CHAPTER XXIII.

HISTORY OF THE COMBINATIONS OF PLANE MIRRORSWHICH HAVE BEEN SUPPOSED TO RESEMBLETHE KALEIDOSCOPE.

It has always been the fate of new inventions to have their origin referred to some remote period; and those who labour to enlarge the boundaries of science, or to multiply the means of improvement, are destined to learn, at a very early period of their career, that the desire of doing justice to the living is a much less powerful principle than that of being generous to the dead. This mode of distributing fame, injurious as it is to the progress of science, by taking away one of the strongest excitements of early genius, has yet the advantage of erring on the side of generosity; and there are few persons who would reclaim against a decision invested with such a character, were it pronounced by the grave historian of science, who had understood and studied the subject to which it referred.

The apparent simplicity, both of the theory and the construction of the Kaleidoscope, has deceived very well-meaning persons into the belief that they understood its mode of operation; and it was only those that possessed more than a moderate share of optical knowledge, who saw that it was not only more difficult to understand, but also more difficult to execute, than most of the philosophical instruments now in use. Thepersons who considered the Kaleidoscope as an instrument consisting of two reflectors, which multiplied objects, wherever these objects were placed, and whatever was the position of the eye, provided that it received only the reflected rays, were at no loss to find numerous candidates for the invention. All those, indeed, who had observed the multiplication and circular arrangement of a fire blazing between two polished plates of brass or steel; who had dressed themselves by the aid of a pair of looking-glasses, or who had observed the effects of two mirrors placed upon the rectangular sides of a drawing-room, were entitled, upon such a definition, to be constituted inventors of the Kaleidoscope. The same claim might be urged for every jeweller who had erected in his window two perpendicular mirrors, and placed his wares before them, in order to be multiplied and exhibited to advantage; and for every Dutch toy-maker, and dealer in optical wonders, who had manufactured show-boxes, for the purpose of heaping together, in some sort of order, a crowd of images of the same object, of different intensities, seen under different angles, and presenting different sides to the eye. This mode of grouping images, dissimilar in their degree of light, dissimilar in their magnitude, and dissimilar in their very outlines, produced such a poor effect, that the reflecting show-boxes have for a long series of years disappeared from among the number of philosophical toys.

From these causes, the candidates for the merit of inventing the Kaleidoscope have been so numerous, that they have started up in every part of the world; and many individuals, who are scarcely acquainted with the equality of the angles of incidence and reflexion, have notscrupled to favour the world with an account of the improvements which they fancy they have made upon the instrument.[19]

The earliest writer who appears to have described the use of two plane mirrors, was Baptista Porta, who has given an account of several experiments which he performed with them, in the second chapter of the seventh book of hisMagia Naturalis.

As the combination of plane mirrors which he there describes has been represented as the same as the Kaleidoscope, we shall give the passage at full length:—

Speculum è planis multividum construere.

“Speculum construitur, quodpolyphatonid est multorum visibilium dicitur, illud enim aperiendo et claudendo solius digiti viginti et plura demonstrat simulacra. Sic igitur id parabis. Ærea duo specula vel crystallina rectangula super basim eandem erigantur, sintque in hemiolia proportione, vel alia, et secundum longitudinis latus unum simul colligentur, ut libri instar apte claudi et aperiri possint, et anguli diversentur, qualia Venetiis factitari solent: faciem enim unam objiciens, in utroque plura cernes ora, et hoc quanto arctius clauseris, minorique fuerint angulo: aperiendo autem minuentur; et obtusiori cernes angulo, pauciora numero conspicientur. Sic digitum ostendens, non nisi digitos cernes, dextra insuper dextra, et sinistra sinistra convisuntur; quod speculis contrarium est: mutuaque id evenit reflexione, et pulsatione, unde imaginum vicissitudo.”—Edit. Amstelod, 1664.

—Edit. Amstelod, 1664.

The following is an exact and literal translation of this passage:—

How to construct a multiplying speculum out of plane ones.

