'jf9%.-: - ' O"' THE UNIVERSITY TO FEE DUKE OF ARGYLL, LlLD. P.R.S.E. LORD PRIVY SEAL, CHANCELLOR OF THE UNIVERSITY OF ST. ANDREW'S, THIS VOLUME IS INSCRIBED, IN TESTIMONY OF THE AUTHOR'S ADMIRATION OF HIS TALENTS, AND OF THE ZEAL WITH WHICH THEY ARE DIRECTED IN PROMOTING THE MORAL, RELIGIOUS, AND INTELLECTUAL PROGRESS OF MANKIND. ST. LEONARD'S COLLEGE, ST. ANDREW'S, March 1. 1855. CONTENTS. Page INTRODUCTION - - - - - -1 PART I. ON THE REFLEXION AND REFRACTION OF LIGHT. CATOPTRICS. CHAP. L Reflexion by Specula and Mirrors - -4 Reflexion of Rays from Plane Mirrors - -6 Reflexion of Rays from Concave Mirrors - - 8 Reflexion of Rays from Convex Mrirors . -13 CHAP. II. Images formed by Mirrors - - - - - 15 Images formed by Apertures - - - 16 Images formed by Concave Mirrors - - - - 16 Images formed by Convex Mirrors - - - - 18 Images formed by Plane Mirrors . . - -19 DIOPTRICS. CHAP. III. Refraction - .... - 20 Law of Refraction - - . . - 28 Refractive Power of Bodies - . . - 26 CHAP. IV. Refraction through Prisms and Lenses - - . - 26 On the total Reflexion of Light - - . - 31 Refraction of Light through Plane Glasses - . .32 Refraction of Light through Curved Surfaces - - 34 Refraction of Light through Spheres - - - 35 Refraction of Light through Convex and Concave Surfaces - 38 Refraction of Light through Convex Lenses - - - 39 Refraction of Light through Concave Lenses - - - 42 Refraction of Light through Meniscuses and Concavo-convex Lenses of Glass - - - - -44 Vi CONTENTS. CHAP. V. Page On the Formation of Images by Lenses, and on their magnifying Power - ... 45 CHAP. VI. Spherical Aberration of Lenses and Mirrors - - 52 Spherical Aberration of Mirrors - - - 58 On Caustic Curves formed by Reflexion and Refraction - 60 CHAP. VII. On the Form of Images produced by Lenses and Mirrors of different sizes - - - - - -65 PART II. PHYSICAL OPTICS. CHAP. VIII. On the Colours of Light, and its Decomposition - - -72 Decomposition of Light by Absorption - - -77 CHAP. IX. On the Dispersion of Light - - 81 CHAP. X. On the Principle of Achromatic Telescopes - - - 85 CHAP. XI. On the Physical Properties of the Spectrum On the Existence of Fixed Lines fn the Spectrum On the Bright Lines in the Spectra of different Flames On the Illuminating Power of the Spectrum On the Heating Power of the Spectrum On the Chemical Influence of the Spectrum - On the Magnetising Power of the Solar Rays CHAP. XII. On the Inflexion or Dijgraction of Light - - 109 CHAP. XIII. On the Colours of Thin Plates - - - - 117 Table of the Colours of Thin Plates of Air, Water, and Glass - 123 CONTENTS. Vll CHAP. XIV. Page On the Colours of Thick Plates - - - - 129 CHAP. XV. On the Colours of Fibres and grooved Surfaces - 135 On the Colours of Mother-of- Pearl - - - - 137 CHAP. XVI. On the Colours of Mixed Plates - - 149 CHAP. XVII. On Fits of Reflexion and Transmission, on the Interference of Light, and the Undulatory Theory - 155 CHAP. XVIII. On the Direct Interference of Light ... - 166 CHAP. XIX. On the Absorption of Common Light - - - - 171 CHAP. XX. On the Internal Dispersion of Light within Solid and Fluid Bodies 179 CHAP. XXI. On the Optical Figures produced by Reflexion from the Disintegrated Surfaces of Crystals - - 184 CHAP. XXII. On the Double Refraction of Light - - -189 On Crystals with one Axis of Double Refraction - - 193 On the Law of Double Refraction in Crystals with one Negative Axis- - - - - - - 195 On the Law of Double Refraction in Crystals with one Positive Axis - - - - - - 198 On Crystals with two Axes of Double Refraction - - 199 On Crystals with three Axes of Double Refraction - - 202 On Double Refraction in which one of the Pencils is nebulous - 203 On Crystals with innumerable Axes of Double Refraction - 204 On Bodies to which Double Refraction may be communicated by Heat, rapid Cooling, Pressure, and Induration - ib. On Substances with Circular or Rotatory Double Refraction - 206 CONTENTS. CHAP. XXIII. Page On the Polarisation of Light - - 207 On the Polarisation of Light by Double Refraction - - 209 CHAP. XXIV. On the Polarisation of Light by Reflexion - - 214 On the Law of the Polarisation of Light by Reflexion - - 218 On the partial Polarisation of Light by Reflexion - - 222 CHAP. XXV. On the Polarisation of Light by ordinary Refraction - - 226 CHAP. XXVI. On the Colours of Crystallised Plates in Polarised Light - - 233 CHAP. XXVII. On the Method of determining by the Eye alone the Direction of the Plane of Polarisation . - 245 CHAP. XXVIII. On the System of Coloured Rings in Crystals with one Axis - 249 Polarising Intensities of a few Crystals with one Axis - - 259 CHAP. XXIX. On the Systems of Coloured Rings in Crystals with two Axes - 260 Polarising Intensities of some Crystals with two Axes - - 269 CHAP. XXX. On Circular Crystals - - - 269 CHAP. XXXI. Interference of Polarised Light. On the Cause of the Colours of Crystallised Bodies - - . . - 273 CHAP. XXXII. On the Polarising Structure of Analcime ... 277 CHAP. XXXIII. On Lamellar Polarisation - - 279 CHAP. XXXIV. On Conical Polarisation ^ - - 283 CONTENTS. IX CHAP. XXXV. Page On Circular Polarisation in Quartz .... 286 Circular Polarisation in Amethyst - - 289 Circular Polarisation in Fluids - - 297 Crystals which turn the Planes of Polarisation from Right to Left 298 Crystals which turn the Planes of Polarisation from Left to Right ib. On the Crystallographic Structure which produces Circular Polarisation - - 301 CHAP. XXXVI. On Elliptical Polarisation, and on the Action of Metals upon Light 305 On Elliptical Polarisation - - ib. Order in which the Metals polarise most Light in the Plane of Reflexion - - 306 On the Colours of Elliptical and Circular Polarisation - - 313 On Circular Electro-magnetic Polarisation - - 315 CHAP. XXXVII. On the Action of the Surfaces of Crystallised Bodies upon Common and Polarised Light - 320 On Double Reflexion and Polarisation ... 323 CHAP. XXXVIII. On the Polarising Structure produced by Heat, Cold, Compression, Dilatation, and Induration .... 324 1. Transient Influence of Heat and Cold - - ib. (1.) Cylinders of Glass with one positive Axis of Double Refraction . _ ib. (2.) Cylinders of Glass with a negative Axis of Double Re- fraction ------ 325 (3.) Oval Plates of Glass with two Axes of Double Refraction 326 (4.) Cubes of Glass with Double Refraction - - ib. (5.) Rectangular Plates of Glass with Planes of no Double Refraction - - 327 (6.) Spheres of Glass, &c. with an infinite Number of Axes of Double Refraction - - - 329 (7.) Spheroids of Glass with one Axis of Double Refraction along the Axis of Revolution and two Axes along the Equatorial Diameters - - 330 (8.) Influence of Heat on regular Crystals - - ib. 2. On the permanent Influence of sudden and quick Cooling - 333 3. On the Influence of Compression and Dilatation - - 335 4. On the Influence of Compression and Dilatation on regularly Crystallised Bodies - - - - 338 (1.) On Crystals without Double Refraction - - ib. (2.) On Doubly Refracting Crystals - - - ib. 5. On the Influence of Induration - - - - 340 X CONTENTS. CHAP. XXXIX. Page Phenomena of Composite or Tesselated Crystals - 341 Phenomena of Harmotome - ... 342 Phenomena of Sulphate of Potash - - - ib. phenomena of Apophyllite . - 343 Phenomena of Chabasie - - 347 Phenomena of Brazilian Topaz ... - 348 Phenomena of Aplome Garnet .... 349 Phenomena of Calcareous Spar - - 351 CHAP. XL. On the Dichroism, or Double Colour, of Bodies ; and the Absorption of Polarised Light - - - - - 353 Colours of the two Images in Crystals with one Axis - - 354 Colours of the two Images in Crystals with two Axes - - 356 On the Production of Crystalline Structure by Pressure and Traction in Dichroitic and other Crystals - 359 General Observations on Double Refraction . - - 360 PART III. ON THE APPLICATION OF OPTICAL PRINCIPLES TO THE EXPLAN- ATION OF NATURAL PHENOMENA. CHAP. XLI. On unusual Refraction . 362 CHAP. XLII. On the Polarisation of the Atmosphere - - . - 372 CHAP. XLIII. On the Rainbow - - - - - - 377 CHAP. XLIV. On Halos, Coronae, Parhelia, Paraselenae, and Anthelia - - 381 Researches of M. Bravais - - - . - 388 On Bravais' Parhelioscope - - 392 On the Polarisation of the Light of Halos - - 393 On Converging Beams .... 396 CHAP. XLV. On the Colours of Natural Bodies .. . , 398 CONTENTS. XI CHAP. XLVI. Page On the Eye and Vision - - . - - 405 On the Phenomena and Laws of Monocular Vision - - 409 1. On the Seat of Vision - - - - 409 2. On the Law of visible Direction - - - 412 3. On the Cause of Erect Vision - - - 414 4. On the Law of Distinct Vision - - - 415 5. On the Insensibility of the Eye to direct Impressions of faint Light - 419 6. On the Duration of Impressions of Light on the Retina - 420 The Thaumatrope - - 421 The Phenakistoscope - - . ib. 7. On the Cause of Single Vision - 422 8. On the Accommodation of the Eye to different Distances 423 9. On the cause of Longsightedness and Shortsightedness - 425 10. On the Cylindrical form of the Cornea - 426 CHAP. XLVII. On Binocular Vision and the Stereoscope ... 426 Lenticular Stereoscope - .... 428 Total Reflexion Stereoscope with a single Figure - - 429 CHAP. XLVIII. On accidental Colours and coloured Shadows - - 430 Colour Blindness - - . . .438 PART IV. ON OPTICAL INSTRUMENTS. CHAP. XLIX. On Plane and Curved Mirrors - - . - - 442 Kaleidoscope ---._. 443 Plane Burning Mirrors - .... 446 Convex and Concave Mirrors .... 447 Cylindrical Mirrors - . 448 CHAP. L. On Single and Compound Lenses - - . - 449 Burning and illuminating Lenses - . - - 450 CONTENTS. CHAP. LI. Page On Simple and Compound Lenses .... 453 Prismatic Lenses - - - - ib. Compound and variable Prisms - - 455 Multiplying Glass - 458 CHAP. LIL On the Camera Obscura, Magic Lantern, and Camera Lucida - 459 Camera Obscura - - - - - - ib. Magic Lantern - - - - - - 461 Camera Lucida - ... 463 CHAP. LIU. On Microscopes ------ 465 On Single Microscopes - - ib. Hemispherical Reflecting Lens - - 468 Grooved Lens .-..-- 470 Semi-Lenses and Quarter Lenses - - - 471 Reading Glasses - - ib. Extempore Microscope .... - 472 On Compound Microscopes - - ib. Wollaston's Doublet - - - - - 477 On Reflecting Microscopes * - 478 On Test Objects - - - 480 Rules for Microscopical Observations - - - ib. Solar Microscope - - 481 On the Illumination of Microscopic Objects - 482 On the Polarising Microscope - ... 484 The Microscopic Finder - - 486 CHAP. LIV. On Refracting and Reflecting Telescopes - 486 Astronomical Telescope - - ib. Terrestrial Telescope - - 488 Galilean Telescope - - - 489 Gregorian Reflecting Telescope - - ib. Cassegrainian Telescope - - 492 Newtonian Telescope - - ib. with Achromatic Prism .... 494 Sir W. Herschel's Telescope - - 495 Mr. Ramage's Reflecting Telescopes - - 496 Lord Rosse's Telescopes - ... 497 Mr. Lassell's Telescope - ... 500 Mr. Nasmyth's Telescope - - - - - 500 CONTENTS. Xlll CHAP. LV. Page On Achromatic Telescopes - - 502 Rev. Mr. Craig's Achromatic Telescope ... 506 On Achromatic Eyepieces - 508 Ramsden's Positive Eyepiece - 509 Prism Telescope - - 513 Achromatic Eye Glasses with single Lenses ... 515 Mr. Barlow's Achromatic Telescope . - - 516 Mr. Rogers's Achromatic Telescope - - 517 Achromatic Solar Telescopes with single Lenses - - 518 On the Improvement of imperfectly Achromatic Telescopes - 520 APPENDIX - - - - - - 521 A TREATISE OPTICS u r i i ^ ^313,^ /y'y* o* THE ^^S, tlTITBRSITTJ . ,jm^ INTRODUCTION. (1.) OPTICS, from a Greek word which signifies to see, is that branch of knowledge which treats of the pro- perties of light, and of the phenomena and laws of vision as performed by one or both eyes. (2.) Light is an emanation, or something which pro- ceeds from bodies, and by means of which we are enabled to see them. All visible bodies may be divided into two classes self-luminous and non-luminous. Self-luminous bodies, such as the stars,, flames of all kinds, and bodies which shine by being heated, or rubbed, or electrified, are those which possess in them- selves the property of discharging light. Non-luminous bodies are those which have not the power of dis- charging light of themselves, but which throw back the light which falls upon them from self-luminous bodies. One non-luminous body may receive light from another non-luminous body, and discharge it upon a third ; but in every case the light must originally come from a self-luminous body. When a lighted candle is brought into a dark room, the form of the flame is seen by the light which proceeds from the flame itself; but the objects in the room are seen by the light which they B 2 A TREATISE ON OPTICS. receive from the candle, and again throw back ; while other objects, on which the light of the candle does not fall, receive light thrown back from the white ceiling and walls, and thus become visible. (3.) All bodies, whether self-luminous or non-lumin- ous, discharge or reflect light of the same colour with themselves. A red flame or a red-hot body discharges red light ; and a piece of red cloth reflects red light, though it is illuminated by the white light of the sun. (4.) Light is emitted from every visible point of a luminous or of an illuminated body, and in every direc- tion in which the point is visible. If we look at the flame of a candle, or at a sheet of white paper, and mag- nify them ever so much, we shall not observe any points destitute of light. (5.) Light moves 'in straight lines, and consists of separate and independent parts, called rays of light. If we admit the light of the sun into a dark room through a small hole, it will illuminate a spot on the wall exactly opposite to the sun, the middle of the spot, the middle of the hole, and the middle of the sun, being all in the same straight line. If there is dust or smoke in the room, the progress of the light in straight lines will be distinctly seen. If we stop a very small portion of the admitted light, and allow the rest to pass, or if we stop nearly the whole light, and allow only the smallest por- tion to pass, the part which passes is not in the slightest degree affected by its separation from the rest. The smallest portion of light which we can either stop or allow to pass is called a ray of light. (6.) Light moves with a velocity of 192,500 miles in a second of time. It travels from the sun to the earth in seven minutes and a half. It moves through a space equal to the circumference of our globe in the 8th part of a second, a flight which the swiftest bird could not per- form in less than three weeks. (7.) When light falls upon any body whatever, part of it is reflected or driven back, and part of it enters the body, and is either lost within it or transmitted through INTRODUCTION. 3 it. When the body is bright and well polished like gold or silver, a great part of the light is reflected, and. the remainder lost within the gold or silver, which can transmit light only when hammered out into the thin- nest film. When the body is transparent, like glass or water, almost all the light is transmitted, and only a small part of it reflected. The light which is driven back from bodies is reflected according to particular laws, the consideration of which forms that branch of optics called catoptrics ; and the light which is trans- mitted through transparent bodies is transmitted ac- cording to particular laws, the consideration of which constitutes the subject of dioptrics. A TREATISE ON OPTICS. PART I. PART I. ON THE REFLEXION AND REFRACTION OF LIGHT. CATOPTRICS. (8.) CATOPTRICS is that branch of optics which treats of the progress of rays of light after they are reflected from plane and spherical surfaces, and of the formation of images from objects placed before such surfaces. CHAP. I. REFLEXION BY SPECULA AND MIRRORS. {9; ANY substance of a regular form employed for the purpose of reflecting light, or of forming images of objects, is called a speculum or mirror. It is generally made of metal or glass, having a highly polished surface. The name of mirror is commonly given to reflectors that are made of glass ; and the glass is always quicksilvered on the back, or silvered by the new electrotype process, to make it reflect more light. The word speculum is used to describe a reflector which is metallic, such as those made of silver, steel, or of grain tin mixed with copper. (10.) Specula or mirrors are either plane, concave, or convex. A plane speculum is one which is perfectly flat, like a looking-glass; a concave speculum is one which is hollow like the inside of a watch-glass ; and a convex speculum is one which is round like the outside of a watch-glass. As the light which falls upon glass mirrors is inter- cepted by the glass before it is reflected from the quick- CHAP. I. INCIDENCE AND REFLEXION. silvered surface,, we shall suppose all our mirrors to be formed of polished metal, as they are in almost all optical instruments. (11.) When a ray of light, AD, fig. 1., falls upon a Fig. 1. plane speculum, M N, at the point D, it will be reflected or driven back in a direction D B, which is as much inclined to E D, a line per- pendicular to M N, as the ray A D was; that is, the angle B D E is equal to A D E, or the circular arc B E is equal to E A. The ray A D is called the incident ray, and D B the reflected ray, A D E the angle of incidence, and B D E the angle of reflexion ; and a plane passing through A D and D B, or the plane in which these two lines lie, is called the plane of incidence, or the plane of reflexion. (12.) When the speculum is concave, as MN,fig. 2., then if C be the centre of the circle of which M N is a part, the incident ray A D and the re- flected ray D B will form equal angles with the line C D, which is perpendicular to the small por- tion of the speculum on which the ray falls at D. Hence in this case also the angle of incidence A D E is equal to the angle of reflexion B D E. (13.) When the speculum is convex, as M N, fig. 3., let C be the centre of the circle of which M N forms a part, and C E a line drawn through D ; then the angle of incidence A D E will be equal to the angle of reflexion BDE. These results are found to be true !>N by experiment; and they may be easily proved by admitting a ray of the sun's light through a hole in the -window- shutter, and making it fall on the mirrors M N in the B 3 A TREATISE ON OPTICS. PART I. direction AD, when it will be seen reflected in the direction DB. If the incident ray AD is made to ap- proach the perpendicular DE, the reflected ray DB will also approach the perpendicular DE ; and when the ray AD falls in the direction ED, it will be reflected in the direction D E. In like manner when the ray A D approaches to D N, the ray D B will approach to DM. (14.) As these results are true under all circumstances, we may consider it as a general law, that when light falls upon any surface, whether plane or curved, the angle of its reflexion is equal to the angle of its incidence. Hence we have a method of universal application for finding the direction of a reflected ray when we know the direction of the incident ray. If A D, for example, figs. 1, 2, 3., is the direction in which the incident ray falls upon the mirror at D, draw the perpendicular D E in fig. 1., and in^. 2. or^. 3. draw aline from D to C, the centre of the curved surface M N ; and, having de- scribed a circle M B E A N round D as a centre, take the distance A E in the compasses and carry it from E to B, and having drawn a line from D to B, D B will be the direction of the reflected ray. Reflexion of Rays from Plane Mirrors. (15.) Reflexion of parallel rays. When parallel or equidistant rays, A D, A' D', fig. 4., are incident upon Fig. 4. a plane mirror, M N, they will continue to be paral- lel after reflexion. By the method already explained, describe arches of circles round D, D' as centres, and make the arch from E towards B equal to that be- CHAP. I. PLANE MIRRORS. tween A D and D E, and also the arch from E' towards B' equal to that between A'D' and D'E'; then drawing the lines D B, D'B', it will be found that these lines are parallel. If the space between AD and A'D' is filled with other rays parallel to A D, so as to constitute a parallel beam or mass of light A A' D'D, the reflected rays will be all parallel to B D, and will constitute a parallel reflected beam. The reflected beam, however, will be inverted; for the side A D, which was uppermost before reflection, will be undermost, as at D B, after reflexion. (16.) Reflexion of diverging rays. Diverging rays are those which proceed from a point, A, and separate as they advance, like AD, A D', A D". When such rays fall upon a plane mirror M N, fig. 5., they will be reflected in directions DB, D' B', D' B", making the angles BDE, B'D'E', B"D"E", respectively, equal to ADE, A D'E', AD"E"; the lines D E, D'E', D"E" being drawn from the points D, D', D", where the rays are incident, perpendicular to MN; and by Fig. 5. continuing the reflected rays backwards, they will be found to meet at a point A' as far behind the mirror MN as A is before it ; that is, if A N A' be drawn perpendi- cular to M N, A' N will be equal to A N. Hence the rays will have the same divergency after reflexion as they had before it. If we consider A D" D as a divergent beam of light included between A D and A D", then the B 4 A TREATISE ON OPTICS. PART I. reflected beam included between J)B and D"B" will diverge from A', and will be inverted after reflexion. (17.) Reflexion of converging rays. Converging rays are those which proceed from several points A, A 7 , A'\ fig. 6., towards one point B. When such rays fall upon Fig. 6. fr a plane mirror, M N, they will be reflected in directions D B', D'B', D"B', forming the same angles with the per- pendiculars D E, D' E', D" E", as the incident rays did, and converging to a point B' as far before the mirror as the point B is behind it. If we consider A D D" A" as a converging beam of light, D" B' D will be its form after reflexion. In all these cases the reflexion does nothing more than invert the incident beam of light, and shift its point of divergence or convergence to the opposite side of the mirror. Reflexion of Rays from Concave Mirrors. (18.) Reflexion of parallel rays. Let MN, fig. 7., be a concave mirror whose centre of concavity is C ; and let AD, AM, AN be parallel rays, or a parallel beam of light falling upon it, at and near to the vertex D. Then, since CM, CN are perpendicular to the surface of the mirror at the points M and N, CM A, CNA will be the angles of incidence of the rays AM, AN. Make the angles of reflexion CMF, CNF equal to CM A, CNA, and it will be found that the lines MF, CONCAVE MIRRORS. NF meet at F in the line AD, and these lines MF, NF will be the reflected rays. The ray AC D being perpendicular to the mirror at D, because it passes through the centre C, will be reflected in an opposite direction D F ; so that all the three rays, AM, AD, and AN, will meet at one point, F. In like manner it will be found that all other rays between AM and AN, falling upon other points of the mirror between M and N, will be reflected to the same point F. The point F, in which a concave mirror collects the rays which fall upon it, is called the focus, or fire-place, be- cause the rays thus collected have the power of burning any inflammable body placed there. When the rays which the mirror collects are parallel, as in the present case, the point F is called its principal focus, or its focus for parallel rays. When we consider that the rays which form the beam AMNA occupy a large space before they fall upon the mirror M N, and by reflexion are condensed upon a small space at F, it is easy to understand how they have the power of burning bodies placed at F. RULE. The distance of the focus F from the nearest point or vertex D of the mirror MN is, in spherical mirrors, whatever be their substance, equal to one half of CD, the radius of the mirror's concavity. The distance FD is called the principal focal distance of the mirror. The truth of this rule may be found by pro- jecting fig. 7. upon a large scale, and by taking the points M, N near to D. (19.) Reflexion of diverging' rays. Let MN,j%. 8., be a concave mirror, whose centre of concavity is C ; 10 A TREATISE ON OPTICS. PART I. and let rays A M, AD, AN, diverging or radiating from the point A, fall upon the mirror at the points M, D, N; Fig. 8. M and N being near to D, and be reflected from these points. The lines CM, CD, and CN being perpen- dicular to the mirror at the points M, D, and N, we shall find the reflected rays M F, N F, by making the angle FMC equal to AMC, and FNC equal to ANC; and the point F, where these rays meet, will be the focus where the diverging rays A M, A N are collected. By comparing fig. 7. with fig. 8. it is obvious that, as the incident ray A M injEgr. 8. is nearer the perpendicular C M than the same ray is mfig. 7., the reflected ray M F will also be nearer the perpendicular C M than the same ray in fig. 7. ; and as the same is true of the reflected ray NF, it follows that the point F must be nearer C in fig. 8. than in fig. 7- ; that is, in the reflexion of diverging rays the focal distance D F of the mirror is greater than its focal distance for parallel rays. If we suppose the point of divergence A., fig* 8., or the radiant point, as it is called, to approach to C, the incident rays AM, AN will approach to the perpen- diculars CM, CN, and consequently the reflected rays M F, N F will also approach to C M, C N ; that is, as the radiant point A approaches to the centre of concavity C, the focus F also approaches to it, so that when A reaches C, F will also reach C ; that is, when rays diverge from the centre, C, of a concave mirror, they will all be re- flected to the same point. If the radiant point A passes C towards D, then the CHAP. I. CONCAVE MIRRORS. 11 focus F will pass C towards A; so that if the light now diverges from F it will be collected in A, the points that were formerly the radiant points being now the foci. From this relation, or interchange, between the radiant points and the foci, the points A and F have been called conjugate foci, because if either of them be the radiant point the other will be the focal point. If in fig. 7 we suppose F to be the radiant point, then the focal point A will be at an infinite distance ; that is, the rays will never meet in a focus, but will be parallel, In like manner it is obvious, that if the point F is at f, as in^. $., the reflected rays will be Ma, Na; that is, Fig. 9. they will diverge from some point, A", behind the mirror M N ; and as / approaches to D, they will diverge more and more, as jf the point A', from which they seemed to diverge, approached to D. The point A' behind the mirror, from which the rays M a, N a seem to proceed, or at which they would meet if they moved backwards in the directions a M, a N is called their virtual focus, because they only tend to meet in that focus. In all these cases the distance of the focus F may be determined either by projection or by the following rule, the radius of the concavity of the mirror, C D, and the distance, A D, of the radiant point being given. RULE. Multiply the distance, AD, of the radiant 12 A TREATISE ON OPTICS. PART I. point from the mirror by the radius, C D, of the mirror, and divide this product by the difference between twice the distance of the radiant point and the radius of the mirror, and the quotient will be F D, the conjugate focal distance required. In applying this rule we must observe, what will be readily seen from the figures, that if twice A D is less than C D (as at /, fig. 9), the rays will not meet before the mirror, but will have a virtual focus behind it, the distance of which from D will be given by the rule. (20.) Reflexion of converging rays. Let M N, fig* 10., Fig. 10. be a concave mirror whose centre of concavity is C, and let rays AM, AD, AN, converging to a point A' behind the mirror, fall upon the mirror at the points M, D, and N, and suffer reflexion at these points, M and N being near to D. The lines CM, CD, and CN being per- pendicular to the mirror at the points M, D, and N, we shall find the reflected rays M F and N F by making the angle FMC equal to AMC, and FNC equal to ANC; and the point F, where these rays meet, will be the focus where the converging rays AM, AN are collected. By comparing fig. 10. with fig. 7. it will be manifest, that, as the incident ray A M in fig. 10. is farther from the perpendicular C M than the same ray A M in fig. 7., the reflected ray MF in fig. 10. will also be farther from the perpendicular C M than the same ray in fig. 7- ; and CHAP. I. CONVEX MIRRORS. 13 as the same is true of the reflected ray NF, it follows that the point F must be farther from C in^r. 10. than in fig. 7. ; that is, in the reflexion of converging rays, the conjugate focal distance DF of the mirror is less than its distance for parallel rays. If we suppose the point of convergence A.', fig. 10., to approach to D, or the rays A M, A N to become more convergent, then the incident rays A M, A N will recede from the perpendiculars CM, C N ; and as the reflected rays M F, N F will also recede from C M, C N, the focus F will likewise approach to D ; and when A' reaches D, F will also reach D. If the rays AM, AN become less convergent, that is, if their point of convergence A' recedes farther from D to the left, the focus F will recede from D to the right ; and when A' is infinitely distant, or when AM, AN are parallel, as in fig. 7j F will be half way between D and C. In these cases the place of the focus F will be found by the following rule. RULE. Multiply the distance of the point of con- vergence from the mirror by the radius of the mirror, and divide this product by the sum of twice the distance of the radiant point and the radius C D, and the quotient will be the distance of the focus, or FD, the focus F being always in front of the mirror. Reflexion of Rays from Convex Mirrors. (21.) Reflexion of parallel rays. Let MN, fig. 11., be a convex mirror whose centre is C, and let A M, AD, AN be parallel rays falling upon it. Continue the lines CM and C N to E, and M E, N E wiU be per- pendicular to the surface of the mirror at the points M and N. The rays AM, AN will therefore be re- flected in directions MB, NB, the angles of reflexion E M B, E N B being equal to the angles of incidence E M A, E N A. By continuing the reflected rays B M, BN backwards, they will be found to meet at F, their A TREATISE ON OPTICS. PART 1. virtual focus behind the mirror; and the focal distance D F for parallel rays will be almost exactly one half of Fig. 11. the radius of convexity C D, provided the points M and N are taken near D. (22.) Reflexion of diverging rays. Let MN,./fyr. 12., be a convex mirror, C its centre of convexity, and A M, Fig. 12. AN rays diverging from A, which fall upon the mirror at the points M, N. The lines C M E and C N E will be, as before, perpendicular to the mirror at M and N; and consequently, if we make the angles of reflexion EMB,ENB equal to the angles of incidence EM A, ENA, MB,NB wiU be the reflected rays which, when continued backwards, will meet at F, their virtual focus behind the mirror. By comparing./^. 12. with fig. 11., CHAP. II. IMAGES FORMED BY MIRRORS. 1 5 it is obvious that the ray AM, fig. 12., is farther from ME than in fig. 11., and consequently the reflected ray MB must also be farther from it. Hence, as the same is true of the ray NB, the point F, where these rays meet, must be nearer to D in fig. 12. than in^. 11. ; that is, in the reflexion of diverging rays, the virtual focal distance D F is less than for parallel rays. For the same reason, if we suppose the point of divergence A to approach the mirror, the virtual focus F will also approach it ; and when A arrives at D, F will also arrive at D. In like manner, if A recedes from the mirror, F will recede from it ; and when A is infinitely distant, or when the rays become parallel, as in fig. 11., F will be half way between D and C. In all these cases, the focus is a virtual one behind the mirror. CHAP. II. IMAGES FORMED BY MIRRORS. (23.) THE image of any object is a picture of it formed either in the air, or in the bottom of the eye, or upon a white ground, such as a sheet of paper. Images are generally formed by mirrors or lenses, though they may be formed also by placing a screen, with a small aperture, between the object and the sheet of paper which is to receive the image. In order to understand this, let C D be a? screen or window-shutter with a small aperture, A, and E F a sheet of white paper placed in a dark room. Then, if an illuminated object, R G B, is placed on the outside of the shutter, we shall observe an in- verted image of this object painted on the paper at rgb. In order to understand how this takes place, let us sup- pose the object RB to have three distinct colours, red at R, green at G, and blue at B ; then it is plain that 16 A TREATISE ON OPTICS. PART I. the red light from R will pass in straight lines through the aperture A, and fall upon the paper E F at r. In Fig. 13. like manner the green light from G will fall upon the paper at g, and the blue light from B will fall upon the paper at b ; thus painting upon the paper an inverted image, rb, of the object, R B. As every coloured point in the object R B has a coloured point corresponding to it, and opposite to it on the paper E F, the image b r will be an accurate picture of the object R B, provided the aperture A is very small. But if we increase the aperture, the image will become less distinct; and it will be nearly obliterated when the aperture is large. The reason of this is, that, with a large aperture, two adjacent points of the object will throw their light on the same point of the paper, and thus create confusion in the image. It is obvious from fig. 13., that the size of the image b r will increase with the distance of the paper E F be- hind the hole A. If A g is equal to A G, the image will be equal to the object ; if A g is less than A G, the image will be less than the object; and if A g is greater than A G, the image will be greater than the object. As each point of an object throws out rays in all directions, it is manifest that those only which fall upon the small aperture at A concur in forming the image b r; and as the number of these rays is very small, the image b r must have very little light, and therefore cannot be used for any optical purposes. This evil is completely remedied in the formation of images by mirrors and lenses. (24.) Formation of images by concave mirrors. Let CHAP. II. IMAGES IN CONCAVE MIRRORS. 1? AB, fig. 14., be a concave mirror whose centre is C, and let MN be an object placed at some distance Fig. 14. before it. Of all the rays emitted in every direction by the point M, the mirror receives only those which lie between MA and MB, or a cone of rays MAB whose base is the spherical mirror, the section of which is A B. If we draw the reflected rays Am, B m, for all the incident rays M A, M B, by the methods already described^ we shall find that they will all meet at the point m, and will there paint the extremity M of the object. In like manner, the cone of rays NAB flowing from the other extremity N of the object will be reflected to a focus at n, and will there paint that point of the ob- ject. For the same reason, cones of rays flowing from intermediate points between M and N will be reflected to intermediate points in the image between m and n, and m n will be an exact inverted picture of the object MN. It will also be vsry bright, because a great num- ber of rays concur in forming each point of the image. The distance of the im^e from the mirror is found by the same rule which we ftave given for finding the focus of diverging rays, the points M, m in fig. 14. corre- sponding with A and F in fig. 8. If we measure the relative sizes of the object M N and its image m n, we shall find that in every case the size of the image is to the size of the object as the dis- tance of the image from the mirror is to the distance of the object from it. If the concave mirror AB is large, and if the object M N is very bright, such as a plaister of Paris statue strongly illuminated^ the image mn will appear suspended IS A TREATISE OX OPTICS. in the air; and a series of instructive experiments may be made by varying the distance of die object, and observ- ing the variation in the size and place of the image, When the object is placed at m n f a magnified repre- sentation of it will be formed at MX. (25.) Formation of images l>y convex mirrors. In concave mirrors there is, in all cases, a real image of r^e object formed in front of the mirror, excepting when the object is placed between the principal focus and the mirror, in which case it gives a virtual image formed behind it. : whereas in convex mirrors the image is always a virtual one formed behind the mirror. Let A B, fig. 15., be a convex mirror whose centre is ^. 15. .iiul M X an object placed be- fore it ; and let the eye of the observer be situated any where in front of the mirror, as at E. Out of the great number of rays which < are emitted in every direction from the points M. X of the object, and are subsequently reflected from die mirror., a few only can enter the eye at E. Those which do enter die eye. such as D E, F E and GE, H E, will be reflected from the portions D F, G H of the mirror so situated with respect to the eye and the points M, X^ that the angles of incidence and reflexion will be equal. Th* ray M V> will be reflected in a direction D E,, forming the same angle that M D does wi:h the perpendicular C X", and the ray X G in the direction G E. In like manner, F E, H E will be the reflected rays corre- sponding to the incident ones M F. X' H. Xow, if we uie backwards the rays D E, F E, they will meet at m; and they will therefore appear to the eye to have come from the point ni as their focus. For the same rays G E, HE will appear to come from the point n as their focus, and m n will be the virtual image of the. object M X". It is called virtual because it is not formed by die actual union of 1 1 :us, and cannot CHAP. IT. IMAGES IN PLANE MIRRORS. 19 be received upon paper. If the eye E is placed in any other position before the mirror, and if rays are drawn from M and N, which after reflexion enter the eye, it will be found that these rays continued backwards will have their virtual foci at m and n. Hence, in every posi- tion of tlie eye before the mirror, the linage will be seen in the same spot m n. If we draw the lines CM, C N from {he centre' of the mirror, we shall find that the points m, n are always in these lines. Hence it is obvious that the image mn is always crc.ct, and less than the object. It will approach to the mirror as the object; M N approaches to it, and it will recede from it as M N recedes ; and when MN is infinitely distant, and the rays which it emits become parallel, the image mn will be half way between C and the mirror. In other positions of the object the distance of the image will be found by the rule already given for diverging rays falling upon convex mirrors. The size of the image is to the size of the object, as C m, the distance of the image from the centre of the mirror, is to C M, the distance of the object. In approaching the mirror, the image and object approach to equality ; and when they touch it, they are both of the same size. Hence it follows that objects are always seen diminished in convex mirrors, unless when they actually touch the mirror. ('>().) /''ormation of imagat ly plane mirror*. Let A I >,////. Hi., be a plane mirror or looking-glass, MN an object situated before it, and E the place of the eye; then, upon the very same principles which we have, explained for a convex mirror, it will be found that an image of M X will be formed at mn, the virtual foci ?/v,, n being determined by continuing back the reflected rays D 1% F K till they meet at m, and <;K, II 10 till they meet at n. If we join the points M, m and N, v/, the lines M -in, N n will be per- pendicular to the mirror A B, and consequently parallel C 2 20 A TREATISE ON OPTICS. PART I* and the image will be at the same distance, and have the same position behind the mirror that the object has before it. Hence we see the reason why the images of all objects seen in a looking-glass have the same form and distance' as the objects themselves. DIOPTRICS. (27.) DIOPTRICS is that branch of optics which treats of the progress of those rays of light which enter trans- parent bodies and are transmitted through their sub- stance. CHAP. III. REFRACTION. (28.) WHEN light passes through a drop of water or a piece of glass, it obviously suffers some change in its direction, because it does not illuminate a piece of paper placed behind these bodies in the same manner as it did before they were placed in its way. These bodies have therefore exercised some action, or produced some change upon the light, during its progress through them. In order te discover the nature of this change, let A B C D be an empty vessel, having a hole H in one of its sides B D, and let a lighted candle S be placed within a few feet of it, so that a ray of its light S H may fall upon the bottom C D of the vessel, and form a round spot of light at a. The beam of light S H R a will be a straight line. Having marked the point a which the ray from S strikes, pour water into the vessel till it rises to the level EF. As soon as the surface of the water has become smooth, it will t>* 6HAP. III. REFRACTION. 21 seen that the round spot which was formerly at a is now at b y and that the ray SHR& is bent at R; HR and R6 being two straight lines meeting at R, a point in the surface of the water. Hence it follows, that all objects seen under water are not seen in their true direction by a person whose eye is not immersed in the water. If a fish, for example,, is lying at b,fig. 17., it will be seen by an eye at S in the direction S a, the direction of the re- fracted ray R S; so that, in order to shoot it with a ball, we must direct the gun to a point nearer us than the point a. For the same reason, every point of an object under water appears in a place different from its true place ; and the difference between the real and apparent place of any point of an object increases with its depth beneath the surface, and with the obliquity of the ray R S by which it is seen. A straight stick, one half of which is im- mersed in water, will therefore appear crooked or bent into an angle at the point where it enters the water. A straight rod SR#, for example, will appear bent like SR6; and a rod bent will, for a like reason, appear straight. This effect must have been often observed in the case of an oar dipping into clear water. If in place of water we use alcohol, oil, or glass, the surfaces of all these bodies coinciding with the line E F, we shall find that they all have the power of bend- ing the ray of light SR at the point R; the alcohol bending it more than the water, the oil more than the alcohol, and the glass more than the oil. In the case of glass, the ray would be bent into the direction Re. The power which thus bends or changes the direction of a ray of light is called refraction, a name derived from a Latin word, signifying breaking back, because the ray S R a is broken at R, and the water is said to refract, or break the ray, at R. Hence we may conclude that if a ray of light, passing through air, falls in an oblique or slanting direction on the surface of solid or fluid bodies that are transparent, it will be refracted towards a line, MN, perpendicular to the surface E F at the point R, where the ray enters it ; and that the quantity of this c 3 22 A TREATISE ON OPTICS. PART I. refraction, or the angle a R b, varies with the nature of the body. The power by which bodies produce this effect is called their refractive power, and bodies that produce it in different degrees are said to have different refractive powers. Let the vessel A B C D be now emptied, and let a bright object, such as a sixpence, be cemented on the bottom of it at a. If the observer places himself a few feet from the vessel, he will find a position where he will see the sixpence at a through the hole H. If water be now poured into the vessel up to E F, the observer will no longer see the sixpence; but if another sixpence is placed at a, and is moved towards 5, it will become visible when it reaches b. Now, as the ray from the sixpence at b reaches the eye, it must come out of the water at a point, R, in the surface, found by drawing a straight line, S H R, through the eye and the hole H ; and consequently b R must be the direction of the ray, which makes the sixpence visible, before its refraction at R. But if this ray had moved onwards in a straight line, without being refracted at R, its path would have been bh; whereas, in consequence of the refraction, its path is RH. Hence it follows, that when a ray of light, passing through any dense medium, such as water, &c., in a direction oblique or slanting to its surface, quits the medium at any point, and enters a rarer medium, such as air, it is refracted from the line perpendicular to the surface at the point where it quits it. When the ray S H R from the candle falls, or is inci- dent upon the surface E F of the water, and is refracted in the direction R6, towards the perpendicular MN, the angle M R H which it makes with the perpendicular, is called the angle of incidence ; and the angle N R 6, which the ray R6 bent or refracted at R makes with the same perpendicular, is called the angle of refraction. The ray HR is called the incident ray, and R6 the refracted ray. But when the light comes out of the water from the sixpence at 6, and is refracted at R in the direction RH, 6R is the incident ray and RH the CHAP. III. LAW OF REFRACTION. refracted ray. The angle NR6 is the angle of inci- dence, and M R H the angle of refraction. Hence it follows, that when light passes out of a rare into a dense medium, as from Air to Water, the angle of incidence is greater than the angle of refraction ; and when light passes out of a dense into a rare medium, as out of Water into Air, the angle of incidence is less than the angle of refraction ; and these angles are so related to one another, that when the ray which was refracted in the one case becomes the incident ray, what was formerly the incident ray becomes the refracted ray. (29.) In order to discover the law or rule according to which the rays of light enter or quit water, or other re- fracting media, so that we may be able to determine the refracted ray when we know the direction of the inci- dent ray, describe a circle MENF upon a square board gr. 18., standing upon a heavy pedestal P, and Fig. 18. draw the two diameters MN, EF j\ r Z_ ,B perpendicular to one another, and also to the sides AB,AC of the piece of wood. Let a small tube, HR, be so made that it may be attached to the board along any radius H R, H' R, or, what would be still better, that it may move freely round R as a centre. Let 1 the board with its pedestal be placed in a pool or tub of water, or in a glass vessel of water, so that the surface of the water may coincide with the line EF without touching the end R ;>f the tube HR. When the tube is in the position MR, perpendicular to the surface E F of the water, admit a ray of light down the tube, and it will be seen that it enters the water at R, and passes straight on to N, without suffer- ing any change in its direction. Hence it follows, that a ray of light incident perpendicularly on a refracting surface experiences no refraction or change in its di- rection. If we now place a sixpence at N, we shall see c 4 24 A TREATISE ON OPTICS. PART I, it through the tube MR; so that the rays from the six- pence quit the water at R, and proceed in the same straight line NRM. Hence a ray of light quitting a re- fracting surface perpendicularly undergoes no refraction or change of direction. If we now bring the tube into the position H R, and make a ray of light pass along it, the ray will be refracted at R in some direction R b, the angle of refraction NR6 being less than the angle of incidence MRH. If we now, with a pair of compasses, take the shortest distance bn of the point b from the perpendicular MN, and make a scale of equal parts, of which b n is one part, the scale being divided into tenths and hundredths, and if we set the distance H m upon this scale, we shall find it to be 1*336 of these parts, or 1^ nearly. If this experiment is repeated at any other position, H'R, of the tube where R V is the refracted ray, we shall find that on a new scale, in which b' n 1 is one part, R f m f will also be 1*336 parts. But the lines Rm, H'm' are called the sines of the angles of incidence HRMjH'RM, and bn,b'n' the sines of the angles of refraction 5RN, &'RN. Hence it follows, that in water the sine of the angle of incidence is to the sine of the angle of refraction as 1*336 to 1, whatever be the position of the ray with respect to the surface E F of the water. This truth is called by optical writers the con- stant ratio of the sines. By placing a sixpence at 6, we shall find that it will be seen through the tube when it has the position HR; and placing it at b', it will be seen through it in the position H'R. Hence, when light quits the surface of water, the sine of its angle of in- cidence 6RN will be to the sine of its angle of re- fraction HRM as 1 to 1*336, as these are the measures of the sines b n,~Rm; and since these are also the measures of l>n f , H'w' upon another scale, in which b'n' is unity, we may conclude that, when light emerges from water into air, the sines of the angles of incidence and refraction are in the constant ratio of 1 to 1*336. If we make the same experiment with other bodies, we shall obtain different degrees of refraction at the same CHAP. III. REFRACTIVE POWERS OP BODIES. 25 angles ; but in every case the sines of the angles of in- cidence and refraction will be found to have a constant ratio to each other. The number 1-336, which expresses this ratio for water, is called the index of refraction for water, and sometimes its refractive index, and refractive power. (30.) As philosophers have determined the index of refraction for a great variety of bodies, we are able, from those determinations, to ascertain the direction of any ray when refracted at any angle of incidence from the surface of a given body, either in entering or quitting it. Thus, in the case of Water, let it be required to find the direction of a ray, HR, fig. 18., after it is refracted at the surface E F of water : draw R M perpendicular to E F at the point R, where the ray H R enters the water, and from H draw Hra perpendicular to MR. Take Hm in the compasses, and make a scale in which this distance occupies 1*336 parts, or 1^- nearly. Then, taking 1 on the same scale, place one foot of the com- passes in the quadrant N F, and move that foot towards or from N till the other foot falls upon some one point n in the perpendicular RN, and in no other point of it. Let b be the point on which the first foot of the com- passes is placed when the second falls upon n, then the line R6 passing through this point will be the refracted ray corresponding to the incident ray H R. (31.) Table I. (Appendix) contains the index of re- fraction for some of the substances most interesting in optics. (32.) As the bodies enumerated in these tables have all different densities, the indices of refraction annexed to their names cannot be considered as showing the relation of their absolute refractive powers, or the re- fractive powers of their ultimate particles. The small refractive index of hydrogen, for example, arises from its particles being at such a distance from one another; and, if we take its specific gravity into account, we shall find that, instead of having a less refractive power than 26 A TREATISE ON OPTICS. PART I. all other bodies, its ultimate particles exceed all other bodies in their absolute action upon light. Sir Isaac Newton has shown, upon the supposition that the ultimate particles of bodies are equally heavy, that the absolute refractive power is equal to the excess of the square of the index of refraction above unity, divided by the specific gravity of the body. In this way Table II. (Appendix) has been calculated. Sir John Herschel has justly remarked, that if, accord- ing to the doctrines of modern chemistry, material bodies consist of a finite number of atoms, differing in their actual weight for every differently compounded substance, the intrinsic refractive power of the atoms of any given medium will be the product arising from multiplying the numbers in Table II. by their atomic weight. (33.) In examining Table II., it appears that the substances which contain fluoric acid have the least absolute refractive power, while all inflammable bodies have the greatest. The high absolute refractive power of Oil of cassia, which is placed above all other fluids, and even above Diamond, indicates the great inflamma- bility of its ingredients. HAP. IV. REFRACTION THROUGH PRISMS AND LENSES. (34.) BY means of the law of refraction explained in the preceding pages, we are enabled to trace a ray of light in its passage through any medium or body of any figure, or through any number of bodies,, provided we can always find the inclination of the incident ray to that small por- tion of the surface where the ray either enters or quits the body. The bodies generally used in optical experiments, and in the construction of optical instruments, where the CHAP. IV. LENSEVt 27 effect is produced by refraction, are prisms, plane glasses, spheres, and lenses, a section of each of which is shown in the annexed figure. Fig. 19. A B C DEFCHl Tl c X""^X A I / ^ \M- I- ( 1. An optical prism, shown at A, is a solid having two plane surfaces A R, AS, which are called its refracting surfaces. The face R S, equally inclined to A R and A S, is called the base of the prism. 2. A plane glass, shown at B, is a plate of glass with two plane surfaces, a b, cd, parallel to each other. 3. A spherical lens, shown at C, is a sphere, all the points in its surface being equally distant from the centre O. 4. A double convex lens, shown at D, is a solid formed by two convex spherical surfaces, having their centres on opposite sides of the lens. When the radii of its two surfaces are equal, it is said to be equally convex; and when the radii are unequal, it is said to be an unequally convex lens. 5. A plano-convex lens, shown at E, is a lens having one of its surfaces convex and the other plane. 6. A double concave lens, shown at F, is a solid bounded by two concave spherical surfaces, and may be either equally or unequally concave. 7. A plano-concave lens, represented at G, is a lens one of whose surfaces is concave and the other plane. 8. A meniscus, shown at H, is a lens one of whose surfaces is convex and the other concave, and in which the two surfaces meet if continued. As the convexity exceeds the concavity, it may be regarded as a convex lens. 9. A concavo-convex lens, shown at I, is a lens one of whose surfaces is concave and the other convex, and in which the two surfaces will not meet though con- 28 A TREATISE ON OPTICS. PART I. tinued. As the concavity exceeds the convexity, it may be regarded as a concave lens. In all these lenses a line, M N, passing through the centres of their curved surfaces, and perpendicular to their plane surfaces, is called the axis. The figures represent only the sections of the lenses, as if they were cut by a plane passing through their axis ; but the reader will understand that the convex surface of a lens is like the outside of a watch-glass, and the concave sur- face like the inside of a watch-glass. In showing the progress of light through such lenses, and in explaining their properties, we must still use the sections shown in the above figure; for since every section of the same lens passing through its axis has exactly the same form, what is true of the rays passing through one section must be true of the rays passing through every section, and consequently through the whole surface. (35.) Refraction of light through prisms. As prisms are introduced into several optical instruments, and are essential parts of the apparatus used for decomposing light and examining the properties of its component parts, it is necessary that the reader should be able to trace the progress of light through their two refracting surfaces. Let A B C be a prism of plate glass whose index of refraction is 1-500, and let H R be a ray of light falling obliquely upon its first surface A B at the point R. Round R as a centre, and with any radius H R, describe the circle H M b. ' Through R draw M R N per- pendicular to A B, and H m per- pendicular to M R. The angle H R M will be the angle of incidence of the ray H R, and H m its sine, which in the present case is 1*500. Then having made a scale in which the distance H m is 1*500, or 1^ parts, take 1 part or unity from the same scale, and having set one foot of the compasses on the circle somewhere about b, move it to different points of the circle till the other CHAP. IV. REFRACTION BY PRISMS. 29 foot strikes only one point n of the line RN; the point b thus found will be that through which the refracted ray passes, R b will he the refracted ray, and n R b the angle of refraction, because the sine bn of this angle has been made such that its ratio to H m, the sine of the angle of incidence, is as 1 to 1*500. The ray R6 thus refracted will go on in a straight line till it meets the second sur- face of the prism at R', where it will again suffer refraction in the direction R&'. In order to determine this direction, make R'H'equal to RH, and, with this distance as radius, describe the circle H'6'. Draw R'N perpendicular to AC, and H' m' perpendicular to R'N, and form a scale on which H f m f shall be 1 part, or I'OOO, and divide it into tenths and hundredths. From this scale take in the com- passes the index of refraction 1-500, as 1^ of these parts ; and having set one foot somewhere in the line R'w', move it to different parts of it till the other foot falls upon some part of the circle about &', taking care that the point &' is such, that when one foot of the compasses is placed there, the other foot will touch the line R'n' continued only in one place. Join R' b'. Then, since H' R' m f is the angle of incidence on the second surface A C, and H'w'its sine, and since n'5', the sine of the angle 5'R'w', has been made to have to H' w' the ratio of 1*500 to 1, b'R'ri will be the angle of refraction, and R'5' the re- fracted ray. If we suppose the original ray H R to proceed from a candle, and if we place our eye at &' behind the prism so as to receive the refracted ray &' R', it will appear as if it came in the direction DR'6', and the candle will be seen in that direction; the angle HED representing its angular change of direction, or the angle of deviation, as it is called. In the construction of fig. 20., the ray H R has been made to fall upon the prism at such an angle that the refracted ray R R' is equally inclined to the faces A B, A C, or is parallel to the base B C of the prism ; and it will be found that the angle H R B is equal to the angle b f R' C. Under these circumstances SO A TREATISE ON OPTICS. PART I. we shall find, by making the angle H R B either greater or less than it is in the figure, that the angle of deviation H E D is less than at any other angle of inci- dence. If we, therefore, place the eye behind the prism at &', and turn the prism round in the plane BAG, some- times bringing A towards the eye and sometimes pushing it from it, we shall easily discover the position where the image of the candle seen in the direction &'D has the least deviation. When this position is found, the angles H R B and 6'R'C are equal, and R R' is parallel to B C, and perpendicular to A F, a line bisecting the refracting angle B A C of the prism. Hence it may be shown by the similarity of triangles, or proved by projection, that the angle of refraction b R n at the first surface is equal to B A F, half the refracting angle of the prism. But since B A F is known, the angle of refraction b R n is also known ; and the angle of incidence H R M being found by the preceding methods, we may determine the index of refraction for any prism by the following ana- logy. As the sine of the angle of refraction is to the sine of the angle of incidence, so is unity to the index of refraction ; or the index of refraction is equal to the sine of the angle of incidence divided by the sine of the angle of refraction. (36.) By this method, which is very simple in prac- tice, we may readily measure the refractive powers of all bodies. If the body be solid, it must be shaped into a prism ; and if it is soft or fluid, it mus-t be placed in the angle BAG of a hollow prism ABC, fig. 21., made by cementing together three pieces of plate glass, A B, AC, BC. A very simple hollow prism for this purpose may be made by fastening together at any angle two pieces of plate glass, A B, AC, with a bit of wax, F. A drop of the fluid may then be placed in the angle at A, where it will be retained by the force of capillary attraction. When light is incident upon the second surface of a prism, it may fall so obliquely that the surface is in" CHAP. IV. TOTAL REFLEXION. 31 capable of refracting it, and therefore the incident light is totally reflected from the second surface. As this is a curious property of light, we must explain it at some length. On the total Reflexion of Light. (37.) We have already stated, that when light falls upon the first or second surfaces of transparent bodies, a certain portion of it is reflected, and another and much greater portion transmitted. The light is in this case said to be partially reflected. When the light, however, falls v^ery obliquely upon the second surface of a trans- parent body, it is wholly reflected, and not a single ray suffers refraction, or is transmitted by the surface. Let A B C be a prism of glass, whose index of refraction is 1-500: let a ray of light G K,/#. 22., be refracted at K Fig. 22. by the first surface A B, ||L so as to fall on the point R "m^^ of the second surface very ^^ G bliquely, and in the direc- Li^l- "^fes^ tion KR. Upon R as a t* ft " centre, and with any radius, R H, describe the circle H M E N F; then, in order to find the refracted .ray corresponding to H R, make a scale on which H m is equal to 1, and take in the com- passes 1-500 or 1^ from that scale, and setting one foot in the quadrant E N, try to find some point in it, so that the other foot may fall only in one point of the radius RN. It will soon be seen that there is no such point, and that 1-500 is greater even than E R, the sine of an angle E R N of 90. If the distance 1-500 in the compasses had been less than E R, the ray would have been re- fracted at R; but as there is no angle of refraction whose sine is 1-500. the ray does not emerge from the prism, but suffers total reflexion at R in the direction R S, so that the angle of reflexion M R S is equal to the angle of incidence M R H. If we construct fig. 22. so as to make the incident ray H R take different positions be- 32 A TREATISE ON OPTICS. PART I. tween M R and F R, we shall find that the refracted ray will take different positions between R N and R E. There will be some position of the incident ray about H R, where the refracted ray will just coincide with RE; and that will happen when the quantity 1-500, taken from the scale on which H m is equal to 1, is exactly equal to R E, or radius. At all positions of the incident ray between this line and F R, refraction will be impossible, and the ray incident at R will be totally reflected. It will also be found that the sine of the angle of incidence at R, at which the light begins to be totally reflected, is equal to ^-.3^77, or '666, or -J, which is the sine of 41 48' for plate glass. The passage from partial to total reflexion may be finely seen, by exposing one side, A C, of a prism A B C, fig. 20., to the light of the sky, or at night to the light reflected from a large sheet of white paper. When the eye is placed behind the other side, A B, of the prism, and looks at the image of the sky, or the paper, as re- flected from the base, B C, of the prism, it will see when the angle of incidence upon B C is less than 41 48 ', the faint light produced by partial reflexion ; but by turning the prism round, so as to render the incidence gradually more oblique, it will see the faint light pass suddenly into a bright light, and separated from the faint light by a coloured fringe, which marks the boundary of the two reflexions at an angle of 41 48'. But, at all angles of incidence above this, the light will suffer total reflexion. Refraction of Light through Plane Glasses. (38.) Let M N, fig. 23., be the section of a plane glass with parallel faces; and let a ray of light, A B, fall upon the first surface at B, and be refracted into the direction B C : it will again be refracted at its emergence from the second surface at C, in a direction, C D, parallel to A B ; and to an eye at D it will appear to have pro- ceeded in a direction a C, which will be found by con- CHAP. IV. PLANE GLASSES. A A; tinuing I) C backwards. It will thus appear to come from a point a bekw A, the point from which it was Fig. 23. really emitted. This may be proved by projecting the figure by* the method already described; '"' a though it will be obvious also from the consideration, that if we suppose the refracted ray to be- come the incident ray, and to move backwards, the incident ray will become the refracted ray. Thus the refracted ray B C, falling at equal angles upon the two surfaces of the plane glass, will suffer equal refractions at B and C, if we suppose it to move in opposite directions; and con- sequently the angles which the refracted rays BA, C D form with the two refracting mrfaces will be equal, and the rays parallel. If we suppose another ray, A' B', parallel to AB, to fall upon the point B', it will suffer the same refractions at B 7 and C', and will emerge in the direction C'D', parallel to C D, as if it came from a point a'. Hence parallel rays fatting upon a plcine glass will retain their parallelism after passing through it. (39.) If rays diverging from any point, A, fig. 24., such as A B, A B', are incident upon a plane glass M N, Fig. 24. they will be refracted into the directions B C, B' C' by the first surface, and C D, C' D' by the second. By continuing C B, C' B' backwards, they will be f found to meet at a, a point x. farthei from the glass than A. Hence, if we suppose the surface B 1$' to be that of standing water, placed horizontally, an eye within it would see the point A removed to a, the divergency of the rays B C, B' C' having been diminished by refrac- tion at the surface B B'. But whea the rays B C, B'Cf D 34 A TREATISE ON OPTICS. PART I, suffer a second refraction, as in the case of a plane glass, we shall find, by continuing D C, D' C f backwards, that they will meet at ft, and the object at A will seem to be brought nearer to the glass; the rays C D, C'D', by which it is seen, having been rendered more divergent by the two refractions. A plane glass, therefore, diminishes the distance of the divergent point of diverging rays. If we suppose D C, D' C' to be rays converging to &, they will be made to converge to A by the refraction of the two surfaces ; and consequently a plane glass causes to recede from it the convergent point of converging rays. If the two surfaces B B x , C C' are equally curved, the one being convex and the other concave, like a watch-glass, they will act upon light nearly like a plane glass; and accurately like a plane glass, if the convex and concave sides are so related that the rays B A, C D are incident at equal angles on each surface: but this is not the case when the surfaces have the same centre, unless when the radiant point A is in their common centre. For these reasons, glasses with parallel surfaces are used in windows and for watch-glasses, as they produce very little change upon the form and position of objects seen through them. Refraction of Light through Curved Surfaces. (40.) When we consider the inconceivable minute- ness of the particles of light, and that a single ray consists of a succession of those particles, it is obvious that the small part of any curved surface on which it falls, and which is concerned in refracting it, may be regarded as a plane. Tl?e surface of a lake, perfectly still, is known to be a curved surface of the same radius as that of the earth, or about 4000 miles; but a square yard of it, in which it is impossible to discover any curvature, is larger in proportion to the radius of the earth than the small space on the surface of a lens occupied by a ray of light is in relation to the radius of that surface. Now, mathe- maticians have demonstrated that a line touching a curve CHAP. IV. REFRACTION THROUGH SPHERES. 3> at any point may be safely regarded as coinciding with, an infinitely small part of the curve ; so that when a ray of light, A B, fig. 25., falls upon a curved refracting surface Fig. 25. at B, its angle of incidence must be considered as A B D, the angle which the ray A B forms with a line D C, perpendicular to a line M N, which touches, or is a tangent to, the curved surface at B. In all spherical surfaces, such as those of lenses, the tangent M N is perpen- dicular to the radius C B of the surface. * Hence, in spherical surfaces the consideration of the tangent M N is unnecessary ; because the radius C D, drawn through the point of incidence B, is the perpendicular from which the angle of incidence is to be reckoned. Refraction of Light through Spheres. (41.) Let MN be the section of a sphere of glass whose centre is C, and whose index of refraction is 1-500; and let parallel rays,/#. 26., H R, H'R/ fall upon Fig. 26. it at equal distances on each side of the axis G C F. H the ray H R is incident at R, describe the circle H D b round R, through C and R draw the line C R D, which will be perpendicular to the surface at R, and draw H m perpendicular to R D. Draw the ray R b r through a point b found by the method already explained, and so that the sine b n of the angle of refraction & R C may be 1 on the same scale on which H mis 1'500, or 1J; then R b will be the ray as refracted by the first surface of D 2 36 A TREATISE ON OPTICS. PART J. the sphere. In like manner draw R'/for the refracted ray corresponding to H x R'. If we continue the rays R r, R' r', they will meet the axis at E, which will be the focus of parallel rays for a single convex surface RPR'; and the focal dis- tance P E may he found by the following rule. RULE for finding the principal focus of a single convex surface. Divide the index of refraction by its excess above unity, and the quotient will be the principal focal distance, P E ; the radius of the surface, or C R, being 1 . If C R is given in inches, then we have only to mul- tiply the result by that number of inches. When the surface is that of glass, whose index of refraction is 1'5, then the focal distance, PE, will A 1 ways be equal to thrice the radius, C R. Round r as a centre, with a radius equal to R H, describe the circle D' b'h , and, by the method formerly explained, find a point &' in the circle, such that V n, the sine of the angle of refraction b' rn, is 1-500 or 1^ on the same scale on which h m, the sine of the angle of incidence, is 1 part, and rb'F will be the ray re- fracted at the second surface. In the same manner we shall find r F to be the refracted ray corresponding to the incident ray R' /, F being the point where r b' cuts the axis G E. Hence the point F will be the focus of parallel rays for the sphere of glass M N. If diverging rays fall upon the points R, R', it is quite clear, from the inspection of the figure, that their focus will be on some point of the axis G F more remote from the sphere than F, the distance of their focus increasing as the radiant point from which they diverge approaches to the sphere. When the radiant point is as far before the sphere as F is behind it, then the rays will be refracted into parallel directions, and the focus will be infinitely distant. Thus, if we suppose the rays F r, F r to diverge from F, then they will emerge after refraction in the parallel directions R H, R' H'. If converging rays fall upon the points R R / , it is equally manifest that their focus will be at some ^oi^t CHAP. IV. CURVED REFRACTING SURFACES. 37 of the axis, G F, nearer the sphere than its principal focus F; and their convergencymay be so great that their focus will fall within the sphere. All these truths may be rendered more obvious, and would be more deeply im- pressed upon the mind, by tracing rays of different de- agrees of divergency and convergency through the sphere, by the methods already so fully explained. (42.) In order to form an idea of the effect of a sphere made of substances of different refractive powers, in bringing parallel rays to a focus, let us suppose the sphere to be one inch radius, and let the focus F be determined as in fig. 26., when the substances are, Index of Distance, F Q, of the Refraction. Focus from the Sphere. Tabasheer - 1-11145 - - 4 inch. Water - - 1'3358 Glass - - 1-500 - - Zicron - - 2-000 - - Hence we find that in tabasheer the distance FQ is 4 inches ; in water, 1 inch ; in glass, half an inch ; and in zircon, nothing ; that is, r and F coincide with Q, after a single refraction at R. When the index of refraction is greater than 2 '000, as in diamond and several other substances, the ray of light R r will cross the axis at a point somewhere between C and Q. Under certain circumstances the ray R r will suffer total reflexion at r, towards another part of the sphere, where it will again suffer total reflexion, being carried round the circumference of the sphere, without the power of making its escape, till the ray is lost by absorption. Now, as this is true of every possible section of the sphere, every such ray, R r, incident upon it in a circle equidistant from the axis, G F, will suffer similar reflexions. RULE for finding the focus F of a sphere. The dis- tance of the focus, F, from the centre, C, of any sphere may be thus found. Divide the index of refraction by twice its excess above 1, and the quotient is the distance, C F, in radii of the sphere. If the radius of the sphere j> 3 38 , A TREATISE ON OPTICS. PART Ii is 1 inch, and its refractive power 1'500, we shall have C F equal to 1 \ inches, and Q F equal to half an inch. Refraction of Light through Convex and Concave Surfaces. (43.) The method of tracing the progress of a ray which enters a convex surface, is shown mfig.