APPENDIX.

Although I have no doubt that the observations contained in the preceding Chapters are sufficient to satisfy every candid and intelligent person respecting the true nature of all the combinations of plane mirrors that preceded the invention of the Kaleidoscope, yet as there are many who are incapable, from want of optical knowledge, to understand the comparison which has been made between them, I shall here present the opinions of four of the most eminent mathematicians and natural philosophers.

The first of these is contained in a note from the late Professor Wood, Master of St. John’s College, Cambridge, written in reply to a letter, in which I requested him to say, if he had any idea of the effects of the Kaleidoscope when he wrote the thirteenth and fourteenth Propositions of his works on Optics.

“St. John’s,May 19, 1818.“Sir,—The propositions I have given relating to the number of images formed by plane reflectors, inclined to each other, contain merely the mathematical calculation of their number and arrangement.The effects produced by the Kaleidoscope were never in my contemplation.My attention has for some years been turned to other subjects, and I regret that I have not time to read your Optical Treatise, which I am sure would give me great pleasure.—I am, Sir, your obedient humble servant,“J. Wood.”

“St. John’s,May 19, 1818.

“Sir,—The propositions I have given relating to the number of images formed by plane reflectors, inclined to each other, contain merely the mathematical calculation of their number and arrangement.The effects produced by the Kaleidoscope were never in my contemplation.My attention has for some years been turned to other subjects, and I regret that I have not time to read your Optical Treatise, which I am sure would give me great pleasure.—I am, Sir, your obedient humble servant,

“J. Wood.”

The following is the opinion of the late celebrated Mr. James Watt:—

“It has been said here,” says Mr. Watt, “that you took the idea of the Kaleidoscope from an old book on gardening. My friend, the Rev. Mr. Corrie, has procured me a sight of the book. It is Bradley’s Improvements of Planting and Gardening. London, 1731, Part II. Chap. I. It consists of two pieces of looking-glass, of equal bigness, of the figure of a long square, five inches long, and four inches high, hinged together upon one of the narrow sides, so as to open and shut like the leaves of a book, which, being set upon their edges upon a drawing, will show it multiplied by repeated reflexions. This instrument I have seen in my father’s possession seventy years ago, and frequently since, but what has become of it I know not. In my opinion, the application of the principle is very different from that of your Kaleidoscope.”

The following is the opinion of the late Mr. Playfair, Professor of Natural Philosophy in the University of Edinburgh:—

“Edinburgh,May 11, 1818.“I have examined the Kaleidoscope invented by Dr. Brewster, and compared it with the description of an instrument which it has been said to resemble, constructed by Bradley in 1717. I have also compared its effect with an experiment to which it may be thought to have some analogy, described by Mr. Wood in hisOptics, Prop.xiii.andxiv.“From both these contrivances, and from every optical instrument with which I am acquainted, the Kaleidoscope appears to differ essentially, both in its effect and in the principles of its construction.“As to the effect, the thing produced by the Kaleidoscope is a series of figures presented with the most perfect symmetry, so as always to compose a whole, in which nothing is wanting and nothing redundant. It matters not what the object be to which the instrument is directed; if it only be in its proper place, the effect just described is sure to take place, and with an endless variety. In this respect the Kaleidoscope appears to be quite singular among optical instruments. Neither the instrument of Bradley, nor the experiment or theorem in Wood’s book, have any resemblance to this; they go no further than the multiplication of the figure.“Next, as to the principle of construction, Dr. Brewster’s instrument requiresa particular position of the eye of the observer, and of the object looked at, in order to produce its effect. If either of these is wanting, the symmetry vanishes, and the figures are irregular and disunited. In the other two cases, no particular position, either for the eye or the object, is required.“For these reasons, Dr. Brewster’s invention seems to me quite unlike the other two. Indeed, as far as I know, it is quite singularamong optical instruments; and it will be matter of sincere regret, if any imaginary or vague analogy, between it and other optical instruments, should be the means of depriving the Doctor of any part of the reward to which his skill, ingenuity, and perseverance, entitle him so well.“John Playfair,Professor of Natural Philosophy inthe University of Edinburgh.”“P.S.—Granting that there were a resemblance between the Kaleidoscope and Bradley’s instrument, in any of the particulars mentioned above, the introduction of coloured and movable objects, at the end of the reflectors, is quite peculiar to Dr. Brewster’s instrument. Besides this, a circumstance highly deserving of attention, is the use of two lenses and a draw-tube; so that the action of the Kaleidoscope is extended to objects of all sizes, and at all distances from the observer, and united, by that means, to the advantages of the telescope.“J. P.”