A speculum is constructed, calledpolyphaton, that is,which shows many objects, for by opening and shutting it, it exhibits twenty and more images of the finger alone. You will therefore prepare it in the following manner:—Let two rectangular specula of brass or crystal be erected upon the same base, and let their length be one and a half times their width, or in any other proportion; and let two of their sides be placed together, so that they may be opened and shut like a book, and the angles varied,as they are generally made at Venice. For by presenting your face, you will see in both more faces the more they are shut, and the less that the angle is; but they will be diminished by opening it, and you will see fewer as you observe with a more obtuse angle. If you exhibit your finger, you will see only fingers, the right fingers being seen on the right side, and the left on the left side, which is contrary to what happens in looking-glasses, and this arises from the mutual reflexion and repulsion which produce a change of the images.[20]

It is quite obvious, from the preceding passage, that the multiplying speculum described by Porta was not an invention of his own, but had been long made at Venice. In the very next chapter, indeed, where he describes aspeculum theatraleoramphitheatrale(theshow-boxof Harris and other modern authors), he expressly states, that a multiplying speculum was invented by the ancients.—“Speculum autem è planis compactum, cui si unum spectabile demonstrabitur, plura illius rei simulachra demonstrabit,prudens invenit vetustas; ut ex quibusdam Ptolemæi scriptis quæ circumferuntur percipitur;” that is, “a speculum consisting of plane ones, which, when one object is presented to it, will exhibit several images of it, was invented by skilful antiquity, as appears from some of the writings of Ptolemy.” This speculum, which consists of several mirrors arranged in a polygon, with the object within it, ischaracterized by Porta as puerile, and much less wonderful and agreeable than one of his own, which he proceeds to describe. This new speculum consists of ten mirrors, placed within a box, in a sort of polygonal form, with one of the sides of the polygon open. Architectural columns, pictures, gems, pearls, coloured birds, etc., are all placed within the box, and their images are seen heaped together in inextricable disorder, as a whole, but so as to astonish the spectator by their number, and by the arrangement of individual groups. Porta speaks of this effect as so beautiful, “ut nil jucundius nil certe admirabilius oculis occurset nostris,”—that nothing more agreeable, and certainly nothing more admirable, was ever presented to our eyes.

It would be an insult to the capacities of the most ordinary readers to show that the instruments here described by Baptista Porta have no farther connexion with the Kaleidoscope than that they are composed of plane mirrors.

The sole purpose of these instruments was tomultiplyobjects by reflexion; and so little did the idea of producing a symmetrical picture enter into Baptista Porta’s contemplation, that he directs the mirrors to be placed at any angle, because the multiplying property of the mirrors is equally developed, whatever be the angle of their inclination.

The show-box of which Porta speaks with such admiration, has so many mirrors, and these are placed at such angles, that not one of the effects of the Kaleidoscope can be produced from them. Its beauty is entirely derived from the accumulation of individual images.

The next competitor for the invention of the Kaleidoscope is the celebrated Kircher, who describes, as an invention of his own, theconstruction of two mirrors which can be opened and shut like the leaves of a book. This instrument is represented inFig. 54, and is described in the following passage:—

Fig. 54.

Parastasis I.

