dispersive power of the convex lens would be in excess, and the coloured rays in each compound ray could not become parallel. But by forming the concave lens of a more highly dispersive medium, with a less proportional mean refraction than the convex, when the curves of the surfaces and the relative thickness of the lenses are properly adjusted, the dispersive action of the concave lens may be made equal to that of the convex; and being exerted in the opposite direction, the coloured rays will become parallel and meet at a single focus.

This may be elucidated by considering the lenses as composed of prisms. Thus, let fig. 28 represent the compound lens, the two halves of the doubly convex lens acting as two triangular prisms (fig. 19) with their bases opposed, converging the compound white rays w w, and dispersing the coloured elementary rays, which would form spectra at s s. In the plano-concave lens the triangular prisms may be considered as placed with their apices towards each other, and so would tend to disperse the coloured rays in the opposite direction, to form spectra at t t. Then, supposing the dispersions to be equal and in opposite directions, the coloured rays would become parallel and meet at a definite focus, the colour being destroyed. At the same time, the spherical action of the concave lens being opposite to that of the convex, the converging action of the latter will be diminished, so that the focus of the compound lens will be longer than that of the convex alone; but as the dispersive power of the concave is greater relatively than that of the convex, the mean refraction is less altered than the refraction or dispersion of the separate coloured rays; so that the concave wholly opposes or corrects the dispersion produced by the convex, while it only partially corrects its mean refraction.

A lens in which the chromatic and spherical aberrations are corrected or destroyed is commonly called achromatic; although the term properly applies to the correction of the colour only.

If in a compound lens the chromatic aberration is only partially corrected, so that the red rays still meet at a focus beyond the violet, as in a simple uncorrected lens (fig. 20), the lens is said to be under-corrected, or the aberration to be positive; while if the correcting action of the plano-concave lens be too great, so that the violet rays meet before the red, as in a simple concave lens, the lens is said to be over-corrected, and the aberration is called negative. Although the positive chromatic aberration of the extreme rays passing through a convex lens may be corrected by the negative aberration of a concave lens, there still remains a certain amount of uncorrected colour, arising from the irrationality of the spectra of the two refracting media. This evil cannot be overcome, and the remaining colour is said to arise from the secondary spectrum.

The object-glasses of the microscope, consisting of the compound lenses, have their aberrations balanced to a considerable extent on the above principles—the lowest combination being under-corrected, while the upper combinations are over-corrected; and, by suitable adaptation of their distance from each other, further correction may be obtained, the aberration of the object-glass altogether being, however, over-corrected or negative.

The eye-piece consists of two simple plano-convex lenses, the upper or eye-glass (fig. 27 e) having a shorter focus than the lower (f) or field-glass, and the two placed at the distance of half the sum of their focal lengths. The object-glass alone would form an enlarged and reversed image of the object within the body of the microscope, the cones of rays from each point of the object terminating at the larger arrows in the figure (fig. 27). But the rays meeting the field-glass are brought by it to a focus at the position of the smaller arrows, where they form a reduced image; and, subsequently passing through the eye-glass, they are so altered in direction as to enter the eye at a greater angle, and to present a magnified image of the object.

The eye-piece produces several important effects. The refraction being produced by two less convex lenses instead of one of greater convexity, the spherical aberration is considerably reduced; and the convexities of the lenses in the eye-piece being situated in an opposite direction to that of those in the object-glass, the spherical aberration of the former reverses and so neutralizes that of the latter. Also the under-correction of the field-glass compensates the over-correction of the object-glass—the blue rays which are refracted more than the red by the field-glass, being thrown upon the eye-glass nearer its centre, where the refraction is less, and thus the coloured rays become parallel or nearly so on reaching the eye. Moreover the field-glass collects a larger number of rays than the eye-glass could do alone, so that it enlarges the field and increases its brightness.

