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If a ray of light pass through a plate of quartz which has been cut perpendicularly to the axis, or line parallel to the main planes bounding the crystal, it is as usual divided into two; but the vibrations in each ray, instead of being rectilinear and at right angles to one another, are circular and in opposite directions. That is to say, if the motion of vibration in one ray is directed like the hands of a clock, that in the other is directed in the opposite sense; and the light in each ray is then said to be circularly polarised. The motion of a series of particles of ether, which when at rest lie in a straight line, is circular, and, as in plane polarisation, successive; and consequently, at any instant during the motion such a series of particles will be arranged in a helix or corkscrew curve. The sweep of the helix will follow the same direction as that of the circular motion ; and, on that account, a circularly polarised ray is spoken of as right-handed or lefthanded, according to the direction of motion. A righthanded ray is one in which, to a person looking in the direction in which the light is moving, the plane of vibration appears turned in the same sense as the hands of a watch. Or, what is the same thing, to a person meeting the ray, it appears turned in the opposite sense, viz., that in which angles when measured geometrically are usually reckoned as positive.

The question, however, which mainly concerns us is the condition of the vibrations after emerging from the plate of quartz and before entering the analyser. In the passage of the ray through the plate the ether is subjected to a double circular motion, one right-handed, the other left-handed; but, as one of these motions is transmitted with greater velocity than the other, it follows that at any given point and at the same instant of time one of the revolutions will, in general, be more nearly completed than the other, or, to use an expression adopted in plane polarisation, there will be a difference of phase. The motions may be represented by two clock hands moving at the same rate in opposite directions, and the difference of phase by the angle between them when one of them is in the position from which angles are reckoned. As both are supposed to move at the same rate, they will have met in a position midway between their actual positions ; and if we consider a panicle of the ether (say) at the extremity of the clock-hands, it will be solicited when the hands are coincident by forces producing two opposite circular motions. Now, whatever may have been the forces or structural character within the crystal whereby this double circular motion is perpetuated, it is clear that when the ray emerges into air the particle of ether immediately contiguous to the surface of the crystal will be acted on by two sets of forces, one whereby it would be caused to follow the right-handed and the other the left-handed rotation. Each of these may, as is well known, be represented by a pair of forces, one directed towards the centre of the circle, the other in the direction of the motion and at right angles to the first, or, to use geometrical language, one along the radius and towards the centre, the other along the tangent and in the direction of the motion. The two forces acting along the tangent being in opposite directions will neutralise one another, and the resultant of the whole will, therefore, be a force in the direction of the centre. The particle in question, and consequently all those which following in succession serve to compose the entire ray until it enters the analyser, will vibrate in the direction of the diameter drawn through the point under consideranon ; or, to express it otherwise, the ray will be plane-polarised, and the plane of vibration will be inclined to the plane irom which angles are measured by an angle equal to half the, oiiference of phase on emergence due to the thickness of the crystal. The retardation being the same absolute quantity for all rays, will, as in the case of plane polarisation, be a different fraction of the wave-length for rays of different colours, and will be greater for the shorter waves than for the longer. Hence

the planes of vibration of the different coloured rays, after emerging from the quartz, will be differently inclined. Each ray will therefore enter the analyser in a condition of plane polarisation; and if the analyser be turned round, it will cross the vibrations of the various coloured rays in succession, and extinguish each of them in turn. Each of the images will consequently exhibit a gradual change of colour while the analyser is being turned; and the tints will be, as explained before, complementary to those which are successively extinguished. For a given plate of quartz the order of the tints will be reversed when the direction of rotation of the analyser is reversed. But it should be here explained that there are two kinds of quartz, one called right-handed and the other left; and that, for a given direction of rotation of the analyser, these cause the colours to follow one another in opposite orders. A similar effect is produced by turning the polariser round in the opposite direction.