Specula plana multiplicativa sunt specierum unius rei.Vide Fig. 54.Mira quædam et a nemine, quod sciam observata proprietas elucescit in duobus speculis ita constructis, ut ad instar libri claudi et aperiri possint; ponantur illa in plano quopiam, in quo semicirculum in gradus suos descriptum habeas. Si enim punctum, in quo specula committuntur, in centro semicirculi statuas, ita ut utrumque speculi latus diametro insistat, semel tantam videbitur rei imago, apparebuntque duæ res, una extra speculum vera, altera intra, phantastica: Si vero specula itaposueris, ut divaricatio laterum 120 gradus intercipiat, videbis rei intra latera est, quia angulus reflexionis et incidentiæ tantus est, quantus est angulus interceptus a lateribus, videlicet 120 grad. qui cum obtusius sit, non nisi binam imaginem causare potest, ut in Propos. v. fol. 848, ostensum est. Si vero specula interceperint angulum 90 graduum, videbis in plano circulum in quatuor partes divisum, in quibus totidem simulacra rei positæ comparabunt, tria phantastica, et unum verum; cum enim reflectio fiat ad angulos rectos utrumque latus reflectens formam causabit intra se alias duas formas, unde et consequentur pro multiplicatione laterum formæ multiplicabuntur, quæ et in reflectione laterum normam servabunt uti in Propos. v. fol. 848, ostendimus. Porro si speculorum latera interceperint angulum 72 graduum, videbis in plano horizontali efformari perfectum et regulare pentagonum, in quo totidem formæ apparebunt, item, si sexaginta graduum interceperint angulum, videbis hexagonum totidemque formas quinque nimirum phantasticas unam veram. Ita, si speculorum angulus interceperit 51 gradus cum ³/₇ comparebit perfectum heptagonum, cum totidem rei intra specula collocatæ formis; non secus angulus speculorum 45 graduum dabit octogonum; 40 graduum dabit enneagonum; 36 graduum decagonum; 32 graduum angulus cum ⁸/₁₁ dabit endecagonum et denique angulus 30 graduum referet dodecagonum cum totidem formis, et sic in infinitum; ita ut semper tot laterum sit futurum polygonum anacampticum totidemque formarum, quot polygonum cuivis latus speculorum intercipit divaricatio, latera habuerit: quorum omnium rationes dependent a Propos. v. precedentis distinctionis. —Kircheri,Ars Magna Lucis et Umbræ. Rom. 1646, p. 890.

Specula plana multiplicativa sunt specierum unius rei.

Vide Fig. 54.

Mira quædam et a nemine, quod sciam observata proprietas elucescit in duobus speculis ita constructis, ut ad instar libri claudi et aperiri possint; ponantur illa in plano quopiam, in quo semicirculum in gradus suos descriptum habeas. Si enim punctum, in quo specula committuntur, in centro semicirculi statuas, ita ut utrumque speculi latus diametro insistat, semel tantam videbitur rei imago, apparebuntque duæ res, una extra speculum vera, altera intra, phantastica: Si vero specula itaposueris, ut divaricatio laterum 120 gradus intercipiat, videbis rei intra latera est, quia angulus reflexionis et incidentiæ tantus est, quantus est angulus interceptus a lateribus, videlicet 120 grad. qui cum obtusius sit, non nisi binam imaginem causare potest, ut in Propos. v. fol. 848, ostensum est. Si vero specula interceperint angulum 90 graduum, videbis in plano circulum in quatuor partes divisum, in quibus totidem simulacra rei positæ comparabunt, tria phantastica, et unum verum; cum enim reflectio fiat ad angulos rectos utrumque latus reflectens formam causabit intra se alias duas formas, unde et consequentur pro multiplicatione laterum formæ multiplicabuntur, quæ et in reflectione laterum normam servabunt uti in Propos. v. fol. 848, ostendimus. Porro si speculorum latera interceperint angulum 72 graduum, videbis in plano horizontali efformari perfectum et regulare pentagonum, in quo totidem formæ apparebunt, item, si sexaginta graduum interceperint angulum, videbis hexagonum totidemque formas quinque nimirum phantasticas unam veram. Ita, si speculorum angulus interceperit 51 gradus cum ³/₇ comparebit perfectum heptagonum, cum totidem rei intra specula collocatæ formis; non secus angulus speculorum 45 graduum dabit octogonum; 40 graduum dabit enneagonum; 36 graduum decagonum; 32 graduum angulus cum ⁸/₁₁ dabit endecagonum et denique angulus 30 graduum referet dodecagonum cum totidem formis, et sic in infinitum; ita ut semper tot laterum sit futurum polygonum anacampticum totidemque formarum, quot polygonum cuivis latus speculorum intercipit divaricatio, latera habuerit: quorum omnium rationes dependent a Propos. v. precedentis distinctionis. —Kircheri,Ars Magna Lucis et Umbræ. Rom. 1646, p. 890.

The following is a translation of the preceding passage:—

Parastasis I.