“Edinburgh,May 11, 1818.

“I have examined the Kaleidoscope invented by Dr. Brewster, and compared it with the description of an instrument which it has been said to resemble, constructed by Bradley in 1717. I have also compared its effect with an experiment to which it may be thought to have some analogy, described by Mr. Wood in hisOptics, Prop.xiii.andxiv.

“From both these contrivances, and from every optical instrument with which I am acquainted, the Kaleidoscope appears to differ essentially, both in its effect and in the principles of its construction.

“As to the effect, the thing produced by the Kaleidoscope is a series of figures presented with the most perfect symmetry, so as always to compose a whole, in which nothing is wanting and nothing redundant. It matters not what the object be to which the instrument is directed; if it only be in its proper place, the effect just described is sure to take place, and with an endless variety. In this respect the Kaleidoscope appears to be quite singular among optical instruments. Neither the instrument of Bradley, nor the experiment or theorem in Wood’s book, have any resemblance to this; they go no further than the multiplication of the figure.

“Next, as to the principle of construction, Dr. Brewster’s instrument requiresa particular position of the eye of the observer, and of the object looked at, in order to produce its effect. If either of these is wanting, the symmetry vanishes, and the figures are irregular and disunited. In the other two cases, no particular position, either for the eye or the object, is required.

“For these reasons, Dr. Brewster’s invention seems to me quite unlike the other two. Indeed, as far as I know, it is quite singularamong optical instruments; and it will be matter of sincere regret, if any imaginary or vague analogy, between it and other optical instruments, should be the means of depriving the Doctor of any part of the reward to which his skill, ingenuity, and perseverance, entitle him so well.

“John Playfair,Professor of Natural Philosophy inthe University of Edinburgh.”

“P.S.—Granting that there were a resemblance between the Kaleidoscope and Bradley’s instrument, in any of the particulars mentioned above, the introduction of coloured and movable objects, at the end of the reflectors, is quite peculiar to Dr. Brewster’s instrument. Besides this, a circumstance highly deserving of attention, is the use of two lenses and a draw-tube; so that the action of the Kaleidoscope is extended to objects of all sizes, and at all distances from the observer, and united, by that means, to the advantages of the telescope.

“J. P.”

Professor Pictet’s opinion is stated in the following letter:—

“Sir,—Among your friends, I have not been one of the least painfully affected by the shameful invasion of your rights as an inventor, which I have been a witness of lately in London. Not only none of the allegations of the invaders of your patent, grounded on a pretended similarity between your Kaleidoscope and Bradley’s instrument, or such as Wood’s or Harris’s theories might have suggested, appear to me to have any real foundation; but I can affirm,that, neither in any of the French, German, or Italian authors, who, to my knowledge, have treated of optics, nor in Professor Charles’s justly-celebrated and most complete collection of optical instruments at Paris, have I read or seen anything resembling your ingenious apparatus, which, from its numberless applications, and the pleasure it affords, and will continue to afford to millions of beholders of its matchless effects, may be ranked among the most happy inventions that science ever presented to the lovers of rational enjoyment.“M. A. Pictet,Professor of Natural Philosophy inthe Academy of Geneva.”

“M. A. Pictet,Professor of Natural Philosophy inthe Academy of Geneva.”

Those who wish to examine farther the ancient combinations of plane mirrors, and other subjects connected with the Kaleidoscope, are referred to the following works:—

Baptista Porta’sMagia Naturalis. Kircher’sArs Magna Lucis et Umbræ. Schottus’sMagia Universalis Naturæ et Artis. Bradley’sTreatise on Planting and Gardening. Harris’sTreatise on Optics. Wood’sOptics. Dr. Roget on theKaleidoscope, in theAnnals of Philosophy, vol. xi. p. 375.Encyclopædia Britannica, Art.Kaleidoscope,byDr. Roget; and theCompte Rendu des Travaux de L’Académie de Dijon, pour 1818, pp. 108-117.