%6. for the ray H R, and of tracing one entering a concave surface of a rare medium, or quitting a convex surface of a dense one, is shown for the ray R r, in the same figure. When the ray enters the concave surface of a dense medium, or quits a similar surface, and enters the con- vex. surface of a rare medium, the method of tracing its progress is shown in fig. %J. y where M N is a dense Fig. 27. medium (suppose glass) with two concave surfaces, or a thick concave lens. Let C, C' be the centres of the two surfaces lying in the axis C C', and H R, H' R' parallel rays incident on the first surface. As C R is perpen- dicular to the surface at R, H R C will be the angle of incidence; and if a circle is described with a radius R h, hm will be the sine of that angle. From a scale on which hm is 1*500, take in the compasses 1, and find some point, b y in the circle where, when one foot of the compasses is placed, the other will fall only on one point, n, of the per- pendicular R C : the line R b drawn through this point will be the refracted ray. By continuing this ray b R back- wards., it will be found that it meets the axis at F. In like manner it will be seen that the ray H'R' will be re*, fracted in the direction RV, as if it also diverged from F. Hence F will be the virtual focus of parallel rays ,OHAP. IV. REFRACTION THROUGH LENSES. $9 refracted by a single concave surface, and may be found by the following rule. RULE for finding the principal focus of a single con- cave surface. Divide the index of refraction by its excess above unity, and the quotient will be the principal focal distance FE, the radius of the surface or C E being 1. If the radius CE is given in inches, we have only to multiply C F, thus obtained by that number of inches, to have the value of FE in inches. If, by a similar method, we find the refracted ray re at the emergence of the ray rb from the second surface r r' of the lens, and continue it backwards, it will be found to meet the axis at// so that the divergent rays Rr, RV are rendered still more divergent by the second sur- face, and C will be the focus of the lens M N. Refraction of Light through Convex Lenses. (44.) Parallel rays. Rays of light falling upon a con- vex lens parallel to its axis are refracted in precisely the same manner as those which fall upon a sphere; and the refracted ray may be found by the very same methods. But as a sphere has an axis in every possible direction, every incident ray must be parallel to an axis of it; whereas, in a lens which has only one axis, many of the incident rays must be oblique to that axis. In every case, whether of spheres or lenses, all the rays that pass along the axis suffer no refraction at all, because the axis is always perpendicular to the refracting surface. When parallel rays, RL, RC, RL 3 jfo.28., fall upon a double convex lens, L L, parallel to its axis, R F, the ray RC which coincides with the axis will pass through without suffering any refraction, but the other rays, R L, RL, will be refracted at each of the surfaces of the lens ; and the refracted rays corresponding to them, viz. L F, L F, will be found, by the method already given, to meet at some point, F, in the axis. When the rays are oblique to the axis, as SL, SL, TL, TL, the rays SC, TC, which pass through the centre, C 3 of the lens, will suffer refraction at each surface ; { D 4 40 A TREATISE ON OPTICS. PART I. but as the two refractions are equal, and in opposite di- rections, the finally refracted rays Cf, C/' will be parallel Fig. 28. to S C, T C. Hence, in considering oblique rays, such as S L, T L, we may regard lines Sf, Tf r 9 passing through the centre, C, of the lens as the direction of the refracted ray corresponding to S C, T C. By the methods already explained, it will be found that S L, S L will be refracted to a common point, f, in the direction of the central ray S/, and TL, TL, to the point/ 7 . The focal distance FC, or/C, may be found numerically by the following rule, when the thickness of the lens is so small that it . may be neglected. RULE for finding the principal focus, or the focus of parallel rays, for a glass lens unequally convex. Multiply the radius of the one surface by the radius of the other, and divide twice this product by the sum of the same radii. When the lens is of glass, and equally convex, the focal distance will be equal to the radius. RULE /or the principal focus of a plano-convex tens of glass. When the convex side is exposed to parallel rays, the distance of the focus from the plane side will be equal to twice the radius of its convex surface, di- minished by two thirds of the thickness of the lens. When the plane side is exposed to parallel rays, the distance of the focus from the convex side will be equal to twice the radius. (45.) Diverging rays. When diverging rays, R L, RL, fig. 2$)., radiating from the point R, fall upon the* double convex lens L L, whose principal focus is at O CHAP. IV. REFRACTION THROUGH LENSES* 41 and O', their focus will be at some point F more remote than O. If R approaches to LL, the focus F will Fig. 29. recede from L L. When R comes to P, so that P C is equal to twice the principal focal distance C O, the focus F will be at P', as far behind the lens as the radiant point P is before it. When R comes to O.', the focus F will be infinitely distant, or the rays L F, L F will be parallel ; and when R is between O' and C, the refracted rays will diverge and have a virtual focus before the lens. The focus F of a glass lens will be found by the following rule. RULE for finding the focus of a convex lens for diverging rays. Multiply twice the product of the radii of the two surfaces of the lens by the distance, RC, of the radiant point, for a dividend. Multiply the sum of the two radii by the same distance RC, and from this product subtract twice the product of the radii, for a divisor. Divide the above dividend by the divisor, and the quotient will be the focal distance, C F, required. If the lens is equally convex, the rule will be this. Multiply the distance of the radiant point, or RC, by the radius of the surfaces, and divide that product by the difference between the same distance and the radius, and the quotient will be the focal length, CF, required. When the lens is plano-convex, divide twice the pro- duct of the distance of the radiant point multiplied by the radius by the difference between that distance and twice the radius, and the quotient will be the distance of the focus from the centre of the lens. (46.) For converging rays. When rays, RL, RL, converging to a point f,fig. 30., fall upon a convex lens L L, they will be so refracted as to converge to a point or focus F nearer the lens than its principal focus O, 42 A TREATISE ON OPTICS. PART I. As the point of convergence /recedes from the lens, the point F will also recede from it towards 0, which it just reaches when the point / becomes infinitely distant. When / approaches to the lens, F also approaches to it. The focus F of a glass lens, when its thickness is small, may be found by the following rule : RuLE^/br finding the focus of converging rays. Multiply twice the product of the radii of the two surfaces of the lens by the distance fC of the point of convergence, for a diyidend. Multiply the sum of the two radii by the same distance fC, and to this product add twice the product of the radii, for a divisor. Divide the above dividend by the divisor, and the quotient will be the focal distance C F required. If the lens is equally convex, multiply the distance fC by the radius of the surface, and divide that product by the sum of the same distance and the radius, and the quotient will be the focal length F C required. When the lens is plano-convex, divide twice the pro- duct of the distance /C multiplied by the radius by the sum of that distance and twice the radius, and the quo- tient will be the focal distance FC required. Refraction of Light through Concave Lenses. (47-) Parallel rays. Let L L be a doubly concave Fig. 31. ^ r R- R- lens, and RL, RL parallel rays incident upon it; these CHAP. IV. REFRACTION THROUGH LENSES. 43 rays will diverge after refraction in the directions Lr, ~Lr, as if they radiated from a point F, which is the virtual focus of the lens. The rule for finding F C is the same as for a convex lens. (48.) Diverging rays. When the lens L L receives Fig. 32. the rays RL, RL diverging from R, they will be re- fracted into lines, Lr, Lr, diverging from a focus F, less remote from the lens than the principal focus O, and the focal distance, F C, will be found by the follow- ing rule : RULE for finding the focus on a concave lens of glass for diverging rays. Multiply twice the product of the radii by the distance, RC, of the radiant point for a di- vidend. Multiply the sum of the radii by the distance RC, and add to this twice the product of the radii for a divisor. Divide the dividend by the divisor, and the quotient will be the focal distance. . If the lens is equally concave, the rule will be this. Multiply the distance of the radiant point by the radius, and divide the product by the sum of the same distance and the radius, and the quotient will be the focal dis- tance. When the lens is plano-concave, multiply twice the radius by the distance of the radiant point, and divide this product by the sum of the same distance and twice the radius ; the quotient will be the focal distance. (49.) Converging rays. When rays, R L, R L,^ze/. 33., converging to a point / fall upon a concave lens, LL, they will be refracted so as to have their virtual focus at F, and the distance FC will be found by the rule given for convex lenses. The rule for finding the focus of con- 4s 4 A TREATISE ON OPTICS. PART 1. verging rays is exactly the same as that for diverging rays in a double convex lens. Fig. 33. R'- When the lens is plano-concave, the rule for finding the focus of converging rays is the same as for diverg- ing rays on a plano-convex lens. Refraction of Light through Meniscuses and Concavo- convex Lenses of Glass. (50.) The general effect of a meniscus in refracting parallel,, diverging, and converging rays, is the same as that of a convex lens of the same focal length ; and the general effect of a concavo-convex lens is the same as that of a concave lens of the same focal length. RULE for a meniscus with parallel rays. Divide twice the product of the two radii by their difference, and the quotient will be the focal distance required. RULE for a meniscus with diverging rays. Multiply twice the distance of the radiant point by the product of the two radii for a dividend. Multiply the difference between the two radii by the same distance of the ra- diant point, and to this product add twice the product of the radii for a divisor. Divide the above dividend by this divisor, and the quotient will be the focal distance required. The same rule is applicable for converging rays. Both the above rules are applicable to concavo-convex lenses ; but the focus is a virtual one in front of the lens. The truth of the preceding rules and observations are capable of being demonstrated mathematically ; but the reader who has not studied mathematics may obtain an ocular demonstration of them, by projecting the rays CHAP. V. IMAGES FORMED BY LENSES. 45 and lenses in large diagrams, and determining the course of the rays after refraction by the methods already de- scribed. We would recommend to him also to submit the rules and observations to the test of direct experi- ment with the lenses themselves. CHAP. V. ON THE FORMATION OF IMAGES BY LENSES, AND ON THEIR MAGNIFYING POWER. (51.) WE have already described, in Chapter II., the principle of the formation of images by small apertures, and by the convergency of rays to foci by reflexion from mirrors. Images are formed by lenses in the very same manner as they are formed by mirrors ; and it is an universal rule, that when ah image is formed by a con- vex lens, it is inverted in position relatively to the position of the object,, and its magnitude is to that of / the object as ita,disjl!IWi^fi ! oni the lens is to the distance' of the object from the lens. If MN is an object placed before a convex lens, L L, fig. 34., every point of it will send forth rays in every direction. Those rays which fall upon the lens L L will be refracted to foci behind the lens, and at Fig. 34. M such a distance from it as may be determined by the Kules in the last chapter. Since the focus where any 46 A TREATISE ON OPTICS. PART I. ' point of the object is represented in its image is in the straight line drawn from that point of the object through' the middle point C of the lens, the upper end M of the Object 'will be represented somewhere in the line M C m, and the lower end N somewhere in the line N C n, that is, at the points m, n, where the rays L m, L m, L n, L n cross the lilies M C m, N C n. Hence m will re- present the upper, and n the lower end of the object M N. It is also evident, that in the two triangles M C N, m C /i, m n, the length of the image must be to M N the length of the object as C m, the distance of the image, is to C M, the distance of the object from the lens. We are enabled, therefore, by a lens, to form an image of an object at any distance behind the lens we please, greater than its principal focus, and to make this image as large as we please, and in any proportion to the object. In order to have the image large, we must bring the object near the lens, and in order to have it small, we must remove the object from the lens ; and these effects we can vary still farther, by using lenses of different focal lengths or distances. When the lenses have the same focus, we may increase the brightness of the image by increasing the size of the lens or the area of its surface. If a lens has an area of 12 square inches, it will obviously intercept twice as many rays proceeding from every point of the object as if its area were only 6 square inches ; so that, when it is out of our power to increase the brightness of the ob- ject by illuminating it, we may always increase the brightness of the image by using a larger lens. (52.) Hitherto we have supposed the image mn to be received upon white paper, or stucco, or some smooth and white surface on which a picture of it is distinctly formed; but if we receive it upon ground glass, or transparent paper, or upon a plate of glass one of whose sides is covered with a dried film of skimmed milk, and if we place our eye 6 or 8 inches or more behind this semi-transparent ground interposed at m n y we shall see. CHAP. Y. IMAGES FORMED BY LENSES. 47 the inverted image m n as distinctly as before. If we keep the eye in this position, and remove the semi- transparent ground, we shall see an image in the air distinctly and more bright than before. The cause of this will be readily understood, if we consider that all the rays which form by their convergence the points m, n of the image m n, cross one another at m, n, and diverge from these points exactly in the same manner as they would do from a real object of the same size and brightness placed in m n. The image m n therefore of any object may be regarded as a new object; and by placing another lens behind it, another image of the image mn would be formed, exactly of the same size and in the same place as it would have been had mn been a real object. But since the new image of mn must be inverted, this new image will now be an erect image of the object MN, obtained by the aid of two lenses; so that, by using one or more lenses, we can obtain direct or inverted images of any object at plea- sure. If the object M N is a moveable one and within, our reach, it is unnecessary to use two lenses to obtain an erect image of it : we have only to turn it upside, down, and we shall obtain, by means of one lens, an, image erect in reality, though still inverted in relation to the object. (53.) In order to explain the power of lenses in magnifying objects and bringing them near us, or rather in giving magnified images of objects, and bringing the images near us, we must examine the different circumstances under which the same object appears when placed at different distances from the eye. If an eye placed at E lookr it a man a 6, fig. 35., placed at a Fig. 35. A' distance^ his general outline only will be seen., and 48 A TREATISE ON OPTICS. PART I* neither his age, nor his features, nor his dress will be recognised. When he is brought gradually nearer us, we discover the separate parts of his dress, till at the distance of a few feet we perceive his features; and when brought still nearer, we can count his very eye- lashes, and observe the minutest lines upon his skin. At the distance E b the man is seen under the angle b E a, and at the distance E B he is seen under the greater angle B E A or b E A', and his apparent magni- tudes, a b } A'b, are measured in those different positions by the angles b E o, B E A, or b E A'. The apparent magnitude of the smallest object may therefore be equal to the apparent magnitude of the greatest. The head of a pin, for example, may be brought so near the eye that it will appear to cover a whole mountain, or even the whole visible surface of the earth, and in this case the apparent magnitude of the pin's head is said to be equal to the apparent magnitude of the mountain, &c. Let us now suppose the man a b to be placed at the distance of 100 feet from the eye at E, and that we place a convex glass of 25 feet focal distance, half way between the object a b and the eye, that is 50 feet from each, then, as we have previously shown, an inverted image of the man will be formed 50 feet behind the lens, and of the very same size as the object, that is, six feet high. If this object is looked at by the eye, placed 6 or 8 inches behind it, it will be seen exceedingly dis- tinct, and nearly as well as if the man had been brought nearer from the distance of 100 feet to the distance of 6 inches, at which we can examine minutely the details of his personal appearance. Now, in this case, the man, though not actually magnified, has been apparently mag- nified, because his apparent magnitude is greatly in- creased, in the proportion nearly of 6 inches to 1 00 feet, or of 200 to 1. But if, instead of a lens of 25 feet focal length, we make use of a lens of a shorter focus, and place it in such a position between the eye and the man, that its conjugate foci may be at the distance of 20 and 80 feet CHAP. V. MAGNIFYING POWER OF LENSES. 4$ from the lens, that is, that the man is 20 feet before the lens, and his image 80 feet behind it, then the size of the image is four times that of the object, and the eye placed 6 inches behind this magnified image will see it with the greatest distinctness. Now in this case the image is magnified 4 times directly by the lens, and 200 times by being brought 200 times nearer the eye ; so that its apparent magnitude will be 800 times larger than before. If, on the other hand, we use a lens of a still smaller focal length, and place it in such a position between the ye and the man, that its conjugate foci may be at the distance of 75 and 25 feet from the lens, that is, that the man is 7-5 feet before the lens, and his image 25 feet behind it, then the size of the image will be only one third of the size of the object; but though the image is thus diminished three times in size, yet its apparent magnitude is increased 200 times by being brought within 6 inches of the eye, so that it is still magnified, or its apparent magnitude is increased 2 -g-, or 6'7 times nearly. At distances less than the preceding, where the focal length of the lens forms a considerable part of the whole distance, the rule for finding the magnifying power of a lens, when the eye views at the distance of 6 inches, the image formed by the lens, is as follows. From the distance between the image and the object in feet, sub- tract the focal distance of the lens in feet, and divide the remainder by the same focal distance. By this quotient divide twice the distance of the object in feet, and the new quotient will be the magnifying power, or the number of times that the apparent magnitude of the object is increased. When the focal length of the lens is quite inconsider- able, compared with the distance of the object, as it is in most cases, the rule becomes this. Divide the focal length of the lens by the distance at which the eye looks at the image ; or, as the eye will generally look at it at the distance of 6 inches, in order to see it most distinctly, 50 A TREATISE ON OPTICS. PART I- divide the focal length by 6 inches; or, what is the same thing, double the focal length in feet, and the result will be the magnifying power. (54.) Here, then, we have the principle of the sim- plest telescope; which consists of a lens, whose focal ler.gth exceeds six inches, placed at one end of a tube whose length must always be six inches greater than the focal length of the lens. When the eye is placed at the other end of the tube, it will see an inverted image of distant objects, magnified in proportion to the focal length of the lens. If the lens has a focal length of 10 or 12 feet, the magnifying power will be from 20 to 24* times, and the satellites of Jupiter will be distinctly seen through this single lens telescope. To a very short- sighted person, who sees objects distinctly at a distance of three inches, the magnifying pcwer would be from 40 to 48. A single concave mirror is, upon the same principle, a reflecting telescope, for it is of no consequence whether the image of the object is formed by refraction or re- flection. In this case, however, the image mn,fig. 14., cannot be looked at without standing in the way of the object ; but if the reflection is made a little obliquely, or if the mirror is sufficiently large, so as not to intercept all the light from the object, it may be employed as a telescope. By using his great mirror, 4 feet in diameter and 40 feet in focal length, in the way now mentioned, Dr. Herschel discovered one of the satellites of Saturn. But there is still another way of increasing the ap- parent magnitude of objects, particularly of those which are within our reach, which is of great importance in optics. It will be proved, when we come to treat of vision, that a good eye sees the visible outline of an ob- ject very distinctly when it is placed at a great distance, and that, by a particular power in the eye, we can ac- commodate it to perceive objects at different distances. Hence, in order to obtain distinct vision of any object, we have only to cause the rays which proceed from it to enter the eye in parallel lines, as if the object itself was CHAP. V. MAGNIFYING POWER OF LENSES. 51 very distant. Now, if we bring an object, or the image of an object, very near to the eye, so as to give it great apparent magnitude, it becomes indistinct ; but if we can, by any contrivance, make the rays which proceed from it enter the eye nearly parallel, we shall necessarily see it distinctly. But we have already shown that when rays diverge from the focus of any lens, they will emerge from it parallel. If we, therefore, place an object or an image of one in the focus of a lens held close to the eye, and having a small focal distance, the rays will enter the eye parallel, and we shall see the object very dis- tinctly, as it will be magnified in the proportion of its present short distance from the eye to the distance of six inches, at which we see small objects most distinctly. But this short distance is equal to the focal length of the lens, so that the magnifying power produced by the lens will be equal to six inches divided by the focal length of the lens. A lens thus used to look at or mag- nify any object is a single microscope; and when such a lens is used to magnify the magnified image produced by another lens, the two lenses together constitute a com- pound microscope. When such a lens is used to magnify the image pro- duced in the single lens telescope from a distant object, the two lenses together constitute what is called the astronomical refracting telescope; and when it is used to magnify the image produced by a concave mirror from a distant object, the two constitute a reflecting telescope, such as that used by Le Maire and Herschel ; and when it is used to magnify an enlarged image, M N, fig. 14., produced from an object mn, placed before a concave mirror, the two constitute a reflecting microscope. All these instruments will be more fully described in a future chapter. 52 A TREATISE ON OPTICS. PART CHAP. VI. SPHERICAL ABERRATION OF LENSES AND MIRRORS. (55.) IN the preceding chapters we have supposed that the rays refracted at spherical surfaces meet exactly in a focus ; but this is by no means strictly true : and if the reader has in any one case projected the rays by the methods described, he must have seen that the rays nearest the axis of a spherical surface, or of a lens, are refracted to a focus more remote from the lens than those which are incident at a distance from the axis of the lens. The rules which we have given for the foci of lenses and surfaces are true only for rays very near the axis. In order to understand the cause of spherical aberrar tion, let L L be a plano-convex lens one of whose sur- faces is spherical, and let its plane surface L m L be turned towards parallel rays R L, R L. Let R'L', R'L' be rays very near the axis A F of the lens, and let F be their focus after refraction. Let R L, R L be parallel rays incident at the very margin of the lens, and it will JFie. 36. be found by the method of projection that the corre- sponding refracted rays L/, L/ will meet at a point/ much nearer the lens than F. In like manner inter- mediate rays between R L and R' L' will have their foci intermediate between / and F. Continue the rays L/, Lf, till they meet at G and II a plane passing through F, and perpendicular to FA. The distance /F is called the longitudinal spherical aberration, and G H the lateral spherical aberration of the lens. In a plano-convex lens CHAP. VI. SPHERICAL ABERRATION. 53 placed like that in the figure, the longitudinal spherical aberration /F is no less than 4^ times mn the thickness of the lens. It is obvious that such a lens cannot form a distinct picture of any object in its focus F. If it is ex- posed to the sun, the central part of the lens Urn L/, whose focus is at F, will form a pretty bright image of the sun at F ; but as the rays of the sun which pass through the outer part L L of the lens have their foci at points between f and F, the rays will, after arriving at those points, pass on to the plane GH, and occupy a circle whose diameter is GH ; hence the image of the sun in the Fig. 37. focus F will be a bright disc surrounded and rendered - indistinct by a broad halo of light growing fainter and fainter from F to G and H. In like manner, every object seen through sucli a lens, and every image formed by it, will be rendered confused and W indistinct by spherical aberration. These results may be illustrated experimentally by taking a ring of black paper, and covering up the outer parts of the face L L of the lens. This will diminish the halo G H, and the indistinctness of the image, and if we cover up all the lens excepting a small part in the centre, the image will become perfectly distinct, though less bright than before, and the focus will be at F. If, on the contrary, we cover up all the central part, and leave only a narrow ring at the circumference of the lens, we shall have a very distinct image of the sun formed about/. (56.) If the reader will draw a very large diagram of a plano-convex, and of a double convex lens, and deter- mine the refracted rays at different distances from the axis where parallel rays fall on each of the surfaces of the lens, he will be able to verify the following results for glass lenses. 1 . In a plano-convex lens, with its plane side turned to parallel rays as in fig. 36., that is, turned to distant objects if it is to form an image behind it, or turned to the eye if it is to be used in magnifying a near object, the E 3 54 A TREATISE ON OPTICS. PART I. spherical aberration will be 4^ times the thickness, or 4^ times mn. 2. In a plano-convex lens, with its convex side turned towards parallel rays, the aberration is only l-j^ths of its thickness. In using a plano-convex lens, there- fore, it should always be so placed that parallel rays either enter the convex surface or emerge from it. 3. In a double convex lens with equal convexities, the aberration is l T 6 ^ths of its thickness. 4. In a double convex lens having its radii as 2 to 5, the aberration will be the same as in a plano-convex lens in Rule 1, if the side whose radius is 5 is turned towards parallel rays ; and the same as the plano-convex lens in Rule 2, if the side whose radius is 2 is turned to parallel rays. 5. The lens which has the least spherical aberration is a double convex one, whose radii are as 1 to 6. When the face whose radius is 1 is turned towards parallel rays, the aberration is only l T ^ths of its thickness; but when the side with the radius 6 is turned towards parallel rays, the aberration is S^^yths of its thickness. These results are equally true of plano-concave and double concave lenses. If we suppose the lens of least spherical aberration to have its aberration equal to I, the aberrations of the other lenses will be as follows : Best form, as in Rule 5. - 1*000 Double convex or concave, with equal curvatures 1*561 Plano-convex or concave in best position, asl in Rule 2. - Plano-convex or concave in worst positio in Rule 1. - (57.) As the central parts of the lens LL,^r. 36., refract the rays too little, and the marginal parts too much, it is evident that if we could increase the con- vexity at n and diminish it gradually towards L, \ve should remove the spherical aberration. But the ellipse and the hyperbola are curves of this kind, in which the curvature diminishes from n to L ; and mathematicians have shown how spherical aberration may be entirely* curvatures tion, as"! tion, asl CHAP. VI. LENSES WITHOUT ABERRATION. 55 removed, by lenses whose sections are ellipses or hyper- bolas. This curious discovery we owe to Descartes. Fig. 38. If A L D L, for example, is an ellipse whose greater axis AD is to the distance between its foci F,/as the index of refraction is to unity, then parallel rays RL, RL incident upon the elliptical surface L AL will be refracted by the single action of that surface into lines, which would meet exactly in the focus F, if there were no second sur- face intervening between L A L and F. But as every useful lens must have two surfaces, we have only to de- scribe a circle L a L round F as a centre, for the second surface of the lens L L. As all the rays refracted at the surface L A L converge accurately to F, and as the cir- cular surface L a L is perpendicular to every one of the refracted rays, all these rays will go on to F without suf- fering any refraction at the circular surface. Hence it follows that a meniscus whose convex surface is part of an ellipsoid, and whose concave surface is part of any spherical surface whose centre is in the farther focus, will have no spherical aberration, and will refract parallel rays incident on its convex surface to the farther focus. In like manner a concavo-convex lens, L L, whose Fig. 39. concave surface L A L is part of the ellipsoid A L D L, and whose convex surface L a L is a circle described E 4 56 A TREATISE ON OPTICS. PART I. round the farther focus of the ellipse,, will cause parallel rays R L, R L to diverge in directions L r, L r , which when continued backwards will meet exactly in the focus F, which will be its virtual focus. If a plano-convex lens has its convex surface, L A L, part of a hyperboloid formed by the revolution of a hyperbola whose greater axis is to the distance between the foci as unity is to the index of refraction, then pa- rallel rays, RL, RL, falling perpendicularly on the plane surface will be refracted without aberration to the farther focus of the hyperboloid. The same property belongs to a plano-concave lens, having a similar hyperbolic surface, and receiving parallel rays on its plane surface. A meniscus with spherical surfaces has the property of refracting all converging rays to its focus, if its first sur- face is convex, provided the distance of the point of convergence or divergence from the centre of the first surface is to the radius of the first surface as the index of refraction is to unity. Thus, if M L L N is a menis- cus, and R L, R L rays converging to the point E, whose distance E C from the centre of the first surface L A L of the meniscus is to the radius C A or C L as the index of refraction is to unity, that is as 1*500 to 1 in glass; then if F is the focus of the first surface, describe with any radius less than F A a circle M a N for the second surface of the lens. Now it will be found by projection that the rays R L, R L, whether near the axis A E or remote from it, will be refracted accurately to the focus F, and as all these rays fall perpendicularly on the second CHAP. VI. LENSES WITHOUT ABERRATION. 57 surface MN, they will still pass on without refraction to the focus F. In like manner it is obvious that rays Fig. 41. F L, F L diverging from F will be refracted into R L, R L, which diverge accurately from the virtual focus. When these properties of the ellipse and hyperbola, and of the solids generated by their revolution, were first discovered, philosophers exerted all their ingenuity in grinding and polishing lenses with elliptical and hyper- bolical surfaces, and various ingenious mechanical con- trivances were proposed for this purpose. These, how- ever, have not succeeded, and the practical difficulties which yet require to be overcome are so great, that lenses with spherical surfaces are the only ones now in use for optical instruments. But though we cannot remove or diminish the sphe- rical aberration of single lenses beyond 1 T J^ths of their thickness, yet by combining two or more lenses, and making opposite aberrations correct each other, we can remedy this defect to a very considerable extent in some cases, and in other cases remove it altogether. (58.) Sir John Herschel has shown, that if two plano- convex lenses AB, CD, whose focal lengths are as 2'3 to 1, are placed with their convex sides together, AB the least convex being next the eye when the combination is to be used as a microscope, the aberration will be only 0-248, or one fourth of that of a single lens in its best form. When this lens is used to form an image, A B A TREATISE ON OPTICS. PART I. Fig. 42. must be turned to the object. If the focal lengths of the two lenses are equal, the spherical aberration will be 0-603,, or a little more than one half of a single lens in its best form. Sir John Herschel has also shown that the spherical aber- ration may be wholly removed by combining a meniscus C D with a double convex lens A B, as in figs. 43. and 44., the lens AB being turned to the eye when it is used for a microscope, and to the object when it is to be used for forming images, or as a burning glass. Fig. 43. Fig. 44. The following are the radii of curvature for these lenses, as computed by Sir John Herschel : Fig. 43. Fig. 44. Focal length of the double convex~\ lr . ,.__ lens A B - - J + 10<( Radius of its first or outer surface + 5*833 + Radius of its second surface 35 *000 Focal length of the meniscus C D 4- 17*829 + Radius of its first surface - + 3-688 + Radius of its second surface - + 6*291 + Focal length of the compound lens + 6-407 + 10-000 5-833 35-000 5-497 2*054 8-128 3-374 Spherical Aberration of Mirrors. (59.) We have already stated, that when parallel rays, A M, A N, are incident on a spherical mirror, M N, they are refracted to the same focus, F, only when they are in- cident very near the axis, AD. If F is the focus of CHAP. VI. ABERRATION OF MIRRORS. 59 those very near the axis, such as A m, then the focus of Fig. 45. those more remote, such as A M, will be at /between F and D, and /F will be the longitudinal spherical aber- ration, which will obviously increase with the diameter of the mirror when its curvature remains the same, and with the curvature when its diameter is constant. The images, therefore, formed by mirrors will be indistinct, like those formed by spherical lenses, and the indistinct- ness will arise from the same cause. It is manifest that if M N were a curve of such a nature that a line, A M, parallel to its axis, A D, and an- other line, /M drawn from M to a fixed point, /, should always form equal angles with a line, C M, perpendicular to the curve M N, we should in this case have a surface which would reflect parallel rays exactly to a focus f, and form perfectly distinct images of objects. Such a curve is the parabola ; and, therefore, if we could construct mirrors of such a form that their section M N is a para- bola, they would have the invaluable property of reflect- ing parallel rays to a single focus. When the curvature of the mirror is very small, opticians have devised me- thods of communicating to it a parabolic figure; but when the curvature is great, it has not yet been found practicable to give them this figure. In the same manner it may be shown, that when di- verging rays fall upon a concave mirror of a spherical form, they will be reflected to different points of the axis; and that if a surface could be made so that the in- cident and reflected rays should form equal angles with a line perpendicular to the surface at the point of incidence, the reflected rays would all meet in a single point as their f>0 A TREATISE ON OPTICS. PART I, focus. A surface whose section is an ellipse has this property; and it may be proved that rays diverging from one focus of an ellipse will be reflected accuiately to the ether focus. Hence in reflecting microscopes the mirror should be a portion of an ellipsoid; the axis of the mir- ror being the axis of the ellipsoid, and the object being placed in the focus nearest the mirror. On Caustic Curves formed by Reflexion and Refraction. (60.) Caustics formed by reflexion. -As the rays in- cident on different points of a reflecting surface at differ- ent distances from its axis are reflected to different foci in that axis, it is evident that the rays thus reflected must cross one another at particular points, and wher- ever the rays cross they will illuminate the white ground on which they are received with twice as much light as falls on other parts of the ground. These luminous intersections form curve lines, called caustic lines or caustic curves; and their nature and form will, of course, vary with the aperture of the mirror, and the distance of the radiant point. In order to explain their mode of formation and general properties, let M B N be a concave spherical mirror, fig. 46., whose centre is C, and whose focus for Fig. 46. CHAP. VI. CAUSTIC CURVES. 6l parallel and central rays is F. Let RMB be a di- verging beam of light falling on the upper part, MB, of the mirror at the points 1, 2, 3, 4, &c. If we draw lines perpendicular to all these points from the centre C, and make the angles of reflexion equal to the angles of incidence, we shall obtain the directions and foci of all the reflected rays. The ray Rl, near the axis RB, will have its conjugate focus at/, between F and the centre C. The next ray, R 2, will cut the axis nearer F, and so on with all the rest, the foci advancing from f to B. By drawing all the reflected rays to these foci, they will be found to intersect one another as in the figure, and to form by their intersections the caustic curve Mf. If the light had also been incident on the lower part of the mirror, a similar caustic shown by a dotted line would also have been formed between N and f. If we suppose, therefore, the point of incidence to move from M to B, the conjugate focus of any two con- tiguous rays, or an infinitely slender pencil diverging from R, will move along the caustic from M to/. Let us now suppose the convex surface M B N of the mirror to be polished, and the radiant point R to be placed as far to the right hand of B as it is now to the left, it will be found, by drawing the incident and reflected rays, that they will diverge after reflexion ; and that when continued backwards they will intersect one another, and form the imaginary caustic M/' N situated behind the convex surface; and exactly similar to the real caustic. If we suppose the convex mirror M B N to be com- pleted round the same centre, C_, as at M A N, and the pencil of rays still to radiate from R, they will form the imaginary caustic M/'N smaller than M/N, and uniting with it at the points M, N. Let the radiant point R be now supposed to recede from the mirror M B N, the line B/, which is called the tangent of the real caustic M/N, will obviously diminish, because the conjugate focus /will approach to F ; and, for the same reason, the tangent A/' of the imaginary caustic will increase. When R becomes in- A TREATISE ON OPTICS. PART I. finitely distant, and the incident rays parallel, the points f)f' i called the cusps of the caustic, will both coincide with F and F', the principal foci, and will have the very same size and form. But if the radiant point R approaches to the mirror, the cusp f of the real caustic will approach to the centre C, and the tangent B / will increase, the cusp f of the imaginary caustic will approach to A, and its tangent A/' will diminish ; and when the radiant point arrives at the circumference at A, the cusp f f will also arrive at A, and the imaginary caustic will disappear. At the same time, the cusp f of the real caustic will be a little to the right of C, and its two opposite summits will meet in the radiant point at A. If we suppose the radiant point R now to enter within the circle A M B N, as shown in fig. 47-, so that R C is Fig. 47. less than R A, a remarkable double caustic will be formed. This caustic will consist of two short ones of the com- mon kind, ar,br, having their common cusp at r, and of two long branches, af 9 bf, which meet in a focus at /. When RC is greater than RA, the curved branches that meet at/" behind the mirror will diverge, and have a vir- tual focus within the mirror. When R coincides with F, a point halfway between A and C, arid the virtual CHAP. VI. CAUSTIC CURVES. 63 principal focus of the convex mirror MAN, these curved branches become parallel lines ; and when R coincides with the centre C, the caustics disappear, and all the light is condensed into a single mathematical point at C, from which it again diverges, and is again reflected to the same point. In virtue of the principle on which these phenomena depend, a spherical mirror has, under certain circum- stances, the paradoxical property of rendering rays di- verging from a fixed point either parallel, diverging, or converging ; that is, if the radiant point is a little way within the principal focus of a mirror, so that rays very near the axis are reflected into parallel lines, the rays which are incident still nearer the axis will be rendered diverging, and those incident farther from the axis will be rendered converging. This property may be dis- tinctly exhibited by the projection of the reflected rays. Caustic curves are frequently seen in a very distinct and beautiful manner at the bottom of cylindrical vessels of china or earthenware that happen to be exposed to the light of the sun or of a candle. In these cases the rays generally fall too obliquely on their cylindrical surface, owing to their depth ; but this depth may be removed, and the caustic curves beautifully displayed, by inserting a circular piece of card or white paper about an inch or so beneath their upper edge, or by filling them to that height with milk or any white and opaque fluid. The caustic curves produced by a highly polished ring, such as that of a bell-handle, are exceedingly beautiful in the light of the sun. The following method, however, of exhibiting caustic curves I have found exceedingly convenient and in- structive. Take a piece of steel spring highly polished, such as a watch spring, ~MN,fig. 48., and having bent it into a concave form as in the figure, place it vertically on its edge upon a piece of card or white paper AB. Let it then be exposed either to the rays of the sun, or those of any other luminous body, taking care that the plane of the card or the paper passes nearly through the A TREATISE ON OPTICS. PART^T and the two caustic curves shown in the figure will be finely displayed. By varying the size of the spring, and bending it into curves of different shapes, all the va- riety of caustics, with their cusps and points of contrary flexure, will be finely exhibited. The steel may be bent accurately into different curves by applying a portion of its breadth to the required curves drawn upon a piece of wood, and either cut or burned sufficiently deep in the wood to allow the edge of the thin strip of _ metal to be inserted in it. Gold or silver foil answers very well ; and when the light is strong, a thin strip of mica will also answer the purpose. The best substance of all, how- ever, is a thin strip of polished silver. ( 6' 1 . ) Caustics formed by refraction. If we expose a globe of glass filled with water, or a solid spherical lens, or even the widest part of a round decanter, filled with water, to the rays of the sun, or to the light of a lamp or candle, and receive the refracted light on white paper held almost parallel to the axis of the sphere, or so that its plane passes nearly through the luminous body, we shall perceive on the paper a luminous figure bounded by two bright caustics, like af and bf, fig. 4?., but placed . behind the sphere, and forming a sharp cusp or angle at the point f, which is the focus of refracted rays. The production of these curves depends upon the intersection of rays, which, being incident on the sphere at different distances from the axis, are refracted to foci at different points of the axis,, and .therefore cross one another. This result is so easily understood, and may be exhibited so clearly, by projecting the refracted rays, that it is un- necessary to say any more on the subject. Some of the phenomena of caustics produced by re- fraction may be illustrated experimentally in the follow- ing manner : Take a shallow cylindrical vessel of lead, CH. VII. IMAGES PRODUCED BY LENSES AND MIRRORS. 60 M N, two or three inches in diameter, and cut its upper margin, as shown in the figure, leaving two or more opposite projections, ac, bd, &c., forming each about 10 or 15 of the whole circumference. Complete the cir- cumference by cementing on the vessel two strips of g. 49. mica, so as to substitute for the lead that has been removed two transparent cylindrical surfaces. If this vessel is filled with water, or any other transparent fluid, and a piece of card or white pa- per, ABCD, is held almost pa- rallel to the surface of the water, and having its plane nearly passing through the sun or the candle, the caustics A F, D F will be finely displayed. By altering the cur- vature of the vessel, and that of the strips of mica, so as to form refracting solids of different kinds, many inter- esting and instructive variations of the experiment may be made. CHAP. VII. ON THE FORM OF IMAGES PRODUCED BY LENSES AND MIRROR'S OF DIFFERENT SIZES. THE shape of the images of objects as formed by lenses and mirrors with spherical surfaces, has been treated of by various optical writers * ; but I am not aware that any author has treated of the shape of images as affected only by the size of the lenses or mirrors by which they are formed. This subject is of fundamental importance in the new art of Photography, when the images delineated by the solar rays are formed by lenses, and sometimes, too, by mirrors of a larger size. * Smith's " Complete System of Optics," vol. i. chap. xii. p. 238., and vol. ii., Remarks, p. 83. F 66 A TREATISE ON OPTICS. PART I. The images of objects formed upon a plane surface differ from the objects themselves, from many causes which it is unnecessary here to enumerate. The most skilful opticians have striven, and to a great extent successfully, to make the most perfect lenses for photo- graphic purposes ; but the photographer himself has overlooked the greatest imperfection to which his art is subject, arising solely from the size of the lenses in his camera. According to the geometrical principles of perspective, the correct representation of any body or object what- ever, upon a plane surface, is obtained by drawing lines from the point of sight, through every point of the body or object, to that plane. As the pupil of the human eye is little more than two tenths of an inch in diameter, we may regard the picture on the retina as a correct representation of external objects, in so far, at least, as its correctness depends upon the size of the lens which forms the picture. In like manner we may consider the image of objects formed by a lens the size of the pupil of the eye as a correct representation of the object. Now if in perspective we take a new point of sight two tenths of an inch distant from the first, the per- spective representation of the object on a plane will be changed, and the magnitude of the change will in- crease with the distance between the two points of sight. In like manner, if we look at an object from two different points, which are two tenths of an inch distant, we shall obtain two views of that object equally dis- similar. Following out this principle, let us suppose that a lens four inches square is employed to produce upon a plane surface the image of any object, and that the size of the pupil of the eye is two tenths of an inch \ then, as there will be several hundred areas equal to that of the pupil in the lens, the image given by the lens will be a compound image consisting of several hun- dred perspective views of the object taken from several CH. VII. IMAGES PRODUCED BY LENSES AND MIRRORS. 67 hundred different points of sight, each distant two tenths of an inch from its neighbour, and all those on the margin of the lens distant three inches and eight tenths from those opposite to them. Such a jumble of images cannot, under any circumstances, be a true representation of the object. This view of the question, as one of perspective, will be more intelligible if we consider the subject optically. Let L L be either the horizontal or the vertical sec- tion of a lens, by means of which an image or picture Fig. 50. of the object A B C D E is to be taken either on a plane surface, or suspended in the air, and made visible to an eye behind the lens. The solid object ABE con- sists of a cylindrical portion A B D C, whose termi- nation A B is a circle, and of a conical portion C D E. If we continue the lines E C, E D, and C A, D B, they will meet the lens in the points c, a, d, b. If we now cover all the lens except the central portion a b, the Fig. 51. image of the object ABE will be merely a circle, as shown at a 6, fig. 51., because not a single ray from F 2 68 A TREATISE ON OPTICS. PART I. the cylindrical surface A B D C, nor from the conical surface C D E, can reach the lens a b. In like manner, if we cover all the lens except cd, the image of the object ABE will be, as shown in fig. 51., at cd, its circular termination, and the cylindrical part of it only being seen, because not a single ray from its conical part C D E can fall upon the lens c d. But when the whole area L L of the lens is exposed, the whole object will be seen suspended in the air, as at L L, fig. 51. If the image is received upon a plane surface behind the lens, the cylindrical part will be represented by a halo or circle of light surrounding the circle ab, and corresponding in size to the section m n, fy. 50., of the none of rays C c d D ; and the conical part C D E will be represented by another halo or circle, round the halo m n, and corresponding to the section o p of the cone of rays ELL. Results demonstrating the truth of these views, have been obtained photographically by my friend Mr. Buckle, of Peterborough, whose beautiful Talbotypes obtained a Council Medal at the Great Exhibition. The acting diameter of his lens was 3-J inches, and the effect of the combination of the marginal pictures is most dis- tinctly exhibited. Let us now apply these results to the photographical pictures of the human bust as taken in a camera. The human face and head consist superficially of various surfaces, some vertical, some horizontal, and many in- clined at all angles to the axis of the lens by which they are to be represented on a plane surface. A true perspective representation of the human head placed at A B, will be that which is given by a lens a b whose diameter is equal to that of the pupil of the eye, or as formed by lines passing from the centre of the pupil to different points of the head. From such a portrait, all surfaces, such as A C, B D, E C, E D will be excluded ; but if we use the whole lens L L, all these surfaces, and all those of an intermediate inclination between AC OH. VII. IMAGES PRODUCED BY LENSES AND MIRRORS. 69 and E C, B D and D E, will be introduced into the portrait. If, for example, L L is a horizontal section of the lens, the right hand marginal parts of the lens, between a and L, may introduce into the portrait the left eye, or the left ear, or the left side of the nose, and all other parts of a certain inclination to the axis ; thus enlarging all such parts, and widening the picture. If L L be a vertical section of the lens, the lower part of the nose, the interior of the nostrils,, the lower part of the upper lip, and the lower part of the chin, will be introduced into the portrait by the lower marginal parts b L of the lens ; while the top of the head, the upper parts of the lip and the eyelids, will be introduced by the upper marginal parts a L of the lens. The same is true of all other sections of the lens, and a monstrous portrait of the human bust is thus obtained by the photographer, the monstrosity increasing with the size of the lens. The nature and character of the portrait will thus vary with the superficial form of the lens, which may be circular, oval, square, rectangular, triangular, or of any irregular form ; and in this way remarkable modifications of photographic portraits may be produced merely by varying the shape of the lens. The amount of the deformity introduced into por- traits by a, lens three or four inches in diameter may be readily estimated by the fact, that when a portrait is taken from two points two and a half inches distant, such as those taken as seen by each eye separately, the difference between the two is so well marked, that it can be pointed out by a child. A portrait, therefore, consisting of a combination of portraits as seen from every point of a lens triree or four inches in diameter, must give a form and expression to the human coun- tenance very wide of the truth. The hideousness of photographic portraits is uni- versally admitted, and has been ascribed to the im- perfection of the lenses employed, the unsteadiness of the sitter, and the necessary constraint of features and of limb under which he submits to the operation. The F 3 70 A TREATISE ON OPTICS. PART I. true cause, modified doubtless by others, is the size of the lens, even if the lens is optically perfect. The photographer, therefore, who has a genuine in- terest in the perfection of his art, will receive these truths with gratitude ; and by accelerating the photo- graphic processes, with the aid of more sensitive ma- terials, he will be able to make use of lenses of very small aperture, and thus place his art in a higher position than that which it has yet attained. The photographer, on the contrary, whose sordid interests bribe him to forswear even the truths of science, will continue to deform the youth and beauty that may in ignorance repair to his studio, adding scowls and wrinkles to the noble forms of manhood, and giving tx> a fresh and vigorous age the aspects of departing or departed life.* But while small apertures possess such a peculiar advantage as that of giving a true perspective repre- sentation of the object or scene to be delineated, a small lens possesses still greater advantages. In large lenses much light is lost by the absorption of raya in passing through a great thickness of glass, and also by reflection from the four or eight surfaces of the achromatic lens or lenses employed. In such lenses, too, neither the chromatic nor the spherical aberrations, which increase with the aperture, are completely corrected, and no attempt even is made to remove the influence of the secondary spectrum. With small apertures, too, * It is stated in the Athenceum of May 29th, 1852, that, at Lord Rosse's feoir^e of the 22nd May, " M. Claudet exhibited figures showing that an aperture of three and a quarter inches in*p lens can produce as correct a portrait as one of the size of the pupil. Now this is simply a false in- ference deduced from a falsely reported experiment. No experiment whatever can establish such a proposition, but one which shows the per- fect similarity in form and expression of two portraits the one taken by an aperture equal to that of the pupil, and the other by a large lens. The result of no such experiment was exhibited. Lord Rosse did not see the figures in question, and the only competent person who, on a subsequent occasion, did examine them, Mr. Robert Hunt, at once per- 5eived their difference, and pointed out the one obtained by the large lens, t is interesting, however, to find it so expressly declared as the result of a carefully made experiment, that a correct portrait can be produced by an aperture of two tenths of an inch, which is about the average aperture of the pupil. CH. VII. IMAGES PRODUCED BY LENSES AND MIRRORS. ?1 objects, or parts of objects, at different distances, will be delineated with nearly the same distinctness, and a picture produced as nearly resembling the original as it can be made in the present state of practical optics. The same observations, with the exception of those which relate to the achromatism and the thickness of the refracting medium, are applicable to the images pro- duced by mirrors of different sizes. 72 A TREATISE ON OPTICS. PART II. PART II. PHYSICAL OPTICS. (62.) PHYSICAL Optics is that branch of the science which treats of the physical properties of light. These properties are exhibited in the decomposition and recora- position of white light ; in its decomposition by absorp- tion; in the inflexion or diffraction of light ; in the colours of thick and thin plates ; and in the double refraction and polarisation of light. CHAP. VIII. ON THE COLOURS OF LIGHT, AND ITS DECOMPOSITION. (63.) IN the preceding chapters we have regarded light as a simple substance, all the parts of which have the same index of refraction, and therefore suffer the same changes when acted upon by transparent media. This, however, is not its constitution. White light, as emitted from the sun or from any luminous body, appears to be composed of seven different kinds of light, viz., red, orange, yellow, green, blue, indigo, and violet ; and this compound substance may be decomposed, or ana- lysed, or separated into its elementary parts, by two dif- ferent processes, viz., by refraction and absorption. The first of these processes was that which was em- ployed by Sir Isaac Newton, who discovered the com- position of white light. If we admit a beam of the sun's light, SH, through a small hole, H, in the window- shutter, E F,of a darkened room, it will go on in a straight line and form a round white spot at P. If we now in- terpose a prism, BAC, whose refracting angle is BAG, CHAP. VIII. ANALYSIS OF LIGHT BY THE PRISM. 73 so that this beam of light may fall on its first surface C A, and emerge at the same angle from its second surface Fig. 52. B A in the direction g G, and if we receive the refracted beam on the opposite wall, or rather on a white screen, M N, we should expect, from the principles already laid down, that the white beam which previously fell upon P would suffer only a change in its direction, and fall somewhere upon M N, forming there a round white spot exactly similar to that at P. But this is not the case. Instead of a white spot, there will be formed upon the screen M N an oblong image K L of the sun, containing seven colours, viz., red, orange, yellow, green, blue, in- digo, and violet, the whole beam of light diverging from its emergence out of the prism at g, and being bounded by the lines g K, g L. This lengthened image of the sun is called the solar spectrum, or the prismatic spectrum. If the aperture H is small, and the distance g G consi- derable, the colours of the spectrum will be very bright. The lowest portion of it at L is a brilliant red. This red shades off by imperceptible gradations into orange, the orange into yellow, the yellow into green, the green into blue, the blue into a pure indigo, and the indigo into a violet. No lines are seen across the spectrum thus produced ; and it is extremely difficult for the sharpest eye to point out the boundary of the different colours- Sir Isaac Newton, however, by many trials, found the 74 A TREATISE ON OPTICS. i>ART II. lengths of the colours to be as follows, in the kind of glass of which his prism was made. We have added the results obtained by Fraunhofer with flint glass. Newton. Fraunhofer. Red - 45 56 Orange 27 27 Yellow 40 27 Green 60 46 Blue 60 48 Indigo 48 47 Violet - -80 109 Total length 360 360 These seven colours are not equally brilliant. At the lower end, L, of the spectrum the red is comparatively faint, but grows brighter as it approaches the orange. The light increases gradually to the middle of the yellow space, where it is brightest ; and from this it gradually declines to the upper or violet end, K, of the spectrum, where it is extremely faint. (64.) From the phenomena which we have now de- scribed, Sir Isaac Newton concluded that the beam of white light, S, is compounded of light of seven different colours, and that for each of these different kinds of light the glass, of which his prism was made, has dif- ferent indices of refraction ; the index of refraction for the red light being the least, and that of the violet the greatest. If the prism is made of crown glass, for example, the indices of refraction for the different coloured rays will be as follows : Index of Index of Refraction. Red ... 1-5258 Orange - - 1-5268 Yellow - - 1-5296 Refraction* Blue - 1-5360 Indigo - - 1-5417 , Violet - - 1-5466 Green - If we now draw the prism, B A C, on a great scale, and determine the progress of the refracted rays, supposed to be incident upon the same point of the first surface C A, by using for each ray the index of refraction in the pre- CHAP. VIII. RECOMPOSITION OP LIGHT. 75 ceding table, we shall find them to diverge as in the preceding figure, and to form the different colours in the order of those in the spectrum. In order to examine each colour separately, Sir Isaac made a hole in the screen MN, opposite the centre of each coloured space; and he allowed that particular colour to fall upon a second prism, placed behind the hole. This light, when refracted by the second prism, was not drawn out into an oblong image as before, and was not refracted into any other colours. Hence he concluded that the light of each different colour had the same index of refraction; and he called such light homo- geneous or simple, white light being regarded as hetero- geneous or compound. This important doctrine is called the different refrangibility of the rays of light. The different colours as existing in the spectrum are called primary colours; and any mixtures or combinations of any of them are called secondary colours, because we can easily separate them into their primary colours by re- fraction through the prism. ^65.) Having thus clearly established the composition of white light, Sir Isaac also proved, experimentally, that all the seven colours, when again combined and made to fall upon the same spot, formed or recomposed white light. This important truth he established by various experiments ; but the following method of proving it is so satisfactory, that no farther evidence seems to be wanted. Let the screen MN,fig. 5Q., which receives the spectrum, be gradually brought nearer the prism BAG, the spectrum K L will gradually diminish ; but though the colours begin to mix, and encroach upon one another, yet, even when it is brought close to the face B A of the prism, we shall recognise the separation of the light into its component colours. If we now take a prism, B a A, shown by dotted lines, made of the same kind of glass as B A C, and having its refracting angle A B a exactly equal to the refracting angle B A C of the other prism; and if we place it in the opposite di- rection, we shall find that all the seven differently coloured 76 A TREATISE ON OPTICS. PART II. rays which fall upon the second prism, A B a, are again combined into a single beam of white light gP, forming a white circular spot at P, as if neither of the prisms had been interposed. The very same effect will be produced, even if the surfaces, AB, of the two prisms are joined by a transparent cement of the same refractive power as the glass, so as to remove entirely the refractions at the common surface AB. In this state the two prisms combined are nothing more than a thick piece of glass, BCAa, whose two sides, AC, aB, are exactly parallel; and the decomposition of the light by the re- fraction of the first surface, A C, is counteracted by the opposite and equal refraction of the second surface, a B ; that is, the light decomposed by the first surface is re- composed by the second surface. The refraction and re-union of the rays in this experiment may be well ex- hibited by placing a thick plate of oil of cassia between two parallel plates of glass, and making a narrow beam of the sun's light fall upon it very obliquely. The spectrum formed by the action of the first surface will be distinctly visible, and the re-union of the colours by the second will be equally distinct. We may, therefore, consider the action of a plate of parallel glass on the sun's rays passing obliquely through it, that is, its pro- perty of transmitting them colourless, as a sufficient proof of the recomposition of light. The same doctrine may be illustrated experimentally by mixing together seven different powders having the same colours as those of the spectrum, taking as much of each as seems to be proportional to the rays in each coloured space. The union of these colours will be a sort of greyish-white, because it is impossible to obtain powders of the proper colours. The same result will be obtained, if we take a circle of paper and divide it into sectors of the same size as the coloured spaces ; and when this circle is placed upon a humming-top, or any suitable apparatus, made to revolve rapidly, the effect of all the colours when combined will be a greyish- white. CHAP. VIII. NEW ANALYSIS OF LIGHT. 77 Decomposition of Light by Absorption. (66.) If we measure the quantity of light which is reflected from the surfaces and transmitted through the substance of transparent bodies, we shall find that the sum of these quantities is always less than the quantity of light which falls upon the body. Hence we may conclude that a certain portion of light is lost in passing through the most transparent bodies. This loss arises from two causes. A part of the light is scattered in all directions by irregular reflexion from the imperfectly polished surface of particular media., or from the imper- fect union of its parts; while another, and generally a greater portion, is absorbed, or stopped by the particles of the body. Coloured fluids, such as black and red ink, though equally homogeneous, stop or absorb dif- ferent kinds of rays, and when exposed to the sun they become heated in different degrees ; while pure water seems to transmit all the rays equally, and scarcely receives any heat from the passing light of the sun. When we examine more minutely the action of co- loured glasses and coloured fluids in absorbing light, many remarkable phenomena present themselves, which throw much light upon this curious subject. If we take a piece of blue glass, like that generally used for finger glasses, and transmit through it ar beam of white light, the light will be a fine deep blue. This blue is not a simple homogeneous colour, like the blue or indigo of the spectrum, but is a mixture of all the colours of white light which the glass has not absorbed ; and the colours which the glass has absorbed are those which the blue wants of white light, or which, when mixed with this blue, would form white light. In order to determine what these colours are, let us transmit through the blue glass the prismatic spectrum K L, fig. 50. ; or, what is the same thing, let the observer place his eye behind the prism BAG, and look through it at the sun, or rather at a circular aperture made in the window-shutter of a dark room. He will then see 78 A TREATISE ON OPTICS. PART II. through the prism the spectrum K L as far below the aperture as it was above the spot P when shown in the screen. Let the blue glass be now interposed between the eye and the prism, and a remarkable spectrum will be seen, deficient in a certain number of its differently coloured rays. A particular thickness absorbs the middle of the red space, the whole of the orange, a great part of the green, a considerable part of the blue, a little of the indigo, and very little of the violet. The yellow space, which has not been much absorbed, has increased in breadth. It occupies part of the space formerly covered by the orange on one side, and part of the space formerly covered by the green on the other. Hence it follows, that the blue glass has absorbed the red light, which, when mixed with the yellow light, constituted orange, and has absorbed also the blue light, which, when mixed with the yellow, constituted the part of the green space next to the yellow. We have therefore, by ab- sorption, decomposed green light into yellow and blue, and orange light into yellow and red; and it conse- quently follows, that the orange and green rays of the spectrum, though they cannot be decomposed by pris- matic refraction, can be decomposed by absorption, and actually consist of two different colours possessing the same degree of refrangibility. Difference of colour is therefore not a test of difference of refrangibility, and the conclusion deduced by Newton is no longer admis- sible as a general truth : " That to the same degree of re- frangibility ever belongs the same colour, and to the same colour ever belongs the same degree of refrangibility/' With the view of obtaining a complete-analysis of the spectrum, I have examined the spectra produced by dif- ferent bodies, and the changes which they undergo by absorption when viewed through various coloured me- dia, and I find that the colour of every part of the spectrum may be changed not only in intensity, but in colour, by the action of particular media ; and from these observations, which it would be out of place here to de- tail, I conclude that the solar spectrum consists of three spectra of equal lengths, viz. ? a red spectrum, a yellow GHAP. VIII. NEW ANALYSIS OP LIGHT. 79 spectrum, and a blue spectrum. The primary red spec- trum has its maximum of intensity about the middle of the red space in the solar spectrum, the primary yellow spectrum has its maximum in the middle of the yellow space, and the primary blue spectrum has its maximum between the blue and the indigo space. The two minima of each of the three primary spectra coincide at the two extremities of the solar spectrum. From this view of the constitution of the solar spec- trum we may draw the following conclusions : 1. Red, yellow, and blue light exist at every point of the solar spectrum. 2. Asa certain portion of red, yellow, and blue, consti- tute white light, the colour of every point of the spectrum may be considered as consisting of the predominating colour at any point mixed with white light. In the red space there is more red than is necessary to make white light with the small portions of yellow and blue which exist there ; in the yellow space there is more yellow than is necessary to make white light with the red and blue ; and in the part of the blue space which appears violet there is more red than yellow, and hence the excess of red forms a violet with the blue. 3. By absorbing the excess of any colour at any point of the spectrum above what is necessary to form white light, we may actually cause white light to appear at that point, and this white light will possess the remarkable property of remaining white after any* number of refrac- tions, and of being decomposable only by absorption. Such a white light I have succeeded in developing in different parts of the spectrum. These views harmonise in a remarkable manner with the hypothesis of three colours, which had been hazarded by some* philoso- phers, and which others had rejected from its incompa- tibility with the phenomena of the spectrum. The existence of three primary colours in the spec- trum, and the mode in which they produce by their * Tobias Mayer, De Affinitate Color um Commentatio. Opera Inedita, p. 33. ; and Lambert, Ucm. Acad. Berl. 1768 80 A TREATISE ON OPTICS. PART II. combination the seven secondary or compound colours which are developed by the prism, will be understood from Jig. 53, where MN is the prismatic spectrum, consist- ing of three primary spectra of the same lengths, MN, viz. a red, a yellow, and a blue spectrum. The red spec- trum has its maximum intensity at R; and this intensity may be represented by the distance of the point R from MN. The intensity declines rapidly to M and slowly to N, at both of which points it vanishes. The yellow spectrum has its maximum intensity at Y, the intensity declining to zero at M and N ; and the blue has its maximum intensity at B, declining to nothing at M and N. The general curve which represents the total illumination at any point will be on the outside of these three curves, and its ordinate at any point will be equal to the sum of the three ordinates at the same point. Thus the ordinate of the general curve at the point Y will be equal to the ordinate of the yellow curve, which we may suppose to be 10, added to that of the red curve, which may be 2, and that of the blue, which may be 1. Hence the general ordinate will be 13. Now, if we suppose that 3 parts of yellow, 2 of red, and 1 of blue, make white, we shall have the colour at Y equal to 3 + 2 -h 1, equal to 6 parts of white mixed with 7 parts of yellow : that is, the compound tint at Y will be a bright yellvw without any trace of red or blue. As these colours all occupy the same place in the spectrum, they cannot be separated by the prism ; and if we could find a coloured glass which would absorb 7 parts of the yellow, we should obtain at the point Y a white light which the prism could not decompose. See the Transactions of the Royal Society of Edinburgh, vol. xii. p. 1 23. Q11AP, IX. DISPERSION OF LIGHT. 81 CHAP. IX. OX THE DISPERSION OF LIGHT. JN the preceding observations, we have considered the prismatic spectrum,, KL,jig. 50., as produced by a prism of glass having a given refracting angle, BAG. Tlie green ray, or g G, which, being midway between g K and g L, is called the mean ray of the spectrum, has been refracted from P to G, or through an angle of deviation, P#G, which is called the mean refraction or deviation, produced by the prism. If we now increase the angle B A C of the prism, we shall increase the refraction. The mean ray g G will be refracted to a greater distance from P, and the extreme rays g L, g K to a greater dis- tance in the same proportion ; that is, if g G is refracted twice as much, g L and g K. will also be refracted twice as much, and consequently the length of the spectrum K L will be twice as great. For the same reason, if we diminish the angle B A C of the prism, the mean refrac- tion and the spectrum will diminish in the same pro- portion , but, whatever be the angle of the prism, the length K L will always bear the same proportion to G P, the mean refraction. Sir Isaac Newton supposed that prisms made of all substances whatever produced spectra bearing the same proportion to the mean refraction as those produced by prisms of glass ; and it is a remarkable circumstance, that a philosopher of such sagacity should have over- looked a fact so palpable, as that different bodies produced spectra whose lengths were different, when the mean re- fraction was the same. The prism BAC,/#. 52., being supposed to be made of crown glass, let us take another of flint glass or white crystal, with such a refracting angle that, when placed in the position BAG, the light enters and quits it at equal angles, and refracts the mean ray to the same point G. The 82 A TREATISE ON OPTICS. PART II. two prisms ought, therefore, to have the same mean re- fraction. But when we examine the spectrum produced hy the flint glass prism, we shall find that it extends be- yond K and L, and is evidently longer than the spectrum produced by the crown glass prism. Hence flint glass is said to have a greater dispersive power than crown glass, because at the same angle of mean refraction it separates the extreme rays of the spectrum, g L, g K, farther from the mean ray, g G. In order to explain more clearly what is the real mea- sure of the dispersive power of a body, let us suppose that in the crown glass prism, BAG, the index of re- fraction for the extreme violet ray, g K, is 1-54-66, and that for the extreme red ray, g L, 1*5258 ; then the difference of these indices, or -0208, would be a measure of the dispersive power of crown glass, if it and all other bodies had the same mean refraction: but as this is far from being the case, the dispersive power must be measured by the relation between -0208 and the mean refraction, or 1*5330, or to the excess of this above unity, viz., '5330, to which the mean refraction is always proportional. For the purpose of making this clearer, let it be required to compare the dispersive powers of diamond and crown glass. The index of refraction of diamond for the extreme violet ray is 2*467, and for the extreme red, 2*411, and the difference of these is 0-056, nearly three times greater than 0'0208, the same differ- ence for crown glass ; but then the difference between the sines of incidence and refraction, or the excess of the index of refraction above unity, or 1 '439^ is also about three times greater than the same difference in crown glass, viz. 0*533; and, consequently, the dispersive power of diamond is actually a little less than that of crown glass. The two dispersive powers are as fol- lows : Dispersive Powers. Crown Glass - - ! = 0-0390 Diamond - - = 0-0389 CHAP. IX. DISPERSION OP LIGHT. 