Plane specula may be made to multiply the images of one object.See Fig. 54.A wonderful, and, so far as I know, a new property, is exhibited by two specula, so constructed that they may be opened and shut like a book. If they are placed upon any plane, in which there is a semicircle divided into degrees, in such a manner that the point where the specula meet is in the centre of the circle, and the edge of each speculum stands upon the diameter of the semicircle, one image only will be visible, and there will appear two things, namely, a real one, without the specula, and another formed by reflexion behind them,[21]and so on, as in the following table, where the first column shows the inclination of the specula, and the second the figure which is produced:—

Plane specula may be made to multiply the images of one object.

See Fig. 54.

A wonderful, and, so far as I know, a new property, is exhibited by two specula, so constructed that they may be opened and shut like a book. If they are placed upon any plane, in which there is a semicircle divided into degrees, in such a manner that the point where the specula meet is in the centre of the circle, and the edge of each speculum stands upon the diameter of the semicircle, one image only will be visible, and there will appear two things, namely, a real one, without the specula, and another formed by reflexion behind them,[21]and so on, as in the following table, where the first column shows the inclination of the specula, and the second the figure which is produced:—

and so on,ad infinitum, the polygon formed by reflexion having always as many sides as the number of times that the angle of the specula is contained in 360°.

The combination of plane mirrors, which Kircher describes in the preceding extract, is precisely the same as that which is given by Baptista Porta. The latter, indeed, only mentions, that the number of images increases by the diminution of the angle, whereas Kircher gives the number of images produced at different angles, and enumerates theregular polygonswhich are thus formed.

It must be quite obvious to any person who attends to Kircher’s description, that the idea never once occurred to him of producing beautiful and symmetrical forms by means of plane mirrors. Hissole objectwas to multiply a given regular form a certain number of times; and he never imagined that, when the mirrors were placed at the angles marked with an asterisk, there could be no symmetry in the figure, and no union of the two last reflected images, unless in the case where a regular object was placed, either by design or by accident, in a position symmetrically related to both the reflectors.

In Kircher’s mirrors the eye was placed in front of them. The object therefore was much nearer the eye than the images, and the light of the different reflected images was not only extremely unequal, but the difference in their angular magnitude was such that they could notpossibly be united into a symmetrical whole. From the accidental circumstance of his usinglines upon paperas an object, the distortion of the pictures arising from the erroneous position of the eye was prevented; but if the same combination of mirrors were applied to the object-plates of the Kaleidoscope, it would be found utterly incapable of producing any of the fine forms which are peculiar to that instrument.

If it were necessary to prove that Kircher and his pupils were entirely ignorant of the positions of the eye and the object which are necessary to the production of a picture, symmetrical in all its parts, and uniformly illuminated, and that they went no farther than the mere multiplication of forms that were previously regular and symmetrical, we would refer the reader to Schottus’Magia Universalis Naturæ et Artis, printed at Wurtzbourg in 1657, where he repeats, almost word for word, the description of Kircher, and adds the following curious observation:—“But it is not only the objects placed in the semicircle in the angle of the glasses that are seen andmultiplied, but also those which are more distant; for example, a wall, with its windows, and in this case the multiplication produced by the mirrors will create an immense public place, adorned with edifices and palaces.” This passage shows, in the clearest manner, not only that the multiplication of an object, independent of the union of the multiplied objects into a symmetrical whole, was all that Kircher and his followers proposed to accomplish; but also that they were entirely unacquainted with the effects produced by varying the distance of the object from the mirrors. If any person should doubt the accuracy of this observation, we would request him to take Kircher’s two mirrors, todirect them to a “wall with its windows,” either by Kircher’s method, or even by any other way that he chooses, and to contemplate “the public place adorned with edifices and with palaces.” He will see heaps of windows and of walls, some of the heaps being much larger than others; and some being farther from, and others nearer to, the centre; and some being dark, and others luminous; while all of them are disunited. Let him now take a Telescopic Kaleidoscope, and direct it to the same object; he will instantly perceive the most perfect order arise out of confusion, and he will not scruple to acknowledge, that no two things in nature can be more different than the effects which are produced by these two combinations of mirrors.