The angle of rotation of the plane of vibration for any particular colour varies, as stated above, with the thickness of the plate ; while for a given thickness it increases nearly as the square (product of the quantity into itself) of the wave-length decreases. In mathematical language it varies approximately inversely as the square of the wave-length. If this law were accurately true, the product of the angles of rotation into the square of the corresponding wave-lengths (X) would be the same for all rays. The following are some measurements made by Brock, with a quartz plate one millimetre thick, which show that the law may be considered as true for a first approximation.

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If the colours exhibited by a plate of quartz when submitted to polarised light be examined by a spectroscope, in the way described when we were speaking of selenite, the spectrum will be found to be traversed by one or more dark bands, whose position and number depend upon the thickness of the plate. But there will be this difference between plane and circular polarised light, that if the analyser be turned round, the bands will never disappear, but will be seen to move along the spectrum in one direction or the other, according as the plate of quartz be right-handed or left-handed, and according to the direction in which the analyser is turned. This is, in fact, identical with the statement made before, that the analyser in its different positions successively crosses the plane of vibration of each ray in turn, and extinguishes.it.

This being so, it is clear that a change of colour exhibited by a quartz plate when submitted to plane-polarised light and examined with an analyser, forms a test of a change in the plane of original polarisation. And if the plate be composed of two parts, one of right-handed, the other of left-handed quartz, placed side by side, any change in the plane of polarisation will affect the two parts in opposite ways. In one part the colours will change from red to violet, in the other from violet to red. At two positions of the polariser, or analyser, the colours must be identical. With plates, as usually cut, one of these identities will be in the yellow, the other at the abrupt passage from violet to red, or vice vend. In this case the field appears of a neutral tint, teinie sensible or teinte de passage, as the French call it, and the slightest change in the plane of polarisation exhibits a marked distinction of colour, one part verging rapidly to red, the other to violet. This arrangement is called a biquartz, and affords a very delicate test for determining the posi

Ition, or change of position, of the plane of polarisation, especially in cases where feebleness of light or other circumstance interfere with the employment of prismatic analysis.

If the thickness of the plate be such that the difference of rotation of the planes of vibration of the rays corresponding to the two ends of the visible spectrum (or, as it is sometimes termed, the "arc of dispersion") be less than 180°, there will be one dark band in the spectrum; because there can then be only one plane of vibration at a time at right angles to that of the analyser. If the arc of dispersion is greater than 18o° and less than 3600, there will be two bands. And so on for every 1800 of dispersion.

This mode of examination by means of prismatic analysis is the most accurate yet devised for measuring the angle of rotation produced by circular polarisation; especially if solar light be employed, and the fixed lines used to form a scale of measurement.

The property of circular polarisation is, however, not confined to quartz. Among solids, chloride of sodium is the only other known instance, but among fluids and fluid solutions there are not a few.

The following list is given by Verdct. The angles have reference to the red rays given by a plate of glass coloured with oxide of copper, and are affected with the sign -f- in the case of right-handed, and with — in the case of left-handed rotation. The length of the column of the solution is in every case one decimetre.

— 29° 6

+ 55°-3
+19° 08

+ 7i>"'94

— o°'7o
+ I3°i6
+ 65°79
+ 2° 02
+ I6°i4

+ 2°-29
+ IIO-84

+ 3°-29
H 33°-64

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,. peppermint.

„ rosemary

,, marjoram .

,, sassafras

Solution of sugar 50 per cent.

,, quinine 6 per cent, in )

alcohol . )

It will be noticed that the rotary power of all these substances is much less than that of quartz.

A mixture of liquids, one or both of which is active, generally exhibits a rotatory action represented by the sum or difference of their separate powers (a neutral liquid being considered to have a power represented by o); but this law is true only when no chemical action takes place between the elements of the mixture. Saccharine solutions vary not only in the amount but also in the character of their power of rotation ; thus cane sugar is right-handed, but grape sugar left-handed.