83 This similarity of dispersive power might be proved experimentally, by taking a prism of diamond, which, when placed at B A C in fig. 50., produced the same mean refraction as the green ray y G. It would then be seen that the spectrum which it produced was of the same length as that produced by the prism of crown glass. Hence the splendid colours which distinguish diamond from every other precious stone are not owing to its high dispersive power, but to its great mean refraction. As the indices of refraction given in our table of refractive powers are nearly suited to the mean ray of the spectrum, we may, by the second column of the Table of the Dispersive Powers of Bodies, given in the Ap- pendix, No. I., obtain the approximate indices of refraction for the extreme red and the extreme violet rays, by adding half of the number in the column to the mean index of refraction for the index of refraction of the violet, and subtracting half of the same number for the index of the red ray. The measures in the table are given for the ordinary light of day. When the sun's light is used, and when the eye is screened from the middle rays of the spectrum, the red and violet may be traced to a much greater distance from the mean ray of the spectrum. When the index of refraction for the extreme ray is thus known, we may determine the position and length of the spectra produced by prisms of different sub- stances, whatever be their refracting angle, whatever be the positions of the prism, and whatever be the distance of the screen on which the spectrum is received. If we take a prism of crown glass, and another of flint glass, with such refracting angles that they produce a spectrum of precisely the same length, it will be found, that when the two prisms are placed together with their refracting angles in opposite directions, they will not restore the refracted pencil to the state of white light as happens in the combination of two equal prisms of crown or two equal prisms of flint glass. The white G 2 84? r A TREATISE ON OPTICS. PART II. light Y,fig. 52., will be tinged on one side with purple, and on the other with green light. This is called the secondary spectrum, and the colours secondary colours ; and it is manifest that they must arise from the coloured spaces in the spectrum of crown glass not being equal to those in the spectrum of flint glass. In order to render this curious property of the spec- trum very obvious to the eye, let two spectra of equal length be formed by two hollow prisms, one containing oil of cassia, and the other sulphuric acid. The oil of cassia spectrum will resemble AB, fig. 54?., and the Fix. 54. VwUi. liulige. B D sulphuric acid spectrum CD. In the former, the red, orange, and yellow spaces are less than in the latter, while the blue, indigo, and violet spaces are greater ; the least refrangible rays being, as it were, contracted in the former and expanded ia the latter, while the most refrangible rays are expanded in the one and contracted in the other. In consequence 5., Doctor Blair succeeded in refracting parallel J%. 56. ALC rays R A, R B to a single focus F, without the least trace of secondary colour. Before he discovered this property of the muriatic acid, he had contrived another, though a more complicated combination, for producing the same effect ; but as he preferred the combination which we have described, and employed it in the best aplanatic object-glasses which he constructed, it is un- necessary to dwell any longer upon the subject. In these observations, we have supposed that the lenses which are combined have no spherical aberration ; but though this is not the case, the combination of concave with convex surfaces, when properly adjusted, enables us to correct the spherical along with the chromatic aberration of lenses. In the course of an examination of the secondary spectra produced by different combinations, I was led to the conclusion that there may be refraction without colour, by means of two prisms, and that two lenses may converge white light to one focus, even though the prisms and the lenses are made of the same kind of glass. When one prism of a different angle is thus made to correct the dispersion of another prism, a tertiary spec- trum is produced, which depends wholly on the angles at which the light is refracted at the two surfaces of the prisrns. See my Treatise on New Philosophical /n- strumentSy p. 400. CHAP. XI. ON LINES IN THE SPECTRUM. 91 CHAP. XI. ON THE PHYSICAL PROPERTIES OF THE SPECTRUM. (68.) IN the preceding chapter we have considered only those general properties of the solar spectrum on which the construction of achromatic lenses depends. We shall now proceed to take a general view of all its physical properties. On the Existence of Defective Lines, or Lines without Light, in the Solar Spectrum. In the year 1 802, Dr. Wollaston * announced that in the spectrum formed hy a fine prism of flint glass, free of veins, when the luminous object was a slit, the twentieth of an inch wide, and viewed at the distance of 10 or 12 feet, there were six fixed dark lines, one in the red, one in the orange, one in the green, one in the Hue, and one in the violet space. These six lines are found to correspond with those marked B, D, b, F, G, and H, in fig. 57 This discovery did not excite any atten- tion, and was not followed out by its ingenious author. Without knowing of Dr. Wollaston's observations, the late celebrated M. Fraunhofer, of Munich, while viewing through a telescope the spectrum formed, from a narrow line of solar light, by the finest prisms of flint glass, discovered that its surface was crossed throughout its entire length by dark lines of different breadths. None of these lines coincide with the bound- aries of the coloured spaces. They are nearly 600 in number ; and the largest of them subtends an angle of from 5" to 10". I have found this angle to increase enormously as the sun passes from the meridian to the horizon. From their distinctness, and the facility with which they may be found, seven of these lines, viz. B, C, D, E, F, G, H, have been particularly distinguished * Philosophical Transactions for 1802, or Nicholson's Phil. Journal^ 8vo. vol. iv. p. 99. 92 A TREATISE ON OPTICS. PART IT. by M. Fraunhofer. Of these B lies in the red space, near its outer end ; C, which is broad and black, is beyond the middle of the red; D is in the orange, and is a strong double line, easily seen, the two lines being nearly of the same size, and separated by a bright one ; E is in the green, and consists of several, the middle -Fig. 57. one being the strongest ; F is in the blue, and is a very strong line; G is in the indigo, and H in the violet. Besides these lines there are others which deserve to be noticed. At A is a well defined dark line within the red space, and halfway between A and B in Fraunhofer's map of the spectrum is a group of seven or eight, forming together a dark band. Between B and C there are 9 lines ; between C and D there are 30 ; between D and E there are 84 of different sizes. Between E and b there are 24 ; at b there are three very strong lines, with a fine clear space between the two widest ; between b and F there are 52; between F and G 185; and between G and H J90, many being accumulated at G. Many lines and groups of lines are visible beyond the point I, the extreme limit of the spectrum as given by Fraunhofer. The line b of Fraunhofer lies in the green space between E and F. It consists of three strong lines, two of which are nearer to each other than the third. I have found that one of the two nearest, the one nearest to F, is double, and the other triple, and that between these two lines there is a broad band con- sisting of several lines. Between the two most distant lines I have discovered seven bands, some of which are composed of several lines. CHAP. XI. ON LINES IN THE SPECTRU3I. 9- (69.) These lines are seen with equal distinctness in spectra produced by prisms of all bodies, whether solid or fluid ; and, whatever be the lengths of the spectra and the proportion of their coloured spaces, the lines preserve the same relative positions to the boundaries of the co- loured spaces ; and therefore their proportional distances vary with the nature of the prism by which they are produced. Their number, however, their order, and their intensity, are absolutely invariable, provided light coming either directly or indirectly from the Sun be em- ployed. Similar bands are perceived in the light of the Moon andpktnets; and in the light of the fixed stars, of coloured flames , and of the electric spark, defective lines, or lines without light, have also been observed. The spectra from the light of Mars and from that of Venus contain the lines D, E, 6, and F very distinctly, and in the same positions as in Sun-light. In the spectrum from the light of Sirius, no fixed lines could be perceived in the orange and yellow spaces ; but in the green there was a very strong streak, and two other very strong ones in the blue. They had no resemblance, however, to any of the lines in planetary light. The star Castor gives a spectrum exactly like that of Sinus, the streak in the green being in the very same place. The streaks were also seen in the blue, but Fraunhofer could not ascertain their place. In the spectrum of Pollux there were many weak but fixed lines, which looked like those in Venus. It had the line D, for example, in the very same place as in the light of the planets. In the spectrum of Capetta the lines D and b are seen as in the Sun's light. The spectrum of Betalgeus contains numerous fixed lines sharply defined, and those at D and b are precisely in the same places as in im-light. It resembles the spectrum of Venus. In the spectrum of Procyon Fraunhofer thought he saw the line D in the orange; but though he observed other lines, yet he could not determine their place with any degree of ac- curacy. All the stars in whose light defective lines were discovered by Fraunhofer are colourless, that is, 94? A TREATISE ON OPTICS. PART II. the defective rays are equally numerous in the differ- ently coloured spaces of their spectra, or are so balanced that the abstraction of light at these places does not diminish the whiteness of their light. It occurred to me that in coloured stars the colour was owing to the defective rays being more numerous in one part of the spectrum than in another, and I had an opportunity many years ago of confirming this conjecture by ex- amining with a fine rocksalt prism the orange coloured star of the double star f Herculis when seen through Sir James South's large achromatic telescope. One defective band was observed in the red space, and two or more in the blue space, and therefore the orange colour of the star was owing to there being a greater defect of blue than of red rays. (70.) Having observed that the light which passed through nitrous acid gas gave a spectrum covered with dark lines and bands of the most remarkable kind, I was led to compare these lines with those in Fraunhofer's map of the solar spectrum. In this comparison I found that there existed between these two classes of pheno- mena a remarkable coincidence. In order to obtain an ocular proof of this, I formed the solar and the gaseous spectrum with light passing through the same aperture, so that the lines on the one stood opposite to those on the other, like the division lines on the vernier and limb of a divided instrument, and their coincidence or non -coincidence became a matter of simple observation. I then superimposed the two spectra when they were both formed by solar light, and thus exhibited at once the two series of lines, with all their coincidences and all their apparent deviations. The one set of lines indeed were seen through the other. In these obser- vations some of the larger lines in the gaseous spectrum coincided with some of the larger ones in the solar one, yet in many cases faint and narrow lines in the one coincided with strong and broad lines in the other, and there were some strong gaseous lines and even broad bands to which I could discover nothing corresponding CHAP. XI. ON LINES IN THE SPECTRUM. Q5 in the map of the solar spectrum by Fraunhofer. This discrepancy was very embarrassing, and therefore I was obliged to enter upon the Herculean task of making a new map of the solar spectrum. In this inquiry I used very fine rocksalt prisms, prisms of oil of cassia, and prisms of glass, the largest I believe in existence, executed for me by M. Merz at Munich. These prisms were applied to a telescope made on purpose by Dollond, in which, according to a formula of Sir John Herschel's, the spherical aberration was corrected while the aberration of colour remained. After a little practice in observing, I discovered most of the lines which I had in vain sought for in Fraunhofer's map, as the counterpart of those in the gaseous spectrum. I saw well-marked groups of which he had only given one of the lines, and shaded bands, and well-defined lines. The action of the gas upon invisible lines ren- dered them visible by slightly enlarging them, and this enlargement of a solar line indicated a corresponding line in the gaseous spectrum. In this way I have been able to execute three different maps of the spectrum; 1st, a map of the lines themselves ; 2nd, a map of the same spectrum, showing the lines and bands produced by the action of nitrous acid gas; and, 3rd, a map showing the action of the gas upon a continuous and uninterrupted spectrum of artificial white light The length of Fraunhofer's spectrum is 1 5^ inches : mine, upon the same scale, is 17 inches, from having traced the red space much farther than Fraunhofer did. The length of the general spectrum which I have delineated is about 5 feet 6 inches ; but in order to exhibit the numerous lines and bands in some parts of it, 1 have used a scale corresponding to a spectrum 1 7 feet long. In this spectrum I have inserted 2000 lines, the number in Fraunhofer's being only 354. I have constructed also what I call an atmospheric spectrum, exhibiting the lines and bands produced by the action of the atmosphere. The atmosphere acts very powerfully on the rays round the line D, and on the 96 A TREATISE ON OPTICS. PART II. space immediately on the least refrangible side of it. It developes a beautiful line in the middle of the double line D, and by enlarging a group of small lines on the red side of D., it creates a band almost as dark as the triple line D itself. It widens generally all the lines, but especially the darkest of them, which I call m, between C and D. It developes a band on the least refrangible side of m ; and it acts specially on several lines and developes several bands on the most refrangible side of C. The lines A, B, and C are greatly widened, and lines and bands are particularly developed between A and B, and generally throughout all the red space. The absorptive action of the atmosphere shows itself in a less precise manner in the production of dark bands whose limits are not distinctly defined. A very remark- able narrow one, corresponding to a gaseous line, is situated on the most refrangible side of C. Another very broad one lies on the most refrangible side of D, close to a sharp and broad band of yellow light. There is also an imperfectly defined atmospheric action corre- sponding to a group of lines where Dr. Wollaston placed his line C. I have observed and delineated with great difficulty a large space full of lines beyond A, the red extremity of the spectrum as observed by Fraunhofer.* (71.) One of the most important practical results of the discovery of these fixed lines in the solar spectrum is, that they enable us to take the most accurate measures of the refractive and dispersive powers of bodies, and by measuring the distances of the lines B, C, D, &c. Fraun- hofev computed the table of the indices of refraction of different substances, given in the Appendix, No. III. From the numbers in the table here referred to we may compute the ratios of the dispersive powers of any two of the substances, by the method already explained in a preceding chapter, and thus obtain the most accurate data for the construction of achromatic object glasses. * See Edinburgh Transactions, vol. vii. p, 12., Report of the British Association, 1842, p. 15., and 1847, p. 38., and Comptes Rendus, Sfc., 18SO, Urn. xxx. p. 378. CHAP. XI. ON LINES IN THE SPECTRUM. 97 This method, however, requires very nice observation, and the difficulty of obtaining and fixing the Sun when his light is wanted, and of procuring glass sufficiently pure to show very distinctly such narrow lines as E, or the two which constitute D, are great obstacles to the general adoption of so refined a method of measuring dispersive powers. The discovery of lines in the nitrous acid gas spectrum relieves us from these difficulties. Lines so broad of black are seen with prisms of or- dinary purity, and the artificial light of a lamp can be commanded at any time, and its rays absolutely fixed for the purposes of observation. In examining the solar spectrum several observers have noticed longitudinal lines perpendicular to the transverse lines we have been describing. These have been generally ascribed to minute irregularities, such as particles of dust on the edges of the slit or line of light, and it is only when thus produced that I have seen them. But it appears from the observations of Pro- fessor Zantedeschi, of Venice*, and of Professor Ragona- Scinat, that the lines are produced when a lens is used along with the prism. These longitudinal lines have different magnitudes, some being very broad and others very narrow like the transverse ones, depending of course on the focal length and nature of the lens. M. Zantedeschi has given beautiful drawings of them both as existing alone and as coexisting with the fixed transverse lines. M. Ragona-Scina and M. Babinet have come to the conclusion that they are lines of interference which must exist in light which has passed through a convex glass.J On the bright Lines in the Spectra of different Flames. (72.) In the spectrum of the light of a lamp, and generally of all white flames, none of the defective lines are found, and consequently all such flames contain Ricerche-FisicO'Chemico-Fisiolog'che svlla Luce. Cap. 3. Venezia, 1846. f Phil. Magazine, May, 1852, p. 347. j Comptes Bendus, #c., Sept. 27th, 1852, vol. xxxv. p. 413. H 98 A TREATISE ON OPTICS. PART II. rays which do not exist in the light of the Sun and stars. Fraunhofer, however, observed in the orange space of the spectrum from the light of a lamp a bright line more distinct than the rest of the spectrum. He found it to be double, each bright line corresponding with each of the two dark lines forming the line D of the solar spectrum, already described in the preceding section. If we throw any of the salts of soda into the flame, the bright orange line D becomes more brilliant, and I have discovered in the salted-wick flame a bright line placed nearly half way between the two that compose D. On the less refrangible side of D, I have found three equi- distant bright lines in the salted-wick spectrum, the least refrangible of the three, corresponding with a defective line in the solar spectrum lying between D and D 1 of Fraunhofer. I have discovere4 also a band in the solar spectrum corresponding with the space between the two of the most refrangible of these three bright lines. Designating the two lines of D by the letters a, 6, and the other three bright lines by c, rf, A, and the small line between a and b by e, we have a 6 = cd dh ; bc= Ifffft, and ae less than eb. When nitrate of strontian is thrown into an alcohol flame, a great number of brilliant red lines are exhibited on the most refrangible side of D 9? corresponding with defective lines in the pure light, and a few on the less refrangible side of D. In the spectrum produced by the combustion of nitre upon charcoal I have observed brilliant red lines corre spending with the double lines A and B, and with the group of eight lines between A and B in Fraunhofer's map.* In a series of experiments on the spectra produced in the combustion of various mineral and saline substances in oxygen and carburetted hydrogen gas, I observed many defective bands and lines which gave to the flames the colour of the predominating rays ; and also nume- * See Comptes Rendus, $c. t 1850, torn. xxx. p. 578. CHAP. XI. ILLUMINATING BAYS IN THE SPECTRUM. 99 rous bright lines analogous to those which have already been described.* On the Illuminating Power of the Spectrum. (73.) Before the time of M. Fraunhofer, the illumin- ating power of the different parts of the spectrum had been given only from a rude estimate. By means of a photometer he obtained the following results : The place of maximum illumination he found to be at M,fig. 57., so situated that D M was about one third or one fourth of DE ; and therefore this place is at the boundary of the orange and yellow. Calling the illu- minating power at M, where it is a maximum, 100, then the light of other points will be as follows : Light at the red extremity 0*0 B- - - 3-2 C - - -9-4 D - - - 64-0 Maximum light at M - 1000 Light at E - - 48'0 Light at F- - - 17'0 G- - - 3-1 the violet ex- , tremity o-oo Calling the intensity of the light in the brightest space DE 100, Fraunhofer found the light to have the follow- ing intensity in the other spaces : Intensity of light in BC - 2'1 CD 29-9 DE 100-0 Intensity of light in EF 32-5 FG 18-5 GH 3-8 From these results it follows that, in the spectrum examined by Fraunhofer, the most luminous ray is nearer the red than the violet extremity in the propor- tion of 1 to 3 '5, and that the mean ray is almost in the middle of the blue space. As a great part, however, of the violet extremity of the spectrum is not seen under ordinary circumstances, these results cannot be applied to spectra produced under such circumstances. Sir John Herschel has succeeded in rendering visible what were considered only as chemical fays beyond the * See a brief notice of these experiments in the Reports of the British Association for 184-i, p. 15., and the North British Review, vol. vi. p. 237. H 2 100 A, TREATISE ON OPTICS. PART II* visible violet rays of the spectrum. These rays are so faint that they can be seen only when concentrated by a lens ; and when thus rendered visible, their colour is that of lavender grey.* On the Heating Power of the Spectrum. (74.) It had always been supposed by philosophers that the heating power in the spectrum would be pro- portional to the quantity of light ; and Landriani, Kochon, and Sennebier found the yellow to be the warmest of the coloured spaces. Sir W. Herschel, however, proved by a series of experiments that the heating power gradually increased from the violet to the red extremity of the spectrum. He found also that the thermometer continued to rise when placed beyond the red end of the spectrum, where not a single ray of light could be perceived.f Hence he drew the important conclusion, that there were invisible rays in the light of the sun which had the power of producing heat, and which had a less degree of rpfrangibility than red light. Sir W. Herschel was desirous of ascertaining the refrangibility of the ex- treme invisible ray which possessed the power of heat- ing, but he found this to be impracticable; and he satisfied himself with determining that, at a point 1| inches distant from the extreme red ray, the invisible rays exerted a considerable heating power, even though the thermometer was placed at the distance of 52 inches from the prism. These results were confirmed by Sir Henry Englefield, who obtained the following measures : Temperature. Red - - - 72 Beyond Red- - 79 Temperatun Blue - - - 56 Green - - - 58 Yellow- - - 62 When the thermometer was returned from beyond the red into the red, it fell again to 72. * See Phil. Trans. 1840, pp. 1922. f- In the experiments on the spectrum described in (68. 1 ) I observed light at- the point where Sir W. Herschel found the maximum heating power. CHAP. XI. BEATING BAYS* 301 M. Berard obtained analogous measures ; but he found that the maximum of heat was at the very ex- tremity of the red rays when the bulb of the thermome- ter was completely covered by them, and that beyond the red space the heat was only one fifth above that of the ambient air. Sir Humphry Davy ascribed Berard's results to his using thermometers with circular bulbs, and of too large a size ; and he therefore repeated the experiments in Italy and at Geneva with very slender thermometers, not more than one twelfth of an inch in diameter, with very long bulbs filled with air confined by a coloured fluid. The result of these experiments was a confirma- tion of those of Sir W. HerscheL* M. Seebeck, who has more recently studied this sub- ject, has shown that the place of maximum heat in the spectrum varies with the substance of which the prism is made. The following are his results : Substance of the Prism. Coloured space in -which the heat is a maximum. "Water - Yellow- Alcohol - - ' Yellow. Oil of turpentine - - Yellow. Sulphuric acid concentrated - Orange. Solution of sal-ammoniac - Orange. Solution of corrosive sublimate Orange. Crown glass - Middle of the red. Plate glass - Middle of the red. Flint glass - Beyond the red. The observations on Alcohol and Oil of turpentine were made by M. Wunsch. The calorific or thermic spectrum has been recently examined by Sir John Herschel by means of a new and ingenious process, namely, by the drying power of the heat itself. A piece of thin paper, such as is used for foreign correspondence, is blackened on one side by Indian ink, or, what is better, by a smoky flame, and the other, or * See Edinburgh Encyclopaedia, vol. x. p. 69., where they were first pub* lished, as communicated to me by Sir Humphry. H 3 102 A TREATISE ON OPTICS. PART II. white side, is saturated with good rectified spirit of wine, which will make it uniformly black. The solar spectrum being thrown upon this wet side of the paper, its heating power will be displayed by the whiteness produced by the evaporation of the alcohol. By this process, and with an object glass of crown and flint glass and a prism of flint glass, he obtained the ' following results. The thermic spectrum is continuous throughout the length of the luminous spectrum, but at a point a, considerably beyond the extreme red, the heating power is a maximum, having gradually increased up to this point. It then diminishes slightly for a short space, and again reaches a second maximum at j3 : near this point it diminishes and ceases altogether. It then reappears, and reaches another maximum at y, diminishes again, ceases, and reaches a fourth maxi- mum at S. Traces of a fifth maximum were seen at e. Calling the length of the luminous spectrum 57 parts, viz. 43 on the violet side of the yellow line D, and 14* on the red side, the distances of the maxima will be as follows : c 18'2 parts from the line D. = 26-7 7 = S5'7 5 = 4.5-1 6 = 55 the thermic spectrum thus extending the whole length of the luminous spectrum beyond the line D. With a crown glass prism and lens, " the insulation of y," says Sir John Herschel, white 5 m 71 77 53\ 573 37, 49 The preceding colours are those which are seen when light is reflected and transmitted nearly perpendicularly ; but Sir Isaac Newton found that when the light was reflected and transmitted obliquely, the rings increased in size, the same colour requiring a greater thickness to produce it. The colour of any film, therefore, will de- scend to a colour lower in, or nearer the beginning of the scale, when it is seen obliquely. Such are the general phenomena of the coloured rings when seen by white light. When we place the lenses in homogeneous light, or make the different colours of the solar spectrum pass in succession over the lenses, the rings, which are always of the same colour as the light, will be found to be largest in red light, and to contract gradually as they are seen in all the succeeding colours, till they reach their smallest size in the violet rays. Upon measuring their diameters, Newton found them to have the following ratio in the different colours at their boundaries : Extreme Red. Orange. 1 0-924 Yellow. 0-885 Indieo. Violet. Extreme. ". 0-711 0-681 0-630 Since white light is composed of all the preceding co- ' lours, the rings seen by it will consist of all the seven differently coloured systems of rings superposed as it were, and forming, by their union, the different colours in the Table. In order to explain this we have con- structed the annexed diagram, fig. 62., on the sup- position that each ring or spectrum has the same breadth in homogeneous light which they actually have when they are formed between surfaces nearly flat, or when the thickness of the plate varies with the distance from CHAP. XIII. COLOURS OP THIN PLATES. 125 the point of contact.* Let us then suppose that we form such a system of rings with the seven colours of the spectrum, and that a sector is cut out of each system, and placed, as in the figure, round the same centre C. Let the angle of the red sector be 50, of the orange 30, the yellow 40, the green 60, the blue 60, the indigo 40, and the violet 80, being 360 in all, so as to complete the circle. From the centre C set off the first, second, and third rings in all the sectors, with radii corresponding to the values in the preceding small Table. Then, since the proportional diameters of the extreme red and the extreme orange are 1 and 0*924, the middle of the red will be in the middle between these numbers, or 0'962 ; and consequently the propor- tional diameter, or the radius of the first red ring for the middle of the red space R, will be 0*962. In like manner, the radius for the orange will be 0*904, for the yellow 0-855, for the green 0*794, for the blue 0'737, for the indigo 0*696, and for the violet 0*655. Let the red rings be coloured red as they appear in the experi- ment, the orange rings orange, and so on, each colour resembling that of the spectrum as nearly as possible. If we now suppose all these coloured sectors to revolve rapidly round C as a centre, the effect of them all thus * This supposition is made in order to simplify the diagram. 126 A TREATISE ON OPTICS. PART II. mixed should be the production of the coloured rings as seen by white light. As the diameter of each ring varies from the beginning of the red space to the end of it, and so on with all the colours, the portion of the ring in each sector should be part of a spiral, and all these separate parts should unite in forming a single spiral, the red forming the commencement, and the violet the termination of the spiral for each ring. This diagram enables us to ascertain the composition of any of the rings seen in white light. Let it be re- quired, for example, to determine the colour of the ring at the distance C m from the centre, m being in the middle of the second red ring. Round C as a centre, and with the radius C m, describe a circle, mnop, and it will be seen from the different colours through which it passes what is its composition. It passes nearly through the very brightest * part of the second red ring, at m, and through a pretty bright part of the orange. It passes nearly through the bright part of the yellow, at n; through the brightest part of the green ; through a less bright part of the blue ; through a dark part of the indigo, at p ; and through the darkest part of the third violet ring. If we knew the exact law according to which the brightness of any fringe varied from its darkest to its brightest point, it would thus be easy to ascertain with accuracy the number of rays of each colour which entered into the composition of any of the rings seen by white light. In order to determine the thickness of the plate of air by which each colour was produced, Newton found the square of the diameters of the brightest parts of each to be in the arithmetical progression of the odd numbers, 1, 3, 5, 7) 9> &c., and the squares of the diameters of the obscurest parts in the arithmetical progression of the even numbers, 2, 4, 6, 8, 10 ; and as one of the glasses was plane, and the other spherical, their inter- vals at these rings must be in the same progression. * In the figure, the brightest part is the most shaded. CHAP. XIII. COLOURS OF THIN PLATES. 127 He then measured the diameter of the first dark ring, and found that the thickness of the air at the darkest part of the FIRST dark ring, made by perpendicular rays, was the -g-g-Jo Q" part of an inch. He then multiplied this number by the progression 1, 3, 5, 7> 9* & c -> an d 2, 4, 6, 8, 10, and obtained the following results : Thickness of the air at the Thickness of the air at the FIRST Ring - TT J,oM - " n&mf or SECOND Ring - THIRD Ring - FOURTH Ring - - Newton found that the diameter of the rings in- creased with the obliquity of incidence, and he inferred that the thickness of the plate of air at which the same colour was produced was proportional to the sine of an angle, whose sine had to the sine of the angle of inci- f dence the constant ratio of - - -, m being the index of refraction. MM, Provostaye and Desains have, how- ever, found that the thickness is simply proportional to the secant of the angle of incidence, as indicated by the undulatory theory.* When Newton admitted water between the lenses, he found the colours to become fainter, and the rings smaller ; and upon measuring the thicknesses of water at which the same rings were produced, he found them to be nearly as the index of refraction for air is to the index of refraction for water, that is, nearly as I'OOO to 1*336. From these data he was enabled to compute the three last columns of the Table given in pages 123 and 124, which show the thicknesses in millionth parts of an inch at which the colours are produced in plates of air, water, and glass. These columns are of exten- sive use, and may be regarded as presenting us with a micrometer for measuring minute thicknesses of trans- parent bodies by their colours, when all other methods would be inapplicable. * Comptes Rendus, 1850, torn, xxx. p. 498. 128 A TREATISE OX OPTICS. PART II. We have already seen that when the thickness of the film of air is about TTil8o~odth of an inch, which corre- sponds to the seventh ring, the colours cease to become visible, owing to the union of all the separate colours forming white light ; but when the rings are seen in homogeneous light they appear in much greater numbers, a dark and a coloured ring succeeding each other to a considerable distance from the point of contact. In this case, however, when the rings are formed between ob- ject glasses, the thickness of the plate of air increases so rapidly that the outer rings crowd upon one another, and cease to become visible from this cause. This effect would obviously not be produced if they were formed by a solid film whose thickness varied by slow gradations. Upon this principle, Mr. Talbot has pointed out a very beautiful method of exhibiting these rings with plates of glass and other substances even of a tangible thick- ness. If we blow a glass ball so thin that it bursts *, and hold any of the fragments in the light of a spirit lamp with a salted wick, or in the light of any of the monochromatic lamps which I have elsewhere described, all of which discharge a pure homogeneous yellow light, the surface of these films will be seen covered with fringes alternately yellow and black, each fringe mark- ing out by its windings the lines of equal thickness in the glass film. Where the thickness varies slowly, the fringes will be broad and easily seen ; but where the va- riation takes place rapidly, the fringes are crowded toge- ther, so as to require a microscope to render them visible. If we suppose any of the films of glass to be only the thousandth part of an inch thick, the rings which it ex- hibits will belong to the 89th order ; and if a large rough plate of this glass could be got with its thickness descending to the millionth part of an inch by slow gradations, the whole of those 89 rings, and probably many more, would be distinctly visible to the eye. In order to produce such effects, the light would require to be perfectly homogeneous. * Films of mica answer the purpose still better. CHAP. XIV. COLOURS OF THICK PLATES. 129 The rings seen between the two lenses are equally visible whether air or any other gas is used, and even when there is no gas at all ; for the rings are visible in the exhausted receiver of an air pump. M. Jamin has very recently observed some interest- ing phenomena in the colours of thin plates when the reflected rings are formed between two prisms and illuminated with the light of the spectrum. When the angle of incidence increases, the rings enlarge, and un- dergo a singular change. Each dark ring has in con- tact with it externally if it is violet a very brilliant fringe, and internally if it is red. As the angle of incidence increases, there arises in the bright and very wide space which separates two dark rings, obscure lines which are all bordered with a brilliant fringe, and have the same appearance as the principal^ring. Comple- mentary phenomena are seen in the transmitted rings. These phenomena disappear only at the angle of total reflexion ; but when the angle of incidence is very near the angle of total reflexion, there is an instant when the reflected and transmitted rings are so enlarged that they go out of the field of vision, and there is now seen a considerable number of new bright and dark fringes produced at thicknesses of the thin plate of air, too small for producing the ordinary rings. M. Jamin remarks that the theory does not afford any certain explanation of these fringes.* CHAP. XIV. ON THE COLOURS OF THICK PLATES. (79.) THE colours of thick plates were first observed and described by Sir Isaac Newton, as produced by concave glass mirrors. Admitting a beam of solar light, R, into a dark room, through an aperture a quarter of an inch See Comptes Rendus, fyc., Juillet. 1852, torn. xxxv. p. 14. Jf ISO A TREATISE ON OPTICS. PART II. in diameter formed in the window shutter M N, he allowed it to fall upon a glass mirror, A B, a quarter of Fig. 63. ^ m ISSJ an inch thick, quicksilvered behind, having its axis in the direction R r, and the radius of the curvature of both its surfaces being equal to its distance behind the aperture. When a sheet of paper was placed on the window shutter M N, with a hole in it to allow the sun-beam to pass, he observed the hole to be surrounded with four or five coloured rings, with sometimes traces of a sixth and seventh. When the paper was held at a greater or a less distance than the centre of its concavity, the rings became more dilute, and gradually vanished. The colours of the rings succeeded one another like those in the transmitted system in thin plates, as given in column 3d of the Table in pages 123. and 124. When the light R was red the rings were red, and so on with the other colours, the rings being largest in red and smallest in violet light. Their diameters preserved the same proportion as those seen between the object glasses ; the squares of the diameters of the most lumi- nous parts (in homogeneous light) being as the numbers 0, 2, 4, 6, &c., and the squares of the diameters of the darkest parts as the intermediate numbers, 1, 3, 5, 7, &c. With mirrors of greater thickness the rings grew less, and their diameters varied inversely as the square roots of the thickness of the mirror. When the quick- silver was removed the rings became fainter ; and when the back surface of the mirror was covered with a mass of oil of turpentine, they disappeared altogether. These facts clearly prove that the posterior surface of the CHAP. XIV. COLOURS OF THICK PLATES. 131 mirror concurs with the anterior surface in the produc- tion of the rings. When the mirror A B is inclined to the incident beam R r, the rings grow larger and larger as the in- clination increases, and so also does the whife round spot ; and new rings of colour emerge successively out of their common centre, and the white spot becomes a white ring accompanying them, and the incident and reflected beams always fall upon the opposite parts of this white ring, illuminating its perimeter like two mock suns in the opposite parts of an iris. The colours of these new rings were in a contrary order to those of the former. The duke de Chaulnes observed similar rings upon the surface of the mirror when it was covered with gauze or muslin, or with a skin of dried skim milk; and Sir W. Herschel noticed analogous phenomena when he scattered hair powder in the air before a concave mirror on which a beam of light was incident, and received the reflected light on a screen. (80.) The method which I have found to be the most simple for exhibiting these colours, is to place the eye im- mediately behind a small flame from a minute wick fed with oil or wax, so that we can examine them even at a perpendicular incidence. The colours of thick plates may be seen even with a common candle held before the eye at the distance of 10 or 12 feet from a common pane of crown glass in a window that has accumulated a little fine dust upon its surface, or that has on its surface a fine deposition of moisture. Under these circumstances they are very bright, though they may be seen even when the pane of glass is clean. The colours of thick plates may, however, be best displayed, and their theory best studied, by using two plates of glass of equal thickness. The phenomena thus produced, and which presented themselves to me in 1817, are highly beautiful, and, as Sir John Herschel has shown, are admirably fitted for illustrating the law? of this class of phenomena. In order to obtain p^.tes 132 A TREATISE ON OPTICS. PART II. of exactly the same thickness, I formed out of the same piece of parallel glass two plates, A B, C D and having placed between them two pieces of soft wax, I pressed Fig. 64. them to the distance of about one tenth of an inch from each other ; and by pressing above one piece of wax more than another, I was able to give the two plates any small inclina- tion I chose. Let AB, CD then be a section of the two plates thus inclined at right angles to the common section of their surfaces, and let RS be a ray of light incident nearly in a vertical direction and proceeding from a candle, or, what is better, from a circular disc of condensed light subtending an angle of 2 or 3. If we place the eye behind the plates, when they are parallel we shall see only an image of the circular disc ; but when they are inclined, as in the figure, we shall observe in the di- rection VR several reflected images in a row besides the direct image. The first or the brightest of these will be seen crossed with fifteen or sixteen beautiful fringes or bands of colour. The three central ones consist of blackish or whitish stripes ; and the exterior ones of brilliant bands of red and green light. The direction of these bands is always parallel to the common section of the inclined plates. These coloured bands increase in breadth by diminishing the inclination of the plates, and diminish by increasing their inclination. When the light of the luminous circular object falls obliquely on the first plate, so that the plane of incidence is at right angles to the section of the plates, the fringes are not distinctly visible across any of the images ; but their distinctness is a maximum when the plane of in- cidence is parallel to that section. The reflected images of course become more bright, and the tints more vivid, as the angle of incidence becomes greater; when the CHAP. XIV. COLOURS OF THICK PLATES. 135 angle of incidence increases from to 90* the images that have suffered the greatest number of reflexions are crossed by other fringes inclined to them at a small angle. If we conceal the bright light of the first image so as to perceive the image formed by a second reflexion within the first plate, and if we view the image through a small aperture, we shall observe coloured bands across the first image far surpassing in precision of outline and richness of colouring any analogous phenomenon. When these fringes are again concealed, others are seen on the image immediately behind them, and formed by a third reflexion from the interior of the first plate. If we bring the plate C D a little farther to the right hand, and make the ray R S fall first upon the plate C D, and be afterwards reflected back upon the first plate AB, from both the surfaces of C D, the same coloured bands will be seen. The progress of the rays through the two plates is shown in the figure. When the two plates have the form of concave and convex lenses, and are combined, as in the double and triple achromatic object glass, a series of the most splendid systems of rings are developed ; and these are sometimes crossed by others of a different kind. I observed these rings in a double achromatic object glass made by Berge 2^- inches in diameter, and 30 inches in focal length. Between the two lenses there was a meniscus of air A 2 B 3 A, as shown in fig. 65. Fig. 65. In order to observe fringes at a perpendicular inci- dence, I placed a minute flame at S, about 4 or 5 inches from the object glass A D, and interposing a small K3 134 A TREATISE ON OPTICS. screen, G, between the flame and the eye at E, I held the eye as close to S as possible, and varied the distance of the object glass till the inverted greenish * coloured flame, reflected from the surface A 1 B, seemed to cover the whole area of the object glass. By a slight change in the position of the object glass, or by screen- Fig. 66. ing the image formed by one reflexion from A 1 B, the rings will now be seen dis- tinctly over the expanded but enfeebled image formed by a second reflexion from the same surface. At a per- pendicular incidence of the light the rings appear as in fig. 66. The rings mmmm, nnnn being distinguished from the rest by their blackness, and by the whiteness of the space between them. By inclining the object glass so that A is further from the eye than B, the rings will become smaller and closer on the side A, and broader and wider on the side B, till they assume the appearance in fig. 6?- Fig. 67. Fig. 68. * It is green from the light having passed twice through the thickness of the green crown glass lens A B. The similar letters \nfigs. 66, 67. show the change produced upon the rings by inclining the object glass. CHAP. XV. COLOURS OF FIBRES. 135 At greater incidences these four groups of rings assume the form shown in fig. 68., where they are so closely packed together that it is very difficult to see them. These phenomena undergo interesting modifications in object glasses, when the meniscus has a different form, when it is filled with fluids of different re- fractive powers, when it is widened at A or at B by separating the lenses, and when homogeneous light is used. In a triple object glass, the system of rings shown in fig. 68. was crossed by numbers of minute fringes parallel to xx. In viewing films of blown glass in homogeneous yel- low light, and even in common day-light, Mr. Talbot has observed that when two films are placed together, bright and obscure fringes, or coloured fringes of an ir- regular form, are produced between them, though ex- hibited by neither of them separately. CHAP. XV. JON THE COLOURS OF FIBRES AND GROOVED SURFACES. (81.) WHEN we look at a candle or any other lu- minous body through a plate of glass covered with vapour or with dust in a finely divided state, it is surrounded with a corona or ring of colours, like a halo .round the sun or moon. These rings increase as the size of the particles which produce them is diminished ; and their brilliancy and number depend on the uniform size of these particles. Minute fibres, such as those of silk and wool, produce the same series of rings, which increase as the diameter of the fibres diminishes ; and hence Dr. Young proposed an instrument called an erio- meter, for measuring the diameters of minute particles and fibres, by ascertaining the diameter of any one of K 4 136 A TREATISE ON OPTICS. the series of rings which they produce. For this pur- pose, he selected the limit of the first red and green ring as the one to be measured. The eriometer is formed of a piece of card or a plate of brass, having an aperture about the fiftieth of an inch in diameter in the centre of a circle about half an inch in diameter, and perforated with about eight small holes. The fibres or particles to be measured are fixed in a slider, and the eriometer being placed before a strong light, and the eye assisted by a lens applied behind the small hole, the rings of colours will be seen. The slider must then be drawn out or pushed in till the limit of the red and green ring coincides with the circle of perforations, and the index will then show on the scale the size of the particles or fibres. The seed of the lycoperdon bovista was found by Dr. Wollaston to be the 8500dth part of an inch in diameter ; and as this substance gave rings which indicated 3J on the scale, it follows that 1 on the same scale was the 29> 750th part of an inch, or the 30,000dth part. The following Table contains some of Dr. Young's measurements in thirty-thousandths of an inch : Milk diluted indistinct - 3 Dust of lycoperdon bovista 3^ Bullock's blood - - 4^ Smut of barley - - 6^ Blood of a mare '- - 6 Human blood diluted with water - - -6 Pus - - - - ?J Silk - 12 Beaver's wool - - 13 Mole's fur - - 16 Shawl wool - - - 19 Saxon wool - - -22 Lioneza wool - - - 25 Alpacca wool - - 26 Farina of laurustinus - 26 Ryeland Merino wool - 27 Merino South Down - 28 Seed of Jycopodium - - 32 South Down ewe - - 39 Coarse wool - - - 46 Ditto from some worsted - 60 (82.) By observing the colours produced by reflexion from the fibres which compose the crystalline lenses of the eyes of fishes and other animals, I have been able to trace these fibres to their origin, and to determine the number of poles or septa to which they are related. The same mode of observation, and the measurement of the dis- CHAP. XV. COLOURS O* 1 FIBRES. 13J tance of the first coloured image from the white image, has enabled me to determine the diameter of the fibres, and to prove that they all taper like needles, diminishing gradually from the equator to the poles of the lens, so as to allow them to pack into a spherical superficies as they converge to their poles or points of origin. These coloured images, produced by the fibres of the lens, lie in a line perpendicular to the direction of the fibres, and by taking an impression on wax from an indurated lens the colours are communicated to the wax. In several lenses I observed coloured images at a great dis- tance from the common image, but lying in a direction coincident with that of the fibres ; and from this I in- ferred, that the fibres were crossed by joints or lines, whose distance was so small as the ll,000dth part of an inch; and I have lately found, by the use of very power- ful microscopes, that each fibre has in this case teeth like those of a rack, of extreme minuteness, the colours being produced by the lines which form the sides of each tooth.* (83.) In the same class of phenomena we must rank the superficial colours of mother-of-pearl. This substance, obtained from the shell of the pearl oyster, has been long employed in the arts, and the fine play of its colours is therefore well known. In order to observe its colours, take a plate of regularly formed mother-of- pearl, with its surfaces nearly parallel, and grind these surfaces upon a hone or upon a plate of glass with the powder of schistus, till the image of a candle reflected from the surfaces is of a dull reddish- white colour. If we now place the eye near the plate, and look at this reflected image C, we shall see on one side of it a pris- matic image, A, glowing with all the colours of the rainbow, and forming indeed a spectrum of the candle as distinct as if it had been formed by an equilateral prism of flint glass. The blue side of this image is next the image C, and the distance of the red part of the image * Phil. Trans. 1833. p. 332. 138 A TREATISE ON OPTICS. PART II. is in one specimen 7 22' ; but this angle varies even in the same specimen. Upon first looking into the mother- Fig. 69. A V\ A of-pearl, the image A may he ahove or helow C, or on any side of it ; but, by turning the specimen round, it may be brought either to the right or left hand of C. The distance AC is smallest when the light of the candle falls nearly perpendicular on the surface, and in- creases as the inclination of the incident ray is increased. In one specimen it was 2 7' at nearly a perpendicular incidence, and 9 14' at a very great obliquity. On the outside of the image A there is invariably seen a mass, M, of coloured light, whose distance M C is nearly double AC. These three images are always nearly in a straight line, but the angular distance of M varies with the angle of incidence according to a law different from that of A. At great angles of incidence the nebulous mass is of a beautiful crimson colour ; at an angle of about 37 it becomes green ; and nearer the perpendicular it becomes yellowish-white, and very lu- minous. If we now polish the surface of the mother-of-pearl, the ordinary image C will become brighter and quite white, but a second prismatic image, B, will start up on the other side of C, and at the same distance from it. This second image has in all other respects the same properties as the first. Its brightness increases with the polish of the surface, till it is nearly equal to that of A, the lustre of which is slightly impaired by polishing. This second image is never accompanied, like the first, with a nebulous mass M. If we remove the polish, the image B vanishes, and A resumes its brilliancy. CHAP. XV. COLOURS OF FIBRES. 139 The lustre of the nebulous mass M is improved by polishing. If we repeat these experiments on the opposite side of the specimen, the very same phenomena will be ob- served, with this difference only, that the images A and M are on the opposite side of C. In looking through the mother-of-pearl, when ground extremely thin, nearly the same phenomena will be ob- served. The colours and the distances of the images are the same ; but the nebulous mass M is never seen by transmission. When the second image, B, is in- visible by reflexion it is exceedingly bright when seen by transmission, and vice versa. In making these experiments, I had occasion to fix the mother-of-pearl to a goniometer with a cement of resin and bees' wax ; and upon removing it, I was sur- prised to see the whole surface of the wax shining with the prismatic colours of the mother-of-pearl. I at first thought that a small film of the substance had been left upon the wax ; but this was soon found to be a mistake, and it became manifest that the mother-of-pearl really impressed upon the cement its own power of producing the coloured spectra. When the unpolished mother-of- pearl was impressed on the wax, the wax gave only one image, A ; and when the polished surface was used, it gave both A and B : but the nebulous image M was never exhibited by the wax. The images seen in the wax are always on the opposite side of C, from what they are in the surface that is impressed upon it. The colours of mother-of-pearl, as communicated to a soft surface, may be best seen by using black wax ; but I have transferred them also to balsam of Tolu, to real- gar, to the fusible metal made of bismuth, mercury, and tin, and to clean surfaces of lead and tin by hard pres- sure, or the blow of a hammer. A solution of gum arabic or of isinglass, -when allowed to indurate upon a surface of mother-of-pearl, takes a most perfect im- pression from it, and exhibits all the communicable colours, in the finest manner, when seen either by re- 140 A TREATISE ON OPTICS. PART II. flexion or transmission. By placing the isinglass be- tween two finely polished surfaces of good specimens of mother-of-pearl, we shall obtain a film of artificial mo- ther-of-pearl, which when seen by single lights, such as that of a candle, or by an aperture in the window, will Shine with the brightest hues. If, in this experiment, we could make the grooves of the one surface of mother-of-pearl exactly parallel to the grooves in the other, as in the shell itself, the images, A and B, formed by each surface would coincide, and only two would be observed by transmission and re- flexion : but as this cannot be done, four images are seen through the isinglass film, and also four by re- flexion ; the two new ones being formed by reflexion from the second surface of the film. From these experiments it is obvious that the colours under our consideration are produced by a particular configuration of surface, which, like a seal, can convey a reverse impression of itself to any substance capable of receiving it. By examining this surface with micro- scopes, I discovered in almost every specimen a grooved structure, like the delicate texture of the skin at the top of an infant's finger, or like the section of the annual growths of wood, as seen upon a dressed plank of fir. These may sometimes be seen by the naked eye,* but they are often so minute that 3000 of them are con- tained in an inch. The direction of the grooves is always at right angles to the line MACB, fig. 69. and hence in irregularly formed mother-of-pearl, where the grooves are often circular, and having every possible direction, the coloured images AB are irregularly scat- tered round the common image C. If the grooves were, accordingly, circular, the series of prismatic images, A B, would form a prismatic ring round C, pro- vided the grooves retained the same distance. The general distance of the grooves is from the 200th to the 5000th of an inch, and the distance of the prismatic images from C increases as the grooves become closer. In a specimen with 2500 in an inch, the distance AC CHAP. XV. COLOURS OF MOTHER OF PEARL. 141 was 3 41'; and in a specimen of about 5000 it was about 7 22'. These grooves are obviously the sections of all the concentric strata of the shell. When we use the actual surface of any stratum, none of the colours AB are seen, and we observe only the mass of nebulous light, M, occupying the place of the principal image, C. Hence we see the reason why the pearl gives none of the images, AB, why it communicates none of its colours to wax, and why it shines with that delicate white light which gives it all its value. The pearl is formed of concentric spherical strata, round a central nucleus, which Sir Everard Home conceives to be one of the ova of the fish. None of the edges of its strata are visible, and as the strata have parallel surfaces, the mass of light M is reflected exactly like the image C, and occupies its place ; whereas in the mother-of-pearl it is reflected from surfaces of the strata, inclined to the general surface of the specimen which reflects the image C. The mixture of these diffuse masses of nebulous light, of a pink and green hue, constitutes the beautiful white of the pearls. In bad pearls, where the colours are too blue or too pink, one or other of these colours has predominated. If we make an oblique section of a pearl, so as to exhibit a sufficient number of concentric strata, with their edges tolerably close, we should ob- serve all the communicable colours of mother-of-pearl.* These phenomena may be observed in many other shells besides that of the pearl-oyster; and in every case we may distinguish communicable from incom- municable colours, by placing a film of fluid or cement between the surface and a plate of glass. The commu- nicable colours will all disappear from the filling up of the grooves and the incommunicable colours will be rendered more brilliant. A species of artificial mother- of-pearl was some years ago discovered by Mr. Hornerf, encrusting the dash * See Edinburgh Journal of Science, No. XII., p. 277. f Philosophical Transactions, 1836, p. 49. 142 A TREATISE ON OPTICS. PART !! wheel at the cotton works of Messrs. J. Finlay & Co., at Catrine, in Ayrshire. It resembles in its struc- ture and pearly lustre some species of shells, such as the Meleagrina, Malleus, &c. Mr. Homer found it to consist of carbonate of lime and gelatine, the lime being obtained from the bleaching powder, and the gelatine from the glue used in dressing the cotton cloths. The specific gravity of this substance, which I have called Hornerite, is 2*44, that of mother-of-pearl being 2*19. It has negative double refraction, like calcareous spar, one of the images being nebulous, the consequence of which is that the image of a candle is surrounded with the other image in the form of a halo. Between each daily layer of the Hornerite deposited on the wheel, there is a delicate film derived from the atmosphere when the wheel is at rest. This film, ac- cording to its thickness, gives the most brilliant colours of thin plates, and enables us to explain the cause of the incommunicable colours of mother-of-pearl, which arise from similar films deposited during the rest or sleep of the oyster.* (84.) Sir John Herschel has discovered in very thin plates of mother-of-pearl another pair of nebulous prismatic images, more distant from C than A and B, and also a pair of fainter nebulous images, the line join- ing which is always at right angles to the line joining the first pair.t These images are seen by looking through a thin piece of mother-of-pearl, cut parallel to the natural surface of the shell, and between the 70th and the 300dth of an inch thick. They are much larger than A and B ; and Sir John Herschel found that the line joining them was always perpendicular to a veined structure which goes through its substance. The distance of the red part of the image from C was found to be 16 29', and the veins which produced these colours were so small that 3700 of them were contained in an inch. We have represented them in^. 70. as crossing the ordinary grooves which give the communicable colours. Sir John * Philosophical Transactions, 1836, p. 5257. t In a specimen nowbeforeme, the line joining the two faintest nebulous images is at right angles to the line joining A and B. CHAP. XV. COLOURS OP MOTHER-OF-PfcARL. 1 43 Herschel describes them as crossing these grooves at all angles, " giving the whole surface much the appearance of a piece of twilled silk, or the larger waves of the sea Fig. 70. intersected with minute ripplirigs." The second pair of nebulous images seen by transmission must arise from a veined structure exactly perpendicular to the first, though the structure has not yet been recognised by the microscope. The structure which produces the lightest pair Sir John found to be in all cases coincident with the plane passing through the centres of the two systems of polarised rings. The principle of the production of colour by grooved surfaces, and of the communicability of these colours by pressure to various substances, has been happily applied to the arts by the late Sir John Barton. By means of a delicate engine, operating by a screw of the most accurate workmanship, he has succeeded in cutting grooves upon steel at the distance of from the 2000th to the 10,000th of an inch. These lines are cut with the point of a diamond ; and such is their perfect parallelism and the uniformity of their distance, that while in mother- of-pearl we see only one prismatic image, A, on each side of the common image C, of the candle, in the grooved steel surfaces 6, 7 3 or 8 prismatic images are 144 A TREATISE ON OPTICS. PART II. seen, consisting of spectra, as perfect as those produced by the finest prisms. Nothing in nature or in art can surpass this brilliant display of colours ; and Sir John Barton conceived the idea of forming buttons for gentlemen's dress, and articles of female ornament covered with grooves, beautifully arranged in patterns, and shining in the light of candles or lamps with all the hues of the spectrum. To these he gave the appropriate name of Iris ornaments. In forming the buttons, the patterns were drawn on steel dies, and these, when duly hardened, were used to stamp their impressions upon polished buttons of brass. In day-light the colours on these buttons are not easily distinguished, unless when the surface reflects the margin of a dark object seen against a light one ; but in the light of the sun, and in that of gas or candles, these colours are scarcely if at all surpassed by the brilliant flashes of the diamond. The grooves thus made upon steel are, of course, all transferable to wax, isinglass, tin, lead, and other sub- stances ; and by indurating thin transparent films of isinglass between two of these grooved surfaces, covered with lines lying in all directions, we obtain a plate which produces by transmission the most extraordinary display of prismatic spectra that has ever been exhibited. (85.) In examining the phenomena produced by some of the finest specimens of Sir John Barton's skill, which he had the kindness to execute for me for this purpose, I have been led to the observation of several curious properties of light. In mother-of-pearl well polished the central image, C, of the candle or luminous object is always white, as we should expect it to be, in con- sequence of being reflected from the flat and polished surfaces between the grooves. In like manner, in most specimens of grooved steel, the image C is also perfectly white, and the spectra on each side of it, to the amount of six or eight, are perfect prismatic images of the candle ; the image A, which is nearest C, being the least dispersed, and all the rest in succession more and more dispersed, as if they were formed by prisms of CHAP. XV. COLOURS OF GROOVED SURFACES. 145 greater and greater dispersive power, or greater and greater refracting angles. These spectra contain the fixed lines and all the prismatic colours ; but the red or least refrangible spaces are greatly expanded, and the violet or most refrangible spaces greatly contracted, even more than in the spectra produced by sulphuric acid. In examining some of these prismatic images which seemed to be defective in particular rays, I was surprised to find that, in the specimens which produced them, the image C reflected from the polished original surface of the steel was itself slightly coloured ; that its tint varied with the angle of incidence, and had some relation to the defalcation of colour in the prismatic images. In order to observe these phenomena through a great range of incidence, I substituted for the candle a long narrow rectangular aperture, formed by nearly closing the win- L 146 A TREATISE ON OPTICS. dow shutters, and I then saw at one view the state of the ordinary image and all the prismatic images. In order to understand this, let A B, fig. 71 ., he the ordinary image of the aperture reflected from the flat surface of the steel which lies between the grooves, and a 6, a' b', a!' b", &c., the prismatic images on each side of it, every one of these images forming a complete spectrum with all its different colours. The image A B was crossed in a direction perpendicular to its length with broad coloured fringes, varying in their tints from to 90 of incidence. In a specimen with 1000 grooves in an inch, the following were the colours dis- tinctly seen at different angles of incidence. Angle of incidence. Angle of incidence. White - - 90 0' Blue - 56 0' Yellow - - 80 30 Bluish green - - 54 30 Reddish orange - 77 30 Yellowish green - 53 15 Pink - 76 20 Whitish green - 51 Junction of pink and 1 ,_ - 4Q Whitish yellow - 49 blue - J Yellow -47 15 Brilliant blue - 74 30 Pinkish yellow - 41 Whitish - - 71 Pink red - 36 Yellow . - 64 45 Whitish pink - 31 O Pink - - 59 45 Green - 24 Junction of pink and l-^o j Q Yellow - 10 blue - \ Reddish - These colours are those of the reflected rings in thin plates. If we turn the steel plate round in azimuth, the very same colours appear at the same angle of incidence, and they suffer no change either by varying the distance of the steel plate from the luminous aperture, or the distance of the eye of the observer from the grooves. In the preceding Table there are four orders of colours ; but in some specimens there are only three, in others two, in others one, and in some only one or two tints of the first order are developed. A specimen of 500 grooves in an inch gave only the yellow of the first order through the whole quadrant of incidence. A spe- cimen of 1000 grooves gave only one complete order, with a portion of the next. A specimen of 3333 grooves CHAP. XV. COLOURS OF GROOVED SURFACES. 147 gave only the yellow of the first order. A specimen of 5000 gave a little more than one order ; and a specimen of 10,000 grooves in an inch gave also a little more than one order. In fig. 71. we have represented the portion of the quadrant of incidence from about 22 to 76. In the first spectrum, a b a b, vv is the violet side of it, and r r the red side of it, and between these are arranged all the other colours. At m, at an incidence of 74, the violet light is obliterated from the spectrum a b; and at n } an incidence of 66, the red rays are obliterated ; the intermediate colours, blue, green, &c. being obli- terated at intermediate points between m and n. In the second spectrum, a f b f a' b f , the violet rays are obliterated at m f at an incidence of 66 20', and the red at n' at an incidence of 56. In the third spectrum, a" b 11 a" b", the violet rays are obliterated at m 11 at 57^ and the red at n" at 41 35' ; and in the fourth spectrum, the violet rays are obliterated at m /// at401, and the red at n'" at 23 30". A similar succession of obliterated tints takes place on all the prismatic images at a lesser incidence, as shown at JJL v, p,' v' ; the violet being obliterated at p. and p.', and the red at v and v' } and the intermediate colours at intermediate points. In this second succession the line p. v begins and ends at the same angle of inci- dence as the line m" n" in the third prismatic image a" b", and the line p.' v' in the second prismatic image corresponds with m'" n'" on the fourth prismatic image. In all these cases the tints obliterated in the direction mn jj,Vy &c., would, if restored, form a complete pris- matic spectrum whose length is m n p. v, &c. Considering the ordinary image as white, a similar obliteration of tints takes place upon it. The violet is obliterated at o about 76, leaving pink, or what the violet wants of white light ; and the red is obliterated at p at 74, leaving a bright blue. The violet is obli- terated at q and s, and the red at r and t, as may be inferred from the preceding Table of colours. The analysis of these curious and apparently compli- Fig. 72. 148 A TREATISE ON OPTICS. PART II. cated phenomena becomes very simple when they are examined by homogeneous light. The effect produced on red light is represented in fig. 72., where A B is the image of the narrow aperture re- flected from the original surface of the steel, and the four images on each side of it correspond with the pris- matic images. All these nine images, however, consist of homogeneous red light, which is obliterated, or nearly so, at the fifteen shaded rec- tangles, which are the minima of the new series of periodical colours which cross both the ordinary and the lateral images. The centres p> r, t, n, v, &c., of these rectangles correspond with the points marked with the same letters in fig. 11.; and if we had drawn the same figure for violet light, the centres of the rectangles would have been all higher up in .the figure, and would | have corresponded with o, where SAB is a pencil of light falling upon the diffracting body A B, whose interior fringes are formed at D E, C being the middle one, and therefore white. If we now apply a thin piece of glass or mica G A close to A, the ray A C will be retarded, and therefore will not be in * Ann. de Chim. &c., vol. i. p. 199. Fev. 1816. CHAP. XVIII. DIRECT INTERFERENCE OF LIGHT. 1&9 Fig. 77. accordance with the ray B C, but it will be in accord- ance with B E, and therefore the fringe of E will be white. This displacement of the interior fringes takes place in the experiments on mixed plates already described,, where the opaque edge of the plate acts as the diffract- ing body A B ; and also in an experiment of Mr. Tal- bot's, in which he covered half of his pupil with an extremely thin film of glass, and looked " at a per- fect spectrum formed by a prism of moderate dispersive power." He then saw the spectrum " covered through- out its length with parallel obscure bands," and he men- tions as the cause of this the retardation of the pencil passing through the film. In fact, this is just M. Arago's experiment, with the exception that the light of the spectrum is used in place of common light, the edge of Mr. Talbot's plate being the diffracting body in contact with a transparent screen. In Mr. Talbot's experiment, the eye placed close to the diffracting edge sees the ne- gative fringes of diffraction, already described, which were then not known. In repeating this interesting experiment I discovered the curious fact that the fringes were produced only when the piece of glass was on the blue side of the spectrum, and that no fringes were seen when it was placed on the red side. This fact appeared to me so extraordinary, that I ascribed it to an apparent polarity of light, one side of the rays of the spectrum seeming to have a prbperty not possessed by the other side. Philo- 170 A TREATISE ON OPTICS. PART II. sophers well acquainted with the undulatory theory did not try to give an explanation of it till many years after the fact was announced. Mr. Airy published an elaborate paper on the subject *, in which he gave an explanation of the fact on the supposition that the spec- trum was seen out of focus. This explanation he com- municated to the British Association in 1840, when I assured him that the fringes were best seen when the spectrum was pure and distinct and gave Fraunhofer's minutest lines. He then published a second paper t, accommodating his explanation to this new condition ; but he made the breadth of the fringes dependent on the aperture of the pupil, or of the telescope if it was used, which is not the case. Having devoted much time to the examination of these fringes, I have been led to the conclusion that they do not indicate any polarity in the rays of the spectrum, but that they are the interior diffraction fringes produced by the edge of the thin plate, displaced by the retarding action of the plate, and rendered visible by the action of the prism, when under ordinary cir- cumstances they would not otherwise be seen. There are positions in which the fringes are seen when the plate is on the red side of the spectrum, and I have observed many interesting variations of the phenomena by placing the plate in front of the prism, or in va- rious positions before the object-glass of the telescope, or between the object-glass and the eye-glass, -or be- tween the eye-glass and the eye. Curious phenomena are produced when plates are used in different positions, and with their retarding edges in different directions. The black fringes have sometimes an appearance re- sembling fine screws, or like lines with ragged edges, arising it may be from the same cause as that which produces the appearance which is described in p. 113., the edges of the retarding plates not being lines per- fectly equable and parallel. J * Phil. Trans. 1840, p. 225. + Phil. Trans. 1841, p. 1. t See Reports of the British Association, 1834, 1840, and 1845. CHAP. XIX. ABSORPTION OF C03IMON LIGHT. 1?1 CHAP. XIX. ON THE ABSORPTION OF COMMON LIGHT. (91.) ONE of the most curious properties of bodies, and one which we are persuaded will yet perform a most important part in the explanation of optical pheno- mena, and become a ready instrument in optical re- searches, is their power of absorbing common and polar- ised light.* Even the most transparent bodies in nature, air and water, when in sufficient thickness, are capable of absorbing a great quantity of light. On the summit of the highest mountains, where the light has to pass through a less extent of air, the sky is black and a much greater number of stars is visible to the eye than in the plains below ; and through great depths of water objects become almost invisible. The absorptive power of air is finely displayed in the blue colour of the sky, in the colour of the morning and even- ing clouds, and that of water, in the blue light which it reflects, and in the red colour of the meridian sun, when seen from a diving bell at a great depth in the sea. In both these cases, one class of rays is absorbed more readily than another in passing through the ab- sorbing medium, while the rest make their way in the one case to the clouds, and in the other to the eye. Nature presents us with bodies of all degrees of ab- sorptive power, as shown in the following brief enu- meration : Charcoal. Coal of all kinds. Nitrous acid gas at a high temperature. Metals in general. Silver. Gold. Elack hornblende. Black pleonaste. Obsidian. Rock crystal. Selenite. Glass. Mica. Water and transparent fluids. Air and gases. * The absorption of polarised light will be treated of in a subsequent Chapter. 