In the best object-glasses the aberrations are so well balanced that the mere covering an object with thin glass is sufficient to disturb the balance and render very delicate markings either misty and coloured or wholly invisible. The effect produced by a plate of glass may be understood by reference to fig. 26, the rays being supposed to emanate from the object at a; and it is evident that the refraction of the glass so alters the direction of the rays that they will fall upon the lower combination nearer the centre than if the cover were absent, and thus negative aberration is produced. In the best object-glasses, however, this aberration may almost entirely be removed, the lower combination being susceptible of approximation by a screw movement to the second or next above it, so that the ascending rays, being able to continue their oblique course through the increased distance between the object and the lower combination, may fall upon the same portions of the latter that they did before the cover was applied.

Polarization of Light.—In attempting to give a sketch of this curious and difficult subject, we must suppose the reader to be in possession of a natural crystal of calcareous spar, and either two Nicol’s prisms (forming the ordinary polariscope) or two plates of the mineral called tourmaline cut in the direction of the length or axis of the crystal.

Hitherto we have considered rays of light falling upon transparent substances as simply refracted or reflected according to the ordinary laws of refraction or reflexion. We have now to notice some curious exceptions, forming the basis of many interesting phenomena, especially in connexion with the microscope, in which these laws are more or less deviated from. If we place a plate of tourmaline, cut as above directed, upon or beneath the stage of the microscope, the light will pass through it, appearing tinged with the green or brown colour natural to the tourmaline; but on laying another slice upon the eye-piece, and turning the latter round or rotating it, the light will be transmitted in certain positions only, being partially or entirely arrested in others, so that the field appears black. And, on careful examination, it will be noticed that the change from black to white occurs at each quarter of a rotation, being twice black and twice white in an entire rotation, the changes occurring alternately. The same phenomena may also be exhibited by substituting two Nicol’s prisms for the tourmalines.

Again, if we take a natural crystal of calcareous spar, and paste upon one side of it a piece of black paper with a small hole in the middle, on holding the crystal to the light or over a piece of white paper, with the covered side next the light, two holes or two images of the hole will be seen; and if the crystal without the paper be placed over some print, the print will appear double. Hence the light passing through the hole is twice or doubly refracted, one ray following the ordinary law of refraction, while the other follows a different law, being retarded and pursuing a longer course; and so the two rays are called respectively the ordinary and extraordinary ray. And on viewing these through a tourmaline or a Nicol’s prism, as in the experiment with the two tourmalines, the images will become alternately visible and invisible, just as was then the case with the entire mass of light.

The light which has undergone this singular change is said to be polarized, because the rays appear to have acquired poles or sides. In the above experiments the lower prism or tourmaline is called the polarizer, because it polarizes the light, and the upper is called the analyzer, because it analyzes or tests the light altered by the former.

An idea of the cause of this change may be obtained by reference to the undulatory theory of light. Ordinary light consists of waves or undulations taking place in planes at right angles to each other, or in all planes; while in polarized light the undulations are all in one plane or in parallel planes. This may perhaps be understood by considering that books in a book-case are situated in parallel planes, the shelves being in planes at right angles to the former. And by imagining in polarizing substances the existence of some structure acting like a grating, a notion can be obtained how the rays in the different planes may be transmitted or intercepted. If the grating be so placed that the bars (representing the planes of polarization) are perpendicular, the books can pass between them; while if the grating be turned round a quarter of a circle, they will become transverse, and the books cannot pass, while the shelves could do so. Carrying on this analogy, the tourmaline or Nicol’s prism polarizes the light by transmitting only those rays whose undulations are in planes parallel to the bars; while the analyzer allows these undulations to pass through it when the direction of the planes coincides with that of the bars, but interrupts them when their direction is at right angles to the bars. And it is evident that the planes of polarization of the ordinary and extraordinary rays are opposite, from the opposite action of the analyzer upon them.