The property in question has been turned to practical use by employing the rotatory power of a saccharine solution as a measure of the strength of the solution. For this purpose a tube containing the solution to be examined is placed between two Nicol's prisms. The simple fact of circular polarisation is proved by a feeble exhibition of the phenomena shown by a plate of quartz cut perpendicularly to the axis. But for accurate measurement various expedients have been adopted. 1/ a biquartz be inserted behind the analyser (the end of the apparatus next the eye being considered the front), then for a certain position of the analyser the two halves will appear of the same colour. When the tube for examimtion is inserted the similarity of colour will be disturbed; and the angle through which, right or left, the analyser must be turned in order to restore it will be a measure of the rotary power of the fluid.

Another method is as follows :—Use a single quartz instead of a biquartz; in front of it place a pair of quartz wedges, with the thin end of one opposite the thick end of the other ; the outer surfaces having been cut perpendicularly to the axis. If the plate be right-handed, the

wedges must be left-handed, and vice vrrsd. The wedges must be made to slide one over another so as together to form a plate of any required thickness, and a scale connected with the sliding gear registers the thickness of the plate produced. When the tube is removed the wedge are adjusted so as to compensate the quartz plate, and their position is considered as the zero point of the seal;. When the tube is replaced, the wedges are again adjust J so as to compensate the action of the fluid in the tub?, and the difference of the readings gives the thickness 01 quartz necessary for the compensation. The rotatory effect of a given thickness of quartz being supposed known we know at once the effect of a thickness of the fluid under examination equal to the length of the tube.

Another method has been based upon the principle of Savarts bands; but sufficient has perhaps here been said to illustrate the principle of the saccharometer.

Circular polarisation may, however, be also prodaced by other means, namely, by total reflexion, and by transmission through doubly-refracting plates of suitable thickness.

It will perhaps be best to begin with the list. And in order the better to understand the process we must consider briefly the result of compounding two rectilinear vibrations under different circumstances.

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Suppose a particle of ether to be disturbed from its point of rest O in a direction O A. The attraction of the particles in its neighbourhood would tend to draw it back to O; and let O A be the extreme distance to which under these attractions it would move. Having reached A it would return to O, and passing through O with a velocity equal to that with which it started under the disturbing force, it would move to a point B equidistant from O with A, but in the opposite direction. And if, as is generally supposed, the ether is perfectly elastic, or th.it there are no internal frictions or other conditions whereby the energy of motion is converted into other forms of energy, the oscillations or vibrations of the particle between the points A and B will continue indefinitely. No* suppose that while these vibrations are going on, a seconJ disturbing impulse, equal in intensity, but in a direction at right angles to the first, be communicated to the particle it is clear that the effect on the motion of the particle will be different according as it takes place at the point of greatest velocity O, or at that of no velocity A or li, or at some intermediate point. Our object is to consider the effects under these various circumstances.

A complete vibration consists in the motion from O to A, thence to B, and finally back to O ; so that if O be tho starting point the passage through A will be removed onefourth, th- passage through O from A towards B will be one-half, the passage through B will be three-fourths, and the passage through O from B to A a complete vibration from the commencement. This being so, suppose that the second impulse be communicated while the particle is at O on its way towards A, then the impulses may be considered as simultaneous and the vibrations to which they give rise will commence together, and the waves of

which they form part will be coincident. If the second impulse take place when the particle is at A, the two sets of vibrations or waves to which they belong will have a difference of phase (i.e. the first will be in advance of the second) equal to one-fourth of a vibration or one-fourth of a wave-length. If the second impulse take place when the particle is at O on its way to B, the difference of phase will be half ; if when it is at B the difference will be threefourths of a wave-length.