172 A TREATISE ON OPTICS. PART II Although charcoal is the most absorptive of all bodies yet, when it exists in a minutely divided state, as iu some of the gases and flames, or in a particular state of aggregation, as in the diamond, it is highly transparent. In like manner, all metals are transparent in a state of solution ; and even silver and gold, when beaten into thin films, are translucent, the former transmitting a beautiful blue, and the latter a beautiful green light. Philosophers have not yet ascertained the nature of the power by which bodies absorb light. Some have thought that the particles of light are reflected in all directions by the particles of the absorbing body, or turned aside by the forces resident in the particles ; while others are of opinion that they are detained by the body, and assimilated to its substance. If the particles of light were reflected or merely turned out of their direc- tion by the action of the particles, it seems to be quite demonstrable that a portion of the most opaque matter, such as charcoal, would, when exposed to a strong beam of light, become actually phosphorescent during its illu- mination, or would at least appear white ; but as all the light which enters it is never again visible, we must believe, till we have evidence of the contrary, that the light is actually stopped by the particles of the body, and remains within it in the form of imponderable matter. Some idea may be formed of the law according to which a body absorbs light, by supposing it to consist of a given number of equally thin plates, at the refracting surfaces of which there is no light lost by reflexion. If the first plate has the power of absorbing T \^th of the light which enters it, or 1 00 rays out of a 1 000 ; then ^ths of the original light, or 900 rays, will fall upon the second plate ; and -/^th of these, or 90, being absorbed, 810 will fall upon the third plate, and so on. Hence it is obvious that the quantity of light transmitted by any number of films is equal to the light transmitted through one film multiplied as often into itself as there are films. Thus, since 900 out of 1000 rays are transmitted by one CHAP. XIX. ABSORPTION OF COMMON LIGHT. 173 film, -J^XT^X-^. equal to Jffc, or 729 rays, will be the quantity transmitted by three films ; and therefore the quantity absorbed will be 271 rays. Of the various bodies which absorb light copiously, there are few that absorb all the coloured rays of the spectrum in equal proportions. While certain clouds absorb the blue rays and transmit the red, there are others that absorb all the rays in equal proportions, and exhibit the sun and the moon when seen through them perfectly white. Ink diluted is a fine example of a fluid which absorbs all the coloured rays in equal proportions ; and it has on this account been applied by Sir William Herschel as a darkening substance for obtaining a white image of the sun. A dark glass has been lately made which has nearly the same property, though the transmitted light has a "slight tinge of blue. Black pleonaste and obsidian afford examples of solid substances which absorb all the colours of the spectrum proportionally. (92.) All coloured transparent bodies, however, whether solid or fluid, necessarily do not absorb the colours proportionally , for it is only in consequence of an unequal absorption that they could appear coloured by transmitted light. In order to exhibit this absorp- tive power, take a thick piece of the blue glass that is used for finger glasses, and which is sometimes met with in cylindrical rods of about -f^ths of an inch in diameter, and shape it into the form of a wedge. Form a prismatic image of the candle, or, what is better, of a narrow rectangular aperture in the window' by a prism, and examine this prismatic image through the wedge of coloured glass. Through the thinnest edge the spectrum will be seen nearly as complete as before the interposi- tion of the wedge ; but as we look at it through greater and greater thicknesses, we shall see particular parts or colours of the spectrum become fainter and fainter, and gradually disappear, while others suffer but a slight diminution of their brightness. When the thickness is about the twentieth part of an inch, the spectrum will have the appearance shown in fig. 78., where the 174? A TREATISE ON OPTICS. PART II middle R of the red space is entirely absorbed, the inner red that is left is weakened in intensity ; the orange is entirely absorbed ; the yellow Y is left almost insulated ; Fig. 78. the green G on the side of the Till [yellow is very much absorbed; III and a slight absorption takes V place along the green and blue space. At a greater thickness still, the inner red di- minishes rapidly, and also the yellow, green, and blue ; till, at a certain thickness, all the middle colours of the spectrum are absorbed, and nothing left but the two extreme colours, the red R and the violet V, as shown in fig. 79' As the red light R has much greater in ten - Fig. 79. s ity tnan tne violet, the glass "" has at this thickness the ap- pearance of being a red glass ; whereas at small thicknesses it had the appearance of being a blue glass. Other coloured media, instead of absorbing the spec- trum in the middle, attack it, some at one extremity, some at another, and others at both. Red glasses, for example, absorb the blue and violet with great force. A thin plate of native yellow orpiment absorbs the violet and refrangible blue rays very powerfully, and leaves the red, yellow, and green but little affected. Sulphate of copper attacks both ends of the spectrum at once, ab- sorbing the red and violet rays with great avidity. In consequence of these different powers of absorption, a very remarkable phenomenon may be exhibited. If we look through the blue glass so as to see the spectrum in fig. 79>> and then look at this spectrum again with a thin plate of sulphate of copper, which absorbs the extreme rays at R and V, the two substances thus combined will be absolutely opaque, and not a ray of light will reach the eye. The effect is perhaps more striking if we look at a bright white object through the two media together. (93.) In attempting to ascertain the influence of heat on the absorbing power of coloured media, I was surprised CHAP. XIX. ABSORPTION OP COMMON LIGHT. 175 to observe that it produced opposite effects upon differ- ent glasses, diminishing the absorbing power in some, and increasing it in others. Having brought to a red heat a piece of purple glass, that absorbed the greater part of the green, the yellow, and the interior or most refrangible red, I held it before a strong light ; and when its red heat had disappeared, I observed that the transparency of the glass was increased, and that it transmitted freely the green, the yellow, and the interior red, all of which it had formerly, in a great measure, absorbed. This effect, however, gradually disappeared, and it recovered its former absorbent power when com- pletely cold. When yellowish-green glass was heated in a similar manner, it lost its transparency almost entirely. In re- covering its green colour, it passed through various shades of olive green ; but its tint, when cold, con- tinued less green than it was before the experiment. A part of the glass had received in cooling a polarising structure, and this part could be easily distinguished from the other part by a difference of tint. A plate of deep red glass, which gave a homogeneous red image of the candle, became very opaque when heated, and scarcely transmitted the light of the candle after its red heat had subsided. It recovered, however, its transparency to a certain degree ; but when cold, it was more opaque than the piece from which it was broken. I have observed analogous phenomena in mi- neral bodies. Certain specimens of topaz have their absorbing power permanently changed by heat. In subjecting the Balas Ruby to high degrees of heat, I observed that its red colour changed into green, which gradually faded into brown as the cooling advanced, and resumed by degrees its original red colour. In like manner, M. Berzelius observed the Spinette to become brown by heat, then to grow opaque as the heat in- creased, and to pass through a fine olive green before it recovered its red colour. A remarkable change of absorbent power is exhibited by heating very consider- A TREATISE ON OPTICS. PART II. ably, but so as not to inflame it, a plate of yellow native orpiment, which absorbs the violet and blue rays. The heat renders it almost blood red, in consequence of its now absorbing the greater part of the green and yellow rays. It resumes its former colour, however, by cool- ing. A still more striking effect may be produced with pure phosphorus, which is of a slightly yellow colour, transmitting freely almost all the coloured rays. When melted, and suddenly cooled, it acquired the power of absorbing all the colours of the spectrum at thicknesses at which it formerly transmitted them all. The black- ness produced upon pure phosphorus was first observed by Thenard. Mr. Faraday observed, that glass tinged purple with manganese had its absorptive power altered by the mere transmission through it of the solar rays. By the method above described of absorbing parti- cular colours in the spectrum, I was led to propose a new method of analysing white light. The experiments with the blue glass incontestably prove that the orange and green colours in solar light are compound colours, which, though they cannot be decomposed by the prism, may be decomposed by absorption, by which we may exhibit alone the red part of the orange and the blue part of the green, or the yellow part of the orange and the yellow part of the green ; and, by submitting the other colours of the spectrum to the scrutiny of absorbent media, I was led to the conclusions respecting the spec- trum which are explained in Chapter VIII. We have already seen that in the solar spectrum, as described by Fraunhofer, there are dark lines, as if rays of particular refrangibilities had been absorbed in their course from the sun to the earth. The absorption is not likely to have taken place in our atmosphere, other- wise the same lines would have been wanting in the spectra from the fixed stars, and the rays of solar light reflected from the moon and planets would probably have been modified by their atmospheres. But as this is not the case, it is probable that the rays which are want- ing in the spectrum have been absorbed by the sun's CHAP. XIX. ABSORPTION OF COMMON LIGHT. 177 atmosphere. In a future Chapter on the Colours of Natural Bodies, the reader will find Sir Isaac New- ton's theory of Absorption stated and controverted. The true theory of absorption has not been satisfac- torily established. Sir, John Herschel conceives, that light may be lost within bodies by the interference of different parts of a ray, which after taking two routes of different lengths meet again in a condition to interfere, Dr. Whewell conceives a medium to consist of certam particles regularly distributed, and that each vibration propagated through it proceeds in part straight forward, and in part round the particles, and then rejoining the direct course in a condition to interfere and suffer extinction. As this is not the place to give the nu- merous details which the discussion of such a subject requires, we must refer the reader to the Philosophical Transactions* and to the Encyclopedia Britannica^ for some new views which I have given on the cause of absorption. (94.) Connected with the preceding phenomena is the subject of coloured flames, which, when examined by a prism, exhibit spectra deficient in particular rays, and resembling the solar spectrum seen through coloured glasses. Pure hydrogen gas burns with a blue flame, in which many of the rays of light are wanting. The flame of an oil lamp contains most of the rays which are wanting in sunlight, Alcohol mixed with water, when heated and burned, affords a flame with no other rays but yellow. Almost all salts communicate to flames a peculiar coloiir, as may be seen by introducing the pow- der of these salts into the exterior flame of a candle, or into the wick of a spirit lamp. The following results have been obtained by different authors : ^ Colours produced. Bodies which give them, JlED - Intense crimson - Strontium. Reddish purple ... Lithia. Brick red - - - - Lime. * 1837, p. 245. t Art. OPTICS, p. 475* 178 A TREATISE ON OPTICS. PART II. Colours produced. Bodies which give them. ORANGE - Orange, with a tinge of green - Iodide of mercury. Copious orange - loduret of iron. YELLOW Intense homogeneous yellow - Soda. Feeble brownish yellow - Water. GREEN - Full green - Copper. Full green - Tellurium. Intense emerald green - - Iodide of copper. Ditto, mixed with blue - - Bromide of copper. Very dark green, feeble - - Ammonia. Dark green - Boracic acid. Dark green ... - Iron wire. Pale green .... Phosphoric acid. Pale apple green - Barytes. Intense whitish green - - Zinc. BLUE - Fine intense blue - Chloride of copper Blue ..... Selenium. Light blue - - - Arsenic. Pale clear blue ... Lead. Greenish blue - - - Antimony. Blue mixed with green - - Bromide of copper. VIOLET - Pale violet .... Potash. In a series of experiments which I made upon 184 substances which were exposed in a platinum cup to the flame of oxygen and carburetted hydrogen gas, I observed and noted a great variety of colours and tints of the same colour during the combustion of these bodies, though my main object was to discover fixed lines in their spectra. In addition to the two which I have placed in the preceding table under the head Orange, I shall give a few of the results I obtained. Nitrate of mercury ... Pink. ammonia - Brownish yellow. magnesia ... Fine and copious yellow. Chloride of iridium ... Pink. Chromate of ammonia - - Beautiful green. .it.. lead ... Lilac. Peroxide of lead ... Blue and purple. Indigo - Pink. Litharge ..... Pink yellow. Bisulphate of mercury - - Reddish. Prussian blue - Yellow. Chromate of mercury - Pale lilac. OHAP. XX. INTERNAL DISPERSION OF LIGHT. 1?9 Borax native ... Acetate of nickel - - - Chlorate of potash Chloride of tin Tartrate of potash and antimony Oxalate of chromium and potash Sulphite of soda - Selenium - Metallic antimony Orange. Red. Blue. Violet pink. Blue. Splendid blue. Purple. Beautiful blue. Splendid blue. Blue and purple. CHAP. XX. ON THE INTERNAL DISPERSION OF LIGHT WITHIN SOLID AND FLUID BODIES. (95.) THE internal dispersion of light within fluor spar was first pointed out in a paper which I communicated to the British Association at Newcastle in 1838.* The light thus dispersed had been noticed by others, and was ascribed by Sir John Herschel to a structure of " the surface of the spar whether natural or artificial which could not be removed by any polishing." f In examining various specimens of fluor spar from different localities, I had no difficulty in proving that the fine blue light emitted by the spar was not super- ficial but internal) and by throwing a conical beam of the sun's light, A CB, upon a fine green crystal from Alston Moor, as shown in fig. 80., I found that different veins of the spar dispersed light of different colours blue light from some veins, pink light from others, white light from others ; and no light at all from some inter- mediate veins. In the figure the veins with points are the blue veins, the veins marked with short lines are the pink ones, the white veins the white ones, and the shaded veins those that dispersed no light at all. The same property of dispersing coloured light I have found in various coloured glasses, especially in yellow Bohemian glass, now called Canary ylass, and also in colourless plate and colourless flint glass. * Reports, $c. t 1838, p. 10. f Treatise on Light, 1076. K 2 180 A TREATISE ON OPTICS. . Fig. 80. PART II. Chemists had long ago observed the blue colour in a weak solution of sulphate of quinine, but Sir John Her- schel was the first person who studied this interesting phenomenon, which is precisely similar to that observed influor spar, and he has given the results of his expe- riments in two papers in the Philosophical Transac- tions.* As the views which these papers contained were incompatible with those which I had previously published, I resumed the investigation of the subject, and discovered the property of internal coloured dis- persion in a great variety of solid and fluid bodies. I had long ago found this property beautifully displayed In the dispersion of a blood-red light from the interior of an alcoholic solution of the green leaves of plants, in an alcoholic solution of the seeds of the colchicum autumnale, in guaiacum, sulphate of strychnine, and in almost all the oils, in some of which it is exceedingly beautiful, varying from a pale green to a blue. The mode of exhibiting it which I adopted is shown in fig. SI., where MNOP is the glass vessel containing t\\e fluid, and LL a lens from which a condensed beam * " On a case of superficial colour presented by a homogeneous liquid internally colourless, Phil. Trans. 184p. ii. 143., and " On the Epipolic ('vtvoXv, a surface) dispersion of light," Id. p. 147. CHAP. XX. INTERNAL DISPERSION OP LIGHT. 181 of the sun's light is conveyed into the fluid, and ex- hibits within the cone ACB the blue light which it disperses. In this way I have placed it beyond a doubt that in all fluids and solids hitherto examined the light is dispersed from every part of the fluid, as in fluor spar, from every part of the dispersing vein. In sulphate of quinine and esculine the rays are dispersed to the greatest degree when they enter the fluid either through the sides of the glass vessel, or downwards through its surfaces, as infy. 81* Fig. 81. In examining the blue light with a prism Sir John Herschel found that it consisted of a Jan. 1853, p. 16., where the original paper is illustrated by thirty -three figures. * These figures are figs. 19. and 20. in the original memoir. CHAP. XXII. DOUBLE REFRACTION OP LIGHT. 189 CHAR XXII. ON THE DOUBLE REFRACTION OF LIGHT. (97.) In the preceding chapters of this work it has always "been supposed, when treating of the refraction of light, either through surfaces, lenses, or prisms, that the transparent or refracting body had the same structure, the same temperature, and the same density in every part of it, and in every direction in which the ray could enter it. Transparent bodies of this kind are gases, fluids, solid bodies, such as different kinds of glass, formed by fusion, and slowly and equally cooled, and a numerous class of crystallised bodies, the form of whose primitive crystal is the cube, the regular octahe- dron, and the rhomboidal dodecahedron. When any of these bodies have the same temperature and density, and are not subject to any pressure, a single pencil of light incident upon any single surface of them, perfectly plane, will be refracted into a single pencil according to the law of the sines explained in Chapter III. In almost all other bodies, including salts and crys- tallised minerals not having the primitive forms above mentioned; animal bodies, such as hair, horn, shells, bones, crystalline lenses of animals and elastic integu- ments ; vegetable bodies, such as certain leaves, stalks, and seeds ; and artificial bodies, such as resins, gums, jellies, glasses quickly and unequally cooled, and solid bodies having unequal density either from unequal tem- perature or unequal pressure; in all such bodies a single pencil of light incident upon their surfaces will be refracted into two different pencils, more or less in- clined to one another, according to the nature and state of the body, and according to the direction in which the pencil is incident. The separation of the two pencils is sometimes very great, and in most cases easily observed and measured ; but in other cases it is not visible, and its existence is inferred only from certain effects which 190 A TREATISE ON OPTICS. PART II. could not arise except from two refracted pencils. The refraction of the two pencils is called double refraction, and the bodies which produce it are called doubly re- fracting bodies or crystals. As the phenomena of double refraction were first discovered in a transparent mineral substance called Iceland spar, calcareous spar, or carbonate of lime, and as this substance is admirably fitted for exhibiting them, we shall begin by explaining the law of double refrac- tion as it exists in this mineral. Iceland spar is com- posed of 56 parts of lime, and 44 of carbonic acid. It is found in almost all countries, in crystals of various shapes, and often in huge masses ; but, whether found in crystals or in masses, we can always cleave it or split it into shapes like that represented in fig. 88., which is called Fig. $8. a rhomb of Iceland spar, a solid bounded by six equal and similar rhom- boidal surfaces, whose sides are parallel, and whose angles BAG, A C D are 101 55' and 78 5'. The inclination of any face A B C D to any of the adjacent faces that meet at A is 105 5', and to any of the adjacent faces that meet at X 74 55'. The line A X, called the axis of the rhomb or of the crystal, is equally inclined to each of the six faces at an angle of 45 23'. The angle between any of the three edges B A, C A, E A that meet at A, or of the three that meet at X, and the axis A X is 66 44' 46", and the angle between any of the six edges and the faces is 1 1 3 1 5' 14" and 66 44' 46". (98.) Iceland spar is very transparent, and gene- rally colourless. Its natural faces, when it is split, are commonly even and perfectly polished ; but when they are not so, we may, by a new cleavage, replace the im- perfect face by a better one, or we may grind and polish any imperfect face. Having procured a rhomb of Iceland spar like that in the figure, with smooth and well-polished faces, and so large that one of the edges A B is at least an inch CHAP. XXII. DOUBLE REFRACTION OF LIGHT. IQl long, place one of its faces upon a sheet of paper, having a black line M N drawn upon it, as shown in fig. 89- If we then look through the upper surface of the rhomb with the eye about R, we shall probably see the line M N double ; but if it is not, it will become double by turning the crystal a little round, Two lines, MN, mn, will then be distinctly visible ; and upon turning the crystal round, preserving the same side always upon the paper, the two lines will coincide with one another, and appear to form one at two opposite points during a whole revolution of the crystal ; and at two other opposite points, nearly at right angles to the former, the lines will be at their greatest distance. If we place a black spot at O, or a luminous aperture, such as a pin-hole in a wafer, with light passing through the hole, the spot or aperture will appear double, as at O and E ; and by turning the crystal round as before, the two images will be seen separate in all positions ; the one, E, revolving, as it were, round the other, O. Let a ray or pencil of light, R r, fall upon the surface of the rhomb at r, it will be refracted by the action of the surface into two pencils, r O, r E, each of which, being again refracted at the second surface at the points O, E, will move in the directions O o, E e, parallel to one another and to the incident ray R r. The ray R r has therefore been doubly refracted by the rhomb. 1 92 A TREATISE ON OPTICS. PART II. If we now examine and measure the angle of re- fraction of the ray r O corresponding to different angles of incidence, we shall find that, at of incidence, or a perpendicular incidence, it suffers no refraction, but moves straight through the crystal in one unbroken line ; that at all other angles of incidence the sine of the angle of refraction is to that of incidence as 1 to 1 *654 ; and that the refracted ray is always in the same plane as that of the incident ray. Hence it is obvious that the ray r O is refracted according to the ordinary law of re- fraction, which we have already explained. If we now examine in the same way the ray r E, we shall find that, at a perpendicular incidence, or one of 0, the angle of refraction, in place of being 0, is actually 6 12'; that at other incidences the angle of refraction is not such as to follow the constant ratio of the sines ; and, what is still more extraordinary, that the refracted ray r E is bent to one side, and lies entirely out of the plane of incidence. Hence it follows that the pencil r E is refracted according to some new and extraordi- nary law of refraction. The ray r O is therefore called the ordinary ray, and r E the extraordinary ray. If we cause the ray R r to be incident in various dif- ferent directions, either on the natural faces of the rhomb or on faces cut and polished artificially, we shall find that in Iceland spar there is one direction, namely, A X, along which if the refracted pencil passes, it is not re- fracted into two pencils, or does not suffer double refrac- tion. In other crystals there are two such directions, forming an angle with each other. In the former case the crystal is said to have ONE AXIS of double refrac- tion, and in the latter case TWO AXES of double refrac- tion. These lines are called axes of double refraction, because the phenomena are related to these lines. In some bodies there are certain planes, along which if the refracted ray passes, it experiences no double re- fraction. An axis of double refraction, however, is not, like the axis of the earth, a fixed line within the rhomb or crys. CHAP. XXII. DOUBLE REFRACTION OF LIGHT. 1.Q3 tal. It is only a fixed direction : for if we divide,, as we can do, the rhomb A B C,fig- 88., into two or more rhombs, each of these separate rhombs will have their axis of double refraction ; but when these rhombs are again put together, their axes will be all parallel to A X. Every line, therefore, within the rhomb parallel to A X, is an axis of double refraction ; but as these lines have all one and the same direction in space, the crystal is still said to have only one axis of double refraction. In making experiments with different crystals, it is found that in some the extraordinary ray is refracted towards the axis A X, while in others it is refracted from the axis A X. In the first case the axis is called a positive axis of double refraction, and in the second case a negative axis of double refraction. On Crystals with one Axis of Double Refraction, (99-) In examining the phenomena of double refrac- tion in a great number of crystallised bodies, I found that all those crystals whose primitive or simplest form had only ONE AXIS of figure, or one pre-eminent line round which the figure was symmetrical, had also ONE AXIS of double refraction ; and that their axis of figure was also the axis of double refraction. The primitive forms which possess this property are as follows : The rhomb with an obtuse summit. The rhomb with an acute summit. The regular hexaedral prism. The octohedron with a square base. The right prism with a square base. (100.) The following Table con tains the crystalswhich have one axis of double refraction, arranged under their respective primitive form, the sign -f- being prefixed to those that have positive double refraction, and to those that have negative double refraction. o 194 A TREATISE ON OPTICS, Fig. 90. Fig. 91. A PAKT II. Fig. 92. 1 . Rhomb with obtuse summit, fig. 90. Carbonate of lime (Iceland spar). Carbonate of lime and iron. Carbonate of lime and mag- nesia, Phosphato-arseniate of lead. Carbonate of zinc. Nitrate of soda. Phosphate of lead. Ruby silver. Levyne. Tourmaline. - Rubellite. Alum stone. Gmelinite. Chlorate of soda. + Dioptase. + Quartz. 2. Rhomb with acute summit, fig. 91. Corundum. Sapphire. -Ruby. Cinnabar. Arseniate of copper. 3. Regular Hexaedral Prism, fig. 92. Emerald. -Beryl. Phosphate of lime (apatite). Fig. 93. Nepheline. Arseniate of lead. f Hydrate of magnesia. Fig. 94. CHAP. XXII. DOUBLE REFRACTION OF LIGHT. 4. Octahedron with a square base, fig. 93. + Zircon. + Oxide of tin. + Tungstate of lime. Mellite. 5. Right Prism with Idocrase. Wernerite. Paranthine or Scapolite. Meionite. Somervillite. Edingtonite. Arseniate of potash. Sub-phosphate of potash. Phosphate of ammonia and magnesia. Molybdate of lead. Octohedrite. Prussiate of potash. Cyanide of mercury. a square base^fig t 94 Sulphate of nickel and cop- per. Hydrate of strontites. -f Apophyllite of Uton. + Oxahverite. + Superacetate of copper am* lime. + Titanite. + Ice (certain crystals). Murio-carbonate of lead. In all the preceding crystals, and in the primitive forms to which they belong, the line AX is the axis of figure and of double refraction, or the only direction along which there is no double refraction. The follow- ing bodies have one axis of double refraction, but their primitive form has not been determined. Muriate of lime - Muriate of strontium Hy posulphate of lime * - Mica from kariat - Mica with amianthus Hornerite or Nacritef - + Boracite - ... -f Apophyllite (sur composee of Haiiy) - + Sulphate of potash and iron - Tortoise shell.* Position of the Axis." Axis of hexagonal prism. Axis of hexagonal prism. Axis of hexagonal tables. Perpendicular to lamina?. Perpendicular to lamina?. Perpendicular to laminae. Axis of rhomb of 90. Perpendicular to laminae. Axis of hexagonal prism. On the Law of Double Refraction in Crystals with one Negative Axis. (101.) In order to give a familiar explanation of the * Sir J. Herschel, See Phil Trans., 1836, p,49. A TREATISE ON OPTICS. PART II. Fig. 95. law of double refraction, let us suppose that a rhomb of Iceland spar is turned in a lathe to the form of a sphere, as shown in fig. $5., A X being the axis of both the rhomb and the sphere. If we now make a ray pass along the axis A X, after grinding or polishing a small flat surface at A and X, perpendicular to A X, we shall find that there is no double refraction ; the ordinary and extraordinary ray forming a single ray. Hence, The index of refraction along \ 1 -654 for ordinary ray. the axis A X will be - j 1 -654 for extraordinary ray. 0-000 difference. If we do the same at any point, a, about 45 from the axis, we shall have The index of refraction along the line"| 1 -654 for ordinary ray. Ra&O, which is nearly perpen- 1 1 -572 for extraordinary dicular to the face of the rhomb - J ray. 0-082 difference. If we do the same at any point of the equator C D, inclined 90 to the axis, we shall have The index of refraction per- \ 1 '654 for ordinary ray. pendicular to the axis - J 1-483 for extraordinary ray. 0-171 difference. Hence it follows that the index of extraordinary re- fraction decreases from the axis A X to the equator C D, or to a line perpendicular to the axis, where it is the greatest. The index of extraordinary refraction is the same at all equal angles with the axis A X ; and "hence, in every part of a circle described on the surface of the sphere round the pole A or X, the index of ex- traordinary refraction has the same value, and conse- quently the double refraction or separation of the rays will be the same. In crystals, therefore, with one axis CHAP. XXII. DOUBLE REFRACTION OP LlGHT. 197 of double refraction, the lines of equal double refraction are circles parallel to the equator or circle of greatest double refraction. The celebrated Huygens, to whom we owe the dis- covery of the law of double refraction in crystals with one axis, has given the following method of determining the index of extraordinary refraction at any point of the sphere, when the ray of light is incident in a plane passing through the axis of the crystal AX: Let it be required, for example, to determine the index of refraction for the extraordinary ray Rab,fig.95., A X, being the axis, and C D the equator of the crystal ; the ordinary index of refraction being known, and also the least extraordinary index of refraction, or that which takes places in the equator. In calcareous spar these numbers are 1*654 and 1*483. From O set off in the lines O C, O D continued, O c, O d, so that O C or O D is to O c or O d as y.-g-^ is to y.^^ 1 or as '604? is to '674 ; and through the points A, c, X, d, draw an ellipse, whose greater axis is c d, and whose lesser axis is A X. The radius O a of the ellipse will be what is called the reciprocal of the index of refraction at a; and as we can find O 0, either by projecting the ellipse on a large scale, or by calculation, we have only to divide 1 by O a to have that index. In the present case O a is *6S6, and .-g-^-g- is equal to 1*572, the index required. As the index of extraordinary refraction thus found always diminishes from the pole A to the equator C D, and is always equal to the index of ordinary refraction minus another quantity depending on the difference between the radii of the circle and those of the ellipse, the crystals in which this takes place may be properly said to have negative double refraction. In order to determine the direction of the extraordi- nary refracted ray, when the plane of incidence is obliqut to a plane passing through the axis, the process, either by projection or calculation, is too troublesome to be given in an elementary work. In every case the force which produces the double o S 198 A TREATISE ON OPTICS. PART II. refraction exerts itself as if it proceeded from the axis, and the doubly refracted ray is as it were repelled from the axis. Every plane passing through the axis is called a prin- cipal section of the crystal. On the Law of Double Refraction in Crystals with one Positive Axis. (102.) Among the crystals best fitted for exhibiting the phenomena of positive double refraction is rock crystal or quartz, a mineral which is generally found in 'Fig. 96. six-sided prisms, like fig. 96., terminated with six-sided pyramids, E, F. If we now grind down the summits A and X, and replace them by faces well polished, and D perpendicular to the axis A X; and if we trans- mit a ray through these faces, so that it may pass along the axis AX, we shall find that there is no double refraction, and that the index of refraction is as follows : Index of refraction along"! 1 '5484 for ordinary ray. the axis AX - - J 1-5484 for extraordinary ray. 0-0000 difference. IF we now transmit the ray perpendicularly through the parallel faces E F, which are inclined 38 20' to the axis A X, the plane of its incidence passing through A X, we shall obtain the following results : Index of refraction perpen-") , r ,,/ j- c 1*5484 for ordinary ray. dicular to the faces of >,--.. ^^ j- the pyramid - - J 1<5 * 44 for ext r 3 G 56 5 20 6 7 24 10 35 10 30 11 28 13 18 14 18 18 19 30 19 34 25 27 51 28 42 28 7 300,310,320,340,37 35 8 37 24 37 42 J37 40 ,38 48 {40 41 42 42 4 42 20 45 43 24 44 41 43 48 45 45 45 8 44 28 46 49 48 Carbonate of lead - Sulphato-carbonate of lead- Mother-of-pearl - . Hydrate of barytes - Mica, certain specimens, about Arragonite - Prussiate of potash, certain specimens Mica, certain specimens - Cymophane- ----- Positive Negative Positive Ditto - Ditto - Negative Ditto - Positive Ditto - Negative Positive Ditto - Negative Negative Anhydrite ------ Mica(Biot) Apophyllite, biaxal - Sulphate of magnesia - - - - Sulphate of barytes - Spermaceti, about - - - - Tincal, or native borax - Nitrate of zinc, estimated at about - Sulphate of nick el - Tartrate of ammonia (Miller) - Tartrate of ammonia (Herschel) Carbonate of ammonia - Anhydrite (Herschel) - Negative Ditto - Positive Negative Positive Negative Lepidolite - - - - .- Benzoate of ammonia - - Sulphate of zinc . - - - - Sulphate of magnesia and soda - opei e CHAP. XXII. DOUBLE REFRACTION OF LIGHT. 201 Names of Minerals. Brazilian topaz - - ... Positive Sulphate of ammonia - - Ditto - Sugar ------- Negative Sulphate of strontites - - Positive Murio-sulphate of magnesia and iron Negative Sulphate of ammonia and magnesia - Positive Heulandite (Herschel) - - - - Phosphate of soda - Negative Comptonite- ----- Positive Felspar --_..- Negative Sulphate of lime- - ... Positive Oxynitrate of silver ... - Ditto - Dichroite or lolite - Negative Topaz (Aberdeenshire) - Positive Sulphate of potash - ... Ditto - Carbonate of soda ... - Negative Acetate of lead ----- Ditto - Citric acid --*-.- Positive Tartrate of potash - Negative Benzoic acid (Miller) - Ditto - Tartaricacid Ditto - Sulphate of oxide of iron and am- 7 monia (Miller) J Tartrate of potash and soda - - Positive Carbonate of potash - Kyanite ------ Positive Chlorate of potash ... Hydrochlorate of copper - Epidote, about - - - - Peridot Crystallized Cheltenham salts - Hyposulphate of soda (Marx) - Succinic acid, estimated at about Sulphate of iron, about Character of Prim-i- pal 4xis. Inclination of Resultant Axes. 49 50 49 or 42 50 50 51 51 22 54 17 65 20 56 6 58 30 60 62 16 60 50 65 67 70 1 70 25 ' 70 29 71 20 [75 79 79 80 80 30 81 48 82 84 30 84 19 87 56 88 14 89 20 90 90 Many of the measures in the preceding table were taken with much care ; but some of them were only estimated, and others will admit of correction by the use of better specimens than I was able to procure. In crystals with one axis of double refraction, the axis has the same position whatever be the colour of the pencil of light which is used ; but in crystals with two axes, the axes change their position according to the colour of the light employed, so that the inclination of the two axes varies with differently coloured rays. This discovery we owe to Sir John Herschel, who found that in. tartrate of potash and soda (Rochelle salts) the inclination of the axis for violet light was about 56, while in red light it was about 76. In other crystals, such as nitre, 202 A TREATISE ON OPTICS. PART II. the inclination of the axes for the violet rays is greater than for the red rays ; but in every case the line joining the extremity of the axes for all the different rays is a straight line. In examining the properties of Glauberite, I found that it had two axes for red light inclined about 5, and only one axis for violet light. It was at first supposed that in crystals with two axes, one of the rays was refracted according to the ordi- nary law of the sines, and the other by an extraordinary law ; but M. Fresnel demonstrated experimentally what he had previously deduced from theory, that, excepting in two sections, the two pencils did not follow either of the general laws of refraction. In a section perpendicular to the line bisecting the two resultant axes, one of the two pencils conforms to the general laws of extraordi- nary refraction ; and in the section perpendicular to the line bisecting the angle supplementary to that be- tween the axes, the other pencil conforms to the general law of ordinary refraction. The general law of extraor- dinary refraction which regulates the pencil in the first of these planes was first given by me in the Philosophical Transactions for 1818, before M. Fresnel had discovered the simple law which applies to every section of the crystal. It will be explained in the next Chapter. On Crystals with three Axes of Double Refraction. (104.) I have already stated that crystals whose primi- tive form is the cube, the octohedron t and the rhomboidal dodecahedron, have no double refraction ; but having found in many of these bodies, such as diamond, alum, garnet, and others, indications of a doubly refracting structure, I was led to suppose that all crystals what- ever have three rectangular axes of double refraction. The ONE axis of uniaxal crystals is the resultant of two axes of an opposite name lying in a plane perpen- dicular to it, and the strength of that axis is increased or diminished by the original axis there, according as it . is of the same or jof an opposite name. CHAP. XXII. DOUBLE REFRACTION OF LIGHT. 203 The TWO axes of biaxal crystals are the resultant of three axes, two or all of which are unequal. In crystals with three equal axes of double refraction, of the same name, two of them form an equal axis of the opposite name at right angles to each other, and this is counteracted by the original axis there of an opposite name, that is, if -f A, +1$ and -f C be three equal axes of the same name, -f- A and -f- B form an axis C coin- cident with -f C, and C and -f C destroy one another; so that crystals having the above-mentioned forms, which are called tessular, and which actually have three equal crystallographic axes, have no double refraction. On Double Refraction, in which one of the Pencils is nebulous. (105.) In examining the double refraction of agate*, chalcedony, and certain specimens of carbonate of ba- rytes"\, and carbonate of potash, and nitre f , and the sub^ stance called Hornerite or Nacrite, and mother of pearl, I found that one of the pencils was completely nebulous, the light of the nebulous image covering sometimes an irregularly circular space, and sometimes having a linear form. The same property is possessed by various sub- stances of animal and vegetable origin, such as oil of mace and certain fatty substances, which exhibit the curious phenomena of circular crystals.]: The nebulosity exhibited by one of the pencils in these doubly-refracting bodies may be produced arti- ficially in all doubly refracting crystals, by merely roughening their surfaces, and cementing upon these sur- faces a plate of glass by means of a balsam or oil of the same refractive power nearly as one of the pencils. This pencil will be seen with great distinctness, while the other* will be nebulous. If we do the same with another balsam or oil of the same refractive power as the other pencil, it will now be seen distinctly, while the one that was first distinct will now be nebulous. * Phil. Trans., 1813, p. 101.; 1814, pp. 189. 212. t Eddn. Trans., 1814, vol. vii. pp. 289. 302. I Phil. Trans., 1815, p. 49. 204 A TREATISE ON OPTICS. PART II. When the refractive power of the fluid is intermediate between that of the two pencils, they will be equally indistinct. These experiments I have repeatedly made with calcareous spar t arragonite, nitrate of potash, and other crystals.* On Crystals with innumerable Axes of Double Refraction. (1 06.) In the various doubly refracting bodies hitherto mentioned, the double refraction is related to one or more axes ; but I have found that in Analcime there are several planes, along which if the refracted ray passes, it will not suffer double refraction, however various be the directions in which it is incident. Hence we may consider each of these planes as containing an infinite number of axes of double refraction, or rather lines in which there is no double refraction. When the ray is incident in any other direction, so that the refracted ray is not in one of these planes, it is divided into two rays by double refraction. No other substance has yet been found possessing the same property. On Bodies to which Double Refraction may be com- municated by Heat, rapid Cooling, Pressure, and In- duration. (107.) If we take a cylinder of glass, C D, fig. 98., Fig. 98. an d having brought it to a red heat, roll it along a plate of metal upon its cylindrical sur- face till it is cold, it will acquire a permanent doubly refracting structure, and it will become a cylinder with one positive axis of double re- fraction, A X, coinciding with the axis of the cylinder, and along which there is to double refraction. This axis differs from that in quartz, as it is a fixed line in the cylinder, while it is only a fixed direction in the quartz ; that is, any other line parallel to A X, fig. 98., is not an axis of double * Phil Trans., 1819, p. 146. CHAP. XXII. DOUBLE REFRACTION OV LIGHT. 205 refraction, but the double refraction along that line in- creases as it approaches the circumference of the cylin- der. The double refraction is a maximum in the direction C D, being equal in every line perpendicular to the axis, and passing through it. If, in place of heating the glass cylinder, we had placed it in a vessel and surrounded! it with boiling oil or boiling water, it would have acquired the very same doubly refracting structure when the heat had reached the axis A X ; but this structure is only transient, as it disappears when the cylinder is uniformly heated. * If we had heated the cylinder uniformly in boiling oil, or at a fire, so as not to soften the glass, and had placed it in a cold fluid, it would have acquired a tran- sient doubly refracting structure as before, when the cooling had reached the axis AX; but its axis of double refraction A X will now be a negative one, like that of calcareous spar. Analogous structures may be produced by pressure and by the induration of soft solids, such as animal jellies, isinglass, &c. If the cylinder in the preceding explanation is not a circular one, but has its section perpendicular to the axis every where an ellipse in place of a circle, it will have two axes of double refraction. In like manner, if we use rectangular plates of glass instead of cylinders in the preceding experiment, we shall have plates with two planes of double refraction ; a positive structure being on one side of each plane, and a negative one on the other. If we use perfect spheres, there will be axes of double refraction along every diameter, and consequently an infinite number of them. The crystalline lenses of almost all animals, whether they are lenses, spheres, or spheroids, have one or more axes of double refraction. All these phenomena will be more fully explained when we treat of the colours produced by double re- fraction. 206 A TREATISE ON OPTICS. On Substances with Circular or Rotatory Double Refraction. (1 08.) When we transmit a pencil of light along the axis A X, fig. 96., of a crystal of quartz, it suffers no double refraction ; but certain phenomena, which will be afterwards described, are seen along this axis, which induced M. Fresnel to examine the light which passed along the axis. He found that it possessed a new kind of double refraction, and he distinctly observed the refraction of the two pencils. This kind of double refraction has, from its properties, been called circular; and it is divided into two kinds, positive or right- handed, and negative or left-handed. The following substances possess this remarkable property : Positive Substances. Right to Left. Rock crystal, certain speci- mens. Dextrine.* Camphor. Oil of turpentine. Solution of camphor in al- cohol. Essential oil of laurel. Vapour of turpentine. Oil of anise seeds. Oil of mint. Oil of rhue. Naphtha. Gum from Senegal. Paratartrates, certain speci- mens. Negative Substances. Left to Right. Rock crystal, certain speci- mens. Concentrated syrup of sugar. Essential oil of lemon. Oil of fennel seeds. Oil of caraway seeds. Oil of marjoram. Oil of bitter oranges. Oil of lemons. Oil of bergamot. Neroli. Tartaric acid. Tartrates. Paratartrates, certain speci- mens. In examining this class of phenomena, I found that the Amethyst possessed in the same crystal both the positive and the negative circular double refraction. This subject will be more fully treated of when we come to that of circular polarisation. * An uncrystallisable syrup found in the farina of rice and wheat CHAP. XXIII. POLARISATION OF LIGHT. 207 CHAP. XXIII. ON THE POLARISATION OP LIGHT. (109.) IF we transmit a beam of the sun's light through a circular aperture into a dark room, and if we reflect it from any crystallised or un crystallised body, or transmit it through a thin plate of either of them, it will be reflected and transmitted in the very same manner and with the same intensity, whether the surface of the body is held above or below the beam, or on the right side or left, or on any other side of it, provided that in all these cases it falls upon the surface in the same manner; or, what amounts to the same thing, the beam of solar light has the same properties on all its sides; and this is true, whether it is white light as directly emitted from the sun, or whether it is red light, or light of any other colour. The same property belongs to light emitted from a candle, or any burning or self-luminous body, and all such light is called common light. A section of such a beam of light will be a circle, like AC BD,/^, 99., and Fig. 99. we shall distinguish the section of a beam of common light by a circle with two diameters, AB, CD, at right angles to each other. If we now allow the same beam of light to fall upon a rhomb of Iceland spar, as in fig. 89.* and examine the two circular beams, O 0, E e, formed by double refrac- tion, we shall find, 208 A TREATISE ON OPTICS. FART II. 1. That the beams O o, E e, have different properties on different sides ; so that each of them differs, in this Jrespect, from the beam of common light. 2. That the beam O o differs from E e in nothing, excepting that the former has the same properties at the sides A' and B' that the latter has at the sides C f and D ; , as shown in fig. 9^. ; or, in general, that the diameters of the beam, at the extremities of which the beam has similar properties, are at right angles to each other, as A' B' and C' D', for example. These two beams, O o, E e, fig. 99., are therefore said to be polarised, or to be beams of polarised light, because they have sides or poles of different properties; and planes passing through the lines A B, C D, orA'B', C'D', are said to be the planes of polarisation of each beam, because they have the same property, and one which no other plane passing through the beam possesses. Now, it is a curious fact, that if we cause the two polarised beams O o, E e to be united into one, or if we produce them by a thin plate of Iceland spar, which is not capable of separating them, we obtain a beam which has exactly the same properties as the beam A B C D of common light. Hence we infer, that a beam of common light, A B C D, consists of two beams of polarised light, whose planes of polarisation, or whose diameters of similar properties, are at right angles to one another. If O o is laid above E e, it will produce a figure like A B C D, and we shall therefore represent common light by such a figure. If we were to place O o above E e, so that the planes of polarisation A'B' and C f D' coincide, then we should have a beam of polarised light twice as luminous as either O o or E e, and possessing exactly the same properties ; for the lines of similar property in the one beam coincide with the lines of similar property in the other. Hence it follows that there are three ways of convert- ing a beam of common light, A B C D, into a beam or beams of polarised light. CHAP. XXIII. POLARISATION OF LIGHT. 209 1. We may separate the beam of common light, A B C D, into its two component parts, O o and E e. 2. We may turn round the planes of polarisation, A B, CD, till they coincide or are parallel to each other. Or, 3. We may ahsorb or stop one of the beams, and leave the other, which will consequently be in a state of polarisation. The first of these methods of producing polarised light is that in which we employ a doubly refracting crystal, which we shall now consider. On the Polarisation of Light by Double Refraction* (110.) When a beam of light suffers double refrac- tion by a negative crystal, as in Iceland spar, fig. 89. , where the ray R r is incident in the plane of the prin- cipal section, or, what is the same thing, in a plane passing through the axis, the two pencils rO, rE are each polarised ; the plane of polarisation of the ordinary ray r O coinciding with the principal section, and the plane of polarisation of the extraordinary ray r E being at right angles to the principal section, as shown in fig. 100., where O is a section of the ordinary beam r O, fid' &9'y and E a section of the extraordinary beam r E. Fig. 100. Fig. 101. If the beam of light R r is incident upon a positive crystal like quartz, the plane of polarisation of the or- dinary ray, O, fig. 101., is horizontal, and the plane of the extraordinary ray, E, vertical. The phenomena which arise from this opposite polaris- ation of the two pencils may be well seen in Iceland spar. For this purpose let A r X be the principal section of 210 A TREATISE ON OPTICS. PART II. a rhomb of Iceland spar, Jfy. 102., through the axis A X, and perpendicular to one of the faces, and let A' F X' be the similar section of another rhomb, all the lines of the one being parallel to all the lines of the other. A ray of light, R r, incident^perpendicularly at r, will be divided into two pencils ; an ordinary one, r D, and an Oo extraordinary one, r C. The ordinary ray falling on the second crystal at G., again suffers ordinary refraction, and emerges at K an ordinary ray^ O o, with its plane of polarisation vertical as at O, fig. 100. In like manner the extraordinary ray, r C, falling again on the second crys- tal at F, suffers extraordinary refraction, and emerges at H an extraordinary ray, E e, with its plane of polar- isation horizontal. These results are exactly the same as if the two crystals had formed a single crystal by being united at their surfaces C X, A' G, either by na- tural cohesion or by a cement. Let the upper crystal A X now remain fixed., with the same ray Rr falling upon it, and let the second crystal A' X' be turned round 90, so that its prin- cipal section is perpendicular to that of the upper one, as shown in fig. 103. ; then the ray r D ordinarily re- CHAP. XXIII. POLARISATION OF LIGHT. 211 fracted by the first rhomb will be extraordinarily re- fracted by the second, and the ray r C extraordinarily refracted by the first rhomb will be ordinarily refracted by the second. The pencils or images formed from the ray R r, in the two positions shown in figs. 102. and 103., may be thus described as marked in the figures : O is the pencil refracted ordinarily by the first rhomb. E is the pencil refracted extraordinarily by the first rhomb. o is the pencil refracted ordinarily by the second rhomb. e is the pencil refracted extraordinarily by the second rhomb. O o is the pencil refracted ordinarily by both rhombs in fig. 102. E e is the pencil refracted extraordinarily by both rhombs in fig. 1 03. O e is the pencil refracted ordinarily by the first, and extraordinarily by the second rhomb in fig. 103. E o is the pencil refracted extraordinarily by the first, and ordinarily by the second rhomb in fig. 103. In both the cases shown in figs. 102. and 103., when the planes of the principal sections of the two rhombs are either parallel, as in fig. 102., or perpendicular to each other, as in^. 103,, the lower rhomb is not ca- pable of dividing into two any of the pencils which fall upon it ; but in every other position between the paral- lelism and the perpendicularity of the principal sec- tions, each of the pencils formed by the first rhomb will be divided into two by the second. In order to explain the appearances in all interme- diate positions, let us suppose that the ray R r proceeds- from a round aperture, like one of the circles at A, fig. 104., and that the eye is placed behind the two rhombs at H K, fig. 102., so as to see the images of this aperture. Let the two images shown at A be the appearance of the aperture at R, seen through one of the rhombs by p 2 212 A TREATISE ON OPTICS, PART II; Fig. 104. ABC D E FG H , I K an eye placed behind C D, fig. 1 02., then ~B,fig. 104., will represent the images seen through the two rhombs in the position in^. 102., their distance being doubled, from suffering the same quantity of double refraction twice. If we now turn the second rhomb, or that nearest the eye, from left to right, two faint images will appear, as at C, between the two bright ones, which will now be a little fainter. By continuing to turn, the four images will be all equally luminous, as at D; they will next appear as at E; and when the second rhomb has moved round $0, as in fig. 103., there will be only two images of equal brightness, as at F. Continuing to turn the second rhomb, two faint images will appear, as at G ; by a far- ther rotation, they will be all equally bright, as at H ; farther on they will become unequal, as at I ; and at 180 of revolution, when the planes of the principal section are again parallel, and the axes A X, A' X 7 at right angles nearly to each other, all the images will coalesce into one bright image, as at K, having double the brightness of either of those at A, B, or F, and four times the brightness of any one of the four at D and H. If we now follow any one of the images A, B from the position in fig. 102., where the principal sections are inclined to one another, to the position in fig. 103., where it disappears at F, we shall find that its bright- ness diminishes as the square of the cosine of the angle formed by the principal sections, while the brightness of any image, from its appearance between B and C, fig. 104., to its greatest brightness at F, increases as the square of the sine of the same angle. By considering the preceding phenomena it will ap- pear, that whenever the plane of polarisation of a polar- ised ray, whether ordinary or extraordinary, coincides CHAP. XXIII. POLARISATION OF LIGHT. 213 with or is parallel to the principal section, the ray will be refracted ordinarily ; and whenever the plane of po- larisation is perpendicular to the principal section, it will be refracted extraordinarily. In all intermediate posi- tions it will suffer both kinds of refraction, and will be doubly refracted; the ordinary pencil being the brightest if the plane of polarisation is nearer the position of pa- rallelism than that of perpendicularity, and the extraor- dinary pencil the brightest if the plane of polarisation is nearer the position of perpendicularity than that of parallelism. At equal distances from both their posi- tions, the ordinary and extraordinary images are equally bright. (111.) It does not appear from the preceding ex- periments that the polarisation of the two pencils is the effect of any polarising force resident in the Iceland spar, or of any change produced upon the light. The Iceland spar has merely separated the common light into its two elements, according to a different law, in the same man- ner as a prism separates all the seven colours of the spectrum from the compound white beam by its power of refracting these elementary colours in different de- grees. The re-union of the two oppositely polarised pencils produces common light, in the same manner as the re-union of all the seven colours produces white light. The method of producing polarised light by double refraction is of all others the best, as we can procure by this means, from a given pencil of light, a stronger po- larised beam than in any other way. Through a thick- ness of three inches of Iceland spar we can obtain two separate beams of polarised light one third of an inch in diameter; and each of these beams contains half the light of the original beam, excepting the small quantity of light lost by reflexion and absorption. By sticking a black wafer on the spar opposite either of these beams, we can procure a polarised beam with its plane of polarisation either in the principal section or at right angles to it. In all experiments on this subject, the reader should recollect that every beam of polarised light, whether it is pro- A TREATISE ON OPTICS. PART II. duced by the ordinary or the extraordinary refraction, or by positive or negative crystals, has always the same properties, provided the plane of its polarisation has the same direction. CHAP. XXIV. ON THE POLARISATION OF LIGHT BY RELEXION. (112.) IN the year 1810, the celebrated French phi- losopher M. Malus, while looking through a prism of calcareous spar at the light of the setting sun reflected from the windows of the Luxembourg palace in Paris, was led to the curious discovery, that a beam of light reflected from glass at an angle of 56, or from water at an angle of 52 45', possessed the very same pro- perties as one of the rays formed by a rhomb of calca- reous spar ; that is, that it was wholly polarised, having its plane of polarisation coincident with or parallel to the plane of reflexion. This most curious and important fact, which he found to be true when the light was reflected from all other transparent or opaque bodies,, excepting metals, gave birth to all those discoveries which have, in our own day, rendered this branch of knowledge one of the most interesting, as well as one of the most perfect, of the physical sciences. In order to explain this and the other discoveries of Malus, let C D, fig. 105., be a tube of brass or wood, Fig. 105. CHAP. XXIV. POLARISATION BY REFLEXION. 215 having at one end of it a plate of glass, A, not quick- silvered, and capable of turning round an axis, so that it may form different angles with the axis of the tube. Let D G be a similar tube a little smaller than the other, and carrying a similar plate of glass B. If the tube D G is pushed into C D, we may, by turning the one or the other round, place the two glass plates in any position in relation to one another. Let a beam of light, Ry, from a candle or a hole in the window-shutter fall upon the glass plate A, at an angle of 56 45' ; and let the glass be so placed that the re- flected ray r s may pass along the axis of the two tubes, and fall upon the second plate of glass B at the point s. If the ray rs falls upon the second plate B at an angle of 56 45' also, and if the plane of reflexion from this plate, or the plane passing through s E and s r, is at right angles to the plane of reflexion from the first plate, or a plane passing through r R, r s, the ray r s will not suffer reflexion from B, or will be so faint as to be scarcely visible. The very same thing will happen if r s is a ray polarised by double refraction, and having its plane of polarisation in the plane passing through r R, r s. Here then we have a new property or test of polarised light, that it will not suffer reflexion from a plate of glass B, when incident at an angle of 56, and when the plane of incidence or reflexion is at right angles to the plane of polarisation of the ray. If we now turn round the tube D G with the plate B, without moving the tube C D, the last reflected ray s E will become brighter and brighter, till the tube has been turned round 90, when the plane of reflexion from B is coincident with or parallel to that from A. In this position the reflected ray s E is brightest. By con- tinuing to turn the tube D G, the ray s E becomes fainter and fainter, till, after being turned 90 farther, the ray ^ E is faintest, or nearly vanishes, which happens when the plane of reflexion from B is perpendicular to that from A. After a farther rotation of 90, the ray s E will recover its greatest brightness ; and when, by a still p 4 216 A TREATISE ON OPTICS. farther rotation of 90, the tube D G or plate B are brought back into their first position, the ray s E will again disappear. These effects may be arranged in a table, as follows : Inclination of the planes of the two re- flexions, or the planes R r s and r s E, 01- azimuths of the planes r*E. State of brightness of the imat;e or ray t E reflected from the second plate B. 900 At angles between 90 and 180 1800 At angles between 180 and 270 270 At angles between 270 and 360 3600 or QO . At angles between and 90 - 90 Scarcely visible. The image grows brighter and brighter. Brightest. The image grows fainter and fainter. Scarcely visible. The image grows brighter and brighter. Brightest. The image grows fainter and fainter. Scarcely visible. If we now substitute in place of the ray r s one of the polarised rays or beams formed by Iceland spar, so that its plane of polarisation is in the plane R r s, it will experience the very same changes as the ray Rr does when polarised by reflexion from A at an angle of 56 45'. Hence it is manifest, that a ray reflected at 56 from glass has all the properties of polarised light as produced by double refraction. (113.) In the preceding observations, the ray R r is supposed to be reflected only from the first surface of the glass ; but Malus found that the light reflected from the second surface of the glass was polarised at the same time with that reflected from the first, although it ob- viously suffers reflexion at a different angle, viz. at an angle equal to the angle of refraction at the first surface. The angle of 56 45', at which light is polarised by reflexion from glass, is called its maximum polarising angle, because the greatest quantity of light is polarised at that angle. When the light was reflected at angles greater or less than 56 45', Malus found that a portion of it only was polarised, the remaining portion possessing all the properties of common light. The polarised por- tion diminished as the angle of incidence receded on either side from 56, and was nothing at 0, or a per- pendicular incidence, and also nothing at 90, or the most oblique incidence. CHAP. XXIV. POLARISATION BY REFLEXION. 21? In continuing his experiments on this subject, Malus found that the angle of maximum polarisation varied with different bodies ; and., after measuring it in various substances, he concluded that it follows neither the order of the refractive powers nor that of the dispersive powers, but that it is a property of bodies independent of the other modes of action which they exercise over light. After he had determined the angles under which complete polarisation takes place in diiferent bodies, such as glass and water, he endeavoured to ascertain the angle at which it took place at their separating surfaces when they were put in contact. In this enquiry, however, he did not succeed ; and he remarks, c that the law accord- ing to which this last angle depends on the two first remains to be determined." If a pencil or beam of light reflected at the maximum polarising angle from glass and other bodies were as completely polarised as a pencil polarised by double re- fraction, then the two pencils would have been equally invisible when reflected from the second plate, B, at the azimuths 90 and 270; but this is not the case : the pencil polarised by double refraction vanishes entirely when it passes through a second rhomb, even if it is a beam of the sun's direct light; whereas the pencil polarised by reflexion vanishes only if its light is faint, and if the plates A and B have a low dispersive power. "When the sun's light is used, there is a large quantity of unpolarised light, and this unpolarised light is greatly increased when the plates A and B have a high dis- persive power. This curious and most important fact was not observed by Malus. A very pleasing and instructive variation of the ge- neral experiment shown in fig. 105. occurred to me in examining this subject. If, when the plates of glass A and B have the position shown in the figure where the luminous body from which the ray s E proceeds is in- visible, we breathe gently upon the plate B, the ray s E will be recovered, and the luminous body from which it proceeds will be instantly visible. The cause of this i 218 r A TREATISE ON OPTICS. PART II. obvious : a thin film of water is deposited upon the glass by breathing, and as water polarises light at an angle of about 53 11', the glass B should have been inclined at an angle of 53 11' to the ray r s, in order to be inca- pable of reflecting the polarised ray* ; but as it is inclined 56 45' to the incident ray r s, it has the power of re- flecting a portion of the ray r s. If the glass B is now placed at an angle of 53 11' to the ray r s, it will then reflect a portion of the po- larised ray r s to the eye at E ; but if we breathe upon the glass B, the reflected light will disappear, because the reflecting surface is now water, and is placed at an angle of 53 11', the polarising angle for water. If we therefore place two glass plates at B, the one inclined 56 45', and the other 53 II 7 , to the beam r s, suffi- ciently large to fall upon both, the luminous object will be visible in the one but not in the other ; but if we breathe upon the two plates, we shall exhibit the paradox of reviving an invisible image, and extinguishing a visible one by the same breath. This experiment will be more striking if the ray r s is polarised by double refraction. On the Law of the Polarisation of Light by Reflexion. (114.) From a very extensive series of experiments made to determine the maximum polarising angles of various bodies, both solid and fluid, I was led, in 1814, to the following simple law of the phenomena : The index of refraction is the tangent of the angle of polarisation. In order to explain this law, and to show how to find the polarising angle for any body whose index of refrac- tion is known, let M N be the surface of any transpa- rent body, such as water. From any point, r, draw r A perpendicular to M N,fy. 106., and round r as a centre * We neglect the consideration of the separating surface of the water and glass, and suppose the glass B to be opaque. CHAP. XXIV. POLARISATION BY REFLEXION. Fig. 106. 219 describe a circle, M AN D. From A draw A F, touching the circle at A, and from any scale on which A r is 1 set off A F equal to 1'336, the index of refraction for water. From F draw F r, which will be the incident ray that will be po- larised by reflexion from the water in the direction r S. The angle A r R will be 53 II 7 , or the angle of maximum polarisation for water. This angle may be obtained more readily by looking for 1'336 in the column of natural tangents in a book of logarithms, and there will be found opposite to it the corresponding angle of 53 II 7 . If we calcu- late the angle of refraction T r D, corresponding to the angle of incidence A r R, or determine it by projection, we shall find it to be 36 49'. From the preceding law we may draw the following conclusions : ] . The maximum polarising angle, for all substances whatever, is the complement of the angle of refraction. Thus, in water, the complement of 36 49' is 53 11', the polarising angle. 2. At the polarising angle, the sum of the angles of incidence and refraction is a right angle, or 90. Thus, in water, the angle of incidence is 53 II 7 , and that of refraction 36 49', and their sum is 90. 3. When a ray of light R r, is polarised by reflexion, the reflected ray, r S, forms a right angle with the re- fracted ray, r T. When light is reflected at the second surface of bodies, the law of polarisation is as follows : The index of refraction is the cotangent of the angle of polarisation. In order to determine the angle in this case, let M N be the second surface of any body such as water. From r draw r A perpendicular to M N,fig. 107., and round r describe the circle M A N D. From A draw A F, 220 A TREATISE ON OPTICS. Fig. 107. touching the circle at A, and upon a scale in which r N is 1 or 10 take A F equal to 7485 or 7'485, that is to T'-g-g-g- the reciprocal of the index r of refraction, or y^.^, and from F draw F r ; the ray R r will be polarised when reflected in the di- rection r S. The maximum polar- ising angle A r R will be 36 49', exactly equal to the angle of refraction of the first surface. Hence it follows, 1. That the polarising angle at the second surface of bodies is equal to the complement of the polarising angle at the first, or to the angle of refraction at the first sur- face. The reason is, therefore, obvious why the por- tions of a beam of light reflected at the first and second surfaces of a transparent parallel plate are simultaneously polarised. 2. That the angle which the reflected ray r S forms with the refracted ray r T is a right angle. The laws of polarisation now explained are appli- cable to the separating surfaces of two media of different refractive powers. If the uppermost fluid is water, and the undermost glass, then the index of refraction of their separating surface is equal to -pf f , to the greater index divided by the lesser, which is 1*141 5. By using this index it will be found that the polarising angle is 48 47'. When the ray moves from the least refractive sub- stance into the greatest, as from water to glass, as in the preceding case, we must make use of the law and the method above explained for the first surface of bodies ; but when the ray moves from the greatest re- fractive body into the least, as from oil of cassia to glass, we must use the law and method for the second surfaces of bodies. If we lay a parallel stratum of water upon glass whose index of refraction is 1*508, the ray reflected from the refracting surfaces will be polarised when the CHAP. XXIV. POLARISATION BY REFLEXION. 221 angle of incidence upon the first surface of the water is 90. (115.) The preceding observations are all applicable to white light, or to the most luminous rays of the spectrum ; but, as every different colour has a different index of re- fraction,, the law enables us to determine the angle of polarisation for every different colour, as in the following table, where it is supposed that the most luminous ray of the spectrum is the mean one : Index Difference between of He- the greatest and frac- tion. Polarising Angle. least Polarising Angles. f Red rays - WATER - - -j Mean rays (_ Violet rays 1 '330 1 -336 1-342 53 4'-] 53 11 I 53 19 J 15' f Red rays - PLATE GLASS j Mean rays (_ Violet rays 1-515 1-525 1-535 56 34 | 56 45 1 56 55 J 21' {Red rays - Mean rays Violet rays 1-597 1-642 1-687 57 57 "] 58 40 I 59 21 J 1 24' The circumstance of the different rays of the spectrum being polarised at different angles, enables us to explain the existence of unpolarised light at the maximum po- larising angle, or why the ray s E, in fig. 105., never wholly vanishes. If we were to use red light, and set the two plate's at angles of 56 34/, the polarising angle of glass for red light, then the pencil s E would vanish entirely. But when the light is white, and the angle at which the plates are set is 56 45', or that which belongs to mean or yellow rays, then it is only the yellow rays that will vanish in the pencil s E. A small portion of red and a small portion of violet will be reflected, because the glasses are not set at their polarising angles ; and the mixture of these two colours will produce a purple colour, which will be that of the unpolarised light which remains in the pencil s E. If we place the plates at the angle belonging to the red ray, then the red only will 222 A TREATISE ON OPTICS. PART II. vanish, and the colour of the unpolarised light will be bluish green. If we place the plates at the angle cor- responding with the blue light, then the blue only will vanish, and the unpolarised light will be of a reddish cast. In oil of cassia, diamond, chromate of lead, realgar, specular iron, and other highly dispersive substances, the colour of the unpolarised light is extremely brilliant and beautiful. Certain doubly refracting crystals, such as Iceland spar, chromate of lead, &c., have different polarising angles on different surfaces, and in different direc- tions on the same surfaces ; but there is always one direction where the polarisation is not affected by the doubly refracting force, or where the tangent of the polarising angle is equal to the index of ordinary re- fraction. On the partial Polarisation of Light by Reflexion. (116.) If in the apparatus in^. 105., we make the ray R r fall upon the plate A at an angle greater or less than 56 45', then the ray s E will not vanish entirely ; but, as a considerable part of it will vanish like polarised light, Malus called it partially polarised light, and con- sidered it as composed of a portion of light perfectly polarised, and of another portion in the state of common light. He found the quantity of polarised light to diminish as the angle of incidence receded from that of maximum polarisation. M. Biot and M. Arago also maintained that partially polarised light consisted partly of polarised and partly of common light ; and the latter announced that, at regular angular distances above and below the maximum polarising angle, the reflected pencil contained the same proportion of polarised light. In St. Gobin's glass he found that the same proportion of light was polarised at an angle of incidence of 82 48' as at 24 18'; in water he found that the same proportion was polarised at 16 12' as at 86 31' ; but he remarks "that the mathe- matical law which connects the value of the quantity of CHAP, XXIV. POJ^ti.^ATION BY REFLEXION. polarised light with the angle of incidence and the refractive pov/er of the body has not yet been disco- vered." In the investigation of this subject, I found that though there was only one angle at which light could be completely polarised by one reflexion, yet it might be polarised at any angle of incidence by a sufficient number of reflexions, as shown in the following Table. BELOW THE POLARISING ANGLE. ABOVE THE POLARISING ANGLE. No. of Reflexions. {Angle at which the Light is polarised. No. of Reflexions. Angle at which the Light is polarised. 