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ON PHYSICS, OR NATURAL PHILOSOPHY.

No. LIV.

(Continued from page 412.)

THE EYE CONSIDERED AS AN OPTICAL

INSTRUMENT.

Polariscopes or Analysers.-These names are given to small instruments which serve to show when light is polarised and to determine its plane of polarisation. The analysers in most frequent use are a plate of black glass, a thin plate of turmalin, the double refracting prism, Nichol's prism, and the piles of glasses which we have mentioned before.

1. Black Glass.-It will be seen by the figure which we give below (fig. 349) that in the apparatus there represented a black glass, m, shows whether the light is polarised by not reflecting it at the angle of polarisation when the plane of incidence upon this glass is perpendicular to the plane of polarisation; consequently the glass, m, is a polariser.

2. Turmalin.-The most simple analyser is a plate of brown turmalin cut parallel to the axis of crystallisation. This mineral, which is double refracting, has the property of not allowing any but natural light, and light polarised in a place perpendicular to its axis, to pass through it; but it acts as an opaque body with regard to polarised light whose plane of polarisation is parallel to the axis. To make use of this analyser, we interpose it between the eye and the luminous pencil which we wish to observe. We then turn the turmalin slowly in its own plane, and if the pencil always exhibits the same intensity, it does not contain polarised light; but if the brightness successively decreases and increases, the pencil contains so much more polarised light as the variations of brightness are more considerable. At the moment when it is least, the plane of polarisation is determined by the axis of the turmalin and by the visual ray. It is the extraordinary ray which goes through turmalin cut parallel to the axis; the ordinary ray is completely absorbed, at least if the turmalin is sufficiently coloured.

3. Double Refracting Prism.-Double refracting prisms are made of Iceland spar, and employed as analysers in many optical instruments, particularly in Biot's apparatus for studying circular polarisation (fig. 351). It is necessary for these prisms to be achromatic, for when the light which passes through them is not simple, it is decomposed by refraction. For this purpose we attach to the prism of Iceland spar a second prism of glass placed at such an angle that, by refracting the light in an opposite direction, it almost completely destroys the effect of dispersion.

The double refracting prism being fixed at the extremity of a copper tube (fig. 346), we know that a luminous pencil Fig. 346.

transmits only a single polarised ray in the direction of its axis. To form it, take a parallelopiped of Iceland spar about an inch and a half to two inches and a half high, and about a third of an inch broad. Cut it in two, in a plane perpendicular to the plane of the large diagonals of the bases, and passing through the obtuse vertices which are nearest each other. Then join the two halves in the same order as balsam of Canada. The parallelopiped thus constructed constitutes Nichol's prism (fig. 347). The index of refraction for balsam of

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the ordinary ray undergoes a total reflection on the surface, ab, and takes the direction co, while the extraordinary ray ce alone passes through; that is to say, Nichol's prism, like turmalin, only allows the extraordinary ray to pass through it, and may therefore be used as an analyser. It is also employed to obtain a pencil of white polarised light. The double refracting prism is also employed for the same purpose.

Noremberg's Apparatus.-Noremberg has invented an apparatus, by means of which, at no great expense, most of the experiments relating to polarised light may be performed.. This apparatus is composed of two upright supports, b and d, fig. 349, made of copper, which sustain a glass n, not plated, and Fig. 350.

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Fig. 349.

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which is made to pass through this tube is completely polarised, when on turning the tube about itself, we find four rectangular positions in the course of one revolution in which we perceive only one image. It is the ordinary image which disappears when the plane of the principal section is perpendicular to the plane of polarisation, and it is the extraordinary image which disappears whenever the plane of polarisation coincides with the principal section. In all other positions which the double refracting prism assumes, the relative intensity of the images varies. We see, at the same time, that the double refracting prism may serve to determine the direction of the plane of polarisation, since it is sufficient to seek for that position of the principal section of the prism in which, the incident pencil being perpendicular, the extraordinary image disappears. Nichol's Prism.-This is the most valuable analyser, because it is altogether colourless, completely polarises the light, and

VOL. V.

132

moveable about a horizontal axis. A small circle e, at the side of it, which is graduated, shows the angle made by the glass with the vertical line. Between the feet of the two supports is a plated glass p, which is fixed and horizontal. At the top of the supports is a graduated rim i, in which a circular disc o, can turn round. This last, in the centre of which is a square opening, contains a black glass m, making, with the vertical, an angle equal to that of polarisation. Lastly, an annular disc k, is capable of being fixed at any height by means of a thumb-screw. A second circle a, supported by the other, is capable of being inclined at various angles, and has a screen e, with a circular opening at its centre.