Works by SIR DAVID BREWSTER.MORE WORLDS THAN ONE:the Creed of the Philosopher, the Hope of the Christian. Cr. 8vo., 4s. 6d.THE MARTYRS OF SCIENCE:Galileo, Tycho Brahe, and Kepler. Cr. 8vo., 4s. 6d.THE KALEIDOSCOPEPractically Described. Cr. 8vo.,with Illustrations, 4s. 6d.THE STEREOSCOPEPractically Described. Cr. 8vo.,with Illustrations, 4s. 6d.London:JOHN CAMDEN HOTTEN,74, PICCADILLY.

Works by SIR DAVID BREWSTER.

MORE WORLDS THAN ONE:the Creed of the Philosopher, the Hope of the Christian. Cr. 8vo., 4s. 6d.

THE MARTYRS OF SCIENCE:Galileo, Tycho Brahe, and Kepler. Cr. 8vo., 4s. 6d.

THE KALEIDOSCOPEPractically Described. Cr. 8vo.,with Illustrations, 4s. 6d.

THE STEREOSCOPEPractically Described. Cr. 8vo.,with Illustrations, 4s. 6d.

London:JOHN CAMDEN HOTTEN,74, PICCADILLY.

Footnotes:[1]An account of the experiments above alluded to was given in theAnalyse des Travaux de la Classe des Sciences Mathématiques et Physiques de l’Institut Royal de France, pendant l’année 1815, par M. le Chev. Delambre, p. 29, &c. The colours produced by repeated reflexions from plates of silver are those ofElliptical Polarization, and are explained at great length in my paper on that subject, published in thePhilosophical Transactionsfor 1830.[2]As this Patent, in so far as the simple Kaleidoscope is concerned, was to a great extent infringed, it has been supposed that it was reduced in a Court of Law. The validity of the Patent was never questioned by any lawyer, or any philosopher acquainted with its theory and construction, as will appear from the opinion of four competent judges, given in theAppendix.In a trial for the infringement of a Patent several years ago, a distinguished judge (we believe it was Judge Alderson) stated it as a fact, that the Patent for the Kaleidoscope had been set aside in a Court of Law. The party whose case was prejudiced by this erroneous assertion, applied to me for an affidavit, by which he was enabled to contradict it in Court, and remove any unfavourable impression it might have made upon the jury.[3]See Chapter X.[4]See the articleAccidental Colours, in theEdinburgh Encyclopædia, vol. i. p. 88.[5]An instrument calledThe Improved Kaleidoscopehas been recently brought out in Paris. It is merely the Telescopic Kaleidoscopedeteriorated. It consists of a lensfixedat the distance of about two inches in front of the reflectors, and can therefore give symmetrical pictures of objects only atone distance, while it cannot be used as an ordinary Kaleidoscope. The instrument described in the preceding page, with a lens that can be slipped off, is a much better Kaleidoscope.[6]See Chapter X.[7]When this chapter was written (1818), it was very difficult to procure glass sufficiently homogeneous for this purpose: but it can now be procured from the Glass Works of Messrs. Chance & Co., at Smethwick, near Birmingham.[8]This light was first proposed by myself. SeeEdinburgh Review, April 1833, vol. lvii. p. 192.[9]See myTreatise on Optics, Edit. 1853, Chaps.xxviii, xxix.[10]Treatise on Optics, p. 120.[11]See myTreatise on the Stereoscope, Chap. xi. p. 86.[12]SeeEdinburgh Encyclopædia, Art. Civil Architecture, platecli.[13]See Hope’sCostume of the Ancients, vol. ii. plates 230, 264, 278, figs 1 and 298, fig. 2.[14]SeeJournal of the Royal Institution, vol. v. p. 99.[15]See p. 93.[16]A thin lens of rock crystal will transmit more of the actinic rays than one rendered achromatic.[17]See theJournal of the Photographic Society, vol. iv. p. 137.[18]This work is entitled,L’Optique des Couleurs, fondée sur les simples observations et tourné surtout à la pratique de la peinture, de la teinture, et des autres arts coloristes. Par le R. P. Castel, Jesuite. Paris, 1740.[19]It would be an easy matter to amuse the reader with an account of these improvements. One of the most notable of them consists in covering the back of the reflectors with white paint, for the purpose of increasing the light of the circular field. This scheme is identically the same as if the author had proposed to improve the magnificent telescopes of Herschel, when rendered dark with a high magnifying power, bywhite-washingthe interior of the tube.[20]We request that the reader will take the trouble of comparing with the original the following translation of Baptista Porta’s description, which was published in London, and copied into all the foreign newspapers, etc. We hope the translator of it had no improper motive in altering the obvious meaning of the original; yet it is singular, that in the journal where this translation appeared, the specification of the patent was published under the title of Directions for making the Kaleidoscope, purporting to be an original communication to that journal, the name of the patentee, and the technical parts of the specification having been left out, apparently to promote the belief that there was no patent, and that every person might make them with impunity. The following is the translation alluded to:—“In the following manner we may construct a mirror for seeing a multitude of objects on a plain surface. This kind of mirror, when constructed, is what is calledpolyphaton, that is to say, multiplying, for by opening and shutting, it shows twenty and more images of one single finger. If, therefore, you wish to prepare it, let two brazen or crystal rectangular mirrors be erected on the same base, and let the proportion of length be one and a half of the width, or any other proportion; and let each side for the whole of its length be so connected together that they may easily be shut and opened like a book, and that the angles may be varied, as they are usually constructed at Venice; for if you placeone object opposite to the face of each, you will seeseveral figures; and this in proportion as you shut it closer, and the angle shall be less. But, by opening,the objectswill be reduced in number, and the more obtuse the angle under which you see it, thefewer objectswill be seen. So if you exhibit your fingeras the object, you will see nothing but fingers. The right fingers will be seen on the right side, and the left on the left side, which is contrary to the usual custom with looking-glasses; but this happens from the mutual reflexion and repulsion which produce a change of the images.”[21]I have thrown the rest of the passage into a tabular form, that the reader may see, more readily, the effect produced by the variation of the angle.[22]See Appendix, p. 185.[23]See Chap. I. pp. 11, 12, where we have shown that Harris was not even acquainted with the way in which the last sector is formed by reflexion.