The particle being at O, and subject to two simultaneous impulses of equal strength, one in the direction of A, the other in that of C, must move as much in the direction of C as in that of A, that is, it must move in a straight line equally inclined to both, namely O E in the same figure. And inasmuch as the two impulses in no way impede one another, the particle will move in each direction as far as it would have done if the other had not taken place. In other words, if we draw a square about O with its sides at distance equal to O A or O B, the extent of the vibration will be represented by O E where E is a corner of the square. The complete vibration will then be represented by the diagonal E F in the same way as it was by the line A B in the first instance. If the impulse had been communicated at the instant of passage through O on the way to B, it is clear that a similar train of reasoning would have shown that the vibration would have been in the other diagonal G H. We conclude, therefore, that if two sets of rectilinear vibrations, or plane waves, at right angles to one another combine, then when they are coincident they will produce a rectilinear vibration, or Wave, whose plane is equally inclined to the two, and lying in the direction towards which the motions are simultaneously directed. In the figure this is represented by the dexter diagonal. When the two sets of waves have a difference of phase equal to half a wave length, their combination gives rise to a wave represented in the figure by the sinister diagonal.

Suppose now that the second impulse is communicated at the instant when the particle is at A; in other words, that the two sets of waves have a difference of phase equal to one-fourth of a wave-length. At that instant the particle will have no velocity in the direction of A B (for convenience, say eastwards), and will consequently begin to move in the direction of the second impulse, say northwards. Hut as time goes On the paiticle will have an increasing velocity westwards and a diminishing velocity n.orthwards, it will therefore move in a curve which gradually and uniformly bends, until when it has reached its greatest distance northwards it will be moving wholly westwards. And as the motion not only will be the same in each quadrant, but would be the same even if the directions of the impulses were reversed, it is clear that the curvature of the path will be the same throughout, that is to say, if two sets of waves of the same magnitude in planes perpendicular to one another, and with a difference of phase equal to one-fourth of a wave-length combine, they will produce a wave with circular vibrations.

If the second impulse be given when the particle arrives at B, that is, if the waves have a difference of phase equal to three-fourths of a wave-length, similar considerations will show that the motion will be circular, but in the opposite direction.

Suppose, therefore, that wc allow plane-polarised light to fall upon a plate of doubly refracting crystal cut perpendicularly to the axis in the case of a uniaxal crystal, or in the case of a biaxal to the plane containing the two axes, say a plate of mica which splits easily in that direction ; then the vibrations will, as before explained, be re solved in two directions, at light angles to one another. And further, if the original directions of vibration be equally inclined to the new directions, i.e., if it be inclined at 45u to them, the amount or extent of vibration resolved in each direction will be equal. Further, if the thickness of the plate be such as to produce retardation or differ

ence of phase equal to a quarter of a wave, or an odd number of quarter wave-lengths, for the particular ray under consideration ; then the two sets of vibrations on emerging from the mica plate will recombine, and. in accordance with the reasoning given above, they will form a circular vibration, left-handed or right-handed according as the retardation amounts to an integral number of threequarter wave-lengths or not.

It thus appears that a plate of mica which retards one of the sets of waves into which it divides an incident set by an odd multiple of quarter-wave lengths, affords a means of producing circular from plane polarisation. It remains to be shown that, with the same plate in different positions, right or left handed circular polarisation may be produced at pleasure. Suppose tbat the original vibrations are in the direction E F in the foregoing figure; the mica plate will resolve them into the two directions AB, CD, one of the rays, say the first, will be transmitted with greater velocity than the other, and the vibrations along C D will be one-fourth of a wave-length behind those along A B. This will correspond to the case discussed above, and will give rise to a circular vibration in a direction opposite to that of the hands of a clock. Suppose, however, that the plate be turned round through a right angle, so that the vibrations which are transmitted with greater velocity are placed parallel to C D, and those which are transmitted with lesser along A B. The ray whose vibrations are along A B will then be a quarter wave-length in advance, or, what comes to the same thing, they are three-quarters of a wave-length in rear of the others j arid this condition of things produces, as explained before, a circular vibration in a direction the reverse of the former. It thus appears that the plate placed in one direction will convert plane into right-handed circular polarisation; and if turned round through a right angle from that position will convert plane into left-handed circular polarisation. A like change from right-handed to left-handed circular polarisation, or vice-verstt, may obviously be effected byturning the orginal plane of polarisation through a right angle; so that it shall lie between lines of concurrent instead of between lines of discordant motion.