1 56 45' 1 56 45' 2 50 26 2 62 30 3 46 30 3 65 33 4 43 51 4 67 33 5 41 43 5 69 1 6 40 6 70 9 7 38 33 7 71 5 8 37 20 8 71 51 In polarising light by successive. reflexions, it is not necessary that the reflexions be performed at the same angle. Some of them may be above and some below the polarising angle, or all the reflexions may be per- formed at different angles. From the preceding facts it follows as a necessary consequence, that partially polarised light, or light re- flected at an angle different from the polarising angle, has suffered a physical change, which enables it to be more easily polarised by a subsequent reflexion. The light, for example, which remains unpolarised after five reflexions at 70, in place of being common light, has suffered such a physical change that it is capable of being completely polarised by ONE reflexion more at 7 ; This view of the subject has been rejected by M. Arago, as incompatible with experiments and specu- lations of his own ; and, in estimating the value of the 224 A TREATISE ON OTTf-S. ?: PART II. two opinions, Sir John Herschel has rejected mine as the least probable. It will be seen, however, from the following facts that it -is capable of the most .rig&rous demonstration. It does not appear, from the preceding enquiries, how a beam of common light is converted into polarised light by reflexion. By a series of experiments made in 1829; I have been able to remove this difficulty. It has been long known that a polarised beam of light has its plane of polarisation changed by reflexion from bodies. If its plane is inclined 45 to the plane of re- flexion, its inclination will be diminished by a reflexion at 80, still more by one at 70, still more by one at 60; and at the polarising angle the plane of the polar- ised ray will be in the plane of reflexion, the inclination commencing again at reflexions above the polarising angle, and increasing till at 0, or a perpendicular inci- dence, the inclination is again 4,5.* I now conceived a beam of common light, constituted as in^. 99- 3 to he incident on a reflecting surface, so that the plane of re- flexion bisected the angle of 90 which the two planes of polarisation, A B, C D, formed with each other, as shown in fig. 108., No. 1., where M N is the plane of reflexion, and A B, C D the planes of polarisation of the beam of white light, each inclined 45 to M N. By a reflexion from glass, where the index of refraction Fig. 108. No. 2. * No. 3. is J'525,, at 80, the inclination of A B to M N will be the tangent of the inclination required CHAP. XXIV. POLARISATION BY REFLEXION. 225 33 13', as in No. 2., instead of 45 ; and in like man- ner the inclination of C D to M N will be 33 13', in place of 45; so that the inclination of A B to C D in place of 90 is 66 26', as in No. 2. At an incidence of 65 the inclination of A B to C D will be 25 36', as in No. 3. ; and at the polarising angle of 56 '45' the planes A B, C D of the two beams will be parallel or coincident, as in No. 4. At incidences below 56 45' the planes will again open, and their inclination will increase till at of incidence it is 90, as in No. 1., having been 25 36' at an incidence of about 48 15', as in No. 3., and 66 26' at an incidence of about 30, as in No. 2. In the process now described, we see the manner in which common light, as in No. 1., is converted into polarised light, as in No. 4., by the action of a reflecting surface. Each of the two planes of its component po- larised beams is turned round into a state of parallelism, so as to be a beam with only one plane of polarisation, as in No. 4. ; a mode of polarisation essentially different in its nature from that of double refraction. The num- bers in fig. 108. present us with beams of light in different stages of polarisation from common light in No. 1. to polarised light in No. 4. In No. 2. the beam has made a certain approach to polarisation, having suffered a physical change in the inclination of its planes ; and in No. 3. it has made a nearer approach to it. Hence we discover the whole mystery of partial polarisation, and we see that partially polarised light is light whose planes of polarisation are inclined at angles between and 90. The influence of successive reflexions is therefore obvious. A reflexion at 80 will turn the planes, as in fig. 108. No. 2.; another reflexion at 80 will bring them closer; a third still closer; and so on: and though they never can by this process be brought into a state of exact parallelism, as in No. 4. (which can only be done at the polarising angle), yet they can be brought infinitely near it, so that the beam will appear as completely polarised as if it had been reflected at the polarising angle. The correctness 226 A TREATISE ON OPTICS. of my former experiments and views is, therefore, de- monstrated by the preceding analysis of common light. It is manifest from these views that partially po- larised light does not contain a single ray of completely polarised light ; and yet if we reflect it from the second plate B, in fig. 105., at the polarising angle, a certain portion of it will disappear as if it were polarised light, a result which led to the mistake of Malus and others. The light which thus disappears may be called appa- rently polarised light ; and I have explained in another place* how we may determine its quantity at any angle of incidence, and for any refractive medium. The fol- lowing table contains some of the results for glass, whose index of refraction is 1*525. The quantity of reflected light is calculated by a rule given by M. Fresnel. Angles of Incidence. Inclination of the Planes of Polarisation, A B, C D,./fe. 108. Quantity of re- flecied Ravs out of 1000. Quantity of polarised Kays out of 1000. 0' 90 0' 43-23 0* 20 80 26 43-41 7-22 40 47 22 49-10 33-25 56 45 79'5 79-5 70 37 4 162-67 129-8 80 66 26 391-7 156-6 85 78 24 616-28 123-75 90 90 1000- o- CHAP. XXV. ON THE POLARISATION OF LIGHT BY ORDINARY REFRACTION. (117.) ALTHOUGH it might have been presumed that the light refracted by bodies suffered some change, correspond- ing to that which it receives from reflexion, yet it was * Sfie Phil. Transactions, 1830, p. 76., or Edinburgh Journal of Science, New Series, No. V. p. 160. , CHAP. XXV. POLARISATION BY REFRACTION. 227 not till 1811 that it was discovered that the refracted portion of the beam contained a portion of polarised light.* To explain this property of light, let R r,fig. 109., be a beam of light incident at a great angle between 80 and 90 on a horizontal plate of glass, No. 1. ; a por- tion of it will be reflected at its two surfaces, r and Fig. 109, a, and the refracted beam a is found to contain a small portion of polarised light. If this beam a again falls upon a second plate. No. 2., parallel to the first, it will suffer two reflexions; and the refracted pencil b will contain more polarised light than a. In like manner, by transmitting it through the plates Nos. 3,4,5, and 6., the last refracted pencil, /#, will be found to consist entirely, so far as the eye can judge, of polarised light. But, what is very interesting, the beam f g is not polarised in the plane of refraction or reflexion, but in a plane at right angles to it ; that is, its plane of polarisation is not represented by A' B', fi9* 99-j like the ordinary ray in Iceland spar,, or as light polarised by reflexion, but by C f D', like the extraordinary ray in Iceland spar. From a great num- ber of experiments, I found that the light of a wax candle at the distance of 10 or 12 feet was polarised at the following angles, by the following number of plates of crown glass. * This discovery was made by independent observation by Malus, Biot, and the author of this work. Q 2 228 A TREATISE ON OPTICS. PART II. Na of Plates of Crown Glass. Observed Angles at which the Pencil is polarised. No. of Plates of Crown Glass. Observed Angles at which the Pencil is polarised. 8 79 11' 27 57 10' 12 74 31 53 28 16 69 4 35 50 5 21 63 21 41 45 35 24 60 8 47 41 41 It follows from the above experiments, that if we divide the number 41*84 by any number of crown glass plates, we shall have the tangent of the angle at which the beam is polarised by that number. Hence it is obvious that the power of polarising the refracted light increases with the angle of incidence, being nothing or a minimum at a perpendicular incidence, or 0, and the greatest possible or a maximum at 90 of incidence. I found likewise, by various experiments, that the power of polarising the light at any given angle increased with the refractive power of the body, and consequently that a smaller number of plates of a highly refracting body was necessary than of a refracting body of low power, the angle of incidence being the same. As Malus, Biot, and Arago considered the beams a, 5, &c., before they were completely polarised, as par- tially polarised, and as consisting of a portion of polar- ised and a portion of unpolarised light ; so, on the other hand, I concluded from the following reasoning that the unpolarised light had suffered a physical change, which made it approach to the state of complete polarisation. For since sixteen plates are required to polarise com- pletely a beam of light incident at an angle of 6'9, it is clear that eight plates will not polarise the whole beam at the same angle, but will leave a portion unpolarised. Now, if this portion were absolutely unpolarised like common light, it would require to pass through other sixteen plates, at an angle of 69, in order to be com- pletely polarised ; but the truth is, that it requires to pass through only eight plates to be completely polarised. Hence I conclude that the beam has been nearly half CHAP. XXV. POLARISATION BY RKFBACTION. 229 polarised by the first eight plates 3 and the polarisation completed by the other eight. This conclusion, though rejected by both the French and English philosophers, is capable of rigid demonstration, as will appear from the following observations. In order to determine the change which refraction produced in the plane of polarisation of a polarised ray, I used prisms and plates of glass, plates of water, and a plate of a highly refractive metalline glass; and I found that a refracting surface produced the greatest change at the most oblique incidence, or that of 90; and that the change gradually diminished to a perpendicular incidence, or 0, where it was nothing. I found also that the greatest effect produced by a single plate of glass was about 16 39', at an angle of 86; that it was 3 5' at an angle of 55, 1 12' at an angle of 35, and at an angle of 0. * A beam of common light, therefore, constituted as in fig. 110, No. 1., with each of its planes A B, C D in- Fig. 110. clined 45 to the plane of refraction, will have these planes opened 16 39' each, by one plate of glass at an incidence of 86 ; that is, their inclination, in place of 90, will be 123 18', as in No. 2. By the action of the other two or three plates they will be opened wider, as in No. 3. ; and by 7 or 8 plates they will be opened to near 180, or so that A B, C D nearly coincide, as in * The rule for finding the inclination is as follows : Find the difference" between the angles of incidence and refraction, and take the cosine of this difference. This number will be the cotangent of the inclination required: and twice this inclination will be the inclination of A B to CD. Q 3 230 A TREATISE ON OPTICS. PART II No. 4>., so as to form a single polarised beam, whose plane of polarisation is perpendicular to the plane of refraction. I have shown, in another place *, that these planes -can never be brought into mathematical coin- cidence by any number of refractions ; but they approach so near to it that the pencil is, to all appearance, com- pletely polarised with lights of ordinary strength. All the light polarised by refraction is only partially po- larised, and it has the same properties as that which is partially polarised by reflexion. A certain portion of the light of a beam thus partially polarised, will disap- pear when reflected at the polarising angle from the plate Tl,fig. 105.; and this quantity, which I have else- where shown how to calculate, is given in the following table for a single surface of glass, whose index of re- fraction is 1*525. Angle of Incidence. Inclination of the Planes of Polarisation ABCD, .fig. 110. Quantity of transmitted Kays out of 1UOO. Quantity of polarised Kays out of 1000. 90 0' 956-77 20 90 26 956-59 7-22 40 92 950-90 32-2 56 45' 94 58 920-5 79-5 70 98 56 837-33 129-8 80 40 7 104 55 608-3 156-7 85 108 44 383*72 123-7 90 112 58 Although the quantity of light polarised by refraction, as given in the last column of this Table, is calculated by a formula essentially different from that by which the quantity of light poralised by reflexion was calculated ; yet it is curious to see that the two quantities are pre- cisely equal. Hence we obtain the following law : When a ray of common light is reflected and refracted by any surface, the quantity of light polarised by refrac- tion is exactly equal to that polarised by reflexion. This law is not at all applicable to plates, as it ap- peared to be from the experiments of M. Arago. * See Phil. Transactions, 1830, p, 137-,or Edinburgh Journal of Science* New Series, No. VI. p. 218. CHAP. XXV. POLARISATION BY REFRACTION. 23 When the preceding method of analysis is applied to the light reflected by the second surfaces of plates, we obtain the following curious law : A pencil of light reflected from the second surfaces of transparent plates, and reaching the eye after two refrac- tions and an intermediate reflexion, contains at all angles of incidence, from to the maximum polarising angle, a portion of light polarised in the plane of reflexion. Above the polarised angle, the part of the pencil polarised in the plane of reflexion diminishes, till the incidence becomes 78 1' in glass, when it disappears, and the whole pencil has the character of common light. Above this last angle the pencil contains a quantity of light polarised perpen- dicularly to the plane of reflexion, which increases to a maximum, and then diminishes to nothing at 90.* (118.) As a bundle of glass plates acts upon light, and polarises it as effectually as reflexion from the surface of glass at the polarising angle, we may substitute a bundle of glass plates in the apparatus Ji#. 105., in place of the plates of glass A, B. Thus,if A(fig. 111.) is a bundle of glass Fig. 111. plates which polarises the transmitted ray st, then, if the second bundle B, is placed as in the figure, with the planes of refraction of its plates parallel to the planes of refraction of the plates of A, the ray s t will penetrate the second bundle ; and if s t is incident on B at the polarising angle, not a ray of it will be reflected by the plates of B. If B is now turned round its axis, the transmitted light vw will giadually diminish, and more and more light will be reflected by the plates of the bundle, till, after a rotation of 90, the ray vw will dis- appear, and all the light will be reflected. By con- * See Phil. Trvns. 1830, p. 145. ; or Edinburgh Journal of Science, No. VI. p. 234. New Series. 32 A TREATISE ON OPTICS. PART II. tinuing to turn round B, the ray v w will re- appear, and reach its maximum brightness at 180, its minimum at 270, and its maximum at 0, after having made one complete revolution. By this apparatus we may perform the very same ex- periments with refracted polarised light that we did with reflected polarised light in the apparatus of fig. 105. We have now described two methods of converting common light into polarised light: 1st, By separating by double refraction the two oppositely polarised beams which constitute common light ; and., 2dly, By turning round, by the action of the reflecting and refracting forces, the planes of both these beams till they coincide, and thus form light polarised in one plane. Another method still remains to be noticed ; namely, to disperse or absorb one of the oppositely polarised beams which constitute common light, and leave the other beam polar- ised in one plane. These effects may be produced by agate and tourmaline, &c. (119.) If we transmit a beam of common light through a plate of agate, one of the oppositely polarised beams will be converted into a nebulous light in one position, and the other polarised beam in another position, so that one of the polarised beams with a single plane of polar- isation is left. The same effect may be produced by Iceland spar, arragonite, and artificial salts prepared in a particular manner, to produce a dispersion of one of the oppositely polarised beams.* When we transmit common light through a thin plate of tourmaline, one of the oppositely polarised beams which constitute common light is entirely absorbed in one position, and the other in another position, one of them always remaining with a single plane of polar- isation. Hence plates of agate and tourmaline are of great use, either in affording a beam of light polarised in one plane, * See Edinburgh Encyclopedia, vol. xv. pp. 600, 601. ; Phil. Trans. 1 819, p. 146. CHAP. XXVI. COLOURS OF CRYSTALLISED PLATES. 233 or in dispersing and absorbing one of the pencils of a compound beam, when we wish to analyse it, or to ex- amine the colour or properties of one of the pencils seen separately. CHAP. XXVI. ON THE COLOURS OF CRYSTALLISED PLATES IN POLARISED LIGHT. (120.) THE splendid colours, and systems of coloured rings, produced by transmitting polarised light through transparent bodies that possess double refraction, are undoubtedly the most brilliant phenomena that can be exhibited. The colours produced by these bodies were discovered by independent observation, first by M. Arago and subsequently by the author of this volume ; and they have been studied with great success by M. Biot and other authors. In order to exhibit these phenomena, let a polarising apparatus be prepared, similar in its nature to that in fig. 105.; but without the tubes as shown in fig. 112., where A is a plate of glass which polarises the ray Fig. 112. R r, incident upon it at an angle of 56 45', and reflects it polarised in the Direction r s, where it is received by a second plate of glass, B, whose plane of reflexion is at right angles to that of the plate A, and which reflects it to the eye at O, at an angle of 56 45'. In order that the polarised pencil r s may be sufficiently brilliant, ten 234 A TREATISE ON OPTICS, PART II. or twelve plates of window glass, or, what is better still, of thin and well-annealed flint glass, should be substituted in place of the single plate A. The plate or plates at A are called the polarising plates, or the Polariser, be- cause their only use is to furnish us with a broad and bright beam of polarised light. The plate B is called the analysing plate, or the Analyser, because its use is to analyse, or separate into its parts, the light trans- mitted through any body that may be placed between the eye and the polarising plate. If the beam of light R r proceeds from the sky, which will answer well enough for common purposes, then an eye placed at O will see, in the direction O s, the part of the sky from which the beam R r proceeds. But as r s will be polarised light, if it is reflected at 5645 / from A, almost none of it will be reflected to the eye at O from the plate B ; that is, the eye at O will see, upon the part of the sky from which R r proceeds, a black spot ; and when it does riot see this black spot, it is a proof that the plates A and B are not placed at the proper inclinations to each other. When a position is found, either by moving A or B, or both, at which the black spot is darkest, the apparatus is properly adjusted. (121.) Having procured a thin film of sulphate of lime or mica, between the 20th and the 6'0th of an inch thick, and which may be split by a fine knife or lancet from a mass of any of these minerals in a transparent state, expose it, as shown at C E D F, so that the po- larised beam r s may pass through it perpendicularly. If we now apply the eye at O, and look towards the black spot in the direction O s, we shall see the surface of the plate of Sulphate of Lime entirely covered with the most brilliant colours. If its thickness is perfectly uniform throughout, its tint will be perfectly uniform ; but if it has different thicknesses, every different thick- ness will display a different colour some red, some green, some blue, and some yellow, and all of the most brilliant description. If we turn the film C E D F round, keeping it perpendicular to the polarised beam, CHAP. XXVI. COLOURS OF CRYSTALLISED PLATES. 235 the colours will become less or more bright without changing their nature, and two lines C D, E F at right angles will be found, so that when either of them is in the plane of reflexion r $ O, no colours whatever are perceived, and the black spot will be seen as if the sulphate of lime had not been interposed, or as if a piece of common glass had been substituted for it. It will also be observed, by continuing the rotation of the sul- phate of lime, that the colours again begin to appear ; and reach their greatest brightness when either of the lines G H, L K, which are inclined 45 to C D, E F, are in the plane of reflexion r s O. The plane R r s, or the plane in which the light is polarised, is called the plane of primitive polarisation ; the lines C D, E F, the neutral axes; and G H, K L, the depolarising axes, because they depolarise, or change the polarisation of the polarised beam r s. The brilliancy or intensity of the colours increase gradually, from the position of no colour, to that in which it is the most brilliant. Let us now suppose the plate C E D F to be fixed in the position where it gives the brightest colour ; namely, when G H is perpendicular to the plane of primitive polarisation R r s, or parallel to the plane r s O, and let the colour be red. Let the analysing plate B be made to revolve round the ray r s, beginning its motion at 0, and preserving always the same inclination to the ray r s, viz. 56 45'. The brightest Ted being now visible at 0, when the plate B begins to move from its position shown in the figure, its brightness will gradually diminish till B has turned round 45, when the red colour will wholly disappear, and the black spot in the sky be seen. Beyond 45 a faint green will make its appearance, and will become brighter and brighter till it attains its greatest brightness at 90. Beyond 90 the green becomes paler and paler till it disappears at 135. Here the red again appears, and reaches its maximum brightness at 180. The very same changes are re- peated while the plate B passes from 1 80 round to its first position at 360 or 0. From this experiment it 236 A TREATISE ON OPTICS. PART II. appears,, that when the film C E D F alone revolves, only one colour is seen ; and when the plate B only revolves, two colours are seen during each half of its revolution. If we repeat the preceding experiment with films of different thickness, that give different colours, we shall find that the two colours are always complementary to each other, or together make white light. (122.) In order to understand the cause of these beautiful phenomena, let the eye be placed between the film and the plate B, and it will be seen that the light transmitted through the film is white, whatever be the position of the film. The separation of the colours is therefore produced, or the white light is analysed, by reflexion from the plate B. Now, sulphate of lime is a doubly refracting crystal ; and one of its neutral axes, C D, is the section of a plane passing through its axis, while E F is the section of a plane perpendicular to the principal section. Let us now suppose either of these planes, viz. E F, to be placed, as in the figure, in the plane of polarisation R r s of the polarised light ; then the ray R r will not be doubled, but will pass into the ordinary ray of the crystallisedfilm ; and falling upon B, it will not suffer reflexion. In like manner, if C D is brought into the plane R r s, it will pass entirely into the ordinary ray, which, falling upon B, will not suffer re- flexion. In these two positions of the film, therefore, it forms only a single image or beam ; and as the plane of polarisation of this image or beam is at right angles to the plane of reflexion from B, none of it is reflected to the eye at O. But in every other position of the doubly refracting film C E D F, it forms two images of different intensities, as may be inferred from fg. 104. ; and when either of the depolarising axesGH or KL is in the plane of primitive polarisation, the two images are of equal brightness, and are polarised in opposite planes ; one in the plane of primitive polarisation, and the other at right angles to it. Now, one of these images is red, and the other green, for reasons which will be afterwards explained ; and as the green is polarised in the plane of CHAP. XXVI. COLOURS OF CRYSTALLISED PLATES. 23? primitive polarisation R r s, it does not suffer reflexion from the plate B ; while the red, being polarised at right angles to that plane, is reflected to the eye at O, and is therefore alone seen. For a similar reason, when B is turned round 90, the red will not suffer reflexion from it ; while the green will suffer reflexion, and be trans- mitted to the eye at O. In this case the plate B analyses the compound beam of white light transmitted through the film of sulphate of lime, by reflecting the half of it which is polarised in the plane of its reflexion, and refusing to reflect the other half, which is polarised in an opposite plane. If the two beams had been each white light, as they are in thick plates of sulphate of lime, in place of seeing two different colours during the revolution of the plate B, the reflected pencil s O would have undergone different variations of brightness, ac- cording as the two oppositely polarised beams of white light were more or less reflected by it ; the positions of greatest brightness being those where the red and green colours were the brightest, and the darkest points being those where no colour was visible. (123.) The analysis of the white beam composed of two beams of red and green light, has obviously been ef- fected by the power of the plate to reflect the one and to transmit or refract the other ; but the same beam may be analysed by various other methods. If we make it pass through a rhomb of Calcareous Spar sufficiently thick to separate by double refraction the red from the green beam, we shall at the same time see both the coloured beams, which we could not do in the former case; the one forming the ordinary, and the other the extraordinary image. Let us now remove the plate B, and substitute for it a rhomb of calcareous spar, with its principal section in the plane of reflexion r s O, or perpendicular to the plane of primitive polarisation R r s, and let the rhomb have a round aperture in the side farthest from the eye, and of such a size that the two images of the aperture, formed by double refraction, may just touch one another. Remove the film C E D F, and the eye 238 A TREATISE ON OPTICS. PART II. placed behind the rhomb will see only the extraordinary image of the aperture, the ordinary one having vanished. Replace the film, with its neutral axes as in the figure, parallel and perpendicular to the plane R r s, and no effect will be produced ; but if either of the depolarising axes are brought into the plane R r s, the ordinary image of the aperture will be a brilliant red, and the extraor- dinary image a brilliant green ; the double refraction of the rhomb having separated these two differently coloured and oppositely polarised beams. By turning round the film, the colours will vary in brightness ; but the same image will always have the same colour. If we now keep the film fixed in the position that gives the finest colours, and move the rhomb of calcareous spar round, so that its principal section shall make a complete revolution, we shall find that, after revolving 45 from its first position, both images become white. After revolving 90, the ordi- nary image that was formerly red is now green, and the extraordinary image that was formerly green is now red. The two images become again white at 135, 225, and 315 ; and at 1 80, the ordinary image is again red, and the extraordinary one green ; and at 270, the ordinary image is green, and the other red. If we use a large circular aperture on the face of the rhomb, the ordinary and extraordinary images O, E will overlap each other, as in fig. 113.; the overlapping parts Fig. 113. at F G being pure white light, and the parts at C and D having the colours above described. This experi- ment affords ocular demonstration that the two colours at C and D are complementary, and form white light. CHAP. XXVI. COLOURS OF CRYSTALLISED PLATES. 23$ The analysis of the compound beam transmitted by the sulphate of lime may also be effected by a plate of Agate, or any of the other crystals, artificially prepared for the purpose of dispersing one of the component beams.* The agate being placed between the eye and the film C E D F, it will disperse into nebulous light the red beam, and enable the green one to reach the eye ; while in another position it will scatter the green beam, and allow the red light to reach the eye. With a proper piece of agate this experiment is both beautiful and instructive; as the nebulous light, scattered round the bright image, will be green when the distinct image is red, and red when the distinct image is green. The analysis may also be effected by the absorption of tourmaline and other similar substances. In one position the tourmaline absorbs the green beam, and allows the red to pass ; while in another position it ab- sorbs the red, and suffers the green to pass. The yellow colour of the tourmaline, however, is a disadvantage. The analysis may also be performed by a bundle of glass plates, such as A or ft, fig. 111. In one position such a bundle will transmit all the red, and reflect all the green ; while in another position it will transmit all the green, and reflect all the red, in the opposite manner, but according to the same rules as the analysing plate B^. 112. (124.) In all these experiments the thickness of the sulphate of lime has been supposed such as to give a red and a green tint ; but if we take a film 0*00046 of an English inch thick, and place it at C E D F in fig. 112., it will produce no colours at all, and the black spot in the sky will be seen, whatever be the position of the film. A film 0*00124 thick will give the white of the first order in Newton's scale of colours, given in p. 123, 124. ; and a plate O'Ol 8 1 8 of an inch thick, and all plates of greater thickness, will give a white composed of all the colours. Films or plates of intermediate thicknesses * See p. 232. 240 A TREATISE ON OPTICS. PART II. between Q'00124 and 0-01818 will give all the inter- mediate colours in Newton's Table between the white of the first order and the white arising from the mixture of all the colours. That is, the colours reflected to the eye at O will be those in column 2d, while the colours observed by turning round the plate B will be those in column 3d ; the one set of colours corresponding to the reflected tints, and the other to the transmitted tints of thin plates. In order to determine the thickness of a film of sulphate of lime which gives any particular colour in the Table, we must have recourse to the num- bers in the last column for glass, which has nearly the same refractive power as sulphate of lime. Suppose it is required to have the thickness which corresponds to the red of the first spectrum or order of colours. The number in the column for glass, opposite red, is 5|; then, since the white of the first order is produced by a film 0*00124 of an inch thick, the number corresponding to which is 3 in the column for glass, we say, as 3|- is to 5, so is 0-00124 to 0*00211, the thickness which will give the red of the first order. In the same manner, by having the thickness of any film of this substance, we can determine the colour which it will produce. Since the colours vary with the thickness of the plate, it is manifest, that if we form a wedge of sul- phate of lime, with its thickness varying from 0'00124 to 0*01818 of an inch, we should observe at once all the colours in Newton's Table in parallel stripes. An experiment of the same kind may be made in the fol- lowing manner : Take a plate of sulphate of lime, MN^jfyr. 114., whose thickness exceeds 0'0181 8 of an CHAP. XXVI. COLOURS OF CRYSTALLISED PLATES. 241 inch. Cement it with isinglass on a plate of glass ; and placing it upon a fine lathe, turn out of it with a very sharp tool a concave or hollow surface between A and B, turning it so thin at the centre that it either begins to break or is on the eve of breaking. If the plate M N is now placed in water, the water will after some time dissolve a small portion of its substance, and polish the turned surface to a certain degree. If the plate is now held at C E D F,fig. 112., we shall see all the colours in Newton's Table in the form of con- centric rings, as shown in the figure. If the thickness diminishes rapidly, the rings will be closely packed together, but if the turned surface is large, and the thickness diminishes slowly, the coloured bands will be broad. In place of turning out the concavity, it might be better to grind it out, by applying a convex surface of great radius, and using the finest emery. When the plate M N is thus prepared, we may give the most perfect polish to the turned surface by cementing upon it a plate of glass with Canada balsam. The balsam will dry, and the plate may be preserved for any length of time. By the method now described, the most beautiful patterns, such as are produced in bank notes, &c., may be turned upon a plate of Sulphate of lime O0181 8 of an inch thick, cemented to glass. All the grooves or lines that compose the pattern may be turned to different depths, so as to leave different thicknesses of the mineral, and the grooves of different depths will all appear as different colours, when the pattern is held in the apparatus in fig. 1 ] 2. Coloured drawings of figures and landscapes may in like manner be executed, by scraping away the mineral to the thickness that will give the required colours ; or the effect may be produced by an etching ground, and using water and other fluid solvents of sulphate of lime to reduce the mineral to the required thicknesses. A cipher might thus be executed upon the mineral ; and if we cover the surface upon which it is scratched, or cut, or dissolved, with a balsam or fluid of exactly the same B 242 A TREATISE ON OPTICS. PART II. refractive power as the sulphates, it will be absolutely illegible by common light, and may be distinctly read in polarised light, when placed at C E D F in fig. 112. As the colours produced in the preceding experiments vary with the different thicknesses of the body which produces them, it is obvious that two films put together, as they lie in the crystal with similar lines coincident or parallel, will produce a colour corresponding to the sum of their thicknesses, and not the colour which arises from the mixture of the two colours which they produce se- parately. Thus, if we take two films of sulphate of lime, one of which gives the orange of the first order, whose number in the last column in Newton's Table, p. 123., is 5J, while the other gives the red of the 2d order, whose number is 1 1 1 ; then by adding these numbers, we get 17, which corresponds in the Table to green of the 3d order. But if the two plates are crossed, so that similar lines in the one are at right angles to similar lines in the other, then the tint or colour which they produce will be that which belongs to the difference of their thick- nesses. Thus, in the present case, the difference of the above numbers is 6j|, which corresponds in the Table to greenish yellow of the second order. If the plates which are thus crossed are equally thick, and produce the same colours, they will destroy each other's effects, and black- ness will be produced ; the difference of the numbers in the Table being 0. Upon this principle, we may produce colours by crossing plates of such a thickness as to give no colours separately, provided the difference of their thickness does not exceed 0-01818 ; for if the difference of their thickness is greater than this, the tint will be white, and beyond the limits of the Table. This may be illustrated by grinding a plate of sul- phate of lime of uniform thickness with the powder of schistus, and polishing it by the action of water, or any other means, or by cementing it between two plates of glass with Canada balsam, or any other fluid of nearly the same refractive power. When a plate of this kind, such as A D, is placed at G H,/#. 1 15., its surface will CHAP. XXVI. COLOURS OF CRYSTALLISED PLATES. 243 Fig. 115. be seen covered with fringes parallel to a d, the thin side of the wedge. If the plate is as thin as the 0'00124th of an inch, the fringe or dotted line above a b will be one of the first order of colours, and those above it of the 2nd, 3rd, 4th, and 5th orders, provided the thick- ness at A B corresponds to that of the 5th order. If A B is thicker than this, we shall have higher orders, and the fringes will be packed close to each other. If the wedge is thinner at AB, there will be fewer fringes. If the thickness at a & is too great to give the first fringe, then the fringes between a b and A B will correspond with the thickness of the wedge between these two lines. If we now cut this wedge into two equal halves, A B, Fig. 116. C D, and place them as in the figure, a new set of fringes will be seen in the intersectional square M N O P, parallel to its diagonal M N. The line N P will be black, and from that line to M and O the fringes will be exactly the same as those shown in fig. 11 6. If the plate A B had been placed above C D, so that A B coincided with C D, we should have had a set of fringes corresponding with double the thickness of the sulphate of lime ; and if the thick edge of the one were placed above the thin edge of the other, the plate, being thus made one of equal thickness, would give a uniform tint corresponding with that at A B or C D, whereas, when they are placed at right angles to each other, as in fig. 11 6., we have a set of fringes cor- responding with the difference of thickness at any point. Along the whole of the diagonal N P, for example, the R2 244 A TREATISE ON OPTICS. PART II. difference of thickness of the two wedges is nothing, so that there can be no colour, and hence the line N P is black. Along the fringe next to NP on either side, the difference of thickness is the same as in the single wedge at the fringe 1,1, and so on with the other fringes on each side of N P. If the two wedges A B, C D, in place of being cut out of the same plate so that C D is parallel to A B, had been cut out so that C D was at right angles to A B, and were then crossed as in fig. 11 6., there would be only one set of fringes in the intersectional square MNOP, commencing with black at the point P, where the two tints are a minimum, and running parallel to the diagonal M O, the fringes being closer and more numerous, and having their maximum tint at N cor- responding to twice the thickness of the wedge at that point in the single plates. When the wedges are placed parallel to each other, so that A B coincides with C D, the tints will corre- spond with the difference of their thickness, which is nothing, that is, there will be no fringes. If the plates are so placed as that the thin edge of the one coincides with the thick edge of the other, the tints mil still correspond with the differences of thick- ness at any point. At each edge the difference of thick- ness will be equal to the thickest edge of each plate, and therefore we shall have a tint or fringe corresponding to that thickness, but in the middle the difference of the thicknesses will be nothing, so that the middle line will be black, with fringes of the same order running from it to the outer edges of the combined plates. The colours of polarised light may be well shown by plates of Ice, either when regularly or irregularly frozen, placed in a polarising apparatus at G H, fig. 112. If in a severe frost, when ice can be handled without melting it, we take a plate of uniform thickness and form a pattern upon it by heat so applied as to dissolve only the parts of it to be made thinner, and give different colours, we may produce phenomena of the most splendid CHAP. XXVII. MR. HAIDINGERS BRUSHES. 245 kind. By means of patterns cut out of paper or zinc, the heat may be transmitted through the openings, in order to produce the desired patterns. If the polarised light employed in the preceding ex- periments is homogeneous, then the colours reflected from the plate B will always be those of the homogeneous light employed. In red light, for example, the colours or rather shades which succeed each other, with different thicknesses of the mineral, will be red at one thickness, black at another, red at another, and black at another, and so on with all the different colours. If we place the specimen shown in fig. 114. in violet light, the rings A B will be less than in red light ; and in intermediate colours they will be of intermediate mag- nitudes, exactly as in the rings of thin plates formerly described. When white light is used, all the different sets of rings are combined in the very same manner as we have already explained, in thin plates of air, and will form by their combinations the various coloured rings in Newton's Table. CHAP. XXVII. ON THE METHOD OP DETERMINING BY THE EYE ALONE THE DIRECTION OP THE PLANE OP POLARISATION. (125.) IT is an easy matter to determine the direction of the plane in which light is polarised, by various methods explained in the preceding chapters ; but Mr. Haidinger, of Vienna, has recently discovered a very singular pro- perty of the eye, by which it can determine, without any instrumental assistance, the direction of the plane of polarisation. When we look intently upon polarised light, such as that seen by reflexion or refraction, in the pencils produced by double refraction, or in the blue light of the sky, where there is much polarised light, we may 3 246 A TREATISE ON OPTICS. PART II. perceive at the place of distinct vision two bushels (houppes, aigrettes) brushes or sectors of yellow light. These brushes or sectors are shown at A B, and their Fig. 1 1 7. line of direction, A B, marks exactly the position of the plane of polarisation. These yellow sectors are accompanied with bluish or violet spaces at C and D, which some- times unite and separate A from B, but more frequently A and B are not thus separated. The light of these sectors is so very faint that it is difficult to see them at all, and many observers with good eyes have not succeeded in witnessing this in- teresting phenomenon. I tried it in vain for more than a year, though I have now no difficulty in seeing both the yellow and the blue sectors, the blue sectors being perpendicular to the plane of polarisation, and as much a part of the phe- nomenon as the yellow ones. The four sectors of coloured light thus seen by the eye, at the extremity of its optical axis, has always appeared to me analogous to the sectors of circular crystals, crossed by a film that depolarised a tint which, when added and subtracted from that of the crystal, produced yellow and blue light. The angular magnitude of these four sectors does not seem to have been observed by Mr. Haidinger. Owing to the exceeding faintness of their light, it is difficult to make the observation with accuracy ; but when the sectors were most distinct, I found that they subtended an angle not exceeding 4 or 4J . This simple phenomenon has excited much interest in the scientific world, and various attempts have been made to explain it. It no doubt depends upon the structure of the eye ; and though we do not venture to give a correct theory of the phenomenon, we may men- tion the general principles upon which a sound theory must rest. The explanations hitherto published are two-fold. In the one, the yellow and blue sectors are CHAP. xxvu. ML. HAIDINGEB'S BRUSHES. 247 supposed to be produced by depolarising films giving a yellow tint, which is subsequently analysed by a polar- ising structure within the eye. In the other explana- tion, the yellow light is supposed to be the colour of light polarised by transmission, and the blue to be the result merely of contrast. This explanation has been given by M. Jamin * upon two principles which I had established long ago. 1. In my paper on the Law of the Tangents t, I have shown, by experiment as well as by theory, that the light of a white ray is bluish when reflected at the maximum polarising angle, and that of the trans- mitted ray yellowish a result which the Abbe Moigno has by mistake ascribed to Sir John HerscheLj 2. In 1840 I described the phenomenon of the cylindrical polarisation of light, as produced by a number of concave films of decomposed glass, similar to a number of watch-glasses. When light vertically polarised passes through such a combination, there will be something like a horizontal dark band, or two ob- scure horizontal bushels or sectors, and consequently two vertical ones, not dark, but yellowish, on the prin- ciple already mentioned. When an analysing plate or rhomb of spar is used, the vertical luminous sectors vanish, and the pencil of light exhibits a distinct black cross, exactly similar to that produced in cir- cular crystals, and shown in fig. 119. The two vertical masses of yellow light seen without the analysing prism, are, according to M. Jamin's explanation, the yellow bushels ofMr.Haidinger, and the blue sectors C,D, are the obscure sectors made blue only by contrast. This explanation does not appear to me to be well- founded. The spherical surfaces of the cornea of the crystalline lens would not produce such distinct sectors * Comptes Rendus, torn. xxvi. p. 197. t Phil. Trans. 1815, p. 151. Prop. 24 and 25. \ Repertoire tfOptique Moderne, torn. iv. pp. 1335. 1344, Reports of Brit. Association, 1840, p. 6. R 4 248 A TREATISE ON OPTICS. PART II. as those described by Mr. Haidinger, and which I have seen, and the colour would be much less yellow, and yellow, too, of a different tint from that which is actually observed. Still less could the sectors be produced by the cornea alone, as M. Jamin thinks they could, in order to explain the fact that the yellow sectors are seen by persons who have no crystalline lens. If the yellow light is not the result of a depolarising film, we would suggest another source from which it may be derived. I have shown that light transmitted through the separating surfaces of transparent bodies of different dispersive powers must have a yellow tinge *, and therefore the yellow colour of the sectors may be derived either from this cause alone, or from this cause combined with the one already mentioned. The small angular magnitude of the sectors is another objection to M. Jamin's explanation, because if they are produced by the whole pencil passing through the cornea and the pupil, their size ought to be much 4 larger, and at such a small distance as 2= or 2 3 41 -~ from the optical axis, the crossing of the yellow 2 and blue sectors could not possibly be seen. I am, therefore, of opinion that we must refer the phenomenon to some cause connected with the foramen centrale of the retina, which, as will be seen in a future chapter, shows itself by peculiar optical phenomena ; and that the yellow and blue sectors are the colours of a depolar- ising film or films, subsequently analysed by a structure which will place the sectors in the plane of polarisation, and not inclined 45 to it. If the explanation of M. Jamin is correct, the sec- tors should be seen by oblique or indirect vision, be- cause the two obscure horizontal sectors produced by the cornea would be painted on the retina by an oblique pencil of polarised light. But as the middle point of * See Phil. Trans. 1829, p. 189. ; and Edin. Trans, vol. xvi., 1846, p. 129. CHAP. XXVIII. RINGS IN CRYSTALS WITH ONE AXIS. 249 the sectors is always at the extremity of the optical axis, and therefore its picture formed in the centre of the foramen centrale ; and as the sectors are limited by the size of the foramen, we are compelled to reject every explanation which does not connect the phe- nomenon with that remarkable opening in the retina. We therefore despair of discovering the origin of the sectors till some new light is thrown upon the structure of that part of the eye, or of the choroid and other membranes behind it. CHAP. XXVIII. ON THE SYSTEM OF COLOURED RINGS IN CRYSTALS WITH ONE AXIS. (114.) IN all the preceding experiments the film C E D F must be held at such a distance from the eye, or from the plate B, that its surface may be distinctly seen, and in the apparatus used by different philosophers this dis- tance was considerable. In the year 1813, I adopted another method, namely, that of bringing the film or crystal to be examined as close to the eye as possible, a very small plate, B, not above one fourth of an inch, being interposed, asin^gr. 112., between the crystal and the eye, to reflect the light transmitted through the crystal. By this means I discovered the systems of rings formed along the axes of crystals with one and two axes, which form the most splendid phenomena in optical science, and which by their analysis have led philosophers to the most important discoveries. I discovered them in ruby, emerald, topaz, ice, nitre, and a great variety of other bodies, and Dr. Wollaston afterwards observed them in Iceland spar. In order to observe the system of rings round a single axis of double refraction, grind down the summits or 250 A TREATISE ON OPTICS. Fig. 118. obtuse angles A X of a rhomb of Iceland spar, fig. 90. 9 and replace them by plane and polished surfaces per- pendicular to the axis of double refraction A X. But as this is not an easy opera- tion without the aid of a lapi- dary, I have adopted the fol- lowing method, which enables us to transmit light along the axis A X without injuring the rhomb. Let C D E F, fig. 118., be the principal section of the rhomb; cement upon its surfaces C D, F E, with Canada balsam, two prisms, D L K, F G H, having the angles L D K, G F H, each equal to about 45 ; and by letting fall a ray of light perpen- dicularly upon the face D L, it will pass along the axis A X, and emerge perpendicularly through the face F G. Let the rhomb thus prepared be held in the polarised beam r s, fig. 112., so that r s may pass along the axis A X, and let it be held as near the plate B as possible. When the eye is held very near to B, and looks along O s as it were through the reflected image of the rhomb C E, it will perceive along its axis A X a splen- did system of coloured rings resembling that shown in fig. 119.j intersected by a rectangular black cross, CHAP. XXVIII. RINGS IN CRYSTALS WITH ONE AXIS. 251 A B C D, the arms of which meet at the centre of the rings. The colours in these rings are exactly the same as those in Newton's Table of colours, and con- sequently the same as the system of rings seen by re- flexion from the plate of air between the object glasses. If we turn the rhomb round its axis, the rings will suffer no change ; but if we fix the rhomb, or hold it steadily, and turn round the plate B, then, in the azi- muths 0, 90 180, and 2?0 of its revolution, we shall see the same system of rings ; but at the inter- mediate azimuths of 45, 135, 225, and 315, we shall see another system, like that in fig. 120., in which all the colours are complementary to those in fig. 11 9-> being the same as those seen in the rings formed by Fig. 120. transmission through the plate of air. The superposi- tion of these two systems of rings would reproduce white light. If, in place of the glass plate B, we substitute a prism of calcareous spar, that separates its two images widely, or a rhomb of great thickness, we shall see in the or- dinary image the first system of rings, and in the extra- ordinary image the second system of complementary rings, when the principal section of the prism or rhomb is in the plane r s O as formerly described. As the light which forms the first system of rings is polarised in an opposite plane to that which forms the second system, we may disperse the one system by 252 A TREATISE ON OPTICS. PART II. agate, or absorb it by tourmaline, and thus render the other visible, the first or the second system being dis- persed or absorbed according to the position of the agate or the tourmaline. If we split the rhomb of calcareous spar.^r. 1 1 8., into two plates by the fissure M N, and examine the rings produced by each plate separately, we shall find that the rings produced by each plate are larger in diameter than those produced by the whole rhomb, and that the rings increase in size as the thickness of the plate diminishes. It will also be found that the circular area contained within any one ring is to the circular area of any other ring, as the number in Newton's Table corresponding to the tint of the one ring is to the number corresponding to the tint of the other. If we use homogeneous light, we shall find that the rings are smallest in violet light and largest in red light, and of intermediate sizes in the intermediate colours, consisting always of rings of the colour of the light em- ployed, separated by black rings. In white light all the rings formed by the seven different colours are com- bined, and constitute the coloured system above de- scribed, according to the principles which were fully explained in Chapter XIII. (127.) All the other crystals which have one axis of double refraction, give a similar system of rings along their axis of double refraction ; but those produced by the positive crystals, such as zircon, ice, &c., though to the eye they differ in no respect from those of the nega- tive crystals, yet they possess different properties. If we take a system of rings formed by ice or zircon, and com- bine it with a system of rings of the very same diameter as formed by Iceland spar, we shall find that the two systems destroy one another, the one being negative and the other positive ; an effect which might have been ex- pected from the opposite kinds of double refraction pos- sessed by these two crystals. If we combine two plates of negative crystals, such as Iceland spar and Beryl, the system of rings which CHAP. XXVIII. RINGS IN CRYSTALS WITH ONE AXIS. 253 they produce will be such as would be formed by two plates of Iceland spar, one of which is the plate em- ployed, and the other a plate which gives rings of the same size as the plate of Beryl. But if we combine a plate of a negative crystal with a plate of a positive crystal, such as one of Iceland spar with one of Zircon or ice, the resulting system of rings, in place of arising from the sum of their separate actions, will arise from their difference ; that is, it will be equal to the system produced by a plate of Iceland spar whose thickness is equal to the difference of the thicknesses of the plate of Iceland spar employed, and another plate of Iceland spar that would give rings of the same size as those produced by the zircon or ice. These experiments of combining rings are not easily made, unless we employ crystals which have natural faces perpendicular to the axis of double refraction, such as the variety of Iceland spar called Spath Calcaire basee, some of the Micas with one axis, and well crystallised plates of ice, &c. When two such plates cannot be obtained, I have adjusted the axes of the two plates so as to coincide, by placing between them, at their edges, two or three small pieces of soft wax, by pressing which in different directions, we may produce a sufficiently accurate coincidence of the systems of rings to establish the preceding conclusions. If, when two systems of rings are thus combined, either both negative or both positive, or the one negative and the other positive, we interpose between the plates which produce them crystallised films of Sulphate of Lime or mica, we shall produce the most beautiful changes in the form and character of the rings. This experiment I found to be particularly successful when the film was placed between two plates of the Spath Calcaire basee of the same thickness, and taken from the same crystal. By fixing them permanently with their faces parallel, and leaving a sufficient interval between them for the intro- duction of films of crystals, I had an apparatus by which the most splendid phenomena were produced. The 254 A TREATISE ON OPTICS. PART II. rings were no longer symmetrical round their axis, but exhibited the most beautiful variety of forms during the rotation of the combined plates, all of which are easily deducible from the general laws of double refraction and polarisation. This artificial combination was suggested to me by examining the system of rings produced by specimens of calcareous spar intersected with one or more hemi- trope films of the same substances. The uniaxal system of rings thus produced is shown in figures 121, 122, 123, and 124. The system shown in fig. 122. with Fig. 121. Fig. 122. CHAP. XXVIII. RINGS IN CRYSTALS WITH ONE AXIS. 255 Fig. 123. eight dark radii had a complementary system, in which the inner circle was marked with eight dark spots, cor- responding to the eight luminous sections in fig. 122. These rings undergo beautiful transformations by the motion of the crystal when the analyser is stationary, and by the motion of the analyser when the crystal is stationary. A rhomb of spar, which gave in one part the rings above referred to, exhibited a singular effect in another part where the crystallisation appeared regular, and where Fig. 124. 256 A TREATISE ON OPTICS. PART H. there were no hemitrope films. In one position the crys- tal gave the regular system of rings, as shown in^. 119.; but upon turning it round 45 all the rings became ellip- tical, as shown in fig. 124., the first order of colours in one quadrant having joined the second order in the ad- jacent quadrant. The arms of the black cross took the position a b c, d ef } the continuations of it, viz. am, en, do, fp, being so faint as to show the continuity of the elliptical rings. The figures 1, 2, 3, 4, show the rings of the same order. I observed the very same phe- nomenon in another rhomb of calcareous spar perfectly free of veins, but the rings were less elliptical than in the above figure. The table of crystals that have negative double refrac- tion shows the bodies that have a negative system of rings ; and the table of positive crystals indicates those that have a positive system of rings. (128.) The following is the method which I have used for distinguishing whether any system of rings is positive or negative. Take a film of sulphate of lime, such as that shown at C E D F, fig. 112., and mark upon its surface the lines or neutral axes C D, E F as nearly as may be. Fix this film by a little wax on the surface L D or F G, fig. 118, of the rhomb which produces the negative system of rings. If the film produces alone the red of the second order, it will now, when combined with the rhomb, obliterate part of the red ring of the second order, either in the two quadrants, AC, B D, fig. 119., or in the other two, AD, C B. Let it oblite- rate the red in A C, B D ; then if the line C D of the film crosses these two quadrants at right angles to the rings, it will be the principal axis of the sulphate of lime ; but if it crosses the other two quadrants, then the line E F, which crosses the quadrants A C, B D, will be the principal axis of sulphate of lime, and it should be marked as such. We shall suppose, however, that C D has been proved to be the principal axis. Then, if we wish to examine whether any other system of rings is positive or negative, we have only to cross CHAP. XXVIII. RINGS IN CRYSTALS WITH ONE AXIS. 25? the rings with the axis C D, by interposing the film : and if it obliterates the red ring of the second order in the quadrant which it crosses, the system will be nega- tive ; but if it obliterates the same ring in the other two quadrants which it does not cross, then the system will be positive. It is of no consequence what qolour the film polarises, as it will always obliterate the tint of the same order in the system of rings under examination. Other methods of distinguishing positive and negative crystals by the influence of heat and pressure will be explained in a subsequent chapter. (129.) In order to explain the formation of the sys- tems of rings seen along the axis of crystals, we must consider the two causes on which they depend ; namely, the thickness of the crystal through which the polarised light passes, and the inclination of the polarised light to the axis of double refraction or the axis of the rings. We have already shown how the tint or colour varies with the thickness of the crystallised body, and how, when we know the colour for one thickness, we may determine it for all other thicknesses, the inclination of the ray to the axis remaining always the same. We have now, there- fore, only to consider the effect of inclination to the axis. It is obvious that along the axis of the crystal, where the two black lines AB, CD, fig. 1 19? cross each other, there is neither double refraction nor colour. When the polar- ised ray is slightly inclined to the axis, a faint tint appears, like the blue in the first order of Newton's Scale ; and as the inclination gradually increases, all the colours in New- ton's Table are produced in succession, from the very black of the first order up to the reddish white of the seventh order. Here, then, it appears that an increase in the inclination of the polarised light to the axis corresponds to an increase of thickness ; so that if the light always passed through the same thickness of the mineral, the different colours of the scale would be produced by dif- ference of inclination alone. Now, it is found by ex- periment, that in the same thickness of the mineral, the 5258 A TREATISE otf OPTICS. PART II. numerical value of the tints, or the numbers opposite to the tints in the last column of Newton's Table, vary as the square of the sine of the inclination of the polarised ray to the axis. Hence it follows, that at equal inclina- tions the same tint will be produced ; and consequently, the similar tints will be at equal distances from the axis of the rings, or the lines of equal tint or rings will be circles whose centre is in the axis. Let us suppose that at an inclination of 30 to the axis we observe the blue of the second order, the numerical value of whose tint is 9 in Newton's Table, and that we wish to know the tint which would be produced at an inclination of 45. The sine of 30 is '500, and its square '2500. The sine of 45 is *7071> and its square '5000. Then we say, as -2500 is to 9, so is -500 to 18, which in the Table is the numerical value of the red of the third order. If we suppose the thickness of the mineral to be increased at the inclinations 30 and 45, then the numerical value of the tint would increase in the same proportion. It is obvious from what has been said, that the polar- ising force, or that which produces the rings, vanishes when the double refraction vanishes, and increases and diminishes with the double refraction, and according to the same law. The polarising force, therefore, depends on the force of double refraction ; and we accordingly find that crystals with high double refraction have the power of producing the same tint, either at much less thicknesses, or at much less inclinations to the axis. In order to compare the polarising intensities of different crystals, the best way is to compare the tints which they produce at right angles to the axis where the force of double refraction and polarisation is a maximum, and with a given thickness of the mineral. Thus, in the case given above, we may find the tint at right angles to the axis, by taking the square of the sine of 90, which is 1 ; so that we have the following proportion : as -2500 is to 9? so is 1 to 36, the value of the maximum tint of calcareous spar at right angles to the axis, upon the sup- position that a tint of the value of 9 was produced at an CHAP. XXIX. RINGS IN CRYSTALS WITH ONE AXIS. 259 inclination of 30. If we have measured the thickness of Iceland spar at which the tint 9 was produced, we are prepared to compare the polarising intensity of Iceland spar with that of any other mineral. Thus, let us take a plate of quartz, and let us suppose that at an inclina- tion of 30, and with a thickness 5 1 times as great as that of the plate of Iceland spar, it produces a yellow of the fii^t order, whose value is about 4. Then to find the tint at 90, or at right angles to the axis, we say, as the square of the sine of 30, or *2500, is to 4, so is the square of the sine of 90, or 1, to 1 6, the tint at 90, or the green of the third order. Now the polarising power or intensity of the Iceland spar would have heen to that of the quartz as 36 to 16, or 2 times greater, if the thickness of the two minerals had been the same ; but as the thickness of the quartz was 51 times as great as that of the Iceland spar, the polarising intensity of the Iceland spar will be 51 multiplied by 2 or 115 times greater than that of quartz. The intensities for various crystals have been determined by several ob- servers, but the following have been given by Sir John Herschel : Polarising Intensities of a few Crystals with One Axis. Value of highest Tint. Thicknesses that produce the same Tint. Iceland spar 35801 0-000028 Hydrate of strontia 1246 0-000802 Tourmaline 851 0-C01175 Hyposulphate of lime - 470 0-002129 Quartz 312 0-003024 Apophyllite, 1st variety 109 0-009150 Camphor 101 0-009856 Vesuvian 41 0-024170 Apophyllite, 2d variety 33 0-030374 3 0-366620 y The above measures are suited to yellow light, and the numbers in the second column show the proportions s 2 260 A TREATISE ON OPTICS. PART II. of the thicknesses of the different substances that pro- duce the same tint. The polarising force of Iceland spar is so enormous at right angles to the axis, that it is very difficult to prepare a film of it sufficiently thin to exhibit the colours in Newton's Table. CHAP. XXIX. ON THE SYSTEMS OF COLOURED RINGS IN CRYSTALS WITH TWO AXES. (130.) IT was long believed that all crystals had only one axis of double refraction ; but, after I discovered the double system of rings in topaz and other minerals, I found that these minerals had two axes of double re- fraction as well as of polarisation, and that the possession of two axes characterised the great body of crystals which are either formed by art, or which occur in the mineral kingdom. The double system of rings, or rather one of the sets of the double system of rings in topaz, first presented itself to me when I was looking along the axis of topaz, which reflected a part of the light of the sky that happened to be polarised, so that they were seen without the aid either of a polarising or an analysing plate. In this and some other minerals, however, the axes of double refraction are so much inclined to one another, that we cannot see the two systems of rings at once. I shall therefore proceed to explain them as exhibited by Nitre, in which I also discovered them and examined many of their properties. Nitre, or saltpetre, is an artificial substance which crystallises in six-sided prisms with angles of about 120. It belongs to the prismatic system of Mobs, and has therefore two axes of double refraction along which a ray of light is not divided into two. These axes are each inclined about 2^ to the axis of the prism, CHAP. XXIX. RINGS IN CRYSTALS WITH TWO AXES. 26 1 Fig. 125. Fig. 126. and 5 to each other. If we therefore cut off a piece from a prism of nitre with a knife driven by a smart blow of a hammer, and polish two flat surfaces perpendi- cular to the axis of the prism,, so as to leave a thickness of the sixth or eighth of an inch,, and then transmit the polarised light rs, fig.11%., along the axis of the prism, keeping the crystal as near to the plate B as possible on one side, and the eye as near it as possible on the other, we shall see the double system of rings, A B, shown in fig. 125., when the plane passing through the two axes of the nitre is in the plane of primitive polarisation, or in the plane of reflexion r s O, fig. 112., and the system shown in fig. 1 26. when the same plane is in- clined 45 to either of these planes. In passing from the state of fig. 125. to that of fig. 126., the black lines assume the forms shown in fig. 127. and 128. These systems of rings have, generally speaking, the same colours as those of thin plates, or as those of the s 3 262 A TREATISE ON OPTICS. PART II. Fig. 127. Fig. 128. systems of rings round one axis. The orders of colours commence at the centres A and B of each system ; but at a certain distance, which in fig. 125. corresponds to the sixth ring, the rings, in place of returning and encircling each pole A and B, encircle the two poles as an ellipse does its two foci. When we diminish the thickness of the plate of nitre, the rings enlarge ; the fifth ring will then surround both poles. At a less thickness, the fourth ring will sur- round them, till at last all the rings will surround both poles, and the system will have a great resemblance to the system surrounding one axis. The place of the poles A, B never changes, but the black lines A B, C D become broad and indefinite; and the whole system is distinguished from the single system principally by the oval appearance of the rings. If we increase the thickness of the nitre, the rings will diminish in size ; the colours will lose their re- semblance to those of Newton's Scale ; and the tints do not commence at the poles A, B, but at virtual poles in their proximity. The colour of the rings within the two poles are red, and without them blue ; and the great body of the rings are pink and green. CHAP. XXIX. KINGS IN CRYSTALS WITH TWO AXES. 263 As the same colour exists in every part of the same curve, the curves have heen called isochromatic lines, or lines of equal tint. The lines or axes along which there is no double refraction or polarisation, and whose poles are A, B, fig. 125., have been called optical axes, or axes of no polarisation, or axes of compensation, or resultant axes ; because they have been found not to be real axes, but lines along which the opposite actions of other two real axes have been compensated, or destroy one another. (131.) In various crystallised bodies, such as nitre and arragonite, where the inclination of the resultant axes A, ft, fig. 125., is small, the two systems of rings may be easily seen at the same time ; but when the inclina- tion of the resultant axes is great, as in topaz, sulphate of iron, &c., we can only see one of the systems of rings, which may be done most advantageously by grinding and polishing two parallel faces perpendicular to the axis of the rings. In mica and topaz, and various other * crystals, the plane of most eminent cleavage is equally inclined to the two resultant axes ; so that in such bodies the systems of rings may be readily found and easily exhibited. Let M N, for example,^/. 129j be a plate of topaz, cut or split so as to have its face perpendicular to the axis of the prism in which this body crystallises. If we place this plate, fig. 129-, in the apparatus /#. 112., so that the polarised ray r s,fig. 112., passes along the line AB e E, fig. 129-, and if the eye receives this ray when reflected from the analysing plate B, it will see in Fig. 129. s 4 264 A TREATISE ON OPTICS. the direction of that ray a system of oval rings, like that Fig. 130. fid- 130. In like manner, if the polarised light is transmitted along the line C B d D, the eye will see another system perfectly similar to the first. The lines A B e E and C B d D are, therefore, the i resultant axes of topaz. The angle ABC will be found equal | to about 121 16' ; but if we I compute the inclination of the refracted rays B d, B e, we shall find it, or the angle d B e, to be only 65; which is, therefore, the inclination of the optical or result" ing axes of topaz. If we suppose the plate of nitre fixed in any of the positions which give any of the rings shown in fig. 125, 126, 127, or 128, then, if we turn round the plate B," we shall observe in the azimuths of 90 and 270 a system of rings complementary to each, in which the black cross in fig. 125. and the black hyperbolic curves in fig. 126. 128. are white, all the other dark parts light, and the red green, the green red, &c. as in the single system of rings with one axis. In the preceding observations we have supposed the polarisation of the incident light, and the analysis of the transmitted light, to be necessary to the production of the rings ; but in certain cases they may be shown by common light with the analysing plates, or by po- larised light without the analysing plate B, and in some cases without either the light being polarised or analysed. If in topaz, for example, fig. 129-, we allow common light to fall in the direction A B, so as to be refracted along B e, one of the resultant axes, and sub- sequently reflected at e from the second surface, and reaching the eye at c, we shall see, after reflection from the analysing plate, the system of rings in fig. 130. ; or if A B is polarised light, the rings will be seen by the CHAP. XXIX. RINGS IN CRYSTALS WITH TWO AXES. 265 eye at c without an analysing plate. There are several other curious phenomena seen under these circum- stances, which I have described in the Phil. Transactions for 1814, p. 203. 211. I have found some crystals of nitre which exhibit their rings without the use either of polarised light or an analysing plate ; and Sir John Herschel has found the same property in some crystals of carbonate of potash. (132.) When the preceding phenomena are seen by polarised homogeneous light, in place of white light, the rings are bright curves, separated by dark intervals ; the curves having always the colour of the light employed. In many crystals the difference in the size of the rings seen in different colours is not very great, and the poles A, B of the two systems do not greatly change their place; but Sir John Herschel found that there were crystals, such as tartrate of potash and soda, in which the variation in the size of the rings was enormous, being greatest in red, and least in violet light, and in which the distance AB,fig. 125, 126., or the inclination of the resultant axes varied from 56 in violet light to 76 in red, the inclination having intermediate values for intermediate colours, and the centres of all the dif- ferent systems lying in the line A B. When all these systems of rings are combined, as they are in using white light, the system of rings which they form is ex- ceedingly irregular, the two oval centres, or the halves of the first order of colours, being drawn out with long spectra or tails of red, green, and violet light, and the ends of all the other rings being red without the re- sultant axes, and blue within. Sir John Herschel found other crystals in which the rings are smallest in red, and largest in blue light, and in which the inclination of the axes or A B is least in red, and greatest in violet light. In all crystals of this kind, the deviation of the tints, or the colours of the rings seen in white light, from Newton's Tables is very considerable, and may be cal- 266 A TREATISE ON OPTICS. PART II. culated from the preceding principles. This deviation I found to be very great, even in crystals with one axis of double refraction and one system of rings, such as Apophyllite where the rings have scarcely any other tints than a succession of greenish yellow, and reddish purple ones. By viewing these rings in homogeneous light, Sir John Herschel has found that the system is a nega- tive one for the rays at the one end of the spectrum, a positive one for the rays at the other end of the spec- trum, and that there are no rings at all in yellow light. A similar and equally curious anomaly I have found in Glauberite, which is a crystal which has two axes of double refraction, or two systems of rings for red light, and one negative system for violet light. (133.) All the singularities of these phenomena dis- appear, and may be rigorously calculated by supposing the resultant axes of crystals when there are two, or the single axis when there is one, with a system of rings deviating from Newton's Scale as merely apparent axes, or axes of compensation, produced by the opposite action of two or more rectangular axes, the principal one of which is the line bisecting the angle formed by the two resultant axes. Upon this principle, I have shown that all the phenomena presented by such crystals may be computed with as much accuracy as we can compute the motions of the heavenly bodies. The method of doing this may be understood from the following observations. Let A C B D, fig. 1 3 1 ., be a crystal with two axes turned into a sphere. Let P, P be Fig. 131. the poles of axes, O the point bisect- ing them, and AB a line passing through O, and perpendicular to C D, a line passing through P, P. Let us suppose an axis to pass through O, perpendicular to the plane A C B D, then we may ac- count for all the phenomena of such crystals, by supposing the axis at O to be the principal one and the other CHAP. XXIX. RINGS IN CRYSTALS WITH TWO AXES. 26? axis to be along either of the diameters A B or C D. If we take C D, then the axis O and C D must be both of the same name, either both positive or both negative; but if we take A B, the axes must be one positive and the other negative ; or, what is perhaps the simplest supposition for illustration, we shall suppose the two rectangular axes which produce all the phenomena to be A B, C D, either both positive or both negative, leaving out the one at O. Supposing A OB, C PPD to be projections of great circles of the sphere, then P, P are the points where the axis A B destroys the effect of the axis CD; that is, where the tints produced by each axis must be equal and opposite. Now, if we suppose the arch C P to be 60, then, since A P is 90, it follows that the axis C D produces at 60 the same tint that A B does at 90, and consequently the polarising intensity of C D will be to that of A B as the square of the sine of 90 is to the square of the sine of 6'0, or as 1 to 0*75, or as 100 to 75. The polarising force of each axis being thus determined, it is easy to find the tint which will be produced by each axis separately at any given inclination to the axis, by the method formerly explained. Let E be any point on the surface of the sphere, and let the tints produced at that point be 9, or the blue of the second order, by C D, and 16, or the green of the third order, by A B. Let the inclination of the planes passing through A E, C E, or the spherical angle CEA be determined, then the tint at the point E will correspond to the diagonal of a parallelogram whose sides are 9 and 16, and whose angle is double the angle C E A.