Footnotes:

[1]An account of the experiments above alluded to was given in theAnalyse des Travaux de la Classe des Sciences Mathématiques et Physiques de l’Institut Royal de France, pendant l’année 1815, par M. le Chev. Delambre, p. 29, &c. The colours produced by repeated reflexions from plates of silver are those ofElliptical Polarization, and are explained at great length in my paper on that subject, published in thePhilosophical Transactionsfor 1830.

[2]As this Patent, in so far as the simple Kaleidoscope is concerned, was to a great extent infringed, it has been supposed that it was reduced in a Court of Law. The validity of the Patent was never questioned by any lawyer, or any philosopher acquainted with its theory and construction, as will appear from the opinion of four competent judges, given in theAppendix.In a trial for the infringement of a Patent several years ago, a distinguished judge (we believe it was Judge Alderson) stated it as a fact, that the Patent for the Kaleidoscope had been set aside in a Court of Law. The party whose case was prejudiced by this erroneous assertion, applied to me for an affidavit, by which he was enabled to contradict it in Court, and remove any unfavourable impression it might have made upon the jury.

In a trial for the infringement of a Patent several years ago, a distinguished judge (we believe it was Judge Alderson) stated it as a fact, that the Patent for the Kaleidoscope had been set aside in a Court of Law. The party whose case was prejudiced by this erroneous assertion, applied to me for an affidavit, by which he was enabled to contradict it in Court, and remove any unfavourable impression it might have made upon the jury.

[3]See Chapter X.

[4]See the articleAccidental Colours, in theEdinburgh Encyclopædia, vol. i. p. 88.

[5]An instrument calledThe Improved Kaleidoscopehas been recently brought out in Paris. It is merely the Telescopic Kaleidoscopedeteriorated. It consists of a lensfixedat the distance of about two inches in front of the reflectors, and can therefore give symmetrical pictures of objects only atone distance, while it cannot be used as an ordinary Kaleidoscope. The instrument described in the preceding page, with a lens that can be slipped off, is a much better Kaleidoscope.

[6]See Chapter X.

[7]When this chapter was written (1818), it was very difficult to procure glass sufficiently homogeneous for this purpose: but it can now be procured from the Glass Works of Messrs. Chance & Co., at Smethwick, near Birmingham.