The power of doubly refracting and polarizing is not possessed by all crystalline bodies, but only those belonging to other than the cubic system; crystals belonging to this system neither doubly refract nor polarize light. In all doubly refracting crystals there are one or more lines or directions in which the light is not doubly refracted. These are called the optic axes, and sometimes they coincide with the geometric axis of the crystals, at others they do not; and they may be regarded as positions or directions of equilibrium of certain molecular forces existing within the crystal, which, acting in opposition, neutralize each other.

If light, polarized by the polarizer, be transmitted through thin doubly refracting crystals, and analyzed by the analyzer, splendid colours will become visible; and on rotating separately either the polarizer or the analyzer, at each quarter rotation the colours will change, being complementary to those at first visible, or such as are requisite with the first to make white light. We have seen (fig. 19) that white light consists of seven coloured rays, or of three primary colours—red, yellow, and blue, which, by superposition, form the others; and thus red is complementary to green, which consists of blue and yellow, the two sets of complementary colours appearing and vanishing as the light and darkness did when the crystals were not used.

These colours are produced by interference. The compound rays of white light (fig. 30 l) passing through the polarizer (t) are all polarized in one plane; the crystal (d) depolarizes this light, i. e. doubly refracts and resolves it into two sets of rays polarized in planes at right angles to each other, forming the ordinary, O, and the extraordinary ray, E. Each of these two sets of rays is resolved by the analyzer (s) into two other sets, polarized in planes at right angles to each other; so that in all there are four sets, two in one plane and two in the other; and, the primary rays of the two sets in each plane being in different stages or phases of undulation, in consequence of the retardation of the extraordinary rays, the undulations of certain coloured rays check and annihilate each other, while the remainder or complementary conspire and pursue their course, producing the appearance of colour, this effect being reversed at each quarter-revolution of the analyzer.

An idea of what is meant by phases of undulation may be obtained by reference to fig. 29, in which the undulations, a, b, are in similar states or phases, and so conspire in action, while the wave c is in a different phase and half an undulation behind the others; hence it would check or interfere with either of the other waves (a, b), the etherial molecules of the two, which vibrate perpendicularly or at right angles to the direction of the wave, acting to the same extent and in opposite directions.

In fig. 30 the analyzer is represented as composed of a natural crystal (rhomb) of calcareous spar, which transmits both sets of rays; but in the ordinary analyzer or Nicol’s prism—which is made by dividing a rhomb through the obtuse angles into two wedge-shaped pieces and cementing them together again with balsam, only one set of rays is transmitted at each quarter-revolution, the other being refracted out of the field. In the case of the tourmaline, one of the sets of rays is absorbed; so that the tourmaline, like the Nicol’s prism, is single-imaged.

Thus the colours produced by polarization are the same as those of the spectrum, but separated in a different way, both arising from the elementary coloured rays of the compound white light. For while the spectral rays are separated by dispersive refraction, the polarized coloured rays are separated by the interference and annihilation of some rays, the remainder passing on to produce the colours.

When the position of the depolarizing crystal is such that the plane of the polarized light coincides with the direction of the optic axis or axes, the light is not doubly refracted nor polarized in certain parts; hence these parts appear white if the plane of the polarizer and analyzer coincide, and black if they be crossed. A crystal cut at right angles to its optic axis, with its length directed towards the polarizer and analyzer, is in this position, and it exhibits alternately a black and white cross, with one or two sets of concentric rings of complementary colours at each quarter of a rotation.

To prepare crystals for examination by polarized light, a little Epsom salt, nitre, or borax should be dissolved in water, a drop placed upon a slide, and dried at a gentle heat. The crystals should then be mounted in balsam, and viewed as transparent objects.

To see the cross and rings, the crystals should be sawn or cut across transversely, the ends being polished on a strained piece of silk moistened with water, and the sections mounted in balsam.

The property of doubly refracting and polarizing light is not confined to crystalline substances, being also possessed by many organic bodies, for the details of which I must refer to the article Polarization in the ‘Micrographic Dictionary.’