Supposing the glass n, to make with the vertical an angle of 35° 25', that is to say, an angle equal to the angle of polarisation for glass, the luminous rays sn, which meet this glass at that angle, are polarised on reflection in the direction ap towards the glass p, which sends them back in the direction par. After having gone through the glass n, the polarised pencil falls on the black glass m, at an angle of 35° 25', since this glass makes precisely the same angle with the vertical. Now, if we move the disc o, to which the glass m is fixed, horizontally, the glass will also move, but without altering its inclination, and two positions will be observed in which it does not reflect the incident pencil nr, that is, when the plane of incidence upon this glass is perpendicular to the plane of incidence cnp on the glass n. Such is the position represented in the accompanying figure. In every other position the polarised pencil is reflected by the glass m, in various degrees, and the maximum of light is reflected when the planes of incidence on the glasses m and n are parallel. If the glass , makes with the vertical an angle greater or less than 35° 25', the polarised pencil is always reflected in all positions of the plane of incidence.

When, instead of receiving the polarised light on the black glass m, it is received by a double refracting prism placed in a tabe g, fig. 350, we obtain only one image whenever the plane

ing prism, and turned about itself, the polarised pencil com-
pletely disappears when the axis of the turmalin is parallel to
the plane of incidence s np.
Thus the different properties of polarised light may be
demonstrated. Noremberg's apparatus may also be employed
in the observation of the colours of polarised light, and the
study of circular polarisation in quartz.

CIRCULAR POLARISATION.

Rotation of the Plane of Polarisation.-When a polarised ray passes through a plate of quartz cut perpendicularly to the axis of crystallisation, this ray is again polarised on emerging, but no longer in the same plane of polarisation as before its entrance. With some specimens, the new plane is turned to the right of the old one, with others to the left. To this phenomenon is given the name of circular polarisation. It was first observed by Seebeck and Arago, but was particularly studied by Biot, who established the following laws.

1. The rotation of the plane of polarisation is not the same for the different simple colours, and is greater in proportion as the colours are more refrangible. 2. For the same simple colour, and plates of the same crystal, the rotation is proportional to the thickness. 3. In the rotation from right to left, or from left to right, the same thickness gives apparently the same rotation.

Substances which turn the plane of polarisation to the right, are called dextrogyral (that is, turning to the right). To this class belong sugar dissolved in water, essence of lemon, alcoholic solution of camphor, dextrine and tartaric acid. Substances which turn the plane of polarisation to the left, are called lævogyral (that is, turning to the left). Essence of turpentine, essence of laurel, and gum Arabic, come under this head.

Coloration produced by Circular Polarisation.-On looking with a double refracting prism at a thin plate of quartz cut perFig. 851.

h

n

of the principal section of the prism coincides with the plane of polarisation on the glass n, and then it is the ordinary ray which is transmitted. Only one image also is seen when the plane of the principal section is perpendicular to the plane of polarisation, and it is the extraordinary image which then passes. In every other position of the double refracting prism, two images are seen, the brightness of which varies with the position of the principal section.

Lastly, if turmalin be substituted for the double refract

pendicularly to the axis and traversed by a pencil of polarised light, we observe two images brightly coloured, whose colours are complementary. On then turning the prism to the right or left, the two images change colours, and successively assume all the colours of the rainbow, still continuing to be complementary to each other. This phenomenon is a consequence of the first law of circular polarisation. It may be very well observed by means of Noremberg's apparatus, fig. 349. For this purpose, place upon a screen e, fig. 350, a plate of quartz

s, cut perpendicularly to the axis and fixed in a cork. Then the glass n, fig. 349, being inclined in such a manner as to transmit a polarised pencil to the quartz, look through a double refracting prism g, fig. 350, at the same time turning the tube in which this prism is, and you will observe the complementary images produced by the passage of the polarised light through the quartz.