* This law, which is general, and applies also to double refraction, has been confirmed by Biot and Fresnel, the last of whom has proved that it coincides rigorously with the law deduced from the theory of waves. If the axes A B, C D are equal, it follows that they will produce the same tint at equal inclinations; that is, they will compensate each other only at one point, viz. O, and will produce round O a system of coloured rings, * See Phil. Trans. 1818, p. 199. 268 A TREATISE ON OPTICS. PART II. the very same as if O were a single axis of double re- fraction of an opposite name to A B, C D. If the axis A B has exactly the same proportional action that C D has upon each of the differently coloured rays_, a com- pensation will take place for each colour exactly at O, the centre of the resultant systems of rings, and the colours will be exactly those of Newton's Scale. But if each axis exercises a different proportional action upon the coloured rays, a compensation will take place at O for some of the rays (for violet, for example), while the compensation for red will take place on each side of O ; consequently, in such a case the crystal will have one axis for violet light and two axes for red light, like Glauberite. The phenomena of Apophyllite may, in a similar manner, be explained by two equal negative axes, A B, CD, and a positive axis at O. According to this method of combining the action of different rectangular axes, it follows that three equal and rectangular axes, either all positive or all negative, will destroy one another at every point of the sphere, and thus produce the very same effect as if the crystal had no double refraction and polarisation at all. Upon this prin- ciple I have explained the absence of double refraction in all the crystals which form the tessular system of Mohs, each of the primitive forms of which has ac- tually three similarly situated and rectangular axes. If one of these axes is not precisely equal to the other, and the crystallisation not perfectly uniform, traces of double refraction will appear, which is found to be the case in muriate of soda, diamond, and other bodies of this class. (134.) The following table contains the polarising intensities of some crystals with two axes, as given by Sir John Herschel : CHAP. XXX. ON CIRCULAR CRYSTALS. 269 Polarising Intensities of some Crystals with Two Axes, Value of highest Tint. Thicknesses that pro- duce the same Tint. Nitre 740Q 0-000135 Anhydrite, inclination of axes 43 48' 1900 0-000526 Mica, inclination of axes 45 1307 0-000765 Sulphate of barytes - Heulandite (colourless), inclination 7 of axes 540 17 - - -j 521 249 0-001920 0-004021 CHAP. XXX. ON CIRCULAR CRYSTALS. (135.) IN a paper on the Depolarisation of Light, pub- lished in the Philosophical Transactions for 1 8 1 5, 1 have described some remarkable phenomena produced by cir- cular crystals in Oil of Mace, in a mixture of Rosin and Oil of Mace, and also in Tallow. When we look at a bright and small light through Oil of Mace properly melted and cooled between two plates of glass, we observe with the naked eye generally one, but sometimes two halos. When the light is polar- ised in a plane A B, and subsequently analysed, the halo is divided into four luminous sectors, 1, 3, 5, 7> fig. 132., separated by a black cross, which has the appear- ance of four obscure sectors, 2, 4, 6, 8, the position of 2?0 A TREATISE ON OPTICS. PART II. the analyser being such as not to transmit the bright image at m. In the opposite position of the analyser, the sectors appear as in fig. 133., the luminous ones at 9, 11, 13, and 15, arid the dark ones at 10, 12, 14, and 16, the bright image being visible at w. In this last position the sectors 9, 13, were more luminous than 11, 15. In some cases the circular space enclosing the sectors was very small, and in others large, and fre- quently, when two halos were produced, there were two sets of sectors separated by an interval equal to that between the halos. It is very obvious that the halos were produced by the particles or groups of particles of the oil of Mace, as explained in Chap. XV. ; and that the second or larger halo was owing to smaller particles existing among the larger ones. In order to explain the formation of the sectors, I inferred that each halo was composed of two, the one lying above the other, and having every alternate sector polarised in opposite planes ; in short, that these two halos were the two images formed by double refraction and oppositely polarised, as such images always are, and as shown in fig. 134. But though Fig. 134. this is undoubtedly the case, I could not see with the microscope the actual form of the particles or groups of particles by which the double refraction and polarisa- tion were produced. In repeating these experiments, and adopting dif- ferent methods of cooling the Oil of Mace under pres- I soon discovered with the microscope, and the CHAP. XXX. ON CIRCULAR CRYSTALS. 2?1 aid of polarising films, when the microscope could not detect the structure, that the phenomena above described were produced by circular crystals varying from in- visibility to the 200th or 300th of an inch, and ex- hibiting very beautiful phenomena when examined with polarised light. In the year 1836 Mr. Talbot described, for the first time, a method of obtaining Circular Crystals of great beauty, by dissolving a crystal of Borax in a drop of Phosphoric Acid. When the solution crystallises pro- perly, and is placed in the polarising microscope, when the field is black, the little circular spots or discs which are seen by common light 15, 21, 27, &c. reflexions at 69 12', and restored to common polarised light at 6, 12, 18, and 24 reflexions at the same angle; and it will be circularly polarised by 12, 20, 28, 36, &c. re- flexions at 74 42', and be restored to common polarised light by 8, 16, 24, 32, &c. reflexions. I have found that circular polarisation can be produced by 21, 7^> 12^, &c. reflexions, or any other number which is a multiple of 2 1 ; for though we cannot see the ray in the middle of a reflexion, yet we can show it when it is restored to a single plane of polarisation, at 5, 10, 15 reflexions.* When we use homogeneous light, we find that the angle at which circular polarisa- tion is produced is different for the differently coloured rays ; and hence these different rays cannot be restored to a single plane of polarisation at the same angle of reflexion. Complementary colours will therefore be produced, such as I described long ago, and which, I believe, have not been observed by any other person.f These colours are essentially different from those of * See Phil. Transactions, 1830, p. 30K f Z&- 1830 p. 309. 325. CHAP. XXXV. ON CIRCULAR POLARISATION. 2Q5 common polarised light, and will be understood when we come to explain those of elliptical polarisation. (144.) Notwithstanding the importance of those dis- coveries by which Fresnel accounted for the colours of cir- cular polarisation in quartz, no attempt was made to ex- plain how this property belonged only to the rays which passed near the axis of the crystal, or to connect the phenomena of circular with those of plane polarisation in directions inclined to the axis. Mr. Airy naturally conceived, that there must be some connecting link be- tween these two kinds of polarisation, and, by combining experiment with theory, he succeeded in discovering it. In place of the two rays in quartz consisting of plane polarised light, as had been believed, Mr. Airy has shown that they both consist of light elliptically polar- ised, the greater axis of the ellipse for one ray being in the principal plane of the crystal, and the greater axis of the other perpendicular to that plane. One of the rays he found to be right-handed elliptically polarised, and the other left-handed elliptically polarised. In an interesting Memoir on the Polarisation of Quartz, M. Jamin has determined the ratio of the axes in each of the ellipses which correspond to the two refracted rays. Angle formed with the Axis. Ratio of the Axes. 1 1OOO 2 5 17' 9 15 15 28 19 42 0-939 0-641 0-309 0-125 0-087 24 30 0-052 The difference of velocity of the two elliptical rays is proportional to the thickness of the plate of quartz. It is represented by the law of Huyghens, when the incident ray has a greater inclination to the axis than 30, but at incidences from to 30 it follows a dif- ferent law. The following are the results obtained by M. Jamin, the difference of velocity in a plate 1 296 A TREATISE ON OPTICS. PART II millimetre ( ^th of an inch) thick being expressed in parts of an undulation. Angle formed with the Axes. Difference of Velocity. 0-120 5 26' 0-135 11 - - - - - 0273 15 33 0-490 20 27 0-219 25 17 1-231 SO 26 1-774 35 3 2-287 M. Cauchy, in applying his theory of double refrac- tion to quartz, has reproduced all the results obtained by Jamin, with a degree of accuracy which can leave no doubt of the soundness of the theory. (144.) The singular system of Spiral Rings shown in Jig. 149. was discovered by Mr. Airy. Having taken two plates of quartz equally thick, the one cut from a right- handed, and the other from a left-handed crystal, and placed them together, he put them between a polarising plate and an analysing plate of unsilvered glass, and ob- Fig. 149. CHAP. XXXV. CIRCULAR POLARISATION IX FLUIDS. 2p7 served the rings in the figure. Four spirals (proceeding from a black cross in the centre, which is inclined to the plane of reflexion) cut a series of circles at every qua- drant, the points of intersection being in the plane of reflexion and perpendicular to it, or, to adopt Mr. Airy's other description, that the form of the colours which graduate most gently, is alternately a spiral and circular arc, quadrant after quadrant. In the preceding experiment the left-handed plate was nearest to the polarising plate ; but when it was farthest from it, the spirals were turned in the opposite direction. The plates of quartz were O'l6 of an inch thick. The black brushes are in both cases at A, B, C, D, at a distance from the centre. M. Noremberg had also observed these spirals by placing a single plate of quartz upon a mirror, and looking into the plate from above to receive the rays that have passed twice through it. When the temperature of the two plates of quartz is greatly increased, the system of rings suffers certain changes which have not yet been carefully examined. M. Dubrunfaut found that the rotatory force of quartz was increased 1 50' by 70 Cent, of additional heat ; and he even succeeded by a spirit lamp in increa- sing it 12. Circular Polarisation in Fluids. (145.) The remarkable property of polarising light Circularly occurs in a feeble degree in certain fluids, in which it was discovered by M. Biot and Dr. Seebeck. Sir John Herschel found it in camphor in a solid state : I discovered it in certain specimens of unannealed glass, and Professor Dove in compressed glass. If we take a tube six or seven inches long, and fill it with oil of tur- pentine, and place it in the apparatus, /#. 112., so that polarised light transmitted through the oil may be reflected to the eye from the plate C, or analysed by a Nicols' prism or rhomb of calcareous spar, we shall 2Q8 A TREATISE ON OPTICS. PART II. observe the complementary colours and a distinct rota- tion of the plane of polarisation from right to left. Other fluids have the property of turning the planes of polarisation from left to right, as shown in the fol- lowing table, which contains the results of M. Biot's experiments. Substances which turn the Planes from Right to Left. Arc of Rotation Relative Thick- for every 25th nesses that pro- of an inch in duce the same Thickness. Effect. Rock crystal Oil of turpentine - Solution of 1753 parts of artificial cam-") phor in 17-359 of alcohol j 18 25' 16 1 1 68* Essential oil of laurel. turpentine. Substances which turn the Planes from Left to Right. Arc of Rotation for every 25th of an inch in Thickness. Relative Thick- nesses that pro- duce the same Effect. 18 2-V 26 33 38 4 * Essential oil of lemons - Concentrated syrup from sugar In this table the rotatory power of the fluids are given in comparison with that of Quartz. The fol- lowing table contains the results obtained by M. Biot from different kinds of sugar. Rotation from Left, to Right. Proportion of Sugar in 1 of the So- lution. Density. Rotation of Red Light in Thicknesses of 152 Milli- metres. Power of Rotation. Sugar of canes, syrup of 0-25 0-50 0-65 1-1052 1-2311 1-3114 23 28' 45") 52 7 30 V 70 11 15 ) 83 94 Sugar of milk 0-14 1-0537 10 21 40 70-18 starch * 0-65 1-2460 48 30 59-99 Crystallisable principle of honey - - - - 0-34 1-1329 16 47 30 43-32 Sugar of grapes - 59-10 CHAP. XXXV. CIRCULAR POLARISATION IN FLUIDS. 2^ Rotation from Right to Left. The rotation being observed for the yellow rays, and the thickness of solution 1 52 millimetres as before. Sugar of grapes in syrup - - - - 10 (V 0" Uncrystallisable principle of honey, alco- holic solution - - - - - 3 38 20 The same dry 11150 M. Biot obtained the following results with various vegetable juices, all of which gave a slight rotation from right to left. Thickness of Fluid. Rotation. Juice of grapes white 1 60 millimetres 6 Do. red and white mixed - 160 6-25 Chasselas - 160 5-50 Muscat - 160 5-33 Verjuice - 160 1-81 Chasselas of Fontainbleau - 160 8-00 Common black grape 160 10-00 Apples for cider > 3-33 Red gooseberries very ripe - 80 l'8l Berries of the service tree - 160 2 '5 One of the most curious discoveries contained in M. Biot's memoir is that of the powerful rotatory pro- perty of Dextrine, an uncrystallisable syrup which is found in the farina of rice, wheat, and even of ligneous tissue. It differs from gum in producing an opposite rotation, and from sugar in its superior power of rota- tion, which is almost triple of that which is exerted by sugar of canes. It surpasses all animal and vegetable substances at present known, at equal densities and thicknesses, in turning round the plane of a polarised ray, rock crystal only being superior to it. The name of dextrine has been given to it in order to mark the direction as well as the energy of its force of rotation.* * Dextrine is obtained from Starch by acids, potash or hot water by rupturing the envelope and liberating the Dextrine. 300 A TREATISE ON OPTICS. PART II. The rotatory polarisation of solutions of Sugar was found by M. Mitscherlich to be altered by heat. M. Du- brunfaut obtained the same result with Dextrine, Glu- cose, and the sugar of fruits, and he found that even the direction of the polarisation might be changed from left to right by a sufficient heat. Dextrine loses y^ths of its ordinary rotatory force by heat. (146.) When the polarisation is very weak, as in vege- table juices, it may be magnified by a very ingenious method proposed by M. Botzenhart, and founded on the law of the rotation of the plane of polarisation produced by refraction, which I established by direct experiment in 1829.* When a plane polarised ray is incident upon a refracting surface, either solid or fluid, the in- clination of its plane of polarisation to the plane of refraction is much greater than its original inclination to the plane of incidence. If, therefore, a polarised ray which has experienced from the action of a fluid a small rotation, is made to pass through one or more plates of glass, its initial rotation, thus greatly magnified, will be obtained from the formula which gives the deviation produced by the plates. When the rotation is 30', for example, and the angle of incidence 70, it will be magnified to 56' 4" by two plates of glass f> or nearly twice; by four plates of glass to 1 44' 46", or above thrice; \>y eight plates to 6 4' 40", or above twelve times. When the rotation is so small as 15', and the angle of incidence 70 as before, it will be magnified by four plates to 52 24', or three and a half times ; and by eight plates to 3 2' 50", or twelve times. A very interesting series of experiments on six of the vegetable alkalis has been made by M. Bouchardat. He found that all of them, Morphine, Narcotine, Strych- nine, Brucine, Cinchonine, and Quinine, dissolved in alcohol or ether, had or left-handed circular polarisa- * Phil. Trans. 1830, p. 136, and chap. XX. of this Treatise. See also Abbe Moigno's Repertoire d'Optique, $c., torn. iv. p. 1548. t The Index of Refraction of the glass being 1-500. CHAP. XXXV. ON CIRCULAR POLARISATION. 301 tion, excepting cinchonine, which had very great + cir- cular polarisation. The rotatory force was distinctly modified on all of them hut morphine by the interven- tion of acids. Upon Narcotine the influence of acids is enormous. In Sulphuric Ether and Alcohol its mole- cular rotatory force is 151'4. In Alcohol 100 and Chlorohydric acid 1, its force is -f 83. In Brucine acids dimmish, and Ammonia increases its circular polarisation. M. Bouchardat found that the molecular rotatory force of Camphoric Acid, which was -f 38*9> was greatly diminished by an alkali, and re-established by the addition of an excess of strong acid. On the Cryst allograph Structure which produces Circular Polarisation. (147.) The first step in this important inquiry was made by M. Biot, when he discovered that there were two kinds of Quartz, or Rock Crystal, one of which turned the planes of polarisation to the right and the other to the left. The next step, made by myself, was in ascertaining that this property did not belong to the ultimate atoms of Quartz, as M. Biot supposed, but was the result of struc- ture, because Quartz lost the property when melted. A very important addition was made to these facts by Sir John Herschel, when he discovered that the direction in which a crystal of Quartz turned the planes of polarisation was indicated, as already described *, by the plagiedral faces on that crystal. Another step was made when I discovered that Amethyst was composed of lamince Right and Left-handed Quartz, the rotatory force of the one destroying the equal rotatory force of the other, while in certain portions symmetrically placed in the crystal, each variety of Quartz exercised separately its full povjer of rotation. These last portions, shown at A, B, C, D, E, and F, in fig. 146., are so large in the specimen from which that figure was drawn, that a lapidary could have cut them out, and exhibited the plates A, C, and E as Right-handed Quartz, and B, D, and F as Left-handed * See page 293. 302 A TREATISE ON OPTICS. PART II. Quartz. Nay, it is quite certain, that if there had been a proper solvent for Amethyst , separate crystals of Right and Left-handed Quartz would have been obtained from the solution. We mention these facts because a suf- ficiently important place has not been assigned to them, either by M. Biot or M. Pasteur in their reports and memoirs on the analogous properties discovered by the latter in the Tartaric and Racemic acids and their de- rivative salts, which we shall now proceed to describe. The Tartaric Acid, and all the Tartrates dissolved in water, turn the planes of polarisation from left to right ; but the Tartrate of Lime, when dissolved in Chlorohydric acid, turns these planes to the left. The Tartaric acid has, according to M. Biot, a special power of dispersing the different colours of the spectrum, that is, the arcs of rotation for these colours are widely dif- ferent. In 1844 M. Mitscherlich showed that the double Tartrates and Paratartrates of Soda and Ammonia, have the same chemical composition, the same crys- talline form with the same angles, the same specific weights, the same double refraction, and consequently the same inclination of their optical axes. Notwith- standing this similarity, M. Biot found that the whole series of the Tartrates turned the planes of polarisation to the right, while the Paratartrates exercised no rota- tory action whatever. This interesting branch of optics has been success- fully studied by M, Pasteur. He has found that the Paratartaric Acid, which is exactly the same as the Racemic acid, and which differs from the Tartaric only in having an additional atom of water, is actually com- posed of two distinct acids, one of which, the leiora- cemic, has a rotatory force from left to right, and the other, the dextroracemic, from right to left, the rota- tory force of both being the same. Hence it follows that when these two acids are combined, as they are in the Paratartrates and Racemates. the two opposite forces compensate one another. The Dextroracemic Acid is CHAP. XXXV. ON CIRCULAR POLARISATION. 303 consequently identical with the common Tartaric Acid, and the Dextroracemates are only Tartrates. In comparing the rotatory forces of these salts with their crystalline forms, M. Pasteur has found that the Tartrates or Dextroracemates have plagiedral faces going from left to right, like right-handed Quartz, while the Levroracematei have their plagiedral faces going from right to left, like left-handed Quartz, while the Paratartrates and Racemates, like Amethyst, con- sist of the two combined. So far, then, the researches of M. Pasteur are analogous with those which deter- mined the relations of Quartz to Amethyst. The subsequent researches of M. Pasteur, however, are still more interesting, and I shall endeavour to give a brief account of them. When crystals are formed, according to the theory of Haiiy, by the aggregation of infinitely small solids of the same form, they must neces- sarily be symmetrical, Hauy himself had recognised several exceptions to this law of symmetry ; but it is to M. Weiss, a celebrated German crystallographer, that we owe the generalisation of these exceptions, to which he gave the name ofhemiedric. In studying the physical relations of hemiedral crystals, M. Pasteur has divided them into two great classes, which he calls superposable and nonsuperposable. When a crystal is hemiedral, we may, in certain cases, imagine another crystal identical with that crystal in all its parts, but which is not superposable, just as our right hand, though identical with the left, is not superposable upon it : on the other hand, all regular Tetrahedrons, and all Rhombohedrons of the same angle, are superposable hemiedral forms. The two plagiedral varieties of Quartz, the Tartrates, the Paratartrates or Racemates, Asparagine and Aspartic acid, the combination of Glucose with sea salt, are examples of nonsuperposable hemiedral crystals, and have all cir- cular polarisation. In the superposable hemiedral crys- tals the rotatory polarising power has never been found ; and there are only two exceptions to its existence in the nonsuperposable hemiedral crystals. These exceptions, 304 A TREATISE ON OPTICS. PART II. according to M. Pasteur, are Formiate of Strontian and Sulphate of Magnesia, both biaxal crystals, and both nonsuperposable in their hemiedral forms. ' In all the crystallisations of the Formiate of Stron- tian M. Pasteur found two species of crystals, the one hemiedral to the right, and the other hemiedral to the left, perfectly identical but not superposable ; and yet the solutions of neither has circular polarisation ! though when crystallised anew, they again yield the two species of crystals. In explanation of this unexpected result, M. Pasteur supposes that the hemiedru-m of the For- rniate does not depend on the arrangement of atoms in the chemical molecules, but on the arrangement of the physical molecules in the entire crystal, so that the crystalline structure at once disappears in the solution, as that of Quartz does in fusion. The want of circular polarisation in Sulphate of Magnesia, M. Pasteur sup- poses may be owing to its being very nearly superpo- sable, as the angle of the prism of this sulphate and its isomorphous bodies is between 90 and 91, so that the right rhomboidal prism is very near the prism with a square base, which is a superposable form, and there- fore should have no circular polarisation. The phenomena of circular polarisation have already had many useful applications. M. Biot and M. Pasteur have shown in their valuable memoirs their application to crystallography and chemistry. M. Biot has pointed out their value in determining the state of the sap in grasses and growing corn at different stages of their growth ; and by the saccharometer of M. Soleil we can ascertain with the minutest accuracy the quality and quantity of sugar in any sacchariferous solution. CHAP, XXXVI. ELLIPTICAL POLARISATION. 305 CHAP. XXXVI. ON ELLIPTICAL POLARISATION, AND ON THE ACTION OP METALS UPON LIGHT. On Elliptical Polarisation. (148.) THE action of metals upon light has always presented a troublesome anomaly to the philosopher. Malus at first announced that they produced no effect whatever ; but he afterwards found that the difference between transparent and metallic bodies consisted in this, that the former reflect all the light which they polarise in one plane, and refract all the light which they polarise in an opposite plane; while metallic bodies reflect what they polarise in both planes. Before 1 was acquainted with any of the experiments of Malus, I had found* that light was modified by the action of me- tallic bodies; and that, in all the metals which I tried, a great portion of light was polarised in the plane of incidence. In February, 1815, I discovered the cu- rious property possessed by silver and gold and other metals, of dividing polarised rays into their complement- ary colours by successive reflexions : but I was misled by some of the results into the belief, that a reflexion from a metallic surface had the same effect as a certain thickness of a crystallised body ; and that the polarised tints varied with the angle of incidence, and rose to higher orders, by increasing the number of reflexions. M. Biot, in repeating my experiments, and in an ela- borate investigation of the phenomena t, was misled by the same causes, and has given a lengthened detail of experiments, formulae, and speculations, in which all the real phenomena are obscured and confounded. Although I had my full share in this rash generalisation, yet I never viewed it as a correct expression of the * Treatise on New Phil. Instruments, p. 347. and Preface. t Traite de Physique, torn, iv. p. 579. 600. X 306 A TREATISE ON OPTICS. PART II. phenomena, and I have repeatedly returned to the subject with the most anxious desire of surmounting its difficulties. In this attempt I have succeeded ; and I have been enabled to refer all the phenomena of the action of metals to a new species of polarisation, which I have called elliptical polarisation, and which unites the two classes of phenomena which constitute circular and rectilineal polarisation. (149.) In the action of metals upon common light, it is easy to recognise the fact announced by Malus, that the light which they reflect is polarised in different planes. I have found that the pencil polarised in the plane of reflexion is always more intense than that polarised in the perpendicular plane. The difference between these pencils is least in silver, arid greatest in galaena, and consequently the latter polarises more light in the plane of reflexion than silver. The following table shows the effect which takes place with other metals : Order in which the Metals polarise most Light in the Plane of Reflexion, Galaena. Steel. Copper. Fine gold. Lead. Zinc. Tin plate. Common silver. Grey cobalt. Speculum metal. Brass. Pure silver. Arsenical cobalt. Platinum. Grain tin. Total reflexion Iron pyrites. Bismuth. Jewellers' gold. from glass. Antimony. Mercury. . By increasing the number of reflexions, the whole of the incident light may be polarised in the plane of reflexion. Eight reflexions from plates of steel be- tween 60 and 80, polarise the whole light of a wax candle ten feet distant, while at angles above 80 and below 60 a greater number is required. With galaena, lead, cobalt, and antimony a small number is necessary. An increased number of reflexions [above 36] is re- quired to do this with pure silver; and in total re- flexions from glass, where the circular polarisation begins, and where the two pencils are equal, the effect cannot be produced by any number of reflexions. In order to examine the action of metals upon po- CHAP. XXXVI. ELLIPTICAL POLARISATION. 307 larised light, we must provide a pair of plates of each metal, flatly ground and highly polished, and each at least l^inches long and half an inch broad. These parallel plates should be fixed upon a goniometer, or other di- vided instrument, so that one of the plates can be made to approach to or recede from the other, and so that their surfaces can receive the polarised ray at different angles of incidence. In place of giving the plates a motion of rotation round the polarised ray, I have found it better to give the plane of polarisation of the ray a motion round the plates, so that the planes of re- flexion and of polarisation may be set at any required angle. The ray reflected from the plates one or more times is then analysed, either by a plate of glass or a Nicol's prism, or rhomb of Iceland spar. When the plane of reflexion from the plates is either parallel or perpendicular to the plane of primitive po- larisation, the reflected light will receive no peculiar modification, excepting what arises from their property of polarising a portion of light in the plane of reflexion. But in every other position of the plane of reflexion, and at every angle of incidence, and after any number of reflexions, the pencil will have received particular modifications, which we shall proceed to explain. One of these, however, is so beautiful and striking, as to arrest our immediate attention. When the plates are silver or gold, the most brilliant complementary colours are seen in the ordinary and extraordinary images, changing with the angle of incidence and the number of reflexions. These colours are most brilliant when the plane of reflexion is inclined 45 to the plane of incidence, and they vanish when the inclination is or 90. All the other metals in the preceding table give analogous colours; but they are most brilliant in silver, and diminish in brilliancy from silver to galaena. In order to investigate the cause of these phenomena, let us suppose steel plates to be used, and the plane of the polarised ray to be inclined 45 to the plane of re- x2 308 A TREATISE ON OPTICS. PART II. flexion. At an incidence of 75 the light has suffered some physical change which is a maximum at that angle. It is not polarised light, because it does not vanish during the revolution of the analysing plate. It is neither partially polarised light, nor common light; because when we reflect it a second time at 75, it is restored to light polarised in one plane. If we transmit the light reflected from steel at 75 along the axis of Iceland spar, the system of rings shown in fig. 120. is Fig. 150. changed into the system shown in fig. 150., as if a thin film of a crystallised body which polarises the blue of the first order had i crossed the system. If we substi- ' tute for the calcareous spar films of sulphate of lime which give different tints, we shall find that these tints are increased in value ,by a quantity nearly equal to a quarter of a tint, according as the metallic action coin- cides with or opposes that of the crystal. It was on the authority of this experiment that I was led to believe that metals acted like crystallised plates. And when I found that the colours were better developed and more pure after successive reflexions, I rashly- concluded, as M. Biot also did after me, that each suc- cessive reflexion corresponded to an additional thick- ness of the film. In order to prove the error of this opinion, let us transmit the light reflected 2, 4, 6, 8 times from steel at 75 along the axis of Iceland spar, and we shall find that the system of rings is perfect, and that the whole of the light is polarised in one plane ; a result absolutely incompatible with the supposition of the tints rising with the number of reflexions. At 1, 3> 5, 1, 9, and 1 1 reflexions, the light when transmitted along the axis of Iceland spar will produce an effect equal to nearly a quarter of a tint, beyond which it never rises. I now conceived that light reflected 1, 3, 5, 1> and 9 CHAP, xxxvi. ELLIPTICAL POLARISATION. 309 times from steel at 75 resembled circularly polarised light. In circularly polarised light produced by two total reflexions from glass, the ray originally polarised + 45 to the plane of reflexion is, by the two reflexions at the same angle,, restored to light polarised 45 to the plane of reflexion ; whereas in steel, a ray polarised + 45, and reflected once from steel at 75, is restored by another reflexion at 75 to light polarised 1 7. With different metals the same effect is produced, but the inclination of the plane of polarisation of the restored ray is different, as the following table shows: Total Reflexions. Inclination of restored Ray. Total Reflexions. Inclination of restored Ray. From glass - 450 o> Bismuth ... 210 0' Pure silver 39 48 Speculum metal 21 Common silver 36 Zinc .... 19 10 Fine gold - 35 Steel .... 17 Jewellers' gold Grain tin - 33 33 Iron pyrites - Antimony - 14 16 15 Brass .... 32 Arsenical cobalt - 13 Tin plate ... 31 Cobalt ... 12 30 Copper 29 Lead .... 11 Mercury ... 26 Galaena ... 2 Platinum ... 22 Specular iron In total reflexions, or in circular polarisation, the cir- cularly polarised ray is restored to a single plane by the same number of reflexions and at the same angle at which it received circular polarisation, whatever be the in- clination of the plane of the second pair of reflexions to the plane of the first pair; but in metallic polarisation, the angle at which the second reflexion restores the ray to a single plane of polarisation varies with the inclin- ation of the plane of the second reflexion to the plane of the first reflexion. In the case of total reflexions, this angle varies as the radii of a circle ; that is, it is always the same. In the case of metallic polarisation, it varies as the radii of an ellipse. Thus, when the plane of the polarised ray is inclined 45 to the plane of primitive polarisation, the ray reflected once at 75 will be restored to polarised light at an incidence of 75; but when the x 3 310 A TREATISE ON OPTICS. PART II. two planes are parallel to one another, the restoration takes place at 80 ; and when they are perpendicular, at 70 ; and at intermediate angles, at intermediate in- clinations. For these reasons, I have called this kind of polarisation Elliptical Polarisation. We have already seen that light polarised -f 45 is elliptically polarised by i, 3, 5, 7 reflexions from steel at 75, and restored to a single plane of polarisation by- 2, 4, 6, 8 reflexions at the same angle ; and we have stated that the ray restored by two reflexions has its plane of polarisation brought into the state of 17. The following are the inclinations of this plane to the plane of reflexion, by different numbers of reflexions from steel and silver : No. of Reflexions. Inclination of the Plane of the polarised Ray. No. of Reflexions. Inclination of the Plane of the polarised Ray. Steel. Silver. Steel. Silver. 2 4 6 8 - 17 + 5 22 - 1 38 + 30 - 380 15 + 31 52 - 26 6 + 21 7 10 12 18 36 9 + 03 + 00 16 56 + 13 30 6 42 + 47 ' These results explain in the clearest manner why common light is polarised by steel after eight reflexions, and in silver not till after thirty-six reflexions. Com- mon light consists of two pencils, one polarised + 45, and the other 45; and steel brings these planes of polarisation into the plane of reflexion after eight re- flexions, while silver requires more than thirty-six re- flexions to do this. (150.) The angles at which elliptical polarisation is produced by one reflexion may be considered as the maximum polarising angles of the metal, and their tan- gents may be considered as the indices of refraction from the different metals, as shown in the following table : CHAP. XXXVI. ELLIPTICAL POLARISATION. 311 Name of Metal. Angles of Maximum Polarisation. Index of Refraction. Grain tin 78 SO 7 4-915 Mercury Galaena - 78 27 78 10 4-893 4-773 Iron pyrites Grey cobalt Speculum metal Antimony melted Steel - 77 30 76 56 76 75 25 75 4-511 4-309 4-011 3-844 3-732 Bismuth 74 50 3-689 Pure silver 73 3-271 Zinc ... 72 30 3-172 Tin plate hammered Jewellers' Gold - 70 50 70 45 2-879 2-864 Elliptical polarisation may be produced by a sufficient number of reflexions at any given angle, either above or below the maximum polarising angle, as shown in the following table for Steel : Number of Reflexions from Steel at which Elliptical Polarisation is pro- duced. Number of Reflexions at which the Pencil is restored to a single Plane. Observed Angle of Incidence. 3 9 15 &c. 6 12 18 &c. 86 O 7 2 i 7 J I2 J &c - 2 6 10 &c. 5 10 15 &c. 4 8 12 &c. 84 82 20 l 4 7 &c. 13 5 &c. 3 6 9 &c. 2 4 6 &c. 79 75 *4 4 i 7 i & c> 3 6 9 &c. 67 40 2 6 10 &c. 4 8 12 &c. 60 20 gl 7! J2i &c. ' 5 10 15 &c. 56 25 3 9 15 &c. 6 12 18 &c. 52 20 When the number of reflexions is an integer, it is easily understood how an elliptically polarised ray begins to retrace its course, and recover its state of polarisation in a single plane by the same number of reflexions by which it lost it ; but it is interesting to observe, when the number of reflexions is 1-J-, 2^, or any other mixed num- ber, that the ray must have acquired its elliptical polaris- ation in the middle of the second and fifth reflexion ; that is, when it had reached its greatest depth within the metallic surface it then begins to resume its state of X* 312 A TREATISE ON OPTICS* polarisation in a single plane, and recovers it at the end of 3, 5, and 7, reflexions. A very remarkable effect takes place when one reflexion is made on one side of the maximum polarising angle, and one on the other side. A ray that has received partial elliptical polarisation by one reflexion at 85 does not acquire more elliptic polarisation by a reflexion at 54, but it retraces its course and recovers its state of single polarisation. By a method which it would be out of place to ex- plain here, I have determined the number of points of restoration which can occur at different angles of in- cidence from to 90, for any number of reflexions ; and I have represented them in fig> 151., where the arches I, I ; II, II ; &c., represent the quadrant of in- Fig. 151. cidence, for one, two, &c. reflexions ; C being the point of 0, and B that of 90 of incidence. In the qua- drant I, I. there is no point of restoration. In II, II. there is only one point or node of restoration, viz. at 73 in silver. In III, III. there are two points of restoration, because a ray elliptically polarised by one and a half reflexion will be restored by three reflexions at 63 43' beneath the maximum polarising angle, and at 79 40' above that angle. It may also be shown that for IV. reflexions there are 3 points of restoration, for V. re- flexions 4 points, and for VI. reflexions 5 points, as shown in the figure. The loops or double curves are drawn to represent the intensity of the elliptic polaris- ation, which has its minimum at 1, 2, 3, &c., and its maximum in the middle of the unshaded parts C 1, &c. CHAP. XXXVI. ELLIPTICAL POLARISATION. 313 These points of maximum intensity do not bisect the loops, or are not equidistant from the minima ; but such is their relation that the maximum for n reflexions is the minimum for 2ra reflexions. These phenomena lead us to the explanation and analysis of the comple- mentary colours which accompany elliptical and circular polarisation. On the Colours of Elliptical and Circular Polarisation. (151.) When the preceding experiments are made with homogeneous light, we find that the points and angles of restoration vary for the differently coloured rays. Thus in silver we have the maximum polarising angle as follows : Corresponding Index of Refraction. For red light 75 J 3*866 For yellow light - 73 - - 3-271 For blue light - 70j 2-824 Hence it is obvious that at the point of restoration where the blue rays are restored, and vanish, the red rays are not restored, and consequently will appear when the principal section of the analysing rhomb is in the plane of reflexion. Here, then, we have the cause of the phenomena of the complementary colours seen in reflexion from metals. They are analogous to the colours in oil of cassia and chr ornate of lead at the maximum polarising angle. But the remarkable result of the preceding measures is, that in metallic as well as in total reflexion, the index of refraction is less for blue than for red light, or, in the language of the undulatory theory, the refractive index increases with the length of the wave. In a recent communication to the Royal Irish Academy, on the propagation of light in un crystallized media, Professor Lloyd has obtained an expression for the velocity of the propagation of light, each of its terms consisting of two parts with opposite signs, one of which is due to the action of the ether and the other to that of the body. . Conceiving, therefore, that there may be bodies in which 314 A TREATISE ON OPTICS, PART II. the principal term is nearly nothing, the principal part of the expression will be that derived from the second term ; and if that term he taken as an approximate value, it will follow that the refractive index of the substance must be in the subduplicate ratio of the length of the wave nearly. " Now," says Professor Lloyd, " it is remarkable that this law of dispersion, so unlike any thing observed in transparent media, agrees pretty nearly with the results obtained by Sir David Brewster in some of the metals. In all these bodies, the refractive index (inferred from the angle of maximum polarisation) increases with the length of the wave. Its values for the red, mean, and blue, ray in silver, are 3*866, 3*271, 2'824, the ratios of the second and third to the first being -8.5 and '73. According to the law above given 3 these ratios should be *88 and '79." Since these researches were published, the subject of Metallic Polarisation has been ardently and successfully pursued in France, experimentally, by M. Senarmont and M. Jamin, and theoretically by M. Cauchy, one of the most distinguished mathematicians of the present day. The narrow limits of a popular treatise will not permit us to give an account of the results obtained by M. Senarmont and M. Jamin on Elliptical Polarisation by metals, or of the interesting facts which the latter has discovered respecting the colours of metals. In the original memoir, in which he extends his theory to Ellip- tical Polarisation, M. Cauchy has shown that his results agree with the experimental ones obtained by myself, and recorded in the preceding pages ; and M. Jamin has pointed out its remarkable agreement with the re- sults of his own experiments. The researches of M. Jamin on the Elliptical Polar- isation of light by reflexion from the surfaces of trans- parent bodies was suggested by the discovery of Mr. Airy, that the light reflected from the diamond was * For a more full account of my experiments on this subject, I must refer the reader to the Philosophical Transactions, 1830 ; or to the Edin* burgh Journal oj Science, Nos. VII. and VIII. new series, April 1831. CHAP. XXXVI. ELECTRO-MAGNETICAL POLARISATION. 315 elliptically polarised. M. Jamin has shown that this species of polarisation is generally produced by re- flexion from almost all transparent bodies, whether they have a high or a low refractive power, and espe- cially by glass, at angles very little different from that deduced from the law of the tangents. Menilite and Alum, cut perpendicular to the axes of the octohedron, exhibited no elliptical polarisation. Mr. Baden Powell had previously discovered that light reflected from a great number of bodies was ellip- tically polarised. He found it, for example, in China ink, chromate of lead, sulphate of copper, sulphate of iron, decomposed glass, plumbago, litharge, and in many ores of copper of different colours from the Isle of Elba ; but it did not exist in various metallic compounds in which he expected to find it.* On Circular Electro-magnetic Polarisation.^ (152.) The remarkable property of the electro- magnetic current to communicate to transparent solid and fluid bodies a structure analogous to, but different from, that possessed by rock crystal and circularly Fig. 152. c polarising fluids, was discovered in 1845 by our dis- tinguished countryman Mr. Faraday. J * See Phil. Trans. 1843, p. 35., and 1845, p. 269. f The name Magno-crystallisation is adopted by Dr. Tyndall. t See Phil. Trans. 1846, Part 1. 316 A TREATISE ON OPTICS. If a piece of flint-glass N S ns, fig. 15%., with two pa- rallel faces, is placed as in the figure on the poles N, S of a powerful electro-magnet NSC, and a powerful galvanic current passed through it in the direction s n, the piece of glass is neither attracted nor repelled, nor moved in any way, but when a ray of polarised light is passed through it and analysed, it is found to turn the plane of polarisation of the incident ray in the same direction as the current. If the polarised light is transmitted through the plate in the direction GH, no effect whatever is produced. If the polarised light enters at the face N*, and the observer looks into S n, the rotation of the plane of polarisation will be from left to right, like the hand of a watch, but if it enter at Sw, and the observer looks into N*, the rotation will be from right to left. In rock crystal and other bodies with circular polarisa- tion, the direction of rotation is the same through what- ever side the light enters. If the length sn of the glass is greater than the dis- tance between the poles N, S, it has opposite poles at the extremities which extend beyond the poles N, S, and the effect of the two portions beyond the poles is contrary to that of the portion, such as sn, between the poles. As the rotatory force depends on the length of the piece of glass, or of the trajectory of the ray, as well as upon the energy of the pile upon the different laminae through which it passes, Mr. Faraday found that by placing reflectors at sN and nS, so as to prevent the ray from emerging till it had made three or five passages between the surfaces, the effect was increased three or five times. It appears from the experiments of M. Bertin that the action of the electro-magnet is simply a function of the distance ; that is, that each of the laminae of a body through which the current passes, is acted upon as if the other laminae did not exist. From some of M. Ber- tin's experiments, it would appear that the intensities in the Soro-silicate of Lead (flint-glass of Faraday), and the Sulphuret of Carbon, are not affected by a variation CHAP. XXXVI. ELECTBO-MAGNETICAL POLARISATION. Blf within verv considerable limits of the electro-magnetic force. M. Bertin, on submitting different substances to the electro-magnetic action, found that among fluids the Bichloride of Tin, and the Sulphuret of Carbon, to which he had assigned a rotatory force three times greater than that of water, olive oil, alcohol, and water itself appeared to be among the most active. This interesting branch of physical optics has been studied with much success by M. Matthiessen of Altona. He found that the rotatory force diminished as the poles N and S were separated, and that this diminution was more rapid as the glasses were thinner. In examining the influence of the contact of the poles with the glasses, he found that the maximum effect did not take place with absolute contact. A plate of cobalt flint-glass, 39 millimetres long, being placed between the poles, when 40 millimetres distant, he found that when each face of the glass was distant | a millimetre, or -^ of an inch, from its pole, the rotation was 9i. When one pole touched the plate, the effect was only 9> and when both poles touched it the rotation was diminished to 8|-. Hence, M. Matthiessen thinks that by contact a part of the magnetism passes freely through the glass as a conductor, without producing rotation. When the body NsnS consists of six plates of the same glass of the same thickness, combined as a single piece of the same glass, the rotatory force was less, nearly in the ratio of 11 to 13, but when the plates were cemented together by Canada Balsam, they had the same rotatory force as the single piece. In studying the effect of the inclination of the axes of the magnet upon the rotatory power of the glasses, and using a series of prisms of the same kind of glass, he found that the rotation diminished approximative^ as the square of the cosine of the angle of deviation of the luminous ray, a result, he remarks, which ought to surprise us if we consider the action of the pole of a magnet as uniform round its centre** # Comptes Rendus, $c., torn. xxv. p. 20, 1847. 318 A TREATISE ON OPTICS. PART II. In the followiag table we have placed a few of the results obtained by M. Matthiessen, who has given a list of 28 vitrified substances which have a greater rotatory force than the Borosilicate of lead of Faraday.* Thickness in Millimetres. Rotation. Silicate seplombique - 15 - - 20 Silicate quadroplombique - 20 18 Silico aluminate of lead - 10 - - 16 Borate triplombique - 17 - - 16 Realgar red - - 12 - - U Borate of Bismuth - - 14 - - 11 Borate of Lead, neutral - 24 - - 1O Silicate of Lead, neutral - 30 - - 10 Glass of 'Antimony 27 9 Borosilicate of Lead 26 9 Rock Salt - 26 6 These experiments were made with an electro-mag- netic force produced by 50 elements of Bunsen's pile, very feebly charged, and capable of raising 25 kilo- grammes by one of the vertical poles of the magnet. " The thickness," says M. Matthiessen, in concluding his communication, " at which a glass gives a maximum rotation, varies not only with the attractive force of the magnet, but also, the force being the same, according as it is produced by a small number of elements strongly charged, or by a great number weakly charged. The action of glasses upon polarised light varies in intensity according as the same attractive force of the magnet on soft iron is generated by an abundant electric cur- rent of feeble tension, or by a current small in quantity and of a high tension. In the action, therefore, of the magnetic fluid on sensitive glasses, there are mani- fested two modifications analogous to, or comparable with, almost all the forces of nature of which we know the effects in the actual state of the sciences." From a series of very interesting experiments recently made by M. Bertint, he obtained the following values of what he calls the Coefficient of Magnetic Polarisation, in * Comptes Rendus, fyc. torn. xxxv. p. 173, 1847. -< Ann. de Chem'- J ~ nt ~- - . xxxiv. p. 500. f Ann. de Chemie et de Physique^ torn, xxiii. p. 5., and Phil. Mag. vol. s CHAP. XXXVI. ELECTRO- MAGNETICAL POLARISATION. 319 different bodies compared with that of Faraday's flint- glass. This coefficient depends on the intensity of the magnetism and the nature of the substance, the distance between the poles of the magnet and the thickness of the body being the same in all. Coefficient. Faraday's flint glass - - 1 -00 Guinand's ditto ... 0*87 Matthiessen's ditto - - - 0'83 Common ditto ... 0*53 Bichloride of Tin - - O77 Sulphuret of Carbon - -074 Protochloride of Phosphorus - - 051 Chloride of Zinc dissolved - - 0*55 Chloride of Calcium dissolved - - 0'45 Water - 0-25 Alcohol ordinary, of 36 Beaume - - 0*18 Ether - - - 0-15 In connexion with the subject of this chapter, we may mention the curious discovery made by M. Plucker, of Bonn, that when a positive uniaxal crystal like Diop- side, or a biaxal crystal like Topaz, is suspended freely between the poles of an electro-magnet, the optical axis in the one case, and the line which bisects the optical axes in the other, places itself perpendicular to the line joining the poles of the magnet. When the crystals are negative, the same lines point in a direction parallel to the lines joining the poles. Hence we have a new method of determining, without the aid of polarised light, the optical axes of doubly refracting crystals, and their character. M. Plucker also found that certain crystals, uniaxal like Oxide of Tin, and biaxal like Kyanite or blue Die- thene, have such a degree of polarity, that they point to the north by the magnetic power of the earth, t Dr. Tyndall has recently shown that a model of white wax, exactly like a crystal of Calcareous Spar, and having been previously compressed in the direction of. the axis of the model, acts exactly like the natural crystal.; Hence he justly concludes that the action is due to the arrangement, and not to the shape of the molecules. 320 A TREATISE ON OPTICS. PART II. CHAP. XXXVII. ON THE ACTION OF THE SURFACES OF CRYSTALLISED BODIES UPON COMMON AND POLARISED LIGHT. (1 53.) IN his experiments on the polarisation of light hy reflecting surfaces, Malus observed that the action of the surface of Calcareous spar upon light was independent of the position of its principal section, and that its sur- face acts like that of any common transparent body.* In examining, however, the superficial action of this mineral, I found that on all the surfaces of the crystal, whether primary or secondary, excepting that per- pendicular to the axis, its angle of maximum polarisation varied in different azimuths, being a minimum in the direction of the axis, or in azimuth 0, and a maximum in a line perpendicular to it, or in azimuth 90. The following were the results which I obtained on different surfaces : On the Summit of the Prism. Angle of Max. Polarisation in all azimuths - 60 0' On the Face of the Rhomb. Ditto in azimuth - 57 14' 50 57' ... 58 32 90 ... 59 32 On the Faces of the Prism. Ditto in azimuth - - - 54 18 90 ... 58 14 The faces of the rhomb were faces of cleavage, and the other faces were natural ones. I found also that the polarisation was most complete in azimuth than in azimuth 90 on all the faces of the rhomb ; but more complete in azimuth 90 than in azimuth on the faces of the prism. In Chromate of * Thtorie de la double Refraction, p. 240., and Blot's Traits de Physique, torn, iv. p. 339. CHAP. XXXVII. CRYSTALLISED SURFACES. 321 Lead and Specular Iron ore, I obtained the following results : Chromate of Lead. Angle of the axis of the prism - - 67 48' Perpendicular to the axes - - 65 42 Specular Iron Ore. In one direction - - - - 72 10' In opposite direction 69 As it was obvious from these experiments that the doubly refracting force of the Iceland spar extended beyond its surface, I was desirous of ascertaining if the light polarised by reflexion suffered any change from that force. I therefore made a series of experiments, of which an account is published in the Philosophical Transactions for 1819* and a second series,, the results of which have not been published. From these ex- periments, some of the results of which are given in the following notice *, it will be seen that crystallised sur- faces exhibit the phenomena of rectilineal, elliptical, and circular polarisation, under very interesting circum- stances. When light is reflected at the separating surface of two media, the lowermost of which is a doubly-refracting one, the reflected ray is exposed to the action of two forces, one of which is the ordinary reflecting force, and the other a force which emanates from the interior of the doubly refracting crystal. When the first medium is air, or even water, the first of these forces over- powers the second ; and, in general, the effects of the one are so masked by the effects of the other, that I was obliged to use Oil of cassia, a fluid of high re- fractive power, in order that the interior force of the Calcareous spar which I wished to examine might ex- hibit its effects independently of those which arise from ordinary reflexion. The separating surface, there- fore, which I used, had a small refractive power ; and * Report of British Association, 1836. Y 322 A TREATISE ON OPTICS. PART II. the reflected pencil is so attenuated, especially with polarised light, that it is almost impossible to employ any other light than that of the sun. When a pencil of common light is reflected from the separating surface of Oil of cassia and Calcareous spar, the general action of the spar is to polarise a part of the ray in a plane perpendicular to that of reflexion, and thus to produce by reflexion the very same effect that other surfaces do by refraction. On the face of Calcareous spar, perpendicular to the axis of the crystal, the effect is exactly the same in all azimuths, but in every other face the effect varies in dif- ferent azimuths; and depends upon the inclination of the face to the axis of double refraction. On the natural face of the rhomb common light is polarised in the plane of reflexion, in of azimuth, or in the plane of the prin- cipal section ; but at 38 of azimuth, the whole pencil is polarised at right angles to the plane of reflexion ; and in other azimuths the effect is nearly the same as I have stated in my paper in the Philosophical Trans- actions. In order, however, to observe the change which is actually produced upon light, it is necessary to use two pencils, one polarised -f 45, and the other 45, to the plane of incidence. The planes of polarisation of these pencils are inclined 90 to each other, and the invariable effect of the new force is to augment that angle in the same manner as is done by a refracting surface, while the tendency of the ordinary reflective force is to diminish the same angle. Hence 1 was led to make an experiment in which these opposite forces might compensate one another. I mixed Oil of olives and Oil of cassia, till I obtained a compound of such a refractive power that its action in bringing together the planes of polarisation should be equal to the action of the new force in sepa- rating them. Upon reflecting the compound pencil from this surface, I was delighted to find that the in- clination of the planes was still 90, and I thus obtained the extraordinary result of a reflecting surface which CHAP. XXXVII. CRYSTALLISED SURFACES. 328 possessed no action whatever upon common or upon polarised light. On the faces of the spar which are inclined 0, 45, or 90, to the axis of double refraction, the action of the new force is symmetrical upon the two pencils of polar- ised light whose planes are inclined + 45 and 45 to the plane of incidence ; whereas in all intermediate faces, whose inclination to the axis is 22^- and 67^> the plane of one of the polarised rays remains stationary, while that of the other is turned round 1 5. Double Reflexion and Polarisation. (154.) In connexion with the subject of this chapter we cannot omit another very remarkable property of light exhibited in its reflexion from the surfaces of certain coloured crystals, such as Chrysammate of Potash, Chrysammate of Magnesia, Murexide, and various other crystals in which I have found it. As the light reflected from transparent bodies had not entered the substance of the body, it was for this reason always believed that it should be colourless whatever might be the colour of the body. Observation confirmed this supposition, till chemistry presented us with various substances in which the reflected light appeared to be distinctly coloured. In examining this class of crystals, the Chrysammate of Potash for example, I found that common light reflected at a perpendicular incidence had the colour of virgin gold, growing less and less yellow as the incidence increases, till, at great incidences, its colour is a pale bluish white. The pencil thus reflected and coloured consists of two oppositely polarised pencils, one polarised in the plane of reflexion and of a pale bluish white colour at all incidences, and the other polarised perpendicular to that plane, and of a golden yellow colour at small incidences, passing successively into a deeper yellow, greenish yellow, green, greenish blue 9 blue, and light pink as the angle of incidence increases. The same property is exhibited at the surface of the crys- tal in contact with fluids or glass, the colours of course 324 A TREATISE ON OPTICS. PART II. being different. The phenomena vary with the azimuth of the plane of incidence, the polarisation of the pencils being interchanged when the plane of incidence is per- pendicular to the length of the prism, though the colours of the pencils are not exactly the same. Seme of the crystals of this class, though they exist only in a powdery state like snuff, may by pressure and traction be spread or drawn out into a transparent film upon glass, and being thus as it were crystallised, they exhibit the same optical properties as if they formed regular prismatic crystals, the line of traction and pres- sure corresponding with the axis of the prism* The property of double reflexion and polarisation, thus exhibited by the reflected rays, is as much a new property of light, as the double refraction and polar- isation of the transmitted rays. CHAP. XXXVIII. ON THE POLARISING STRUCTURE PRODUCED BY HEAT, COLD, COMPRESSION, DILATATION, AND INDURATION. THE various phenomena of double refraction, and the system of polarised rings with one and two axes of double refraction, and with planes of no double refrac- tion, may be produced either transiently or permanently, in glass and other substances, by heat and cold, rapid cooling, compression and dilatation, and induration. 1. Transient Influence of Heat and Cold. (1.) Cylinders of glass with one positive axis of double refraction. (155.) If we take a cylinder of glass, from half an inch to an inch in diameter, or upwards, and about half an inch or more in thickness, and transmit heat from its circumference to its centre, it will exhibit when exposed to polarised light, in the apparatus, fly. ] 12., a system * Proceedings of Phil. Soc., St. Andrew, Jan. 5, Feb. 2, March 1, Dec. 7th 1846, and Jan. 29, 1853. Report Brit. Assoc. 1846, p. 7. GHAP. XXXVIII. POLARISATION BY HEAT. 325 of rings with a black cross, exactly similar to those in fig. 119.; and the complementary system shown in fig. 120. will appear by turning round the plate C 90. In this case we must hold the cylinder at the distance of 8 or 10 inches from the eye, when the rings will appear as it were in the inside of the glass. If we cover up any portion of the surface of the glass cylinder, we shall hide a corresponding portion of the rings, so that the cylinder has its single axis of double refraction fixed in the axis of its figure, and not in every possible direction parallel to that axis as in crystals. By crossing the rings with a plate of sulphate of lime, as formerly explained, we shall find that it depresses the tints in the two quadrants which the axis of the plate crosses ; and consequently that the system of rings is negative) like that of calcareous spar. As soon as the heat reaches the axis of the cylinder, the rings begin to lose their brightness, and when the heat is uniformly diffused through the glass, they dis- appear entirely. (2.) Cylinders of glass with a negative axis of double refraction. (156.) If a similar cylinder of glass is heated uni- formly in boiling oil, or otherwise brought to a con- siderably high temperature, and is made to cool rapidly by surrounding its circumference with a good con- ductor, it will exhibit a similar system of rings, which will all vanish when the glass is uniformly cold. By crossing these rings with sulphate of lime, they will be found to be positive, like those of ice and zircon ; or the same thing may be proved by combining this system of rings with the preceding system, when they will be found to destroy one another. In both these systems of rings, the numerical value of the tint or colour at any one point varies as the square of the distance of that point from the axis. By placing thin films of sulphate of lime between two of these sys- tems of rings, very beautiful systems may be produced. Y 3 326 A TREATISE ON OPTICS. (3.) Oval plates of glass with two axes of double refraction. (157.) If we take an oval plate A B D C, fig. 153., Fig. 153. an d perform with it the two preceding- experiments, we shall find that it has in both cases two axes of double refrac- tion, the principal axis passing through O, being negative when it is heated at its circumference, and positive when cooled at its circumference. The curves A B, C P, correspond to the black ones in fig. 128., and the distance mn, to the inclination of the resultant axes. The effect shown in fig. 153. is that which is produced by in- clining raw 45 to the plane of primitive polarisation; but when m n is in the plane of primitive polarisation, or perpendicular to it, the curves A B, C D, will form a black cross, as in j^gr. 121. In all the preceding experiments, the heat and cold might have been introduced and conveyed through the glass from each extremity of the axis of the cylinder or plate. In this case the phenomena would have been exactly the same, but the axes that were formerly ne- gative will now be positive, and vice versa. (4.) Cubes of glass with double refraction. (158.) When the shape of the glass is that of a cube, the rings have the form shown in fig. 154. and when it is a parallelepiped with its length about three times its breadth, the rings have the form shown in fig. 1 55., the Fig. 154. Fig. 155. curves of equal tint near the angles being circles, as shown in both the figures. CHAP. XXXVIII. POLARISATION BY HEAT. 32? (5.) Rectangular plates of glass with planes of no double refraction. (159.) If a well annealed rectangular plate o glass, E F D C, is placed with its lower edge C D on a piece of iron A B D C,Jig. 156. , nearly red hot, and the two together are placed in the apparatus, fig. 112., so that C D may be inclined 45 to the plane of primitive polarisation, and that polarised light may reach the eye at O from every part of the glass, we shall observe the following phenomena. The instant that the heat enters the surface C D, fringes of brilliant colours will be seen parallel to C D, and almost at the same time before the heat has reached the upper surface E F, or even the central line a b, similar fringes will appear at E F. Co- lours at first faint blue, and then white, yellow, orange, &c., all spring up at a b ; and these central colours will be divided from those at the edges by two dark lines, M N, O P, in which there is neither double refraction nor po- larisation. These lines correspond with the black curves in^r. 128. and fig. 153., and the structure between M N and O P is negative, like that of calcareous spar ; while the structures without M N and O P are positive, like those of zircon. The tints thus developed are those of Newton's scale, and are compounded of the different sets of tints that would be given in each of the homogeneous rays of the spectrum. In these plates there is obviously an infinite number of axes in the planes passing through M N, O P, and all the tints, as well as the double refraction, can be cal- Y 4 328 A TREATISE ON OPTICS. culated by the very same laws as in regular crystals,, mutatis mutandis. If the plate E F D C is heated equally all round, the fringes are produced with more regularity and quickness ; and if the plate, first heated in oil or otherwise, is cooled equally all round, it will develope the same fringes, but the central ones at a b will in this last case be positive, and the outer ones at E F and C D negative. Similar effects to those above described may be pro- duced in similar plates of rock salt, obsidian, fluor spar, copal, and other solids that have not the doubly refract- ing structure. A series of splendid phenomena are produced by crossing similar or dissimilar plates of glass when their fringes are developed. When similar plates of glass, or those produced by heat, as in fig. 156., are crossed, the curves or lines of equal tint at the square of intersection, A B C D, fig. 157., will be hyperbolas. The tint at Fig. 157. the centre will be the difference of the central tints of each of the two plates, and the tints of the succeeding hyperbolas will rise gradually in the scale above that central tint. If the tints pro- duced by each plate are precisely the same, and the plates of the same shape, the central tints will destroy each other, the hyperbo- las will be equilateral ones, and the tints will gradually rise from the zero of Newton's scale. When dissimilar plates are crossed, as infio. 158., viz. one in which the fringes are produced by heat, with one in which they are produced by cold, the lines of equal tint in the square of intersection A B C D (fig. 158.), will be ellipses. The tints in the centre will be equal to the sum of the separate tints, and the tints formed by the combination of the external fringes will be equal to their difference. If the plates and their tints are perfectly equal, the lines of equal tint will be circles. CHAP. XXXVIII. POLARISATION BY HEAT. 329 The beauty of these combinations can be understood only from coloured drawings. When the plates are combined lengthwise they add to or subtract from each other's effect, according as similar or dissimilar fringes are opposed to one another. Fig. 158 (6.) Sphere of glass, $c. with an infinite number of axes of double refraction. (160.) If we place a sphere of glass in a glass trough of hot oil, and observe the system of rings, while the heat is passing to the centre of the sphere, we shall find it to be a regular system, exactly like that in fig. 119- > and it will suffer no change by turning the sphere in any direction. Hence the sphere has an infinite number of positive axes of double refraction, or one along each of its diameters. If a great number of such spheres of a very small size were placed together between two plates of glass, either without Canada balsam, they would exhibit the phenomena of circular crystals. If a very hot sphere of glass is placed in a glass trough of cold oil, a similar system will be produced^ but the axes will all be negative. 330 A TREATISE ON OPTICS. PART II. (7-) Spheroids of glass with one axis of double refraction along the axis of revolution and two axes along the equatorial diameters. (l6l.) If we place an oblate spheroid in a glass trough of hot oil, we shall find that it has one axis of positive double refraction along its shorter axis, or that of revo- lution ; but if we transmit the polarised light along any of its equatorial diameters., we shall find that it has two axes of double refraction, the black curves appearing as in fig. 156. when the axis of revolution is inclined 45 to the plane of primitive polarisation, and changing into a cross when the axis is parallel or perpendicular to the plane of primitive polarisation. The very same phenomena will be exhibited with a prolate spheroid, only the black cross opens in a dif- ferent plane when the two axes are developed. Opposite systems of rings will be developed in both these cases, if hot spheroids are plunged in cold oil. The reason of using oil is to enable the polarised light to pass through the spheres or spheroids without refrac- tion. The oil should have a refractive power as near as possible to that of the glass. A number of very curious phenomena arise from heat- ing and cooling glass tubes, or cylinders, along their axes; the most singular variations taking place according as the heat and cold are applied to the circumference, or to the axis, or to both.* (8.) Influence of heat on regular crystals. (162.) The influence of uniform heat and cold on re- gular crystals is very remarkable. M. Fresnel found that heat dilates sulphate of lime less in the direction of its principal axis than in a direction perpendicular to it ; and Professor Mitscherlich has found that Iceland spar is dilated by heat in the direction of its axis of double refrac- tion, while in all directions at right angles to this axis it * See Phil. Trans. 1816, P. 46115, and Journal de Physique, 1816, torn. Ixxxiii., pp. 309, 389. GHAP. XXX VIII. POLARISATION BY HEAT. 331 contracts ; so that there must be some intermediate di- rection in which there is neither contraction nor dilatation. Heat brings the rhomb of Iceland spar nearer to the cube, and diminishes its double refraction. Jn applying heat to Sulphate of Lime, M. Mitscherlich found that the two resultant axes (P,P.fig. 131.) gradu- ally approach as the heat increases, till they unite at O, and form a single axis. By a still farther increase of heat they opened out on each side towards A and B. A property of a similar kind, but perhaps a still more extraordinary one, I discovered some years ago, subsequent to Professor Mitscherlich's discovery ; and I have slightly noticed it in a paper on Glauberite, pub- lished in the Edinburgh Transactions.* This interesting mineral has at ordinary temperatures the curious pro- perty of two axes of double refraction for red light, and only one axis for violet light. If we apply heat to it, the two optic axes for red light gradually close, and, at a temperature which the hand can endure, the two systems of rings for red light have united into one system, so that the crystal has now only one axis of double refraction for red light. By continuing to in- crease the heat, the two axes separated, and the single system of rings opened out into two systems, lying in a plane at right angles to that in which they were placed at first. The heat was now less than that of boiling water. By increasing it, the inclination of the optic axes gradually increased. I now applied artificial cold to a crystal of glau- berite at the ordinary temperature of the atmosphere. The inclination of the optic axes for red light increased, as might have been predicted ; but, what was very un- expected, a new axis was created for violet light, the plane of the two violet axes being coincident with the plane of the two red optic axes* at and below the ordi- nary temperature. An increase of cold increased the inclination of the optic axes for all the colours of the . Vol. xi. p. 273., 1829. 