W. Spottiswoode {To be continued?)

A COMPLETE SPECIMEN OF A PALA£0THERIUM

FROM La Nature we learn that the pateontological collection of the Museum of Natural History of Paris has just been enriched by the addition of a new specimen of very great scientific interest, which is the entire skeleton of Palaolherium magnum, imbedded in a large block of gypsum and marl, the whole being exhibited in the anatomical department of the museum.

The Palffoiherium magnum', whose name alone indicates its ancient existence, was first recorded by the great French naturalist Cuvier, in his celebrated "Recherches sur les Ossemens Fossiles.".jIt is an animal which is entirely extinct, without any present representative. Individuals of the species must have been extremely abundant during the period that it existed. Modern zoologists place it among the Perissodactylates, that is to say, with the at present existing rhinoceros, tapir, and horse. It forms part of the fauna which is found abundantly embedded in the deposits of gypsum. All pal aeon tological collections, even the most humble, have for a long time been provided with the remains, or more or less complete portions of this fossil form, but none have yet had the good fortune to obtain a complete skeleton.

The principal result of the examination of the new specimen which we are describing has been to show that until now very inexact notions have been entertained as to what this animal truly was when the proportions and general contour of the tapir were assigned to it, as was done even by Cuvier himself.

Far from being bulky and almost massive, as was thought, Palaotherium magnum is now evidently seen to be a very slender animal, with an extremely graceful carriage, with the neck longer than in the horse, and a general contour much on the same type as that of the Llama.

Without attempting a detailed study of its osteological structure, we may mention that Palaotherium magnum had a height a little less than that of a middle

sized horse. Three toes are found on each of the feet: the head, much like that of a tapir, had most probably also the rudiment of a trunk ; the femur has a third trochanter; the dentary system is composed, in each j»«r, of six incisors, two canines, and fourteen molars, these latter corresponding with the same teeth in the rhinoceros.

Palaotlurium magnum, like its congeners, of which about a dozen species are at present known, was herbivorous, and without doubt lived in large herds. Its existence carries us back to that age of our earth which is termed the Eocene period, and it is in the middle of that period, which comprises the gypsum deposits or their geological

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equivalents, that its remains are discovered, as well as those of all the other species of the same genus.

Nevertheless it made its appearance even before the gypsum formation, its presence having been detected in the beds of coarse limestone, which are inferior to and therefore more ancient than that formation.

It is the plaster quarries of Montmartre, Pantin, and La Villette, near Paris, which have for a long time held the privilege of furnishing to palaeontologists the numerous remains that are known of this fossil species. The Palaeotherium, which forms the subject of this notice, was obtained from a plaster-quarry situated at Vitry-sur-Seine.

It was, however, even a few days ago, as we see it to-day, exposed on one side, and on the other encrusted in its stony resting-place in the ceiling of a subterraneous gallery, a little more than four yards high. Only a fe»' have visited it, although M. Fuchs, a civil engineer, the proprietor of the quarry where this magnificent specimen was found, offered to give it to the Museum.

The gift so generously offered was immediately accepted; and Prof. Gervais, with a scientific zeal which ought to be fully acknowledged, occupied himself with the direction of the important task of taking it intact to Paris.

MARS

'Is H E characteristic appearance of this planetary body, *- long familiar to astronomers, has of late become generally known. Remarkable neither for situation, magnitude, brilliancy, retinue or complexity of arrangement, inferior in each of these respects to some, and in many of them to several of the members of the solar family, one circumstance alone invests it with a peculiar interest—its resemblance to ourselves. Such a resemblance obviously does not exist in the mightier and more nobly attended external planets: the banded skies of two and the strong atmospheric absorption of the two others revealed by the spectroscope, sufficiently show that they belong to classes