Rotatory Power of Liquids.-Quartz is the only solid in which circular polarisation has been observed, but Biot found the same property in many liquids and solutions. The same philosopher observed that the displacement of the plane of polarisation may exhibit differences in the composition of bodies, which could not be detected by any chemical analysis. For example, sugar obtained from the grape turns the plane of polarisation to the left, while sugar from the cane turns it to the right, though the chemical composition of the two substances is the same. Biot found that the rotatory power of liquids is much less than that of quartz. For instance, in concentrated syrup of sugar from the cane, which is one of the liquids possessing the rotatory power in the highest degree, this power is thirty-six times less than in quartz, in consequence of which it is necessary to experiment upon liquid columns of considerable length, that is to say, about | eight inches.

Fig. 351 represents the apparatus employed by Biot to measure the rotatory power of liquids. In a copper channel 9, fastened to a support r, is a tube about eight inches long, containing the liquid on which we wish to experiment. This tube

ether, which shows that the plane of polarisation has not turned. But if we fill the tube with a solution of cane sugar, or any other active liquid, the extraordinary image reappears, and to destroy it we must turn the disc a certain number of degrees to the right or left of zero, according as the liquid is dextrogyral or lævogyral, which proves that the plane of polarisation has turned through the same number of degrees. With solution of cane sugar, the rotation takes place to the right, and if with the same solution we take tubes of greater length, we find the rotation is increased in proportion to the length, according to Biot's second law. Lastly, if with a tube of constant length we take solutions containing more and more sugar, we find the rotation increase in proportion to the increase of sugar, whence we see that from the angle of deviation we may deduce the quantitative analysis of the solution.

Soleil's Saccharimeter.-Soleil availed himself of the rotatory property of liquids, which was discovered by Biot, to construct an apparatus for analysing sacchariferous (or sugar-bearing) substances, to which is given the name of saccharimeter. Fig. 352 represents the saccharimeter placed horizontally, and fig. 353 represents a longitudinal section, with all the recent modifications introduced by Doboscq, Soleil's son-in-law and successor. This instrument, which is apparently simple, is very complicated in a theoretical point of view, for it presupposes a knowledge of the principal phenomena of double refraction and polarisation. The principle of this apparatus is not the amount of the rotation of the plane of polarisation,

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is plated internally and terminated at the ends by two parallel glasses, fastened by two collars with screws. At m is a black glass, making with the axis of the tubes b, d, and a, which is the same for all three, an angle equal to the angle of polarisation, the consequence of which is, that the light reflected by the glass m in the direction b da, is polarised. In the centre of the divided circle h, in the tube a, and perpendicular to the axis b da, is a double refracting achromatic prism, which can be turned at will round the axis of the apparatus by means of a button n, fastened to a dial plate with a vernier, which indicates the number of degrees through which the prism is turned. Lastly, the plane of polarisation so d, of the reflected pencil is vertical, and the zero of the graduation on the circle h, is in this plane. Before the tube d, is placed in the channel 9, the extraordinary image given by the double refracting prism vanishes, as often as the disc c, corresponds to the zero of the graduation, because then the double refracting prism is turned in such a manner, that its principal section coincides with the plane of polarisation. It is the same when the tube d is full of water or any other inactive liquid, like alcohol or

like that of Biot, above described, but compensation, that is to say, the employment of a second active substance, acting in a direction opposite to that in which we wish to analyse, and the thickness of which may be varied until the contrary actions of the two substances destroy each other; so that, instead of measuring the deviation of the plane of polarisation, we measure the thickness to be given to the compensating substance (which is a plate of quartz), to obtain a complete compensation. There are three principal parts in the apparatus; a tube containing the liquid to be analysed, a polariser, and an analyser. The tube m, which contains the liquid, is of copper, plated inside, and terminated at its two extremities by two glasses parallel to each other. It rests upon a support k, which has at its ends two tubes, a and r, in which are the crystals that serve as polarisers and analysers, and are represented in fig. 353.

Before the orifice e (fig. 353) is placed a moderator lamp, the light proceeding from which, in the direction of the axis of the instrument, meets a double refracting prism r, which acts as a polariser. Only the ordinary image reaches the eye,

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the extraordinary image being thrown back beyond the field of vision, in consequence of the magnitude of the angle between the ordinary and extraordinary images. Lastly, the double refracting prism is in such a position that the plane of polarisation is vertical, and passes through the axis of the apparatus.

On leaving the double refracting prism, the polarised pencil meets a plate of quartz q, which has a double rotation, that is to say, it turns the plane of polarisation both to the right and the left at the same time. For this purpose it is formed of two plates of quartz, with contrary rotation, placed side by side, as shown in fig. 356, in such a manner that the line of separation is vertical, and in the same plane as the axis of the apparatus.