Fig. 55.Fig. 56.

Fig. 55.

Fig. 56.

We come now to consider the claims of Mr. Bradley, Professor of Botanyin the University of Cambridge. In a work, entitled,New Improvements in Planting and Gardening, published in 1717, this author has drawn and described Kircher’s apparatus as an invention of his own; and, instead of having in any respect improved it, he has actually deteriorated it, in so far as he has made the breadth of the mirrors greater than their height. An exact copy of the mirrors used by Bradley is shown inFig. 55, from which it will be at once seen, that it is precisely the same as Kircher’s, shown inFig. 54. We are far from saying that Bradley stole the invention from Kircher, or that Kircher stole it from Baptista Porta, or that Baptista Porta stole it from the ancients. There is reason, on the contrary, to think that the apparatus had been entirely forgotten, in the long intervals which elapsed between these different authors, and there can be no doubt that each of them added some little improvement to the instrument of their predecessors. Baptista Porta saw the superiority of two mirrors, as a multiplying machine, to a greater number used by the ancients. Kircher showed the relation between the number of images and the inclination of the mirrors; and Bradley, though he rather injured the apparatus, yethe had the merit of noticing, that figures upon paper, which had a certain degree of irregularity, like those inFig. 56, could still form a regular figure.

In order that the reader may fully understand Bradley’s method of using the mirrors, we shall give it in his own words:—

“We must choose two pieces of looking-glass (says he), of equal bigness, of the figure of a long square,fiveinches in length, andfourin breadth; they must be covered on the back with paper or silk, to prevent rubbing off the silver, which would else be too apt to crack off by frequent use. This covering for the back of the glasses must be so put on, that nothing of it may appear about the edges on the bright side.

“The glasses being thus prepared, they must be laid face to face, and hinged together, so that they may be made to open and shut at pleasure, like the leaves of a book; and now the glasses being thus fitted for our purpose, I shall proceed toexplain the use of them.

“Draw a large circle upon paper; divide it into three, four, five, six, seven, or eight equal parts; which being done, we may draw in every one of the divisions a figure, at our pleasure, either for garden-plats or fortifications; as, for example, inFig. 55, we see a circle divided into six parts, and upon the division markedFis drawn part of a design for a garden. Now, to see that design entire, which is yet confused, we must place our glasses upon the paper, and open them to the sixth part of the circle,i.e., one of them must stand upon the lineb, to the centre, and the other must be opened exactlyto the pointc; so shall we discover an entire garden-plot in a circular form (if we look into the glasses), divided into six parts, with as many walks leading to the centre, where we shall find a basin of an hexagonal figure.

“The lineA, where the glasses join, stands immediately over the centre of the circle, the glassBstands upon the line drawn from the centre to the pointC, and the glassDstands upon the line leading from the centre to the pointE: the glasses being thus placed, cannot fail to produce the complete figure we look for; and so whatever equal part of a circle you mark out, let the lineAstand always upon the centre, and open your glasses to the division you have made with your compasses. If, instead of a circle, you would have the figure of a hexagon, draw a straight line with a pen from the pointcto the pointb, and, by placing the glasses as before, you will have the figure desired.

“So likewise a pentagon may be perfectly represented, by finding the fifth part of a circle, and placing the glasses upon the outlines of it; and the fourth part of a circle will likewise produce a square, by means of the glasses, or, by the same rule, will give us any figure of equal sides. I easily suppose that a curious person, by a little practice with these glasses, may make many improvements with them, which, perhaps, I may not have yet discovered, or have, for brevity sake, omitted to describe.

“It next follows that I explain how, by these glasses, we may, from the figure of a circle, drawn upon paper, make an oval; and also, by the same rule, represent a long square from a perfect square. To do this, open the glasses, and fix them to an exact square; place them over acircle, and move them to and fro till you see the representation of the oval figure you like best; and so, having the glasses fixed, in like manner move them over a square piece of work till you find the figure you desire of a long square. In these trials you will meet with many varieties of designs. As for instance,Fig. 56, although it seems to contain but a confused representation, may be varied into above two hundred different representations, by moving the glasses over it, which are opened and fixed to an exact square. In a word, from the most trifling designs, we may, by this means, produce some thousands of good draughts.