332 A TREATISE ON OPTICS. PART II. spectrum, the inclination of the axes being least for the most ref tangible, and greatest for the least refrangible rays. These results appear very complicated when we begin with the effects at an ordinary temperature, and view them in the manner in which they were observed ; but if we commence the experiments at a low tempe- rature, such as the freezing point, the order and con- nexion of the phenomena will be more easily under- stood. At 32 Glauberite has two axes of double refrac- tion for rays of all colours, the inclination of the axes for the violet rays being least, and that for the red the greatest. As the temperature rises, the optic axes for all colours gradually approach, and the axes for violet first unite into one. At this time the crystal has two axes for all the other colours ; but as the heat increases all the other pairs of axes unite in succession, and form a single system of rings. But before this has taken place, the axes for violet rays have opened up again in a plane at right angles to that in which they originally lay, and they are followed by all the other pairs of axes; so that at a temperature much below that of boiling water, each pair of axes appears with different inclina- tions arranged in a new direction. During all the changes which have been described above, the crystal has preserved its constitution ; and by abstracting the heat, the phenomena are all repeated in an inverse order. If the crystal should happen to be observed at that temperature, which very often occurs when the greenish- yellow or most luminous rays have the optic axes corre- sponding to them united, or form a single system of rings, then the blue rays will have two systems of rings lying in one plane, and the red rays also two systems of rings in a plane at right angles to this. In two rectangular positions, namely, when the planes of the double axes coincide with, or are at right angles to, the plane of primitive polarisation, the black cross will be very distinct ; but in intermediate positions it will be CHAP. XXXVIII. POLARISATION BY SUDDEN COOLING. 333 much less so, and the uniaxal system of rings which predominates, from the greater intensity of their light, will have that indistinctness of character which, when- ever it occurs, indicates a peculiar action of the doubly- refracting force on the differently-coloured rays, When the black cross is perfect and equally distinct in all positions, while the colours of the rings deviate from those of Newton's scale, then the axes for all colours are obviously coincident, and the peculiarity in the colour of the rings is owing to an irrationality in the action of the doubly-refracting forces on the differently- coloured rays. Heat exercises a different effect upon different crys- tals, and even upon the ordinary and extraordinary rays in the same crystal. M. Rudberg, of Upsal, found that the Ordinary ray of Calcareous Spar was not changed in its refractive power, while the Extraordinary ray suf- fered an increase in its refractive index of 0*00043 by an increase of 64 of temperature. In Rock Crystal both rays experienced a decrease of about 0*00027. In Arragonite the double refraction decreased a little with a temperature of 64. In crystals which have no double refraction, such as Rock Salt, Fluor Spar, Obsidian, Semiopal, the same effects are produced by heat as those which take place in glass. Similar effects are produced upon Rosin, Gum Copal, Horn, Amber, the ligament of the Chama gigantea, and upon Tortoise Shell.* 2= On the permanent Influence of sudden and quick Cooling. (163.) In March, 1814, I found that glass melted and suddenly cooled, such as prince Rupert's drops, pos- sessed a permanent doubly refracting structure t; and in December, 1814, Dr. Seebeck published an account of * See Phil. Trans. 1816, p. 77. t Letter to Sir Joseph Banks, April 8, 1814., Phil. Trans. 1814. 334? A TREATISE ON OPTICS. PART II. analogous experiments with cubes of glass. Cylinders, plates, cubes, spheres, and spheroids of glass, with a per- manent doubly refracting structure, may be formed by bringing the glass to a red heat, and cooling it rapidly at its circumference, or at its edges. As these solid bodies often lose their shape in the process, the symmetry of their structure is affected, and the system of rings or fringes injured ; so that the phenomena are not produced so perfectly as during the transient influence of heat and cold. It is often necessary, too, to grind and polish the surfaces afresh : an operation during which the solids are often broken, in consequence of the state of constraint in which the particles are held. An endless variety of the most beautiful optical figures, such as those shown in the first section of this chapter, may be produced by cooling the glass upon metallic patterns (metals being the best conductors) applied sym- metrically to each surface of the glass, or symmetrically round its circumference. The heat may be thus drawn off from the glass in lines of any form or direction, so as to give any variety whatever to its structure, and, con- sequently, to the optical figure which it produces when exposed to polarised light. (164.) In all doubly refracting crystals the form of the rings is independent of the external shape of the crystal ; but in glass solids that have received the doubly refracting structure, either transiently or permanently, from heat, the rings depend entirely on the external shape of the solid. If, in ^7. 156., we divide the rectangular plate E F D C into two equal parts through the line a b, each half of the plate will have the same structure as the whole, viz. a negative and two positive structures, sepa- rated by two dark neutral lines. In like manner, if we cut Si piece of a tube of glass, by a notch, through its circum- ference to its centre, or if we alter the shape of cylindrical plates and spheres, &c., by grinding them into different external figures, we produce a complete change upon the optical figures which they had previously exhibited. CHAP. XXXVIII. POLARISATION BY BENDING. 335 3. On the Influence of Compression and Dilatation. (165.) If we could compress and dilate the various solids above mentioned with the same uniformity with which we can heat and cool them., we should produce the same doubly refracting structures which have been described, compression and dilatation always producing opposite structures. The influence of compression and dilatation may be well exhibited by taking a strip of glass, A B D C, fig. 159., and bending it by the force of the hands. When it is held in the apparatus, fig. 112., with its Fig. 159. edge A B inclined 45 to the plane of primitive polaris- ation, the whole thickness of the glass will be covered with coloured fringes, consisting of a negative set separated from a positive set by the dark neutral line M N. The fringes on the convex side A B are negative, and those on the concave side positive. As the bending force increases, the tints increase in number ; and as it diminishes, they diminish in number, disappearing entirely when the 336 A TREATISE ON OPTICS. PART II. plate of glass recovers its shape. The tints which are those of Newton's scale, vary with their distances from M N ; and when two such plates, A B, C D, as that shown in fig. 1 59. slightly bent so as to produce only the first order of colours, cross each other, they show in the square of intersection, as in the annexed figure, rectilineal fringes parallel to the diagonal of the square which JQins the angles where the two concave and the two convex sides of the plates meet. When a plate of bent glass, A B, is made to cross a plate C D crystallised by heat, and suddenly cooled, the fringes in the square of intersection are parabolas, whose vertex will be towards the convex side of the bent plate, if the principal axis of the other plate is positive) but towards the concave side, if that axis is negative. The effects of compression and dilatation may be most distinctly seen by pressing or dilating plates or cylinders of calves' feet jelly or soft isinglass. M. Fresnel applied such a high pressure to Glass that he produced a distinct separation of the doubly refracted pencils. The most remarkable influence of pressure, however, is that which it produces on a mixture of resin and white wax. In all the cases hitherto mentioned of the artificial production of double refraction, the phenomena are related to the shape of the mass in which the change CHAP. XXXVIII. POLARISATION BY COMPRESSION. 337 is induced : but I have been able to communicate to the compound above mentioned a double refraction, similar to that which exists in the particles of crystals. I took a few drops of the melted compound (rosin and bees' wax), and placed them in succession on a plate of thick glass, so as to form a large drop. Before it was cold I laid above the drop a circular piece of glass about two thirds of an inch in diameter, and, by a strong vertical pressure on the centre of the piece of glass, I squeezed out the drop into a thin plate. This plate was now almost perfectly transparent, as if the pressure had brought the particles of the substance into optical con- tact. If we expose this plate to polarised light, we shall find that it possesses one positive axis of double refrac- tion, and exhibits the polarised tints as perfectly as many crystals of the mineral kingdom. The structure thus communicated to the soft film by pressure does not belong to it as a whole, nor has it only one axis passing through its centre, like a circular piece of unannealed glass. In every point of it there is an axis of double refraction perpendicular to the plates, and the doubly- refracting force varies with the inclination of the inci- dent ray to this axis, as in all regular uniaxal crystals. When the two plates of glass are drawn asunder, \ve can remove one or more portions of the compressed plate, and these portions act upon light exactly like plates of uniaxal mica or hydrate of magnesia, and develope a doubly-refracting force of nearly equal intensity. By reasoning from this experiment, I was led to the opinion that double refraction is acquired by the particles of bodies at the instant of their aggregation, and arises from the pressures produced in the direction of three rectangular axes, by the forces of aggregation. When these forces are very weak, double refraction will not be produced ; when they are sufficiently strong arid of equal intensity, they will produce tessular crystals ; when they are equal in two rectangular directions, they will produce uniaxal crystals ; and when they are un- 338 A TREATISE ON OPTICS. PART II. equal in all the three directions, they will form biaxal ones. In this way all the phenomena of cleavage may he readily explained.* 4. On the Influence of Compression and Dilatation on regularly Crystallised Bodies. (166.) 1. On Crystals without Double Refraction. When plates of Rock Salt, Alum, Fluor Spar, Diamond, Garnet, and other minerals that have no double re- fraction are subjected to compressing or dilating forces, they receive the doubly refracting structure like glass, and are therefore temporarily converted into doubly re- fracting crystals, and exhibit the tints of such crystals when exposed in the polariscope, or in the apparatus in Jfr.112. When the pressure is applied by a point at the centre of a small circular piece, or of a larger piece not circular, of any of these bodies, the doubly refracting force is symmetrical round that centre, and is negative as in Calcareous Spar, and the system of coloured rings with the black cross is exhibited in the polariscope, the tints rising of course with the intensity of the pressure, and depending on the compressibility of the crystal. In some recent experiments on this subject, M. Wertheim f found, as I had done before, that a given pressure on all the sides of the cubes of Rock Salt and Fluor Spar produced the same degree of double refrac- tion. When pressure was applied to the cubical and octohedral faces of the crystals of Alum, he found that the double refraction often varied in the ratio of 1 to 4 upon different faces. M. Wertheim also observed a very considerable non-coincidence between the optical and the mechanical axes of certain crytals of Alum and Fluor Spar. 2. On Doubly Refracting Crystals. By applying compressing and dilating forces to minerals, I have * See Phil. Trans. 1815, p. 31., and 1830, p. 37. f Comptes Rendus, #c., Aout, 1852, torn. xxxv. p. 276. CHAP. XXXVIII. succeeded in altering their doubly refracting structure in every direction ; but tbe effect was always most easily seen wben it was produced along the real axes of uniaxal crystals, or the resultant axes of biaxal ones, where the effect of the natural forces was either nothing, or compensated. The following were some of the re- sults to which I was led by applying the forces to parallel surfaces. Axis of Compression and Dilatation parallel to the Axis of the Crystal r Compressed . . . ( Tints rise in New- f < Positive crystals. . Negative crystals . ton's scale. Dilated ( Tints descend in ( Newton's scale. Compressed. . . . C Tints descend in | Newton's scale. Dilated f Tints rise in New- ton's scale. Axis of Compression and Dilatation perpendicular to the Axis of the Crystal f Compressed . . . . { Tints descend in . . I Newton's scale. Posmve crystals. . . . ' ( ton's scale. f Compressed . . . . C Tints rise in New- XT / ton's scale. Negative crystals . . . Dilated ....... * Tmts degcend Jn Newton's scale. The axis of compression and dilatation is the line perpendicular to the two surfaces pressed together or drawn asunder. The above results were obtained by experiments both on uniaxal and biaxal crystals. When the axis of compression was perpendicular to the axis of double refraction of an uniaxal crystal, it was partially converted into a biaxal one with two axes, the poles of the resultant axes being distinctly visible.* * Edin. Transactions, vol. viii. p. 281. 2 2 340 A TREAlISE ON OPTICS. PART II. In repeating these experiments MM. Moigno and Soleii found that in Rock crystal and other positive crystals, the uniaxal system of rings was doubled in the direction of the compression, and in Beryl and other negative crystals, the uniaxal rings were doubled in a direction perpendicular to the direction of the pressure.* 5. On the Influence of Induration. (167.) In 1814 I had occasion to make some ex- periments on the influence of induration in communi- cating double refraction to soft solids. When isinglass is dried in a glass trough of a circular form, it exhibits a system of tints with the black cross exactly like negative crystals with one axis. When a thin cylin- drical plate of isinglass is indurated at its circumference, it produces a system of rings with one positive axis, If the trough in the first of these experiments and the plate in the second are oval, two axes of double refrac- tion will be exhibited. W r hen jelly placed in rectangular troughs of glass is gradually indurated, we have a positive and a negative structure developed, and these are separated by a black neutral line. If the bottom of the trough is taken out, so as to allow the induration to go on at two parallel surfaces, the same fringes are produced as in a rectan- gular plate of glass heated in oil, and subsequently cooled, f Spheres and spheroids of jelly may be made by pro- per induration to produce the same effects as spheres and spheroids of glass when heated or cooled. The lenses of almost all animals possess the doubly refracting structure.:}: In some there is only one structure, which is generally positive. In others there are two structures, a positive and a negative one ; and in many there are three structures, a negative between two positive, and a positive between two negative structures. In some in- * Moipno, Repertoire, fyc., torn. iv. p. 1593. t See Phil. Trans. 1816. p. 105 and 174. J Ib. 1815, p. 41., 1816, p. 311., and 1837, p. 253. CHAP. XXXIX. COMPOSITE OR TESSELATED CRYSTALS. 341 stances we have two structures of the same name toge- ther. By the process of induration we may remove entirely the natural structure of the lens, especially when it is spherical or spheroidal, and superinduce the structure arising from induration. I have now be- fore me a spheroidal lens of the boneto fish, with a beautiful negative system of seven rings along the axis of the spheroid, and two systems along the equatorial diameters. I have also several indurated lenses of the cod, which have been preserved for many years in glass troughs of Canada balsam, and which display in the finest manner their doubly refracting structure. CHAP- XXXIX. * PHENOMENA OF COMPOSITE OR TESSELATEP CRYSTALS. (168.) IN every regularly formed doubly refracting crystal the separation of the two images, the size of the rings, and the value of the tints, are exactly the same in all parallel directions. If two crystals, however, have grown together with their axes inclined to one another, and if we cut a plate out of these united crystals so that the eye cannot distinguish it from a plate cut out of a single crystal, the exposure of such a crystal to polarised light will instantly detect its com- posite nature, and will exhibit to the eye the very lines of junction. This will be obvious upon considering that the polarised ray has different inclinations to the axis of each crystal, and will therefore produce different tints at these different inclinations. Hence the ex- amination of a body in polarised light furnishes us with a new method of discovering structures which cannot be detected by the microscope, or any other method of observation ; and enables us to determine whether minerals and other crystallised bodies are simple or compound. Two good examples of this are exhibited in Harmo- z 3 342 A TREATISE ON OPTICS. tome, or Cross stone, which, notwithstanding the op- posite opinion of Rome cle Lisle, Haiiy thought might be a simple crystal, and in the Bipyramidal Sulphate of Potash, which Count Bournon and other crystallographers have always regarded as a simple crystal.* When a section of the Harmotome is exposed to polarised light, it exhibits the structure in the annexed Fig. 162. A figure, (162.) which proves it to consist of two com- pressed dodecahedrons A B, C D, crossing each other at angles of 90. The Bipyramidal Sulphate of Potash consists, as its name denotes, of two six-sided pyramids united at their base. Upon cutting out of it a plate perpendicular to Fig. 163. > See Edin. Phil. Journal, vol. i. p. 6 3 7, 181S. CHAP. XXXIX, COMPOSITE OR TESSELATED CRYSTALS, 343 the axes of the pyramid, I found it to exhibit the struc- ture in the annexed figure (163.), proving that it was composed of three rhomboidal prisms, A B, CD, and E F, each prism having two axes of double refraction. When we incline the plate to the polarised ray each of the prisms displays different colours, and by turning it round, each of them becomes dark in succession. These results have been lately confirmed by M. Pasteur.* In the examination of minerals and artificial crystals, I have found many examples of this composite structure, a few of which are so interesting as to merit particular notice. (169.) The Apophyllite from Faroe generally crys- tallises in right-angled square prisms, and splits with great facility into plates by planes perpendicular to the axis of the prism. If we remove with a sharp knife the uppermost slice A of the prism A a, fig. l6j., or the undermost a, it will be found to have one axis of double refraction, and to give the single system of rings shown in fig. 119. If we remove another slice at B or 6, it also has one axis, and is surrounded with a border of rectilineal veins, or edges of plates. Another slice from C or e, has also one axis with two borders, and a clear space between, and the central slice at D has the curious tesselated structure shown in fig. 164. The outer case, M O N P, consists of 164. a number o f parallel veins or " plates, sometimes divided into two sets with a space between. In the centre of the figure is a small lozenge, abed, with one axis of double refraction, and round it are four crystals, A, B, C, D, with two axes of double refrac- tion, the plane passing through the axes of A and D being perpendicular to the plane passing through the axes of B and C ; and the former * Comptes Rendus, &c. 1848, torn. xxvi. p. 304. 344 A TREATISE ON OPTICS. plane being in the direction M N, and the latter in the direction O P. In the Barrel Apophyllite from Greenland, of which I received fine specimens from Sir Chas. Giesecke, the first slice has one axis of double refraction. The se- cond slice has a tesselated appearance, which varies in different crystals as shown in figs. 165. and 166. In Fig. 165. both these figures the shaded part has only one axis of double refraction, while the four sectors have two Fig. 166. axes, the plane of the resultant axes in A and C being at right angles to that passing through the resultant axes in B and D, When the polarised light is transmitted through the faces of certain prisms, the beautiful tesselated figure shown in fig. 167. is exhibited, all the differently shaded CHAP. XXXIX. COMPOSITE OR TESSELATED CRYSTALS. 345 parts shining with the most splendid colours. As the prism has everywhere the same thickness, it is Fig. 167. obvious that the doubly refracting force varies in different parts of the crystal ; but this variation takes place in such a symmetrical manner in relation to the sides and ends of the prism, as to set at defiance all the recognised laws of crystallography. With the view of observing the form of the lines of equal colour, I immersed the crystal in oil, and transmitted the polarised light in a direction parallel to a diagonal of the prism ; the effect then exhibited is shown in fig. 168., where A BCD is the crystal; AC, and BD, its edges, where the thickness is nothing, and mn the edge through which the diagonal of the pig. 168. prism passes. A Now, it is ob- vious, that if this had been a regular crystal, the lines of equal tint or of equal double refraction would have been all straight lines parallel to AC or BD; but in the apo- phyllite they present the most sin- gular irregularities, all of which are, however, symmetrically re- lated to certain fixed points with- in the crystal. In the middle of the crystal, half way between m and ra, there are only five fringes or orders of colours ; at points equidistant from this there are six fringes, the sixth returning into itself in the form of an oval. At other two equidistant points c 346 A TREATISE OX OPTICS. PART II. near m and n, the 3d, 4th, and 5th fringes are sin- gularly serrated, and the 6th and 7th fringes return into themselves in the form of a square ; beyond this, near m and w, there are only four fringes, in conse- quence of the fifth returning into itself.* In his beautiful Memoir on Lamellar Polarisation, to which we have had occasion to refer, M. Biot has en- deavoured to give an explanation of these singular phe- nomena in Apophyllite, by showing the effect of a lamellar structure upon the molecular structure, which produces one positive axis of double refraction. " The general idea/' he says, " which we may form of the crystals of Apophyllite, is to conceive that they have a positive molecular axis of double refraction coincident with the axis of the primitive prism, with two orders of lamellar systems, one perpendicular to the axis, and ex- isting always with unequal degrees of intensity, and the others occasional and composed of laminae which may be directed obliquely to this axis with all degrees of in- clination, even till it becomes parallel to it." That a lamellar structure exists in Apophyllite there can be no doubt, and that the hypothetical combination of laminae imagined by M. Biot would explain some of the more general phenomena exhibited by that mineral we willingly admit ; but such a structure is scarcely to be reconciled with the principles of crystallography, and there are many of the phenomena seen both along the axis of the crystal and perpendicular to it which we cannot explain, even with the help of the most complex system of laminae. It is impossible to overrate the talent and ingenuity displayed in the remarkable Me- moir of M. Biot, and we recommend it to our country- men as one of the finest models of inductive research. There is one addition, however, which I would pro- pose to make to M. Biot's hypothesis, and which might be auxiliary to his, namely, that the laminae may have, as I have found them in some other minerals to have, * See Edinburgh Transactions, 1822, vol. ix. p. 270. 11 A P. XXXIX. COMPOSITE OR TESSELATED CRYSTALS. 347 different degrees and kinds of molecular double refrac- tion, varying from a neutral lamina where there is no double refraction to positive and negative double refrac- tion on each side of it. This singular structure exists in certain biaxal crys- tals of Chabasie*; one of which is shown in the annexed figure. The small central rhomb is a crystal Fig. 169. with regular double refraction, but in consequence of some change in the state of the solution, the molecules not only begin to form a hemitrope crystal on all the sides of the rhomboidal nucleus, but each successive stratum has an inferior doubly refracting force till it wholly disappears at the dark lines in the figure. Be- yond this limit it reappears with an opposite charac- ter, and gradually increases till the crystal is complete. In some of the specimens, the lines of equal double refraction parallel to the sides of the rhomb have an angular notch pointing to the nucleus, and indicating some intruding influence that continued during the for- mation of the strata that have the notched lines. In the Chabasie from the Giants' Causeway, which has two axes, and a much greater double refraction, with a less ordinary refraction than the common variety, the structure is singularly composite, and in the Cha- basie from Faro the little transparent rhombohedra * See Phil. Trans. 1830, p. 93. 348 A TREATISE ON OPTICS. PART II. consist of four crystals separated by the two diagonals of the rhombic faces, The Arseniate of Iron is another composite crystal, some of the crystals having a yellow nucleus with green strata around it. The nucleus was a regular crystal, and the strata were hemitrope like those in Chabasie. The Brazilian topaz is also a composite crystal, com- posed as in the annexed figure (170.). The inner nucleus has generally a different colour from the outer portions, which are bounded by curve lines, the one being pink and the other yellow. Sometimes one portion only, A D, is pink and the rest yellow, and in other specimens, rhomboidal spaces of pink appear at the angles C, D. The outer portions consist of minute strata with their neutral axes not parallel but inclined to each other.* One of the most interesting examples of composite crystallisation is exhibited in certain specimens of Aplome Garnety the external dodecohedral form of which is shown in the annexed figure (171.) Each rhomboidal face having a sort of tesselated structure arising from an increase of transparency at the edges, which gives a fine appearance to the crystal when it is completely de- veloped. When a parallel plate is cut out of this solid, it appears to consist of a nucleus of a green colour sur- rounded by various laminae of different thicknesses and See Cambridge Transactions, 1822. CHAP. XXXIX. COMPOSITE OR TESSELATED! CRYSTALS. 34$ Fig. 171. different tints parallel to the sides of the rhomboid. These tints, by common light, vary from pale green to orange yellow, and when this plate was exposed to po- larised light, the internal nucleus exhibited no double refraction, but the surrounding strata possessed dis- tinctly a doubly refracting structure increasing gradually from the nucleus to the external layer, analogous to one of the structures in Chabasie.* (170.) A composite structure of a very different kind, but extremely interesting from the effects which it pro- duces, is exhibited in many crystals of Iceland spar, which are intersected by parallel films or veins of vari- ous thicknesses, as shown in fig. 172. These thin veins or strata are perpendicular to f the short diagonals E F, GH of the faces of the rhomb, and parallel to the edges EG, FH. When we look per- pendicularly through the faces AEBF, DGCH, the light will not pass through JH anv f tne pl anes eb eg, A B C D, afh d, and consequently we shall only see two images of any object just as if the planes were not there. But if we look through any of the other two pair of parallel faces, we shall observe the two common images at their usual distance ; and at * See Phil. Mag. 1836, vol. ix. J6G. 170. Fiy. 172. 350 A TREATISE ON OPTICS. PART II. a much greater distance, two secondary images, one on each side of the common images. In some cases there are four, and in other cases six, secondary images, ar- ranged in two lines ; one line being on each side of the common image, and perpendicular to the line joining their centres. When the interrupting planes are nu- merous, and especially when they are also found per- pendicular to the short diagonals of the other two faces of the rhomb that meet at B, the obtuse summit, the secondary images are extremely numerous, and some- times arranged in pyramidal heaps of singular beauty, vanishing, and reappearing, and changing their colour and the intensity of their light, by every inclination of the plate. If the light of the luminous object is polar- ised, the phenomena admit of still greater variations. When the strata or veins are thick, the images are not coloured, but have merely at their edges the colours of refracted light. Malus considered these phenomena as produced by fissures or cracks within the crystal, and he regarded the colours as those of thin plates of air or space ; but I have found that they are produced by veins or twin crys- tals firmly united together so as to resist separation more powerfully than the natural cleavage planes, and I have found this both crystallographically, by measuring the angles of the veins, and optically, by observing the system of rings seen through the veins alone. This composite structure will be understood from fig. 1?3., where A B D C is the principal section of Fig. 173. a rhomb of Iceland spar whose axis is A D. The CHAP. XXXIX. COMPOSITE OR TESSELATED CRYSTALS. 351 form and position of one of the intersecting veins or rhomboidal plates is shown at M m N n, but greatly thicker than it actually is ; the angles A m M, and D n N, being 141 44/. A ray of common light R 6, incident on the face A C at 6, will be refracted in the lines b c, b d. These rays entering the vein M m N n, at c and d, will be again refracted doubly ; but as the vein is so thin as to produce the complementary colours of polar- ised light by the interference of the two pencils which compose each of the pencils c e, d f, these colours will depend on the thickness of the vein M N, and on the inclination of the ray to the axis of the plate M N. These double pencils will emerge from the vein at ef, and will be refracted again as in the figure into the pencils e m, e n,fo, fp; the colours of e n, f o, being complementary to those of em,fp. That the multiplication and colour of the images are owing to the causes now explained may be proved ocularly, as I have done, by dividing rhombs of calcareous spar, and inserting between them, or in grooves cut in a single plate of calcareous spar, a thin film of sulphate of lime or mica. In this way all the phenomena of the natural compound crystal may be reproduced in the artificial one, and we may give great variety to the phenomena by inserting thin films in different azimuths round the polarised pencils b c, b d, and at different inclinations to the axis of double refraction. The compound crystal shown in fig. 173. is in re- ality a natural polarising apparatus. The part of the rhomb A m N C, polarises the incident light R b. The vein M N is the thin crystallised vein whose colours are to be examined ; and the part B M n D is the analysing rhomb.* (171.) Though but slightly connected with the subject of composite crystals, we may here describe a remarkable structure in Calcareous Spar, in virtue of which beauti- ful rings of light are seen in connection with a luminous * See Phil. Trans., 1815, p. 270. A TREATISE ON OPTICS. PART II. body when viewed through a rhomb of the spar. In one position of the rhomb, the two rings Fig. 174. A, B are equal, passing through S, which consists of the two images formed by double refraction. By inclining the plate, the ring A gradually becomes less and less, while B becomes larger and larger till A disappears in S. By continuing the inclination in the same direction, the ring A reappears, but within the ring B, and always touching S> and gets larger and larger along with B, till the two nearly unite in a straight line, and bend in the op- posite direction. The two rings are produced from the two images formed by double refraction, and hence the li^ht of one ring is oppositely polarised to that of the other. When the rings disappear, the ray to which they belong is refracted in a direction parallel to the edge of the rhomb. By inclining die plate in different azimuths, the rings undergo many changes, which it is unnecessary to describe. At oblique incidences the rings are highly coloured, and when the dispersive action is small, they have a bright silvery whiteness. When with a strong light we look at them through coloured glasses, such as the blue cobalt glass, the effect is singularly fine. I have ascertained that these rings are produced by reflexion from the surfaces of minute tubes in the mineral, of which there are several thousands in an inch, and that these tubes are parallel to the edges of the rhomb, namely, to that edge to which the refracted ray was parallel when each ring disappeared. Luminous rings are produced also in Beryl. They consist of two rings oppositely polarised, and arise from tubular cavities that contain or have contained the new fluids which I found in Topaz.* * See Phil. Mag. 1848, vol. xxxiii. p. 489. CHAP. XL. ABSORPTION OF POLARISED LIGHT. 353 CHAP. XL. ON THE DICHROISM, OR DOUBLE COLOUR, OP BODIES ; AND THE ABSORPTION OF POLARISED LIGHT. (172.) IF a crystallised body has a different colour in different directions when common light is transmitted through its substance, it is said to possess diehroism, which signifies two colours. Dr. Wbllaston observed this property long ago in the potash muriate of palla- dium, which appeared of a deep red colour along the axis, and of a vivid green in a transverse direction ; and 3VI. Cordier observed the same change of colour in a mi- neral called iolite, to which Hatty gave the name of dichroite. Sir John Herschel has observed a similar fact in a variety of sub -oxy 'sulphate of iron, which is of a deep blood red colour along the axis, and of a light green colour perpendicular to the axis. In examining this class of phenomena, I have found that they depend on the absorption of light, being regulated by the in- clination of the incident ray to the axis of double re- fraction, and on a difference of colour in the two pencils formed by double refraction. In a rhomb of yellow Iceland spar the extraordinary image was of an orange yellow colour, while the ordi- nary image was yellowish white. Along the axis the colour and intensity of the .c'S Deep orange. }> gjs^ and 7 1 .2"o Lemon yellow. J ^ 1 J S Deep orange. J A is the real ship, and B, C the images seen by unusual refraction. Upon looking at another ship, Dr. Vince saw inverted images of some of its parts which suddenly appeared and vanished, "first appearing," says he, " below, and running up very rapidly, showing more or less of the masts at different times as they broke out, re- sembling in the swiftness of their breaking out the shooting of a beam of the aurora borealis." As the ship continued to descend, more of the image gradually appeared, till the image of the whole ship was at last ^rf' completed, with the mainmasts in contact. When the ship descended CHAP, XLI. UNUSUAL RKFIIACTION, 365 still lower, the image receded from the ship, but no second image was seen. Dr. Vince observed another, shown in fig. 178., but in which the sea was distinctly p. ,-g seen between the ships B, C. As the ship A came above the horizon, the image C gradually disappeared, and during this time the image B descended, but the ship did not seem so near the horizon as to bring the mainmasts together. The two images were visible when the whole ship was beneath the horizon. Captain Scoresby, when navigat- ing the Greenland seas, observed se- veral very interesting cases of unusual refraction. On the 28th of June, 1820, he saw from the mast-head eighteen sail of ships at the distance of about twelve miles. One of them was drawn out, or lengthened, in a verti- cal direction; another was contracted in the same direction ; one had an inverted image imme- diately above it ; and other two had two distinct inverted images above them, accompanied with two images oi the strata of ice. In 1822, Captain Scoresby recognised his father's ship, the Fame, by its inverted image in the air, although the ship itself was below the horizon. He afterwards found that the ship was seventeen miles be- yond the horizon, and its distance thirty miles. In all these cases, the image was directly above the object ; but on the 17th of September, 1818, MM. Jurine and Soret observed a case of unusual refraction, where the image was on one side of the object. A bark about 4000 toises distant was seen approaching Geneva by the left bank of the lake, and at the same moment there was seen above the water an image of the sails, which, in place of following the direction of the bark, receded from it, and seemed to approach Geneva by the right bank of the lake ; the image sailing from east to west, 366 A TREATISE ON OPTICS. while the bark was sailing from north to south. The image was of the same size as the object when it first receded from the bark, but it grew less and less as it re- ceded, and was only one half that of the bark when the phenomenon ceased. While the French army was marching through the sandy deserts of Lower Egypt, they saw various pheno- mena of unusual refraction, to which they gave the name of mirage. When the surface of the sand was heated by the sun, the land seemed to be terminated at a certain distance by a general inundation. The villages situated upon eminences appeared to be so many islands in the middle of a great lake, and under each village there was an inverted image of it. As the army approached the boundary of the apparent inundation, the imaginary lake withdrew, and the same illusion appeared round the next village. M. Monge, who has described these appearances in the Memoir es sur f Egypt e, ascribes them to reflexion from a reflecting surface, which he supposes to take place between two strata of air of different density. One of the most remarkable cases of mirage was ob j served by Dr. Vince. A spectator at Ramsgate sees the tops of the four turrets of Dover Castle over a hill between Ramsgate and Dover. Dr. Vince, however, on the 6th of August, 1806, at seven P.M., saw the whole of Dover Castle, as if it had been brought over and placed on the Ramsgate side of the hill. The image of it was so strong that the hill itself was not seen through the image. The celebrated fata morgana, which is seen in the straits of Messina, and which for many centuries aston- ished the vulgar and perplexed philosophers, is obviously a phenomenon of this kind. A spectator on an eminence in the city of Reggio, with his back to the sun and his face to the sea, and when the rising sun shines from that point whence its rays fall at an angle of about 45 oh the sea of Reggio, sees upon the water numberless series of pilasters, arches, castles well delineated, regular co- lumns, lofty towers, superb palaces with balconies and windows, villages and trees, plains with herds and flocks, CHAP. XLI. UNUSUAL REFRACTION. Fig. 179. 36? armies of men on foot and on horseback, all passing rapidly in succession on the surface of the sea. These same objects are, in particular states of the atmosphere, seen in the air, though less vividly ; and when the air is hazy they are seen on the surface of the sea, vividly coloured, or fringed with all the prismatic hues. (180.) That the phenomena above described are gene- rally produced by refraction through strata of air of diffe- rent densities may be proved by various experiments. In order to illustrate this, Dr. Wollaston poured into a square phial (fig. 179*) a small quan- tity of clear syrup, and above this he poured an equal quantity of water, which gradually combined with the syrup, as seen at A. The word Syrup upon a card held behind the bottle ap- peared erect when seen thro ugh the pure syrup, but inverted, as represented in the figure, when seen through the mix- ture of water and syrup. Dr. Wollaston then put nearly the same quantity of rectified spirit of wine above the water, as in the same figure at B, and he saw the appearance there represented, the true place of the word Spirit, and the in- verted and erect images below. Analogous phenomena may be seen by looking at ob- jects over the surface of a hot poker, or along the surface of a wall or painted board heated by the sun. The late Mr. H. Blackadder has described some phe- nomena both of vertical and lateral mirage as seen at King George's Bastion, Leith, which are very instruc- tive. The extensive bulwark, of which this bastion forms the central part, is formed of huge blocks of cut sandstone, and from this to the eastern end the pheno- mena arc best seen. To the east of the tower the bulwark is extended in a straight line to the distance of 500 feet. It is eight feet high towards the land, with a footway about two feet broad, and three feet from the A TREATISE ON OPTICS. PART III. ground. The parapet is three feet wide at top, and is slightly inclined towards the sea. When the weather is favourable, the top of the parapet resembles a mirror, or rather a sheet of ice ; and if in this state another person stands or walks upon it, an observer at a little distance will see an inverted image of the per- son under him. If, while standing on the footway another person stands on it also, but at some distance, with his face turned towards the sea, his image will appear opposite to him, giving the appearance of two persons talking or saluting each other. If, again, when standing on the footway, and looking in a direction from the tower, another person crosses the eastern extremity of the bulwark, passing through the water- gate, either to or from the sea, there is produced the appearance of two persons moving in opposite directions, constituting what has been termed a lateral mirage : first one is seen moving past, and then the other in an oppo- site direction, with some interval between them. In looking over the parapet, distant objects are seen variously modified ; the mountains (in Fife) being converted into immense bridges ; and on going to the eastern extre- mity of the bulwark, and directing the eye towards the tower, the latter appears curiously modified, part of it being as it were cut off and brought down, so as to form another small and elegant tower in the form of certain sepulchral monuments. At other times it bears an exact resemblance to an ancient altar, the fire of which seems to burn with great intensity.* (181.) In order to explain as clearly as possible how the erect and inverted image of a ship is produced as in fy. 1?8., let S P (fig. 1 80.) be a ship in the horizon, seen at E by means of rays S E, P E passing in straight lines through a track of air of uniform density lying be- tween the ship and the eye. If the air is more rare at c than at a, which it may be from the coldness of the sea below , its refractive power will be less at c than at a. * Edinburgh Journal of Science, No. V. p. 13. CHAP. XLI. UNUSUAL REFRACTION. 369 In this case, rays S d, P e, which, under ordinary cir- cumstances, never could have reached the eye at E, will rig. iso. he bent into curve lines P c, S d ; and if the variation of density is such that the uppermost of these rays S d crosses the other at any point #, then 8 d will be under- most, and will enter the eye E as if it came from the lower end of the object. If E p, E s, are tangents to these curves or rays, at the point where they enter the eye, the part S of the ship will be seen in the direction E s, and the part P in the direction E p ; that is, the image S p will be inverted. In like manner, other rays, n, P m, may be bent into curves S n E, P m E, whicl^ do not cross one another, so that the tangent E s' to the curve or ray S n will still be uppermost, and the tangent E p f undermost. Hence the observer at E will see an erect image of the ship at s' p 1 above the inverted image s p, as in fig. 178. It is quite clear that the state of the air may be such as to exhibit only one of these images, and hence these appearances may be all keen when the real ship is beneath the horizon. In- one of Captain Scoresby's observations we have seen that the ship was drawn out, or magnified, in a vertical direction, while another ship was contracted or diminished in the same direction. If a cause should exist, which is quite possible, which elongated the ship 370 A TREATISE ON OPTICS. PART III, horizontally at the same time that it elongated it verti- cally, the effect would be similar to that of a convex lens, and the ship would appear magnified, and might be recognised at a distance far beyond the limits of unas- sisted vision. This very case seems to have occurred. On the 26th July, 1798, at Hastings, at five P.M. Mr. Latham saw the French coast, which is about 40 or 50 miles distant, as distinctly as through the best glasses. The sailors and fishermen could not at first be per- suaded of the reality of the appearance; but as the cliffs gradually appeared more elevated, they were so convinced that they pointed out and named to Mr. Latham the different places they had been accustomed to visit: such as the bay, the windmill at Boulogne, St. Vallery, and other places on the coast of Picardy. All these places appeared to them as if they were sailing at a small distance into the harbour. From the eastern cliff or hill, Mr. Latham saw at once Dungeness, Dover cliffs, and the French coast, all the way from Calais,, Boulogne, on to St. Vallery, and, as some of the fisher- men affirmed, as far as Dieppe. The day was extremely hot, without a breath of wind, and objects at some dis- tance appeared greatly magnified. This class of phenomena may be well illustrated, as I have elsewhere * suggested, by holding a mass of heated iron above a considerable thickness of water, placed in a glass trough, with plates of parallel glass. By with- drawing the heated iron, the gradation of density in- creasing downwards, will be accompanied by a decrease of density from the surface, and through such a medium the phenomena of the mirage may be seen. (182.) That some of. the phenomena ascribed to unusual refraction are owing to unusual reflexion arising from difference of density, cannot, we think, admit of a doubt. If an observer beyond the earth's atmosphere at S, fig- 176., were to look at one composed of strata of different refractive powers as shown in the figure, it is obvious * Edinburgh Encyclopedia, art. Heat. CHAP. XLI. UNUSUAL REFRACTION. 37 1 that the light of the sun would he reflected at its passage through the boundary of each stratum, and the same would happen if the variation of refractive power were perfectly gradual. Well described cases of this kind are wanting to enable us to state the laws of the pheno- mena ; but the following fact, as described by Dr. Buchan, is so distinct, as to leave no doubt respecting its origin. " Walking on the cliff," says he, " about a mile to the east of Brighton, on the morning of the 18th of Novem- ber, 1804, while watching the rising of the sun, I turned my eyes directly towards the sea just as the solar disc emerged from the surface of the water, and saw the face of the cliff on which I was standing represented precisely opposite to me at some distance on the ocean. Calling the attention of my companion to this appearance, we soon also discovered our own figures standing on the summit of the opposite apparent cliff, as well as the re- presentation of a windmill near at hand. The reflected images were most distinct precisely opposite to where we stood, and the false cliff seemed to fade away, and to draw near to the real one, in proportion as it receded to- wards the west. This phenomena lasted about ten minutes, till the sun had risen nearly his own diameter above the sea. The whole then seemed to be elevated into the air, and successively disappeared, like the drawing up of a drop scene in a theatre. The surface of the sea was covered with a dense fog of many yards in height, which gradually receded before the rays of the sun. The sun's light fell upon the cliff at an incidence of about 73 from the perpendicular. Another very interesting example of unusual re- flexion occurred in Radnorshire, on the 21st August, 1851. About 2 o'clock P.M. a young lady had ascended to the top of the Mynydd, a steep hill about 500 feet above the valley of New Radnor. The sun was bright and hot, and having picked some flowers on the top of the hill. Miss E. descended a little way to a spot from which she could see the road and the carriage with her friends whom she had left. After waving her victorine, B B 2 372 A TREATISE ON OPTICS. PART IIC. which she held in her hand, to her friends, she sud- denly perceived upon turning round, a figure standing a few yards from her upon a wet spot /row which a little thin mist was rising. The figure stood exactly facing her, and wavered a little, and she did not discover it to he her own image, till she observed that like herself it held a victorine and a bunch of flowers in its hand. The dress and flowers were precisely similar to her own, and the colours so vivid that she could even see her face. The effect was the same as if she was before a looking^ glass. When she moved her hand the figure did the same. The two ladies in the carriage saw the image of Miss E., and asked her when she joined them what companion it was which was with her on the hill ! There can be no doubt that the figure was a reflexion of Miss E. from the thin mist rising from the damp ground. There was no mist but above the wet spot, and it may be proved by experiment, that when the particles of vapour are sufficiently small they reflect light as distinctly as a surface of glass.* CHAP. XLII. ON THE POLARISATION OF THE ATMOSPHERE. (183.) THE subject of the polarisation of the atmosphere, one of the most interesting Branches of modern optics, has been studied by various philosophers, but by none more successfully than by M. Arago. It is only, however, a very brief notice of so extensive a subject that we can give in this place. The first important discovery which requires to be noticed is the existence of a point in the atmosphere nearly opposite the Sun where there is no polarisation. This point, called the neutral point of Arago, by whom it was discovered, is situated about * See my Letters on Natural Magic, Lett. v. p. 125., CHAP. XLII. POLARISATION OF THE ATMOSPHERE. 373 131 above the antisolar point (Or that opposite to the sun) when he is in the horizon ; and the neutral point is in the horizon when the sun's altitude is from 11 to 12, so that the distance of the neutral from the an- tisolar point is then only 11 or 12. This neutral point is, in the lat. of St. Andrew's, above the horizon from the middle of November till the end of January. I have found that it is sometimes accompanied with a secondary neutral point, and we have then the singular phenomenon of two neutral points with horizontal pola- risation between them. A second neutral point, called the neutral point of JSabinet, by whom it was discovered, is situated about 1 8-| above the sun at the time of his rising and setting. When the sun is in the zenith, this point coincides with, the sun's centre, and as the height of the sun diminishes, the neutral point separates from the centre of the sun, or is as it were left behind him, its distance gradually increasing till it reaches 18^ when the sun sets. When the sun is 11 or 12 below the horizon either at sun- rise or sunset, this neutral point is in the horizon, and consequently 11 or 12 from the sun. As the sun rises he approaches nearer and nearer to the neutral point, till the distance between them is a minimum at noon for the day. As the theory clearly indicated the existence of a third neutral point below the sun, I laboured for a con- siderable time to discover it. I soon obtained proofs of its existence from the state of polarisation of the adjacent parts of the sky ; but it was not till the 18th February, 1845, that I obtained a distinct view of it when the sun was near the meridian. Its distance from the sun was then 15 or 16. On the 20th and 26th April, between noon and 3 h. 45 m. its distance from the sun varied from 10 to 17. As the sun's altitude increases, the neutral point approaches to the sun, and when the sun is in the zenith, both it and the neutral point of Babi- net unite in the sun's centre, and the system of lines of equal polarisation is like that of a crvstal with one 3 B 3 3?4 A TREATISE ON OPTICS. PART IIL axis. In all other positions of the sun his system of lines resembles that of biaxal crystals, the line joining the sun and the antisolar point corresponding with the line which divides the angle of the optical axes, and the neutral points corresponding with the centres of the sys- tem of biaxal rings. I have found the maximum polarisation of the at- mosphere to exist between 88 and 92 from the sun, and to be equal to a rotation of 30 of the plane of polarisation, corresponding to the degree of polarisa- tion which is produced by one reflexion from a surface of glass whose index of refraction is 1*483, at an angle of 651. The maximum distance of the neutral point of Arago from the antisolar point takes place just when there is light enough to recognise it after sunset, at which time it frequently amounts to 25. When the altitude of the sun is 45, the neutral point of Babinet is 13 5' distant from the sun, and the neutral point which I discovered is 6 42' above him. A map of the lines of equal polarisation in the at- mosphere, with additional details on the subject, will be found in Johnston's Atlas of Physical Geography, and an account of instruments for measuring degrees of po- larisation will be found in the Transactions of the Royal Irish Academy, vol. xix., part ii. CHAP. XLIII. ON THE RAINBOW. (184.) THE rainbow is, as every person knows, a luminous arch extending across the region of the sky opposite to the sun. Under very favourable circumstances, two bows are seen, the inner and the outer, or the primary and the secondary, and within the primary rainbow, and in contact with it, and without the secondary one, there have been seen supernumerary bows. CHAP. XLIII. ON THE RAINBOW. 3?5 The primary or inner rainbow, which is commonly seen alone, is part of a circle whose radius is 42. It consists of seven differently coloured bows, viz. violet, which is the innermost, indigo, blue, green, yellow, orange, and red, which is the outermost. These colours have nearly the same proportional breadth as the spaces in the prismatic spectrum. This bow is, therefore, only an infinite number of prismatic spectra, arranged in the circumference of a circle ; and it would be easy, by a circular arrangement of prisms, or by covering up all the central part of a large lens, to produce a small arch of exactly the same colours. All that we require, there- fore, to form a rainbow, is a great number of transparent bodies capable of forming a great number of prismatic spectra from the light of the sun. As the rainbow is never seen, unless when rain is actually falling between the spectator and the sky oppo- site to the sun, we are led to believe that the transparent bodies required are drops of rain, which we know to be small spheres. If we look into a globe of glass or water held above the head, and opposite to the sun, we shall actually see a prismatic spectrum reflected 'from the further side of the globe. In this spectrum the violet rays will be innermost, and the spectrum vertical. If we hold the globe horizontal on a level with the eye, so as to see the sun's light reflected in a horizontal plane, we shall see a horizontal spectrum with the violet rays innermost. In like manner, if we hold a globe in a position intermediate between these two, so as to see the sun's light reflected in a plane inclined 45 to the horizon, we shall perceive a spectrum inclined 45 to the horizon with the violet innermost. Now, since in a shower of rain there are drops in all positions relative to the eye, the eye will receive spectra inclined at all angles to the horizon, so that when combined they will form the large circular spectrum which constitute the rainbow. To explain this more clearly, let E, F, fig. 181., be drops of rain exposed to the sun's rays, incident B B 4 3*76 A TREATISE ON OPTICS. PART III. upon them in the directions RE, R F, out of the whole beam of light which falls upon the drop, those Fig. 181. rays which pass through or near the axis of the drop will be reft acted to a focus behind it, but those which fall on the upper side of the drop will be refracted, the red rays least, and the violet most, and will fall upon the back of the drop with sufficient obliquity, that many of them will be reflected as shown in the figure. These rays will be again reflected, and will meet the eye at O, which will perceive a spectrum or prismatic image of the sun, with the red space uppermost, and the violet undermost. If the sun, the eye, and the drops E, F, are all in the same vertical plane, the spectrum produced by E, F will form the colours at the very sum- mit of the bow as in the figure. Let us now suppose a drop to be near the horizon, so that the eye, the drop, and the sun are in a plane inclined to the horizon ; a ray of the sun's light will be reflected in the same manner as at E, F, with this difference only, that the plane of reflexion will be inclined to the horizon, and will form part of the bow distant from the summit Hence it is manifest, that the drops of rain above the line joining the eye and the upper part of the rainbow, and in the plane passing through the eye and the sun, will form the upper part of the bow ; and the drops to the right and left hand of the observer and without the line joining CHAP. XLIII ON THE RAINBOW. 3?7 the eye and the lowest part of the bow, will form the lowest part of the bow on each hand. Not a single drop, therefore, between the eye and the space within the bow is concerned in its production : so that, if a shower were to fall regularly from a cloud, the rainbow would appear before a single drop of rain had reached the ground. If we compute the inclination of the red ray and the violet ray to the incident rays R E, R F, we shall find it to be 42 2' for the red, and 40 17' for the violet > so that the breadth of the rainbow will be the difference of these numbers, or 1 45', or nearly three times and a half the sun's diameter. These results coincide so ac- curately with observation, as to leave no doubt that the primary rainbow is produced by two refractions and one intermediate reflexion of the rays that fall on the upper sides of the drops of rain. It is obvious that the red and violet rays will suffer a second reflexion at the points where they are repre- sented as quitting the drop, but these reflected rays will go up into the sky, and cannot possibly reach the eye at O. But though this is the case with rays that enter the upper side of the drop as at E F, or the side farthest from the eye, yet those which enter it on the under side, or the side nearest the eye, may after two reflexions reach the eye, as shown in the drops H, G, where the rays R, R enter the drops below. The red and violet rays will be refracted in different directions, and after being twice reflected will be finally refracted to the eye at O ; the violet forming the upper part, the red the under part of the spectrum. If we now com- pute the inclination of these rays to the incident rays R, R, we shall find them to be 50 5 1' for the red ray, and 54 1' for the violet ray ; the difference of which or 3 10' will be the breadth of the bow, and the dis- tance between the bows will be 8 55'. Hence it is clear that a secondary bow will be formed exterior to the primary bow, and with its colours reversed, in con- sequence of their being produced by two reflexions and 3?8 A TREATISE ON OPTICS. PART III. two refractions. The breadth of the secondary bow is nearly twice as great as that of the primary one, and its colours must be much fainter, because the bow consists of light that has suffered two reflexions in place of one. (185.) Sir Isaac Newton found the semi-diameter of the interior bow to be 42, its breadth 2 10', and its distance from the outer bow 8 30' ; numbers which agree so well with the calculated results as to leave no doubt of the truth of the explanation which has been given. But if any farther evidence were wanted, it may be found in the fact, which I observed in 1812, and which had been observed by M. Biot in 1811, that the light of both the rainbows is wholly polarised in planes passing through the eye and the radii of the arch. This result demonstrates that the bows are formed by reflex- ion at or near the polarising angle, from the surface of a transparent body. The production of artificial rain- bows by the spray of a waterfall, or by a shower of drops scattered by a mop, or forced out of a syringe, is another proof of the preceding explanation. A still simpler method, first pointed out by Mariotte, is to squirt a mouthful of water towards a dark ground or wall, op- posite to the sun, scattering it into small drops. Even the second bow may sometimes be thus seen. Lunar rainbows are sometimes seen, bnt the colours are faint, and scarcely perceptible. In 1814, I saw, at Berne, a fog-bow, which resembled a nebulous arch, in which the colours were invisible. (186.) Supernumerary bows have been long observed within the primary bow. On the 5th July, 1828, I observed three, each consisting of green and red arches, and in contact with the violet arch of the primary bow. On the outside of the outer or secondary bow also, I saw distinctly a red arch, and beyond it a very faint green one, constituting a supernumerary bow, analogous to those within the primary rainbow. In August, 1833, and on the 5th of November, 1834, I saw these phenomena with peculiar distinctness. Both CHAP. XLIII. ON THE RAINBOW. 379 the rainbows were complete, and continued for a very considerable time. The space between them was of a dark bluish purple colour, a colour far deeper than the paler blue which appeared within the inner and with- out the outer bow. The supernumerary bows were distinctly seen both within the inner and without the outer rainbow. In 1834 the space within the inner was more luminous than that without the outer bow. The supernumerary red and green bows, first explained by Dr. Young, are produced by the interference of the pencils refracted by drops of rain that are so small as the fifth part of a millimetre, or the -f^th of an inch, having the lengths of their paths slightly unequal. One of the most beautiful phenomena in optical meteorology is the simultaneous occurrence of the phe- nomenon of converging beams, with the two rainbows when the sun is near the horizon. The luminous radiations of the beams are the actual radii of the two bows, converging to their centre. This phenomenon I have only once seen, and I am not aware that it has been observed by any other person. The phenomena of rainbows have been in modern times illustrated by obtaining artificial bows from a vertical cylinder of water escaping from a reservoir, and illuminated by a horizontal beam of light, as employed by M. Babinet. The fluid may be more conveniently placed in a cylinder of glass. With such a cylinder, a centimetre in diameter, Fresnel saw fourteen fragments of bows of successive orders, and M. Babinet has ob- tained interesting results with cylinders of substances possessing double refraction. Dr. Halley has shown that the rainbow formed by three reflexions within the drops will encircle the sun itself, at the distance of 40 20', and that the rainbow formed by four reflexions will likewise encircle him at the distance of 45 33'. We have often looked, but in vain, for the first of these rainbows. M. Bravais, however, informs us that it has been seen, though very rarely, with the red rays on its outer margin. The 380 A TREATISE ON OPTICS. PART III. rainbows formed by five reflexions will be partly covered by the secondary bow. The light which forms these two last bows is obviously too faint to make any im- pression on our organs, and these rainbows have there- fore never been observed. Many peculiar rainbows have been seen and described. On the 10th August, 166*5, a faint rainbow was seen at Chartres, crossing the primary rainbow at its vertex. It was formed by reflexion from the river. On the 6th August, 1698, Dr. Halley, when walk- ing on the walls of Chester, observed a remarkable rain- bow, shown in fig. 182., where A B C is the primary bow, D H E the secondary one, and A F H G C the D A new bow intersecting the secondary bow D H E, and dividing it nearly into three parts. Dr. Halley ob- served the points F, G to rise, and the arch F G gradually to contract, till at length the two arches F H G and F G coincided, so that the secondary iris for a great space lost its colours, and appeared like a white arch at the top. The new bow, A H C, had its colours in the same order as the primary one ABC, and con- sequently the reverse of the secondary bow; and on this account the two opposite spectra at G and F counteracted each other, and produced whiteness. The sun at this time shone on the river Dee, which was unruffled, and Dr. Halley found that the bow A H C was only that part of the circle of the primary bow that would have been under the castle, bent upwards by reflexion from the CHAP. XLIV. ON HALOS AND PARHELIA. 381 river. A third rainbow seen between the two common ones, and not concentric with them, is described in Rozier's Journal, and is doubtless the same phenomenon as that observed by Dr. Halley. Red rainbows, distorted rainbows, and inverted rainbows on the grass, have been seen. The latter are formed by the drops of rain sus- pended on the spiders' webs in the fields. CHAP. XLIV. ON HALOS, CORONA, PARHELIA, PARASELENE, AND ANTHELIA. (187.) WHEN the sun and moon are seen in a clear sky, they exhibit their luminous discs without any change of colour, and without any attendant phenomena. In other conditions of the atmosphere the two luminaries not only experience a change of colour, but are surrounded with a variety of luminous circles of various sizes and forms. When the air is charged with dry exhalations, the sun is sometimes as red as blood. When seen through watery vapours, he is shorn of his beams, but preserves his disc white and colourless ; while, in another state of the sky, I have seen the sun of the most brilliant salmon colour. When light fleecy clouds pass over the sun and moon, they are often encircled with one, two, three, or even more, coloured rings, like those of thin plates ; and in cold weather, when particles of ice are floating in the lower regions, and even in warm weather when they are floating in the higher regions, the two lumi- naries are frequently surrounded with the most com- plicated phenomena, consisting of concentric circles, circles passing through their discs, segments of circles, and mock suns or moons, formed at the points where these circles intersect each other. The name halo is given indiscriminately to these 382 A TREATISE ON OPTICS. PART III* phenomena, whether they are seen round the sun or the moon. They are called parhelia when seen round the sun, and paraselenes when seen round the moon. The small halos seen round the sun and moon in fine weather, when they are partially covered with light fleecy clouds, have been also called corona. They are very common round the sun, though, from the overpowering brightness of his rays, they are best seen when he is ob- served by reflexion from the surface of still water. In June, 1692, Sir Isaac Newton observed, by reflexion in a vessel of standing water, three rings of colour round the sun, like three little rainbows. The colours of the first or innermost were blue next the sun, red without, and white in the middle between the blue and red. The colours of the second ring were purple and blue within, and pale red without, and green in the middle. The colours of the third ring were pale blue within and pale red without. The colours and diameters of the rings are more particularly given as follows : 1st Ring - Blue, white, red - Diameter, 5 6 3d Ring - Pale blue, pale red - Diameter, 1 2. On the 19th February, 1664, Sir Isaac Newton saw a halo round the moon, of two rings, as follows : 1st Ring - White, bluish, green, yellow, red - Diameter, 3. 2d Ring - Blue, green, red - Diameter, 5. 1 *. Sir Isaac considers these rings as formed by the light passing through very small drops of water, in the same manner as the colours of thick plates. On the suppo- sition that the globules of water are the 500th of an inch in diameter, he finds that the diameters of the rings should be as follows : 1st Red ring - Diameter, 7]. 2d Red ring - - Diameter, 10]. 3d Red ring . Diameter, 12 33'. OHAP. XLIV. ON HALOS AND PARHELIA. 383 The rings will increase in size as the globules become less, and diminish if the globules become larger. The halos round the sun and moon, which have ex- cited most notice, are those which are about 47 and 94 in diameter. In order to form a correct idea of them, we shall give accurate descriptions of two ; one a parhelion, and the other a paraselene. The following is the original account of a parhelion, seen by Scheiner in 1630 : (188.) The diameter of the circle MQN next to the sun, was about 45, and that of the circle O 11 P was about 95 20' ; they were coloured like the primary rainbow ; but the red was next the sun, and the other colours in the usual order. The breadths of all the arches were equal to one another, and about a third part less than the diameter of the sun, as represented in fig. 183.; though I cannot say but the whitish circle Fig. 183. O G P, parallel to the horizon, was rather broader than the rest. The two parhelia M, N were lively enough, but the other two at O and P were not so brisk. M and N had a purple redness next the sun, and were white in the opposite parts. O and P were all over 384 A TREATISE ON OPTICS. PART III. white. They all differed in their durations ; for P, which shone but seldom and but faintly, vanished first of all, being covered by a collection of pretty thick clouds. The parhelion O continued constant for a great while, though it was but faint. The two lateral parhelia M, N were seen constantly for three hours together. M was in a languishing state, and died first, after se- veral struggles, but N continued an hour after it at least. Though I did not see the last end of it, yet I was sure it was the only one that accompanied the true sun for a long time, having escaped those clouds and vapours which extinguished the rest. However, it vanished at last, upon the fall of some small showers. This phenomenon was observed to last 4J hours at least, and since it appeared in perfection when I first saw it, I am persuaded its whole duration might be above five hours. " The parhelia Q, R were situated in a vertical plane passing through the eye at F, and the sun at G, in which vertical the arches H R C, O R P either crossed or touched one another. These parhelia were some- times brighter, sometimes fainter than the rest, but were not so perfect in their shape and whitish colour. They varied their magnitude and colour according to the different temperature of the sun's light at G, and the matter that received it at Q and R ; and there- fore their light and colour were almost always fluctu- ating, and continued, as it were, in a perpetual conflict. I took particular notice that they appeared almost the first and last of the parhelia, excepting that of N. " The arches which composed the small halo M N next to the sun, seemed to the eye to compose a single circumference, but it was confused, and had unequal breadths ; nor did it constantly continue like itself, but was perpetually fluctuating. But in reality it consisted of the arches expressed in the figure, as I accurately observed for this very purpose.* These arches cut each * The four intersecting circles which form this inner halo are described from four centres, one at each angle of a small square. CHAP. XLIV. ON HALOS AND PARHELIA. 385 other in a point at Q, and there they formed a par- helion ; the parhelia M, N shining from the common intersections of the inner halo, and the whitish circle O N M P." (189.) Hevelius observed at Dantzic, on the 30th of March, l66'0, at one A. M., the paraselene shown in fig. 1 84. The moon A was seen surrounded by an entire whitish circle B C D E, in which there were two mock moons at B and D ; one at each side of the moon, con- sisting of various colours, and shooting out very long and whitish beams by fits. At about two o'clock a larger circle surrounded the lesser., and reached to the Fig. 184. horizon. The tops of both these circles were touched by coloured arches, like inverted rainbows. The infe- rior arch at C was a portion of a large circle, and the superior at F a portion of a lesser. This phenomenon lasted nearly three hours. The outward great circle vanished first. Then the larger inverted arch at C, and then the lesser; and last of all the inner circle BCDE disappeared. The diameter of this inner circle, and also of the superior arch, was 45, and that of the ex- terior circle and inferior arch was 90. c c 386 A TREATISE ON OPTICS. PART III. On another occasion Hevelius observed a large white rectangular cross passing through the disc of the moon, the moon being in the intersection of the cross, and en- circled with a halo exactly like the inner one in the preceding figure. (190.) The frequent occurrence of the halos of 22 and 46 in radius in cold weather, and especially in the northern regions of the globe, led to the belief that they must be formed by crystals of ice and snow floating in the air. Descartes supposed that they were produced by refraction, through flat stars of pellucid ice ; and Huygens, who investigated the subject, both experi- mentally and theoretically, has published an elaborate theory of halos, in which he assumes the existence of particles of hail, some of which are globular and others cylindrical, with an opaque nucleus or kernel having a certain proportion to the whole. He supposes these cylinders to be kept in a vertical position, by ascending currents of air or vapour, and to have their axes at all possible inclinations to the horizon, when they are dis- persed by the wind or any other causes. He considers these cylinders to have been at first a globular collection of the softest and purest particles of snow, to the bottom of which other particles adhere, the ascending currents preventing them from adhering to the sides ; they will, therefore, assume a cylindical shape. Huygens then supposes that the outer part of the cylinders may be melted by the heat of the sun, a small cylinder remain- ing unmelted in the centre, and that if the melted part is again frozen, it may have sufficient transparency to refract and reflect the rays of the sun in a regular man- ner. By means of this apparatus, the existence of which is not impossible, Huygens has given a solution of many of the difficulties which had been encountered in explaining the origin of halos. Sir Isaac Newton regarded the halo of 45, as pro- duced by a different cause from the small prismatic coronse ; and he was of opinion that it arose from re- fraction " from some sort of hail or snow floating in CHAP. XLIV. ON HALOS AND PAREfELIA. 