After having passed through the quartz q, the polarised pencil passes into the liquid contained in the tube m, and there meets with a fresh plate of quartz i, which is simple and of arbitrary thickness.

the phenomenon of diffraction, let a pencil of light pass through a very small aperture in the window-shutter of a dark room, and let it fall upon a convergent lens L, with short focal distance (fig. 357). Place a red glass at the aperture so as to Fig. 357.

B

allow none but red light to pass. An opaque screen e, with a thin edge, placed behind the lens and beyond its focus, intercepts half of the luminous cone, while the other half is projected upon a screen b, the front view of which is at B. We then observe, within the geometrical shadow bounded by the straight line ab, a reddish and rather bright light, which decreases in brightness in proportion as the points of the screen are more distant from the boundary line of the shadow, and on the part of the screen which ought to be uniformly lighted are seen fringes alternately bright and dark, which grow gradually feebler till they completely disappear. All the various colours of the spectrum give rise to the same phenomenon, but with this distinction, that the fringes are narrower, and consequently less dilated, in proportion as the light is less refrangible. The result of this last property Fig. 353.

At n is the compensator intended to destroy the rotation of the liquid column m. It is formed of two plates of quartz, having the same rotation, whether to the right or left, but contrary to that of the plate i. These two plates of quartz, sections of which are represented in fig. 360, are made by obliquely cutting a piece of quartz with parallel faces, in such a manner as to form two prisms with the same angle N and N'. Then by placing the two prisms side by side, as represented in the figure, we get a single plate with parallel faces, which possesses the advantage of being capable of varying in thick

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ness.

Fig. 354.

For this purpose both prisms are fixed in a groove in such a manner as to be capable of sliding in one direction or the other, still preserving their parallelism to the homologous faces.. This motion is produced by means of a double-toothed wheel and a pinion turned by the button b (figs. 352 and 353).

When the plates are displaced in the directions indicated by the arrows in fig. 354, it is evident that their combined thickness increases, and when they are moved in the opposite directions it is diminished. A scale e, and a vernier (fig. 352) follow the plates in their motions and serve to measure the variations of thickness in the compensator. This scale, which, with its vernier, is represented in fig. 355, has two sets of divisions with the same zero for both, the one from left to right for dextrogyral liquids, and the other from right to left for lævogyral liquids. When the vernier is at zero, the combined thickness of the two plates N and N' is precisely equal to that of the plate i, and as the rotation of this latter is contrary to that of the compensator, the effect is nothing. But if we move the plates of the compensator in either direction, this or the quartz i overbalances the other, and there is rotation to the right or left. Next to the compensator, there is a double refracting prism s, which serves as an analyser for the observation of the polarised pencil which has passed through the of quartz. liquid and the various plates Diffraction is a modification to which light is subject when it grazes the outline of a body or passes through a very small opening, a modification in consequence of which the luminous rays appear to bend and penetrate into the shade. To observe

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is, that when we make the experiment with white light, the fringes of each simple colour being separated by their unequal dilation, those which are formed on the screen в exhibit all the colours of the rainbow.

If, instead of interposing between the lens L and the screen b the edges of an opaque body, we put an opaque body which is very narrow, as e. g. a hair or a fine metallic thread, we not only still observe the alternately dark and bright fringes on both sides of the portion of the screen which corresponds to the geometrical shadow of the body, but even in this shadow we perceive the same alternations of dark and bright bands, that is to say, exterior and interior fringes are then produced.

It was Father Grimaldi, of Bologna, who first made known the phenomenon of diffraction and fringes, in 1663, but without giving any explanation of it. Newton tried to explain diffraction in accordance with his theory of the diffusion of light by the emission of rays, but did not account for the interior fringes. Thomas Young also failed to give a satisfactory explanation, but Fresnel explained all the phenomena in Interferences.-This name is given to the mutual action of accordance with the theory of luminous undulations. luminous rays when, having been emitted from the same source, they meet at a very small angle. This action may be easily observed by the following experiment. Through two very small circular apertures of the same diameter and very near each other, two pencils of homogeneous light--as red light, for example-are introduced into a camera obscura, which is accomplished by placing red glasses at the openings so as

to let none but red light through. The two pencils forming, after their entrance into the chamber, two luminous cones, which meet at a certain distance, are received a little beyond the point of their meeting on white paper, and in the common segment of the two discs formed upon this screen, fringes are then observed of remarkable darkness, forming alternations of red and black. But if we close one of the apertures, the fringes disappear, and are replaced by a pretty uniform red tint. From the disappearance of the dark fringes on closing one aperture and intercepting one of the pencils, we conclude that they are the result of the meeting of the two pencils which cross one another obliquely.