“But thatFig. 56may yet be more intelligible and useful, I have drawn on every side of it a scale, divided into equal parts, by which means we may ascertain the just proportion of any design we shall meet within it.

“I have also marked every side of it with a letter, asA,B,C,D, the better to inform my reader of the use of the invention, and put him in the way to find out every design contained in that figure.

“Example I.—Turn the sideAto any certain point, either to the north, or to the window of your room; and when you have opened your glasses to an exact square, set one of them on the line of the sideD, and the other on the line of the sideC, you will then have a square figure four times as big as the engraved design in the plate: but if that representation should not be agreeable, move the glasses (still open to a square) to the number 5 of the sideD, so will one of them be parallel toD, and the other stand upon the line of the sideC, your first design will then be varied; and so by moving your glasses, in like manner, from point to point, thedraughts will differ by every variation of the glasses, till you have discovered at least fifty plans, differing from one another.

“Example II.—Turn the side markedB, ofFig. 56, to the same point whereAwas before, and by moving your glasses as you did in the former example, you will discover as great a variety of designs as had been observed in the foregoing experiment; then turn the sideCto the place ofB, and, managing the glasses in the manner I have directed in the first example, you may have a great variety of different plans, which were not in the former trials; and the fourth side,D, must be managed in the same manner with the others; so that from one plan alone, not exceeding the bigness of a man’s hand, we may vary the figure at least two hundred times; and so, consequently, fromfivefigures of the like nature, we might show about a thousand several sorts of garden-plats; and if it should happen that the reader has any number of plans for parterres or wilderness-works by him, he may, by this method, alter them at his pleasure, and produce such innumerable varieties, that it is not possible the most able designer could ever have contrived.”

In reading the preceding description, the following conclusions cannot fail to be drawn by every person who understands it.

1. Dr. Bradley, like Kircher, considers his mirrors as applicable to regular figures, such as are represented inFig. 55, and was entirely unacquainted with the fact, that the inclination of the mirrors must be anevenaliquot part of a circle. This is obvious, from hisstating that the mirrors may be set at thethird, fourth,fifth, sixth,seventh, or eighth part of a circle; for if he had tried to set an irregular object between the mirrors when placed at thethird,fifth, orseventhpart of 360°, he would have found that a complete figure could not possibly be produced.

2. From the erroneous position of the eye in front of the mirrors, there is such an inequality of light in the reflected sectors, that the last is scarcely visible, and therefore cannot be united into a uniform picture with the real objects.

3. As the place of the eye in Bradley’s instrument is in front, and therefore much nearer the object, or sector, seen by direct vision, the angular magnitudes of all the different sectors are different, and hence they cannot unite into a symmetrical figure. This is so unavoidable a result of the erroneous position of the eye—a position too, rendered necessary from the absurd form of the mirrors—that Bradley actually employs his mirrors to convert a circle into an ellipse, and a square into a rectangle!

4. In Bradley’s instrument, the sectors thus unequally shaped, and unequally illuminated, are all separated from one another, by a space equal to the thickness of the glass plates; and from the same cause, the images reflected from the first surface interfere with those reflected from the second, and produce a confusion or overlapping of images entirely incompatible with a symmetrical picture.

These results are deduced upon the supposition that the object consists of lines drawn upon the surface of paper, the only purpose to which Bradley ever applied his mirrors; but when we attempt to use these mirrors as a Kaleidoscope, and apply them to the objects which areusually adapted to that instrument, we shall fail entirely, as the mirrors are utterly incapable of producing the beautiful and symmetrical forms which belong to that instrument.