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mutually indeed dissimilar, but each differing, and perhaps widely, from our own. With the swift and fiery Mercury we can have as little sympathy; and though Venus would offer a more promising analogy, the configuration of her beautiful surface is not well seen or readily interpreted. Mars therefore remains; and while, fortunately for astronomers, he occupies such a position that his features are fairly accessible, they bear an aspect so comparatively intelligible that, whatever may be the case as to our other fellow-subjects in the solar monarchy, we are ready to claim that globe as a close relation of our own, inferior indeed in magnitude and importance, if importance is indicated by an attendant, but arranged in a corresponding manner by the Great Creator as the seat of life and intelligence. Such a supposition has been gradually and surely ad

vancing from an early period of telescopic astronomy. The polar whiteness detected by Huygensand Cassini I. as far back as 1672 would naturally suggest the idea of a snowy deposit, which assumed almost the form of certainty, when the elder Herschel showed that its extent was regulated by the Martial seasons, and that it wasted steadily down with the advance of vernal heat. From the obvious division of the surface into brighter and darker portions, the existence of an atmosphere at least would be inferred, so long as they were supposed to be variable; but as the evidence of their general permanence increased under the eye of Herschel I. about a century ago, this impression gave place to the more definite recognition of something corresponding to the outlines of lands and oceans, with occasional variation from atmospheric condensations; and thus by degrees we have been led to acknowledge, in that remote and otherwise unimportant globe, a most interesting counterpart of our own.

This conclusion has not, however, been attained by an uninterruptedly continuous or an uniformly satisfactory process of deduction; and even at the present time it is perhaps not universally received. Schroter referred the darker portions to atmospheric obscuration, a notion which pervaded others of his investigations", not to their advantage; and a more recent observer of considerable ability, the late Prof. Kaiser, of Leiden, whose decease in his 64th year took place July 28, 1872, has, in a very elaborate and interesting report of the work done on the planet at that observatory, expressed his doubts as to the certainty of the more customary inference. Whatever may be our own impressions on the subject, his criticisms and conclusions exhibit so much of the genuine spirit of an impartial student that some notice of them, as they are found in vol. iii. of the Annals of the Leiden Observatory, may be worth the attention of our readers. This observatory, it should be noted, is provided with a Merz achromatic of 7 (French ?) inches aperture, and was therefore, under Kaiser's superintendence, fairly competent for physical researches commensurate with the present demands of science ; as it is well known, and indeed especially brought out by the observations we are about to notice, that much larger telescopes are not invariably, or even generally, available in proportion to their magnitude. The addition, in 1872—too late therefore for a share in the professor's observations—of an 8J inch With-Browning reflector, will hereafter not only afford an interesting comparison of instruments, but if the result corresponds with others obtained elsewhere, will be found a step in advance as regards efficiency.*

In selecting Mars as the subject of special inquiry, Prof. Kaiser laid a solid foundation by consulting every work within his reach, representing or describing the physical aspect of the planet, from the earliest and rudest efforts in 1636 to the elaborate delineations of the present day. No less than 412 drawings thus passed through his hands: upwards of 320 others he could not procure; and the aggregate is doubtless much in defect of the existing total. He did however well in securing so many ; more, probably, than any other areographer, if such a word may be allowed. But the result of their comparison and discussion was not as satisfactory as might be wished. The first specimens of representation were of course mere rude attempts. Those of Huygens, however, in 1659, discovered by Kaiser in his "day-book" (of which the most valuable portion was edited by him in 1847) are compararatively well drawn ; and Hook, in 1666, caught the true character of what he saw, though Kaiser doubts whether his spots could be as readily identified as has been supposed. We next find Herschel I. taking up the subject

* A curious error on the part of Prof. Kaiser may here be noticed. He has referred (p. 23) to a drawing of Mars by Browning as having been taken with a silvered mirror by Barnes. This gentleman was merely the proprietor of the speculum, which, like the others mounted by that optician, was th work of a most accomplished artist, Mr. With, of Hereford.

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