This experiment we owe to Grimaldi, who drew from it the remarkable inference, that light added to light produces darkness. In the above experiment there is diffraction because the rays graze the edges of the openings; but without this phenomenon two pencils may be made to interfere by means of the following apparatus of Fresnel.

tints, especially by reflection. Crystals which split into very thin leaves, as mica and gypsum, present this phenomenon; so also do mother-of-pearl and glass when blown into very thin balls. A drop of oil suddenly let fall into a large quantity of water exhibits the same colours of the spectrum in a constant order. A soap bubble appears white at first, but, as we keep on blowing it, we see beautiful rainbow tints appear, especially at the upper part, where the liquid is thinnest. These colours are arranged in concentric horizontal zones round the top, which becomes black when there is no longer thickness enough to reflect the light, and the bubble suddenly

bursts.

Newton was the first who studied the phenomenon of coloured rings in soap-bubbles. Wishing to ascertain the relation existing between the thickness of the thin plate, the colour of the rings, and their size, he produced them by means of a layer of air between two glasses, the one plane and the Fig. 359.

Fig. 360.

Two plane metal mirrors м and N (fig. 358) are placed side by side in such a manner as to form a very obtuse angle MON. A semi-cylindrical lens L, with short focal distance, concentrates in front of the mirrors a pencil of red light introduced into a camera obscura, which falls partly on one of the mirrors and partly on the other. The luminous waves, after having been reflected, meet at a very small angle, as seen in the figure, nearer the mirror N than м'; and if they are then received on a white screen, we observe upon it bands alter- other convex, with very long focal distance (fig. 359). If the nately dark and bright, parallel to the line of intersection of two surfaces have been very carefully wiped and exposed to

Fig. 358.

the two mirrors, and symmetrically arranged on both sides of the plane o KA, which passes through the line of intersection of the mirrors and bisects the angle which the reflected rays form with one another. If we stop the light from falling on one of the mirrors, the fringes disappear as in the preceding experiment. Lastly, if we make the pencil, after being reflected by one of the mirrors, pass through a plate of glass with parallel surfaces, all the fringes are removed to the right or left, at a distance proportional to the thickness of the plate. This last experiment shows that the mutual action of the rays which meet is modified by the substance through which they pass, and it has been hence inferred that light is diffused less rapidly through glass than air.

Colours of Thin Plates; Newton's Rings.-All diaphanous bodies, whether solid, liquid, or gaseous, on being reduced to sufficiently thin plates, appear coloured with extremely bright

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daylight at a window, in such a manner as to see them by reflection, we perceive at the point of contact a black spot surrounded with coloured rings to the number of six or seven, the colours of which gradually grow feebler. If the glasses are seen by transmission, the centre of the rings is white (fig. 360), and the colours of each of them are exactly complementary of those of the rings seen by reflection. With a homogeneous light, as e. g. red, the rings are successively black and red, and with a diameter smaller in proportion to the refrangibility of the colour. But with white light the rings are coloured with the different colours of the spectrum. If the focal distance of the lens (fig. 359) is from ten to thirteen feet, the rings may be observed with the naked eye; but if the focus is nearer, we must look at the rings through a lens.

The colouring of thin plates and Newton's rings is an instance of the phenomenon of interference.

LESSONS IN MORAL SCIENCE.-No. II.
WHETHER CONSCIENCE IS THE SAME AS THE UN-

DERSTANDING, OR A FACULTY DIFFERENT FROM
AND INDEPENDENT OF IT.

SOME have maintained that our moral feelings and judgments
are the exercise of a peculiar sense, and that the perceptions
and feelings of this sense cannot be referred to the under-
standing. Such as maintain this theory suppose, also, that

the dictates of conscience are infallibly correct, if the mind is in a proper state.

the judgments of the understanding, in regard to moral duty, and that, of course, an error in the judgment or the understanding must affect the decisions or dictates of conscience. To clear this subject, if possible, from all obscurity and perplexity, we will make the following remarks:

Others have maintained that the dictates of conscience are

1. The exercise of the moral faculty, or conscience, is not simply an intellectual act; it is complex, including two

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