We come now to consider the method of applying the mirrors to the object shown inFig. 55, which is an exact, but reduced copy of Bradley’s figure. Because the angles of this figure are 90°, he directs that the mirrors “be opened and fixed to an exact square; and that the edge of one of the mirrors must always be placed so as to coincide exactly with one of the sides of the rectangle, and carefully kept in this line when the position of the mirrors is changed.” Hence it is manifest, that Bradley was entirely ignorant of the fundamental principle of the Kaleidoscope, namely, that if the inclination of the mirrors is an even aliquot part of a circle, and if they areset in any position upon any object or set of objects, however confused, or distorted, or irregular, they will create the most perfect and symmetrical designs. But even if Bradley had been aware of this principle in theory, neither he nor any other person was acquainted with the mode of constructing and fitting up the reflectors, in order to render them capable of producing the effect. The position of the eye, for symmetry of light, and for symmetry of form;—the position of the mirrors, to produce a perfect junction of the last sectors;—the position of the object necessary to produce an equality and perfect junction between the object and the reflected images;—and the method of accomplishing this for objects at all distances, were fundamental points, in the combination of plane mirrors, which, so far as I know, have never been investigated by any author. But even though a knowledgeof these theoretical points had been obtained, numerous difficulties in the practical construction of the instrument remained to be surmounted; and it required no slight degree of labour and attention to enable the instrument to develop, in the most simple and efficacious manner, the various effects which, in theory, it was found susceptible of producing.

As the combination of mirrors, described by Kircher and Bradley, had been long known to opticians, and had excited so little attention that they had even ceased to be noticed in works on optical instruments, it became necessary to discover some other origin for the Kaleidoscope. The thirteenth and fourteenth Propositions of Wood’sOptics, and some analogous propositions in Harris’sOptics, were therefore presumed to be an anticipation of the invention. Professor Wood gives a mathematical investigation of the number and arrangement of the images formed by two reflectors, either inclined or parallel to each other. These theorems assign no position to the eye, or to the object, and do not include the principle of inversion, which is absolutely necessary to the production of symmetrical forms. The theorems, indeed, which have no connexion whatever with any instrument, are true, whatever be the position of the eye or the object; and Mr. Wood has frankly acknowledged, “that the effects produced by the Kaleidoscope were never in his contemplation.”[22]

The propositions in Harris’sOpticsrelate, like Professor Wood’s, merely to the multiplication and circular arrangement of the apertures or sectors formed by the inclined mirrors, and to the progress of a ray of light reflected between two inclined or parallelmirrors; and no allusion whatever is made, in the propositions themselves, to any instrument. In the propositions respecting the multiplication of the sectors, the eye of the observer is never once mentioned; and the proposition is true, if the eye has an infinite number of positions; whereas, in the Kaleidoscope, the eye can only have one position. In the other proposition (Prop.xvii.) respecting the progress of the rays, the eye and the object are actually stated to be placedbetween the reflectors; and even if the eye had been placed without the reflectors, as in the Kaleidoscope, the position assigned it, at a great distance from the angular point, is a demonstration that Harris wasentirely ignorant of the positions of symmetry, either for the object or the eye, and could not have combined two reflectors so as to form a Kaleidoscope for producing beautiful or symmetrical forms.[23]It is important also to remark, that all Harris’s propositions relate either to sectors or to small circular objects; and that he supposes the very same effects to be produced when the inclination of the mirrors is anodd, as when it is aneven, aliquot part of a circle. It is clear, therefore, that he was neither acquainted with the fundamental point in the theory of the Kaleidoscope, nor with any of its practical effects. Theonly practical partof Harris’s propositions is the fifth and sixth scholia to Prop.xvii. In the fifth scholium he proposes a sort of catoptric box, or cistula, known long before his time, composed of four mirrors, arranged in a most unscientific manner, and containing opaqueobjectsbetween the speculums. “Whatever they are,” says he, when speaking of the objects, “the upright figures between the speculums should be slender, and not too many in number, otherwise they will too muchobstruct the reflected rays from coming to the eye.” This shows, in a most decisive manner, that Harris knew nothing of the Kaleidoscope, and that he has not even improved the common catoptric cistula, which had been known long before. The principle of inversion, and the positions of symmetry, were entirely unknown to him. In the sixth scholium, he speaks of rooms lined with looking-glasses, and of luminous amphitheatres, which were known even to the ancients, and have been described and figured by all the old writers on optics.

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