[8]This light was first proposed by myself. SeeEdinburgh Review, April 1833, vol. lvii. p. 192.

[9]See myTreatise on Optics, Edit. 1853, Chaps.xxviii, xxix.

[10]Treatise on Optics, p. 120.

[11]See myTreatise on the Stereoscope, Chap. xi. p. 86.

[12]SeeEdinburgh Encyclopædia, Art. Civil Architecture, platecli.

[13]See Hope’sCostume of the Ancients, vol. ii. plates 230, 264, 278, figs 1 and 298, fig. 2.

[14]SeeJournal of the Royal Institution, vol. v. p. 99.

[15]See p. 93.

[16]A thin lens of rock crystal will transmit more of the actinic rays than one rendered achromatic.

[17]See theJournal of the Photographic Society, vol. iv. p. 137.

[18]This work is entitled,L’Optique des Couleurs, fondée sur les simples observations et tourné surtout à la pratique de la peinture, de la teinture, et des autres arts coloristes. Par le R. P. Castel, Jesuite. Paris, 1740.

[19]It would be an easy matter to amuse the reader with an account of these improvements. One of the most notable of them consists in covering the back of the reflectors with white paint, for the purpose of increasing the light of the circular field. This scheme is identically the same as if the author had proposed to improve the magnificent telescopes of Herschel, when rendered dark with a high magnifying power, bywhite-washingthe interior of the tube.

[20]We request that the reader will take the trouble of comparing with the original the following translation of Baptista Porta’s description, which was published in London, and copied into all the foreign newspapers, etc. We hope the translator of it had no improper motive in altering the obvious meaning of the original; yet it is singular, that in the journal where this translation appeared, the specification of the patent was published under the title of Directions for making the Kaleidoscope, purporting to be an original communication to that journal, the name of the patentee, and the technical parts of the specification having been left out, apparently to promote the belief that there was no patent, and that every person might make them with impunity. The following is the translation alluded to:—“In the following manner we may construct a mirror for seeing a multitude of objects on a plain surface. This kind of mirror, when constructed, is what is calledpolyphaton, that is to say, multiplying, for by opening and shutting, it shows twenty and more images of one single finger. If, therefore, you wish to prepare it, let two brazen or crystal rectangular mirrors be erected on the same base, and let the proportion of length be one and a half of the width, or any other proportion; and let each side for the whole of its length be so connected together that they may easily be shut and opened like a book, and that the angles may be varied, as they are usually constructed at Venice; for if you placeone object opposite to the face of each, you will seeseveral figures; and this in proportion as you shut it closer, and the angle shall be less. But, by opening,the objectswill be reduced in number, and the more obtuse the angle under which you see it, thefewer objectswill be seen. So if you exhibit your fingeras the object, you will see nothing but fingers. The right fingers will be seen on the right side, and the left on the left side, which is contrary to the usual custom with looking-glasses; but this happens from the mutual reflexion and repulsion which produce a change of the images.”

“In the following manner we may construct a mirror for seeing a multitude of objects on a plain surface. This kind of mirror, when constructed, is what is calledpolyphaton, that is to say, multiplying, for by opening and shutting, it shows twenty and more images of one single finger. If, therefore, you wish to prepare it, let two brazen or crystal rectangular mirrors be erected on the same base, and let the proportion of length be one and a half of the width, or any other proportion; and let each side for the whole of its length be so connected together that they may easily be shut and opened like a book, and that the angles may be varied, as they are usually constructed at Venice; for if you placeone object opposite to the face of each, you will seeseveral figures; and this in proportion as you shut it closer, and the angle shall be less. But, by opening,the objectswill be reduced in number, and the more obtuse the angle under which you see it, thefewer objectswill be seen. So if you exhibit your fingeras the object, you will see nothing but fingers. The right fingers will be seen on the right side, and the left on the left side, which is contrary to the usual custom with looking-glasses; but this happens from the mutual reflexion and repulsion which produce a change of the images.”

[21]I have thrown the rest of the passage into a tabular form, that the reader may see, more readily, the effect produced by the variation of the angle.

[22]See Appendix, p. 185.

[23]See Chap. I. pp. 11, 12, where we have shown that Harris was not even acquainted with the way in which the last sector is formed by reflexion.

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