387 the air in a horizontal posture, the refracting angle being about 58 or 60." When we consider, however, that water assumes in freezing a great variety of crystalline forms; that these crystals really exist in a transparent state in the atmosphere, in the form of crystals of ice, which actu- ally prick the skin like needles ; and that simple and compound crystals of snow, of every conceivable variety of shape, are often falling through the atmosphere, and sometimes melting in passing through its lower and warmer strata, we do not require any hypothetical cylinders to account for the phenomena of halos and parhelia. Mariotte, Young, Cavendish, and others, have agreed in ascribing the halo of 22 in radius, or 44 in dia- meter, to refraction through prisms of ice, with refract- ing angles of 6*0 floating in the air, and having their refracting angles in all directions. The crystals of hoar-frost have actually such angles, and if we compute the deviation of the refracted rays of the sun or moon incident upon such a prism, with the index of refraction for ice, taken at 1-31, we shall find it to be 21 50', the double of which is 43 40'. In order to explain the halo of 46, Dr. Young supposes that the rays which have been once refracted by the prism may fall on other prisms, and the effect then be doubled by a second re- fraction, so as to produce a deviation of 90. This, however, is by no means probable, and Dr. Young has candidly acknowledged the fc great apparent probability" of Mr. Cavendish's suggestion, that the external halo may be produced by the refraction of the rectangular terminations of the crystals. With an index of refrac- tion of 1*31, this would give a deviation of 45 44', or a diameter of 91 28', and the mean of several accurate measures is 91 40', a very remarkable coincidence. The existence of prisms with such rectangular ter- minations is still hypothetical ; but I have removed the difficulty on this point, by observing in the hoar-frost o c 2 388 . A TREATISE ON OPTICS. PART III. upon stones, leaves, and wood, regular quadrangular crystals of ice, both simple and compound. (191.) The subject of halos, and of what has been called Optical Meteorology, has been recently studied with singular success by M. Bravais, an officer of the French Navy, and a Professor in the Polytechnic School. His memoir on Halos* is a work of great research and talent, and contains a satisfactory explanation of almost all the complex forms which encircle the sun and moon. As the foundation of his calculations he gives the fol- lowing measures of the refractive power of the crystals of ice by which halos are produced. Index of Refraction. Extreme Red .... 1-3043 Limit of Orange and Red 1 '3078 Limit of Yellow and Orange 1 -3088 Limit of Green and Yellow - - 1-3100 Limit of Blue and Green - - 1-3133 Limit of Violet and Blue - - 1-316*2 With these indices of refraction he obtained for the halo of 22, N Q M, fig. 183, or B C D, fig. 184., the following results produced by the angles of 60 of the prisms of ice with their axes in every direction. Red Ring ... 210 371 Orange do. - . - 21 43 Yellow do. - - 21 48 Green do. - 21 57 For the halo of 46, O R P, fig. 183., or O F H, fig. 184, he obtained the following measures, the re- fraction being made by the twelve dihedral angles of 90 which the surfaces of the prism of ice form with the two bases or summits of the prism. Red Ring ... 450 6 / Orange do. - - 45 25 Yellow do. - - - 45 38 Green do. - - - 46 3 Blue do. ... 46 50 * Memoire sur le Halos, Paris, 1847, pp. 266. 4to. Extrait du Journal de VEcole Royale Poly technique, xxxi. cahier. CHAP. XLIV. ON HALOS AND PARHELIA. 38$ These results agree in a remarkable manner with the most accurate observations. The following is a brief explanation of the different parts of halos, as given by M. Bravais. The circumzenithal or upper tangential arc of the halo of 46, which is exceedingly brilliant, and a true rainbow (H R C, fig. 183.) is produced by refraction through the angles of 90 already mentioned, the axes of the prisms being vertical. When the same prisms have their axes in all directions they produce the halo of 46. The upper and lower arcs, which are tangents to the halo of 22 (the upper is shown at M C N, fig. 184., the lower should be at E) are produced by refraction through the angles of 60 when the axes of the prisms of ice are horizontal. The prisms whose axes have their point de fuite 90 from the sun produce the brightest part of these arches. When the altitude of the sun is from 35 to 40 these tangent arcs form an elliptical halo with its smaller axis vertical. They are often reduced at C to a luminous spot elongated hori- zontally, and have been called superior or inferior parhelias according as they appear at C or E, fig. 184. Coloured arches are sometimes seen to touch laterally the halo of 46 at its inferior half. They are large and brightly coloured, with the red rays and their curved side towards the sun, and are nearly great circles of the sphere. The upper tangent arc, M C N, is transformed into two infra-lateral arcs when the axes of the prisms pass from a vertical into a horizontal position. In like manner the lower tangent arc is transformed into two supra-lateral arcs. The Parhelic Circle is a whitish horizontal -circle passing through the sun at G, being either complete or incomplete, and of unequal lustre in its different parts. It is produced by reflexion from the vertical faces of the prisms whose axes are horizontal or vertical. The parhelia of 46, shown at O and P,fig. 183., appear very rarely at these points, which are the intert c c 3 390 A TREATISE ON OPTICS. PART III. sections of the halo of 46 with the parhelic circle. They are formed, according to M. Galle, by refraction through the diedral angles of 90 and by the vertical edge ; but M. Bravais regards it as more probable that they are the secondary parhelia of the parhelia of 22, and are placed at twice its azimuthal distance from the sun ; that is, they are produced by refraction through two prisms of 60. If M. Galle's explanation is cor- rect, the parhelia will cease to be visible when the sun's altitude becomes 32 II 7 8". The extraordinary halos and the extraordinary cir- cumzenithal arcs are produced by the faces of the pyramids, either complete or truncated, which terminate the prisms. The circum zenithal arcs are divided into two kinds, ordinary and extraordinary. They are nearly parallel to the horizon : they cut the vertical of the sun either above or below that luminary, and they are tangents at this point to the corresponding almi- cantar at a small circle of the sphere parallel to the horizon. The ordinary circumzenithal arcs are the tangent arcs already described, belonging to the halos of 22 and 46. The extraordinary ones are the superior arcs, which either cut or touch, or are exterior to the halo of 22, and the inferior ones are those which also cut, touch, or are inferior to the same halo. The parhelia situated on the parhelic circle at different distances from the sun are produced by asterial hexagons of ice or snow, or by asterial dodecagons of different kinds. The vertical columns of light which surmount the sun at his rising are produced by internal reflexion from the lower or upper base of the prisms with their axes vertical, the prisms having slight oscillations round the vertical ; and the lustre as well as the length of these luminous columns is increased by 3, 5, and 7 re- flexions of the same kind. The light which has expe- rienced 2, 4, and 6 reflexions of the same kind gives rise to vertical masses of light with upper and lower branches CHAP. XLIV. ON HALOS AND PARHELIA. 3$l of equal size, which attend the sun till he is from 20 to 30 high. These lights, when combined with a por- tion of the parhelic circle produce the appearance of a cross. The False Suns of Rothman, Bouguer, Cassini, Malesieu, and others may be explained by prisms with their axes vertical, or nearly so, terminated by faces al- most horizontal and inclined 89 53 f to the axis, and by rays which, entering at one of the vertical faces, are reflected twice by the internal faces of the diedral angle of 199 46' (= 2 X 89 53'), and emerge at the ver- tical face opposite to the one by which they entered. The Anthellon is a luminous white spot, which is sometimes seen in the almicantar passing through the sun, and at a point in that circle diametrically opposite to the sun. This spot has not a distinct disc. It fre- quently exceeds the sun in diameter, and is sometimes coloured at its margin. In the majority of cases the anthelion accompanies the parhelic circle, which then makes the entire circuit of the horizon. The anthelion is produced by lamellar crystals with their axes horizontal, their bases vertical, and one of their three diagonals vertical. The rays refracted by the diedral angles of 90 with their edges parallel to this diagonal will then produce the anthelia. If the bases of the crystals are striated, the anthelion may be crossed by arcs en sautoir. M. Bravais has given the name of Paranthelia to certain parhelia of a white colour which appear in the parhelic circle at an azimuthal distance varying from 90 to 140. Their lustre is feeble, and their disc, which is diffuse and nebulous, is nearly equal to that of the sun. M. Bravais admits as the general basis of his theory that the paranthelia are produced by rays of light which have undergone two internal or external reflexions on the vertical faces from vertical, triangular, or hexagonal prisms, or from the section of an asterial hexagon or dodecagon.* * Dr, Young's explanation becomes a very particular case of this theory. c c 4 392 A TREATISE ON OPTICS. PART III. M. Bravais has invented a beautiful apparatus, which may be called a Parhelioscope, for reproducing artificially parhelia and other optical phenomena caused by prisms with their axes vertical. Having seen this apparatus at work in Paris, in the hands of M. Bravais himself, we can recommend it as peculiarly fitted for the study of this class of phenomena. It consists of a hollow prism P made with plates of parallel glass and angles of 60. It Fig. 185. is filled with water at an orifice O, and by means of a metallic mounting at M it may be fixed to the extremity of a vertical axis A, which may be made to revolve by a piece of clockwork beneath. When this prism makes a hundred revolutions in a second, it reproduces in a single instant before the eye of the observer the varied series of positions of the vertical prisms of ice which produce parhelia. When the prism is illuminated with a beam of the sun's light, or with a lamp at the distance of 8 or 10 yards, it will exhibit, 1., The two parhelia opposite the sun with the white tails which accompany them. 2. The two parhelic circles (passing through the sun and parallel to the horizon) which in nature are super- posed upon one another ; the one produced by an external reflexion, and the other by two refractions and CHAP. XLIV. M. BRAVAIS' PABHELIOSCOPE. 393 one reflexion (as in the primary rainbow). 3. The coloured parhelia, which are formed at 98 from the sun by rays which have undergone two refractions and two internal reflexions. It can also produce the par- helion of 1 4^ from the sun, a parhelion which is caused by rays reflected four times from the internal vertical faces, but whose light is too feeble to have been perceived in our atmosphere. If the sun's rays fall upon the upper base of the prism at an angle of 15 or 20 with its surface, we see formed the horizontal arc which in nature is situated 46 above the sun, an arc which is rigorously circular and has the zenith for its centre. By means of the same apparatus M. Bravais repro- duces the anthelion. This is done by substituting for the prism a quadrangular plate of glass turning round one of its vertical edges. If striae are traced upon the surfaces of this plate, this artificial anthelion is crossed by two symmetrical arcs arranged en sautoir. The parhelia situated 120 from the sun may, according to M. Bravais, be explained in different ways, and appear to be produced by grooved prisms, for example, by prisms whose section represents two equi- lateral triangles, the one being turned round their com- mon centre 90. Some of the more extraordinary forms exhibited in the luminous figures produced by crystals of ice may, we think, be produced by a partial disintegration of their crystalline faces, as explained in CHAP. XXI., arid also by interior crystallized cavities or tubes which exist in ice, and the effects of which, in the case of tubes, we have already noticed as exhibited in Iceland spar. Polarisation of the Light of Halos. (192.) M. Arago was the first person who observed that the light of halos was polarised by refraction, or tan- gentially, to use M. Bravais' term in opposition to normally, which indicates polarisation by reflexion. At 20 from the sun the normal polarisation of the atmo- sphere is considerable, and must, to a certain extent, 394 A TREATISE ON OPTICS. PART III. reduce the tangential polarisation. M. Bravais has noticed the singular character of the polarisation with- out the halo of 22, and also the still more remarkable variations of polarisation within it, but as the neutral point of Babinet above the sun, and the one discovered by myself below the sun, were not then known, it was impossible to generalise his observations. When we consider that the neutral point of Babinet is continually oscillating from 10 or 12 above the sun, (that is, from within the halo of 22 to a distance above and beyond it,) and that the neutral point below the sun oscillates in a still greater degree, the polarisation of the halos of 22 and 46, and of the spaces within and beyond them, must undergo the most capricious variations, all of which, however, maybe calculated when the positions of the two neutral points are given. As' an example of this I shall give the following description of a halo which appeared on a day in which I had occasion to measure with great care the polarisation of the atmosphere, both be- fore the appearance of the halo, and after its disappear- ance. On the 28th December, 18 42, when the barometer stood at 29*56 Fahr., I made the following observations. Distance of Arago's Point Distance of Babinet s from the Antisolar Point. from the Sun. llh 38 A. M. - - 17 20' - 13 41' H 58 - - 17 21 - 13 37 1 P.M. - - 18 25 - 25 25 1 28 22 10 27 30 2 33 - 22 15 - 27 48 The following was the state of polarisation of the sky at these hours. Rotation. I lh 38 Max. Pol. in zenith plane - - 29 II 48 Ditto in horizon above sea - - 27| 11 58 Ditto ditto hazy - 26f 2 31 Max. Pol. in zenith plane - - 16 J The singular change in the state of the atmosphere shown in the diminution of the maximum polarisation to nearly one half of what it was three hours before., and in the removal of the neutral point of Babinet to such a CHAP. XLIV. POLARISATION OP HALOS. 395 distance from the sun, arose from the sudden production of a great degree of cold in the region about the sun. At Ih 0' the crystals of ice produced the halo of 46, which continued till 2h 38'. It was white and slightly brown on its inner margin. At Ih 23' its apex coin- cided nearly with the neutral point of Babinet, where the normal polarisation disappeared, and left the tan- gential polarisation unreduced, and much greater than at its lower extremities near the horizon. The singular reduction of the polarisation of the atmosphere, and the retreat of the neutral points, were obviously produced by the crystals of ice in the air. Although halos are generally represented as circles, with the sun or moon in their centres, yet their apparent form is commonly an irregular oval, wider below than above, the sun being nearer their upper than their lower extremity. Dr. Smith has shown that this is an optical deception, arising from the apparent figure of the sky, and he estimates that when the circle touches the horizon, its apparent vertical diameter is divided by the moon, in the proportion of about 2 to 3 or 4> ; and is to the horizontal diameter drawn through the moon as 4 to 3, nearly. With the view of ascertaining if any of the halos are formed by reflexion, I have examined them with doubly refracting prisms, and have found that the light which forms them has not suffered reflexion. The production of halos may be illustrated experi- mentally by crystallising various salts upon plates of glass, and looking through the plates at the sun or a candle. When the crystals are granular and properly formed, they will produce the finest effects. A few drops of a. saturated solution of alum, for example, spread over a plate of glass so as to crystallise quickly, will cover it with an imperfect crust, consisting of flat octo- hedral crystals, scarcely visible to the eye. When the observer, with his eye placed close behind the smooth side of the glass plate, looks through it at a luminous body, he will perceive three fine halos at different dis- A TREATISE ON OPTICS. PART III. tances, encircling the source of light. The interior halo, which is the whitest of the three, is formed by the re- fraction of the rays through a pair of faces in the crystals that are least inclined to each other. The second halo, which is blue without, and red within, with all the prismatic colours, is formed by a pair of more inclined faces; and the third halo, which is large and brilliantly coloured, from the increased refraction and dispersion, is formed by the most inclined faces. As each crystal of alum has three pair of each of these included prisms, and as these refracting faces will have every possible direction to the horizon, it is easy to understand how the halos are completed and equally luminous through- out. When the crystals have the property of double refraction, and when their axis is perpendicular to the plates, more beautiful combinations will be produced. The phenomena of halos may be studied by de- positing moisture upon plates of glass of different tem- peratures, and freezing it either on a frosty day or in artificial cold; and several such plates may be com- bined. (193.) Among the optical phenomena of the atmo- sphere, we may here notice that of converging and Fig. 186. CHAP. XLIV. ON HALOS AND PARHELIA. 397 diverging solar beams. The phenomenon of diverging learns, represented in fig. 186., is of frequent occurrence in summer,, and when the sun is near the horizon ; and arises from a portion of the sun's rays passing through openings in the clouds, while the adjacent portions are obstructed by the clouds. The phenomenon of con- verging beams, which is of much rarer occurrence, is shown in fig. 187 > where the rays converge to a point A, Fig. 187. as far below the horizon M N as the sun is above it. This phenomenon is always seen opposite to the sun, and generally at the same time with the phenomenon of diverging beams, as if another sun, diametrically opposite to the real one, were below the horizon at A, and throw- ing out his divergent beams. In a phenomenon of this kind which I saw in 1824, the eastern portion of the horizon where it appeared was occupied with a black cloud, which seems to be necessary as a ground for rendering visible such feeble radiations. A few minutes after the phenomenon was first seen, the converging lines were black, or very dark ; an effect which seems to have arisen from the luminous beams having become broad and of unequal intensity, so that the eye took up, as it were/ the dark spaces between the beams more readily thaii the luminous beams themselves. 398 A TREATISE ON OPTICS. PART III. This phenomenon is entirely one of perspective. Let us suppose beams inclined to one another like the me- ridians of a globe to diverge from the sun, as these meridians diverge from the north pole of the globe, and let us suppose that planes pass through all these meri- dians, and through the line joining the observer and the sun, or their common intersection. An eye, therefore, placed in that line, or in the common intersection of all the fifteen planes, will see the fifteen beams converging to a point opposite the sun, just as an eye in -the axis of a globe would see all the fifteen meridians of the globe converge to its south pole. If we suppose the axis of a globe or of an armillary sphere to be directed to the centres of the diverging and converging beams, and a plane to pass through the globe parallel to the horizon, it would cut off the meridians so as to exhibit the precise appearances in ^7. 186. and fig. 187.; with this difference only, that there would be fifteen beams in the diverging system in the place of the number shown mfig. 188.* CHAP. XLV. ON THE COLOURS OP NATURAL BODIES. (194.) There is no branch of the application of op- tical science which possesses a greater interest than that which proposes to determine the cause of the colours of natural bodies. Sir Isaac Newton was the first who entered into an elaborate investigation of this difficult subject ; but though his speculations are marked with the peculiar genius of their author, yet they will not stand a rigorous examination under the lights of modern science. That the colours of material nature are not the result * See the Edinburgh Journal of Science, April, 1832, vol. vi. on. 25. , 256. CHAP. XLV. COLOURS OF NATURAL BODIES. 399 of any quality inherent in the coloured body has been incontrovertibly proved by Sir Isaac. He found that all bodies, of whatever colour, exhibit that colour only when they are placed in white light. In homogeneous red light they appeared red, in violet light violet, and so on; their colours being always best displayed when placed in their own daylight colours. A red wafer, for example, appears red in the white light of day, because it reflects red light more copiously than any of the other colours. If we place a red wafer in yellow light, it can no longer appear red, because there is not a particle of red light in the yellow light which it could reflect. It reflects, however, a portion of yellow light, because there is some yellow in the red which it does reflect. If the red wafer had reflected nothing but pure homogeneous red light and not reflected white light from its outer surface, which all coloured bodies do, it would in that case have appeared absolutely black when placed in yellow light. The colours, therefore, of bodies arise from their pro- perty of reflecting or transmitting to the eye certain rays of white light, while they stifle or stop the remain- ing rays. To this point the Newtonian theory is sup- ported by infallible experiments ; but the principal part of the theory, which has for its object to determine the manner in which particular rays are stopped, while others are reflected or transmitted, is not so well founded. As Sir Isaac has stated the principles of his theory with the greatest clearness, we shall give them in his own -words. CentTe . Mean . Humour. 1-3366. 1-3767. 1-3990 1-3839. 1-3394. But as the rays refracted by the aqueous humour pass into the crystalline, and those from the crystalline into the vitreous humour, the indices of refraction of the separating surface of these humours will be : From aqueous humour to outer coat of the crystalline 1-0466 From do. to crystalline, using the mean index - 1 -0353 From vitreous to crystalline outer coat - - - 1 -0445 From do. to do. using the mean index - ] '0332 As the cornea and crystalline lens act upon the rays of light which fall upon the eye exactly like a convex lens, inverted images of external objects will be formed iipon the retina r r r in precisely the same manner as if the retina were a piece of white paper in the focus of a single lens placed at d. There is this difference, how- ever, between the two cases, that in the eye the spherical aberration is corrected by means of the variation in the density of the crystalline lens, which, having a greater refractive power near the centre of its mass, refracts the central rays to the same point as the rays which pass through it near its circumference c c. No provision, however, is made in the human eye for the correc- tion of colour, because the deviation of the differently coloured rays is too small to produce indistinctness of vision. If we shut up all the pupil excepting a portion of its edge, or look past the finger held near the eye, till the finger almost hides a narrow line of white light, we shall see a distinct prismatic spectrum of this line con- taining all the different colours ; an effect which could not take place if the eye were achromatic.* That an inverted image of external objects is formed on the retina has been often proved, and may be ocu- larly demonstrated by taking the eye of an ox, and paring away with a sharp instrument the sclerotic coat till it * See Lond, and Edin. Phil. Mag., March, 1835, vol. vi. pp. 161. and 247. CHAP.XLVJ. ON THE SEAT OF VISION. 409 becomes thin enough to see the image through it. Be- yond this point optical science cannot carry us. In what manner the retina conveys to the brain the impressions which it receives from the rays of light we know not, and perhaps never shall know On the Phenomena and Laws of Monocular Vision. (197.) 1. On the seat of vision. The retina, from its delicate structure, and its proximity to the vitreous humour, had always been regarded as the seat of vision, or the surface on which the refracted rays were con- verged to their foci, for the purpose of conveying the impression to the brain, till M. Mariotte made the curi- ous discovery that the base of the optic nerve, or the circular section of it at O, fig. 189, was incapable of conveying to the brain the impression of distinct vision. He found that when the image of any external object fell upon the base of the optic nerve, it instantly disap- peared. In order to prove this, we have only to place upon the wall, at the height of the eye, three wafers, two feet distant from each other. Shutting one eye, stand opposite to the middle wafer, and while looking at the outside wafer on the same hand as the shut eye, retire gradually from the wall till the middle wafer disappears. This will happen at about five times the distance of the wafers, or ten feet from the wall ; and when the middle wafer vanishes, the two outer ones will be distinctly seen. If candles are substituted for wafers, the middle candle will not disappear, but it will become a cloudy mass of light. If the wafers are placed upon a coloured wall, the spot occupied by the wafer will be covered by the colour of the wall, as if the wafer itself had been removed. According to Daniel Bernoulli, the part of the optic nerve insensible to distinct impressions occupies about the eighth of an inch. This urifitness of the base of the optic nerve for giving distinct vision, induced Mariotte to believe that theCAo- roid coat, which lies immediately below the retina, per- 410 A TREATISE ON OPTICS. PART III. forms the functions ascribed to the retina; for where there was no choroid coat there was no distinct vision. The opacity of the choroid coat and the transparency of the retina, which rendered it an unfit ground for the reception of images, were arguments in favour of this opinion. Comparative anatomy furnishes us with another argument, perhaps even more conclusive than any of those urged by Mariotte. In the eye of the sepia loligo, or cuttle-fish, an opaque membranous pigment is inter- posed between the retina and the vitreous humour * ; so that, if the retina is essential to vision, the impressions of the image on this black membrane must be conveyed to the retina by the vibrations of the membrane in front of it. Now, since the human retina is transparent, it will not prevent the images of objects from being formed on the choroid coat ; and the vibrations which they excite in this membrane, being communicated to the retina, will be conveyed to the brain. These views are strength- ened by another fact of some interest. I have observed in young persons, that the choroid coat (which is gene- rally supposed to be black, and to grow fainter by age), reflects a brilliant crimson colour, like that of dogs and other animals. t Hence, if the retina is affected by rays which pass through it, this crimson light, which must necessarily be transmitted by it, ought to excite the sensation of crimson, which I find not to be the case. The Foramen centrale, or opening in the retina, is the part of the eye where vision is most distinct. It may be rendered visible, by its properties, by looking at a feebly illuminated surface after the eye has been closed for a minute, either by shutting the eyelids or protecting the eye from the action of light. When directed to the illuminated surface, there will be seen a dark brown or reddish circular spot, which quickly dis- appears, and may be renewed by again closing the eye. * Dr. Knox, Edinburgh Journal of Science, No. VI. p. 199. f See Phil. Aa. t 1833, vol. iii. p. 288. CHAP. XLVI. ON THE SEAT OF VISION. 411 If the sensibility of the eye had been previously re- duced by exposure to much light, the circular spot would have been white, or more luminous than the il- luminated surface.* Hence it follows that in the one case the retina is more quickly affected with light than the choroid coat, and in the other that the choroid coat is more readily impressed with it. The diameter of the circular spot subtends an angle of about 4^, and the corresponding foramen in the retina must be about the 3 5th of an inch. In a case where the retina had been rendered insen- sible by a blow on the head, I found that vision was perfect over the space occupied by thefora?nen centrale. When a person was near the patient he could only see his nose or his eye, or a small portion of his face or figure, but he could recognise a friend at a distance when the whole of his face was included within the base of a cone whose angle was 4^.t A French author, M. Lehot, has recently written a work, endeavouring to prove that the seat of vision is in the vitreous humour ; and that, in place of seeing a flat picture of the object, we actually see an image of three dimensions, viz. with length, breadth, and thickness. To produce this effect, he supposes that the retina sends out a number of small nervous filaments, which extend into the vitreous humour, and convey to the brain the impressions of all parts of the image. If this theory were true, the eye would not require to adjust itself to different distances ; and we besides know for certain, that the eye cannot see with equal distinctness two points of an object at different distances, when it sees one of them perfectly. M. Lehot might indeed reply to the first of these objections, that the nervous filaments may not extend far enough into the vitreous humour to render adjustment unnecessary ; but if we admit this, we would be admitting an imperfection of workmanship, in so far as the Creator would then be employing two * Report of British Association. 1848, pp. 48, 49. t lb. ib., 1852. 412 A TREATISE ON OPTICS. PART III. kinds of mechanism to produce an effect which could have been easily produced hy either of them separately. As difficulties still attach to every opinion respecting the seat of vision, we shall still adhere to the usual ex- pression used by all optical writers, viz. that the images of objects are painted on the retina. (198.) 2. On the law of visible direction When a ray of light falls upon the retina, and gives us vision of the point of an object from which it proceeds, it becomes an interesting question to determine in what direction the object will be seen, reckoning from the point where it falls upon the retina. In fig. 190., let F be a point of the retina on which the image of a point of a distant object is formed by means of the crystalline lens, sup- posed to be at L I/. Now, the rays which form the Fig. 1 90. image of the point at F fall upon the retina in all pos- sible directions from L F to I/F, and we know that the point F is seen in the direction F C R. In the same manner, the points /,/ 7 are seen somewhere in the di- rections/ T, /S. These lines FR,/T,/S, which may be called the lines of visible direction, may either be those which pass through the centre C of the lens LL, or, in the case of the eye, through the centre of a lens equi- valent to all the refractions employed in producing the image ; or they may be the resultant of all the directions within the angles L F L/, L/L', Lf L' ; or it may be a line perpendicular to the retina at the points F,f, f. In CHAP. XLVJ. LAW OF VISIBLE DIRECTION. 413 order to determine this point, let us look over the top of a card at the point of the object whose image is at F till the edge of the card is just about to hide it, or, what is the same thing, let us obstruct all the rays that pass through the pupil excepting the uppermost, R L ; we shall then find that the point whose image is at F, is seen in the same direction as when it was seen by all the rays L F, C F, I/ F. If we look beneath the card in a similar manner, so as to see the object by the lower- most ray, R L/ F, we shall see it in the same direction. Hence it is manifest that the line of visible direction does not depend on the direction of the ray, either before or after refraction. This important truth in the physi- ology of vision may be proved in another way. If we look at the sun over the top of a card, as before, so as to impress the eye with a permanent spectrum by means of rays L F falling obliquely on the retina, this spectrum "will be seen along the axis of vision F C. In like manner, if we press the eyeballs at any part where the retina is, we shall see the luminous impression which is produced in a direction opposite to the point of pres- sure ; and if we make the pressure with the head of a pin, so as to press either obliquely or perpendicularly, we shall find that the luminous spot has in both cases the same direction.* (199-) To determine the line of visible direction has been found a matter of great difficulty. It is admitted by all, and may be rigorously proved, that at the point F of the retina, at the extremity of the axis of the eye C F, fig. 1 89,' or d O, fig. 1 9Qi, the line of visible direction is along that axis F C or O d, and consequently per- pendicular to the surface of the retina at F. Dr. Reid and others had maintained that this was true at every point of the retina ; but D'Alembert, though he ad- mitted that this ought to be the law, in conformity with the laws of mechanics which ought to regulate the action of light on the retina, yet he maintained . on * For an account of experiments on the compression and expansion ot )Uie retina, see Phil. Mag., 1832, vol. i. p. 89. 4-14 A TREATISE ON OPTICS. PART III. the authority of direct experiment, and on calculations made on the refraction of the different humours of the eye, that the law could not be true, because, if it were, the apparent magnitudes of small objects would be increased more than one-third, a result so contrary to experience that he could not suppose vision to be thus performed. Hence he is driven to the conclusion, " that any visible point which sends a ray to the cornea is seen sensibly in its true place, and consequently in the direction of a line joining the point itself and its image on the retina."* In subjecting this question to a more rigorous exa- mination, I have been able to prove, by adopting a more correct form of the globe of the eye, and using more accurate measures of the refractive powers of its coats and humours, that the mechanical law of visible direction is true, arid that at an inclination of 20 or 30, the line of visible direction which it gives does not deviate more than half a degree from the true lii>e joining the point on the retina and the corresponding point of the object, a quantity too small to be recog- nised in oblique vision. This ocular parallax, however, may be rendered visible by a slight motion of objects when the head is turned quickly away from them.t (200.) 3. On the cause of erect vision from an in- verted image. As the refractions which take place at the surface of the cornea, and at the surfaces of the crystalline lens, act exactly like those in a convex lens in forming behind it an inverted image of an erect ob- ject ; and as we know from direct experiment that an inverted image is formed on the retina, it has been long a problem among the learned, to determine how an in- verted image produces an erect object. It would be a waste of time to give even an outline of the different opinions which have been entertained on this subject ; but there is one so extraordinary as to merit notice. * D'Alembert adds, tne visible direction of the point f ! y formed by rays coming from the upper end S of the object, will be /'C S, and the visible direction of the point f } formed by rays coming from the lower end T of the object, will be/C T; so that an inverted image necessarily produces an erect object. This conclusion may be illustrated in another way. If we hold up against the sun the erect figure of a man, cut out of a piece of black paper, and look at it steadily for a little while ; if we then shut both eyes, we shall see an erect spectrum of the man when the figure of the paper is erect, and an inverted spectrum of him when the figure is held in an inverted position. In this case, there are no rays proceeding from the object to the re- tina after the eye is shut, and therefore the object is seen in the positions above mentioned, in virtue of the lines of visible direction crossing one another at a point within the eye. (201.) 4. On the law of distinct vision. When the eye is directed to any point of a landscape, it sees with perfect distinctness only that point of it which is di- rectly in the axis of the eye, or the image of which falls upon the central hole of the retina. But, though we d 41 6 A TREATISE ON OPTICS. PART III. not see any other point but one with that distinctness which is necessary to examine it, we still see the other parts of the landscape with sufficient distinctness to enable us to enjoy its general effect. The extreme mo- bility of the eye, however, and the duration of the impressions made upon the retina, make up for this apparent defect, and enable us to see the landscape as perfectly as if every part of it were seen with equal dis- tinctness. The indistinctness of vision for all objects situated out of the axis of the eye increases with their distances from that axis ; so that we are not entitled to ascribe the distinctness of vision in the axis to the circumstance of the image being formed on the central hole of the retina, where there is no nervous matter ; for if this were the case, there would be a precise boundary be- tween distinct and indistinct vision, or the retina would be found to grow thicker and thicker as it receded from the central hole, which is not the case. In making some experiments on the indistinctness of vision at a distance from the. axis of the eye, I was led to observe a very remarkable peculiarity of oblique vision. If we shut one eye, and direct the other to any fixed point, such as the head of a pin, we shall see indistinctly all other objects within the sphere of vision. Let one of these objects thus seen indistinctly be a strip of white paper, or a pen lying upon a green cloth. Then, after a short time, the strip of paper, or the pen, will disappear altogether, as if it were entirely removed, the impression of the green cloth upon the surrounding parts of the eye extending itself over the part of the retina which the image of the pen occupied. In a short time the vanished image will re-appear, and again vanish. When both eyes are open, the very same effect takes place, but not so rea- dily as with one eye. If the object seen indistinctly is a black stripe on a white ground, it will vanish in a similar manner. When the object seen obliquely is luminous, such as a candle, it will never vanish entirely, unless its light is much weakened by being placed at a great dis- CHAP.XLVI. LAW OF DISTINCT AND INDISTINCT VISION. 417 tance, but it swells and contracts, and is encircled with a nebulous halo; so that the luminous impressions must extend themselves to adjacent parts of the retina which are not influenced by the light itself. If, when two candles are placed at the distance of about eight or ten feet from the eye, and about a foot from each other, we view the one directly and the other indirectly, the indirect image will swell, as we have already men- tioned, and will be surrounded with a bright ring of yellow light, while the bright light within the ring will have a pale blue colour. If the candles are viewed through a prism, the red and green light of the indirect image will vanish, and there will be left only a large mass of yellow terminated with a portion of blue light. In making this experiment, and looking steadily and directly at one of the prismatic images of the candles, I was surprised to find that the red and green rays began to disappear, leaving only yellow and a small portion of blue ; and when the eye was kept immovably fixed on the same point of the image, the yellow light became al- most pure white, so that the prismatic image was con- verted into an elongated image of white light. If the strip of white paper which is seen indirectly with both eyes is placed so near the eye as to be seen double, the rays which proceed from it no longer fall upon similar points of the retina, and the two images do not vanish instantaneously. But when the one be- gins to disappear, the other begins soon after it, so that they sometimes appear to be extinguished at the same time. From these results it appears that oblique or indirect vision is inferior to direct vision, not only in distinctness, but from its inability to preserve a sustained vision of objects ; yet though thus defective, it possesses a su- periority over direct vision in giving us more perfect vision of very faint and minute objects, such as the tails of comets and small stars, which cannot be seen by direct vision. This curious fact, which has been long 418 A TREATISE ON OPTICS. PART III. known*, has been noticed by Sir John Herschel and Sir James South, and some of the French astronomers. " A rather singular method/' they remark, {e of obtaining a view, and even a rough measure, of the angles of stars of the last degree of faintness, has often been resorted to, viz. to direct the eye to another part of the field. In this way, a faint star, in the neighbourhood of a large one, will often become very conspicuous ; so as to bear a certain illumination, which will yet totally disappear, as if suddenly blotted out, when the eye is turned full upon it, and so on, appearing and disappearing alter- nately as often as you please. The lateral portions of the retina, less fatigued by strong lights, and less ex- hausted by perpetual attention, are probably more sen- sible to faint impressions than the central ones ; which may serve to account for this phenomenon." The following explanation of this curious phenomenon seems to me more satisfactory : A luminous point seen by direct vision, or a sharp line of light viewed steadily for a considerable time, throws the retina into a state of agitation highly unfavourable to distinct vision. If we look through the teeth of a fine comb held close to the eye, or even through a single aperture of the same nar- rowness, at a sheet of illuminated white paper, or even at the sky, the paper or the sky will appear to be covered with an infinite number of broken serpentine lines, pa- rallel to the aperture, and in constant motion ; and as the aperture is turned round, these parallel undulations will also turn round. These black and white lines are obviously undulations on the retina, which is sensible to the impressions of light in one phase of the undulation, and insensible to it in another phase. An analogous effect is produced by looking steadfastly, and for a con- siderable time, on the parallel lines which represent the sea in certain maps. These lines will break into por- tions of serpentine lines, and all the prismatic tints will be seen included between the broken curvilinear por- * Phil. Trans., 1810, p. 23., or Young's Elements of Nat. Phil., vol. ii. p. 582. CHAP. XLVI. EFFECT OF WEAK LIGHT ON THE EYE. 419 tions. A sharp point or line of light is therefore un- able to keep up a continued vision of itself upon the retina when seen directly.* Now, in the case of indirect vision, we have already seen that a luminous object does not vanish, but is seen indistinctly, and produces an enlarged image on the re- tina, beside that which is produced by the defect of con- vergency in the pencils. Hence, a star seen indirectly, will affect a larger portion of the retina from these two causes, and, losing its sharpness, will be more easily seen. It is a curious circumstance, too, that in the experiment with the two candles mentioned above, the candles seen indirectly frequently appear more intensely bright than the candle seen directly. Hence it follows that the retina is more sensible to luminous impressions, whether strong or feeble, in proportion to their distance from the axis of the eye. (202.) 5. On the insensibility of the eye to direct im- pressions of faint light. The insensibility of the retina to indirect impressions of objects ordinarily illuminated, has a singular counterpart in its insensibility to the di- rect impression of very faint light. If we fix the eye steadily on objects in a dark room that are illuminated with the faintest gleam of light, it will be soon thrown into a state of painful agitation ; the objects will appear and disappear according as the retina has recovered or lost its sensibility These affections are no doubt the source of many optical deceptions which have been ascribed to a super- natural origin. In a dark night, when objects are feebly illuminated, their disappearance and reappearance must seem very extraordinary to a person whose fear or curi- osity calls forth all his powers of observation. This defect of the eye must have been often noticed by the sportsman in attempting to mark, upon the monotonous" heath, the particular spots where moor-game had alighted. Availing himself of the slightest difference of tint in the adjacent heath, he endeavours to keep his * See Phil. Mag., 1832, vol. i. p. 169. E E 2 420 A TREATISE ON OPTICS. PART III. eye steadily upon it as he advances ; but whenever the contrast of illumination is feeble, he almost always loses sight of his mark, or if the retina does take it up a Second time, it is only to lose it again.* (203.) 6. On the duration of impressions of light on the retina. Every person must have observed that the effect of light upon the eye continues for some time. During the twinkling of the eye, or the rapid closing of the eyelids for the purpose of diffusing the lubricating fluid over the cornea, we never lose sight of the objects we are viewing. In like manner, when we whirl a burning stick with a rapid motion, its burning extre- mity will produce a complete circle of light, although that extremity can only be in one part of the circle at the same instant. The most instructive experiment, however, on this sub- ject, and one which it requires a good deal of practice to make well, is to look for a short time at the window at the end of a long gallery, and then quickly direct the eye to the dark wall. In general, the ordinary observer will see a picture of the window, in which the dark bars are white and the white panes dark ; but the practised observer who makes the observation with great prompt- ness, will see an accurate representation of the window with dark bars and bright panes ; but this representation is instantly succeeded by the complementary picture, in which the bars are bright and the panes dark. M. D'Arcy found that the light of a live coal moving at the distance of 165 feet, maintained its impression on the retina during the seventh part of a second, or Q"'133. Dr. Young found that the impression continued half a second, or 0"*5, and more recently M. Plateau has found it to be very nearly the third of a second, or 0"'34, being for White light * - 0"-35 Yellow do. - - - 0-35 Red do. ... 0*34 Blue do. ... 0-32 * See the Edinburgh Journal of Science, No. VI. p. 288. CHAP. XLVI. THAUMATROPE PHENAKISTOSCOPE. 421 The impression disappears with unequal rapidity, quickest in the white, less quick in the yellow, still less quick in the red, and slowest in the blue. Hence the im- pression is least intense in the blue, and most intense in the white. Various interesting phenomena in the natural world have their origin in this property of the retina. Jets of gas and of water appear as streams of light and of fluid, though they are detached portions only. A stone rapidly projected appears a continuous line. A de- scending meteor is seen as a long train of light, and in forked lightning, the eye combines the successive posi- tions of an electrical discharge. Many beautiful and ingenious instruments, too, are founded on the duration of impressions on the retina. The Thaumatrope, or wonder turner, invented by Dr. Paris, consists of a disc of card about 2 inches in diameter, with a drawing on each side of it. When it is twirled round by two strings, one at each end of a diameter of the circle, the two pictures are combined. If a bird is drawn on one side, and a cage on the other, the bird is seen in the cage during the twirling of the disc. The PhenaJcistoscope, or magic disc, an invention of M. Plateau, is a beautiful instrument depending on the same cause. It consists of a circular disc of paste- board, 8 or 9 inches in diameter, having twelve rectilineal slits or chinks in its margin, placed at equal distances, and in the direction of its radii. This disc can be made to revolve rapidly about its axis, and if we look into a mirror through one of the chinks when it is re- volving, they will appear to stand still in the mirror, owing to the motions of the object and its image being equal and opposite. Had there been a figure beneath each chink, each figure seen in the mirror would be stationary. If the figures were 11 in number, in place of 12, they would all appear to move in one direction ; and if they were 13, they would appear to move in the opposite direction. If we now suppose twelve gates to E E 3 422 A TREATISE ON OPTICS. PART III. be drawn on a separate disc smaller than the main one, and placed upon it so as not to interfere with its slits, these gates will stand still during the revolution of the disc. If we then place thirteen horses with their riders near the gate, one horse just before he begins to leap, the second horse with its fore legs raised from the ground, and all the other horses in the different posi- tions of leaping, till the thirteenth horse reaches the ground, the effect will be, that each horse and its rider will come up to the chink through which we look faster than the gate, and as each gate arrives, the horse will have advanced ^ part of -fa of the circumference of the disc; that is, in one complete revolution, it will have moved forward through T ^ of the circle. Had there been only eleven slits, it would have moved backward. Now, during this motion, the horse has taken thirteen different positions in succession, and therefore leaps the gate. In like manner there are twelve hedgerows, with several hounds, each of which are thirteen in number, and have thirteen different positions, so that they ap- pear in the act of crossing the hedges, and we have exhibited before us a portion of a foxhunting scene. It is obvious that if, instead of a mirror, another person whirls round in an opposite direction, and with the same velocity, a similar disc, the effect will be the same. The similar motion of the two phenakistoscopes could be obtained by machinery. Another instrument invented by Plateau, he calls the Anorthoscope, which, by means of two discs revolving with different velocities, rectifies or makes regular, and multiplies an extremely shapeless and irregular figure. (204.) 7 On the cause of single vision with two eyes. Although an image of every visible object is formed on the retina of each eye, yet when the two eyes are capable of directing their axes to any given object, it always appears single. There is no doubt that, in one sense, we really see two objects, but these objects appear as one, in consequence of the one occupying exactly the same place as the other. Single vision with two eyes, or CHAP. XLVI. ACCOMMODATION OF THE EYE. 423 with any number of eyes, if we had them, is the neces- sary consequence of the law of visible direction. By the action of the external muscles of the eyeballs, the axes of each eye can be directed to any point of space at a greater distance than 4 or 6 inches. If we look, for example, at an aperture in a window shutter, we know that an image of it is formed in each eye ; but, as the line of visible direction from any point in the one image meets the line of visible direction from the same point in the other image, each point will be seen as one point, and, consequently, the whole aperture seen by one eye will coincide with or cover the whole aperture seen by the other. If the axes of both eyes are directed to a point beyond the window, or to a point within the room, the aperture will then appear double, because the line of visible direction from the same points in each image do not meet at the aperture. If the muscles of either of the eyes is unable to direct the two axes of the eyes to the same point, the object will in that case also appear double. This inability of one eye to follow the motions of the other is frequently the cause of squinting, as the eye which is, as it were, left behind, necessarily looks in a different direction from the other. The same effect is often produced by the imperfect vision of one eye, in consequence of which the good eye only is used. Hence the imperfect eye will gradually lose the power of fol- lowing the motions of the other, and will therefore look in a different direction. The disease of squinting may be often easily cured, without having recourse to the admirable operation of cutting the muscles introduced by M. Dieffenbach. (205.) 8. On the accommodation of the eye to different distances. When the eye sees objects distinctly at a great distance, it is unable, without some change, to see objects distinctly at any less distance. This will be readily seen by looking between the fingers at a distant object. When the distant object is seen distinctly, the fingers will be seen indistinctly ; and, if we look at the fingers so as to see them distinctly, the distant object K B 4 424 A TREATISE ON OPTICS. PART III. will be quite indistinct. The most distinguished phi- losophers have maintained different opinions respecting the method by which the eye adjusts itself to different distances. Some have ascribed it to the mere enlarge- ment and diminution of the pupil ; some to the elon- gation of the eye, by which the retina is removed from the crystalline lens ; some to the motion of the crystal- line lens ; and others to a change in the convexity of the lens, on the supposition that it consists of muscular fibres. I have ascertained, by direct experiment, that a variation in the aperture of the pupil, produced arti- ficially, is alone incapable of producing adjustment; and as an elongation of the eye would alter the curvature of the retina, and consequently the centre of visible direc- tion, and produce a change of place in the image, we consider this hypothesis as quite untenable. In order to discover the cause of the adjustment, I made a series of experiments, from which the following inferences may be drawn: 1st, The contraction of the pupil, which necessarily takes place when the eye is adjusted to near objects, does not produce distinct vision by the diminution of the aperture, but by some other action which necessa- rily accompanies it. 2dly, That the eye adjusts itself to near objects by two actions ; one of which is voluntary, depending wholly on the will, and the other involuntary, depend- ing on the stimulus of light falling on the retina. 3dly, That when the voluntary power of adjustment fails, the adjustment may still be effected by the invo- luntary stimulus of light. Reasoning from these inferences, and other results of experiment, it seems difficult to avoid the conclusion that the power of adjustment depends on the mechanism which contracts and dilates the pupil ; and as this ad- justment is independent of the variation of its aperture, it must be effected by the parts in immediate contact with the base of the iris. By considering the various ways in which the mechanism at the base of the iris CHAP. XLVI. LONG AND SHORT-SIGHTEDNESS. 425 may produce the adjustment, it appears to be almost certain that the lens is drawn forward, and consequently removed from the retina by the contraction of the pupil.* / (206.) 9 On the cause of longsightedness and short- sightedness. -Between the age of 30 and 50, the eyes of most persons begin to experience a remarkable change, which generally shows itself in a difficulty of reading small type or ill-printed books, particularly by candle- light. This defect of sight, which is called longsight- edness, because objects are seen best at a distance, arises from a change in the state of the crystalline lens, by which its density and refractive power, as well as its form, are altered. It frequently begins at the margin of the lens, and takes several months to go round it, and it is often accompanied with a partial separation of the laminae and even of the fibres of the lens. "If the human eye," as I have elsewhere remarked, " is not managed with peculiar care at this period, the change in the condition of the lens often runs into ca- taract, or terminates in a derangement of fibres, which, though not indicated by white opacity, occasions im- perfections of vision that are often mistaken for amau- rosis and other diseases. A skilful oculist, who tho- roughly understands the structure of the eye, and all its optical functions, would have no difficulty, by means of nice experiments, in detecting the very portion of the lens where this change has taken place ; in determining the nature and magnitude of the change which is going on ; in applying the proper remedies for stopping its progress ; and in ascertaining whether it has advanced to such a state that aid can be obtained from convex or * concave lenses. In such cases, lenses are often resorted to before the crystalline lens has suffered an uniform change of figure or of density, and the use of them cannot fail to aggravate the very evils which they are intended to remedy. In diseases of the lens, where the * For a fuller account of these experiments, see Edinburgh Journal of Science, No. I. p. 77. 426 A TREATISE ON OPTICS. PART IIT. separation of fibres is confined to small spots, and is yet of such magnitude as to give separate coloured images of a luminous object, or irregular halos of light, it is often necessary to limit the aperture of the spectacles, so as to allow the vision to be performed by the good part of the crystalline lens." This defect of the eye, when it is not accompanied with disease, may be completely remedied by a convex lens, which makes up for the flatness and diminished refractive power of the crystalline, and enables the eye to converge the pencils flowing from near objects to distinct foci on the retina. , Shortsightedness shows itself in an inability to see at a distance ; and those who experience this defect bring minute objects very near the eye in order to see them distinctly. The rays from remote objects are in this case converged to foci before they reach the retina, and therefore the picture on the retina is indistinct. This imperfection often appears in early life, and arises from an increase of density in the central part of the crystal- line lens. By using a suitable concave lens the conver- gency of the rays is delayed, so that a distinct image can be formed on the retina. (207.) 10. Cylindrical form of the cornea or crystal- line. In some eyes imperfection of vision is not cured either by the ordinary convex or concave lenses. In this case, it is probable that either the cornea or the crystalline lens has a cylindrical form, which can be remedied only by cylindrical lenses either convex or concave, which can be easily made by opticians. CHAP. XLVII. ON BINOCULAR VISION AND THE STEREOSCOPE. (208.) IT has been long known to optical writers, and in- deed to every person accustomed to make observations on vision, that when we view with both eyes, or with each eye CHAP. XLVII. BINOCULAR VISION. 427 successively, any solid object, that is, any object in relief, such as a statue or the human head itself, each eye sees the object differently, or two dissimilar pictures of the object are painted on the retince* In virtue of the law of visible position, each two corresponding points of the two pictures are seen in the same place, namely,, at the convergency of the optic axes, the eyes uniting each pair of points in succession, and giving the mind the im- pression of a solid. By simply inverting this process, that is, by making dissimilar pictures of a solid, as seen by each eye, and uniting them again by squinting, or, what is the same thing, by converging the optic axes to a point nearer the eye till the one picture is laid upon the other, the combined pictures will have the appearance of a solid. In a paper on The Law of visible Position in Bino- cular Vision t, I have shown that the combined pictures are seen by the very same process as that by which we see the solid itself. Mr. Wheatstone and others had given a very different explanation. They imagined that the lines of the two pictures, though of very different lengths, actually coalesced as if by some magical elasticity of the retina, a power which must also have been ex- erted in viewing the real solid. Such a coalescence, however, is contrary to the fundamental law of vision, for whether we look at the real solid itself, or to its representative when constituted by its two dissimilar pictures, we see only individual points of the object single, but the eyes, with the rapidity of light, run over all its parts, converging the optical axes upon each, and recognising by this operation the third dimension in space which constitutes a solid figure. As very few persons are able to combine the two dis- similar pictures with their eyes alone, Mr. Wheatstone constructed an apparatus consisting of two reflecting mirrors, by which their union was effected. Mr. Elliot, * See North British Review, 1852, vol. xvii. p. 165204. t Edin. Trans, vol. xv. pt. 2., and Phil. Mag. vol. xxiv. p. 356. 428 A TREATISE ON OPTICS. PART IIJ. of Edinburgh, had united the pictures in another way, but had not published any account of his invention.* But whatever it was, the effects produced by the instru- mental union of two pictures had excited little notice till I invented the Lenticular Stereoscope, and showed its application tp photographic portraits, which could be combined either when taken in Daguerreotype or Talbo- type into solid figures, t I constructed also a Binocular Camera, by which these portraits could be taken at one sitting, and pointed out various forms of the stereoscope for uniting the dissimilar portraits. 1. The Lenticular Stereoscope is shown in fig. 191* where A, B are two eye tubes, containing each a semi- lens, or a quarter of a lens, with their curved sides turned towards each other, so that by looking through their edges, objects in their focus are so refracted that the one picture can be placed above the other. If we now place the annexed drawings of a six-sided pyramid A and B in the bottom of the box by sliding * " I constructed,*' says he, " a stereoscope in everything but the name ittore than thirteen years ago, which, though since neglected by me, is still in existence, and can be produced, with evidence of its date." Phil. Mag. May, 1852, vol.iii. new series, p. 397. t Trans, of Royal Scottish Society of Arts, 1849. CHAP. XLVII. TOTAL REFLEXION STEREOSCOPE. them in at C D, and look into the instrument with the right eye at A and the left at B, we shall see a solid pyra- mid with its apex rising to the eye. Fig. 192. Fig. 193. If the two figures had been united by squinting, they would have produced a hollow pyramid. If the two annexed drawings of a four-sided pyramid Fig. 194. Fig. 195. are put into the instrument, they will form a hollow pyramid, with the top away from the eye, but if they are united by the eye, they will form a raised pyramid. In like manner, two binocular portraits may be united to give the appearance of a solid bust. 2. The total Reflexion Stereoscope with a single Figure. A. curious form of the stereoscope, which I have constructed, is shown in fig. 196., where the in- strument actually creates one of the two figures to be united. If D m w, the drawing of a hollow cone as 430 A TREATISE ON OPTICS. PART III. 19G. seen by the right eye, is viewed through the prism ABC, its image being received by the left eye while the right eye R views it directly, the inverted image formed after re- flexion at E, will be a drawing of the cone as seen by the left eye, and the two will therefore produce a hollow cone by their union. The part of the prism A c d is of no use, and may be cut off. This form of the stereoscope is suited only for pictures or portraits that are perfectly symmetrical, that is, those pictures one half of which is the reflected image of the others CHAP. XLVIII. ON ACCIDENTAL COLOURS AND COLOURED SHADOWS. (2090 WHEN the eve has been strongly impressed with any particular species of coloured light, and when in this state it looks at a sheet of white paper, the paper does not appear to it white, or of the colour with which the eye was impressed, but of a different colour, which is said to be the accidental colour of the colour with which the eye was impressed. If we place, for ex- ample, a bright red wafer upon a sheet of white paper, and fix the eye steadily upon a mark in the centre of it, then if we turn the eye upon the white paper we shall see a circular spot of bluish green light, of the same size as the wafer. This colour, which is called the accidental colour of red, will gradually fade away. The bluish green image of the wafer is called an ocular spectrum, because it is impressed on the eye, and may be carried about with it for a short time. If we make the preceding experiment with differently CHAP. XLVIII. ON ACCIDENTAL COLOURS. 431 coloured wafers^ we shall obtain ocular spectra whose colours vary with the colour of the wafer employed, as in the following table. Colour of the Wafer. Accidental Colour, or Colour of the Ocular Spectrum. Red. Bluish green. Orange. Blue. Yellow. Indigo. Green. Reddish violet. Blue. Orange red. Indigo. Orange yellow. Violet. Yellow green. Black. White. White. Black. In order to find the accidental colour of any colour in the spectrum,, take half the length of the spectrum in a pair of compasses, and setting one foot in the colour whose accidental colour is required, the other will fall upon the accidental colour. Hence the law of accidental colours derived from observation may be thus stated : The accidental colour of any colour in a prismatic spectrum, is that colour which in the same spectrum is distant from the first colour half the length of the spectrum ; or, if we arrange all the colours of any prismatic spectrum in a circle, in their due proportions, the accidental colour of any particular colour will be the colour exactly opposite that particular colour. Hence two colours have been called opposite colours. If the primitive colour, or that which impresses the eye, is reduced to the same degree of intensity as the accidental colour, we shall find that the one is the com- plement of the other, or what the other wants to make it white light ; that is, the primitive and the accidental colours will, when reduced to the same degree of in- tensity which they have in the spectrum, and when mixed together, make white light. On this account acci- dental colours have been called complementary colours. With the aid of these facts the common theory of accidental colours will be readily understood. When the eye has been for some time fixed on the red wafer, 432 A TREATISE ON OPTICS. PART III. the part of the retina occupied by the red image is strongly excited, or, as it were, deadened by its con- tinued action. The sensibility to red light will there- fore be diminished ; and, consequently^ when the eye is turned from the red wafer to the white paper, the deadened portion of the retina will be insensible to the red rays which form part of the white light from the paper, and consequently will see the paper of that colour which arises from all the rays in the white light of the paper but the red; that is, of a bluish green colour, which is therefore the true complementary colour of the red wafer. When a black wafer is placed on a white ground, the circular portion of the retina, on which the black image falls, in place of being deadened, is rer freshed, as it were, by the absence of light, while all the surrounding parts of the retina, being excited by the white light of the paper, will be deadened by its con- tinued action. Hence, when the eye is directed to the white paper, it will see a white circle corresponding to the black image on the retina ; so that the accidental colour of black is white. For the same reason, if a white wafer is placed on a black ground, and viewed stedfastly for some time, the eye will afterwards see a black circular space ; so that the accidental colour of white is black. Such are the phenomena of accidental colours when weak light is employed ; but when the eye is impressed powerfully with a bright white light, the phenomena have quite a different character. The first person who made this experiment with the bright light of the sky in a dark room was Joseph Bonacursius, and Kircher afterwards repeated it with the bright light of the sun. At the desire of Locke, Sir Isaac Newton sent him an account of the results which he obtained in repeating the experiment, but they were not published till 1829-* Many years before l691> Sir Isaac having shut his left eye, directed the right one to the image of the sun re- flected from a looking-glass. In order to see the im- * In Lord King's Ti/ of Locke. HAP. XLVIII. IMPRESSIONS ON THE RETINA. 433 pression which was made, he turned his eye to a dark corner of the room, when he observed a bright spot made by the sun, encircled by rings of colours. This " phantom of light and colours," as he calls it, gradually vanished ; but whenever he thought of it, it returned, and became as lively and vivid as at first. He rashly repeated the experiment three times, and his eye was impressed to such a degree, " that whenever I looked upon the clouds, or a book, or a bright object, I saw upon it a round bright spot of light like the sun ; and, which is still stranger, though I looked upon the sun with my right eye only, and not with my left, yet my fancy began to make an impression on my left eye as well as upon my right ; for if I shut my right eye, or looked upon a book or the clouds with my left eye, I could see the spectrum of the sun almost as plain as with my right eye," The effect of this experiment was such, that Sir Isaac durst neither write nor read, but was obliged to shut himself completely up in a dark chamber for three days together, and by keeping in the dark, and employing his mind about other things, he began, in about three or four days, to recover the use of his eyes. In these experiments, Sir Isaac's attention was more taken up with the metaphysical than with the optical results of them, so that he has not described either the colours which he saw, or the changes which they underwent. Experiments of a similar kind were made by M. ^pinus. When the sun was near the horizon, he fixed his eye steadily on the solar disc for 15 seconds. Upon shutting his eye he saw an irregular pale sulphur yellow image of the sun, encircled with a faint red border. As soon as he opened his eye upon a white ground, the image of the sun was a brownish red, and its surround-* ing border sky blue. With his eye again shut, the image of the sun became green with a red, border, different from the last. Turning his eye again upon a white ground, the sun's image was more red, and its border a brighter sky blue. When the eye was shut, the green 4<34f A TREATISE ON OPTICS. PART III. spectrum became a greenish sky blue, and then a fine sky blue, with the border growing a finer red ; and when the eye was open, the spectrum became & finer red, and its border a finer blue. M. JEpinus noticed, that when his eye was fixed upon the white ground, the image of the sun frequently disappeared,, returned, and disap- peared again. About the year 1803, I was led to repeat the pre- ceding experiments of ^Epinus ; but, instead of looking at the sun when of a dingy colour, I took advantage of a fine summer's day., when the sun was near the meridian, and I formed upon a white ground a brilliant image of his disc by the concave speculum of a reflecting telescope. Tying up my right eye, I viewed this luminous disc with my left eye through a tube, and when the retina was highly excited, I turned my left eye to a white ground, and observed the following spectra by alter- nately opening and shutting it : Spectra with left eye open. . Spectra with left eye shut. 1. Pink surrounded with green. Green. 2. Orange mixed with pink. Blue. 3. Yellowish brown. Bluish pink. 4. Yellow. Pinkish blue. 5. Pure red. Sky blue. 6. Orange. Indigo. Upon uncovering my right eye, and turning it to a white ground, I was surprised to observe that it also gave a coloured spectrum, exactly the reverse of the first spectrum, which was pink with a green border. The reverse spectrum was a green with a pinkish border. This experiment was repeated three times, and always with the same result ; so that it would appear that the impression of the solar image was conveyed by the optic nerve from the left to the right eye. Sir Isaac Newton supposed that it was his fancy that transferred the image from his left to his right eye ; but we are disposed to think that in his experiment no transference took place, because the spectrum which he saw with both eyes was the same, whereas in my experiment it was the reverse CHAP. XLVIII. IMPRESSIONS ON THE RE1. 4*35 one. We cannot however speak decidedly on this point, as Sir Isaac did not observe that the spectra with the eye shut were the reverse of those seen with the eye open. If a spectrum is strongly formed on one eye, it is a very difficult matter to determine on which eye it is formed, and it would be impossible to do this if the spectrum was the same when the eye was open and shut. The phenomena of accidental colours are often finely seen when the eye has not been strongly impressed with any particular coloured object. It was long ago ob- served by M. Meusnier, that when the sun shone through a hole a quarter of an inch in diameter in a red curtain, the image of the luminous spot was green. In like manner, every person must have observed in a brightly painted room, illuminated by the sun, that the parts of any white object on which the coloured light does not fall, exhibit the complementary colours. In order to see this class of phenomena, I have found the following method the simplest and the best. Having lighted two candles, hold before one of them a piece of coloured glass, suppose bright red, and remove the other candle to such a distance that the two shadows of any body formed upon a piece of white paper may be equally dark. In this case one of the shadows will be red, and the other green. With blue glass, one of them will be blue, and the other orange yellow ; the one being invariably the accidental colour of the other. The very same effect may be produced in daylight by two holes in a window- shutter; the one being covered with a coloured glass, and the other transmitting the white light of the sky. Accidental colours may also be seen by looking at the image of a candle, or any white object seen by reflexion from a plate or surface of coloured glass sufficiently thin to throw back its colour frpm the second surface. In this case the reflected image will always have the complementary colour of the glass. The same effect may be seen in looking at the image of a candle reflected from the water in a blue finger glass ; the image of the candle is yellowish : but the effect is not so decided in JF P 2 436 A TREATISE ON OPTICS. PART III. this case, as the retina is not sufficiently impressed with the blue light of the glass. These phenomena are obviously different from those which are produced by coloured wafers ; because in the present case the accidental colour is seen by a portion of the retina which is not affected, or deadened as it were, by the primitive colour. A new theory of accidental colours is therefore requisite, to embrace this class of facts. As in acoustics, where every fundamental sound is actually accompanied with its harmonic sound, so in the impressions of light, the sensation of one colour is ac- companied by a weaker sensation of its accidental or harmonic colour.* When we look at the red wafer, we are at the same time, with the same portion of the re- tina, seeing green ; but being much fainter, it seems only to dilute the red, and make it, as it were, whiter, by the combination of the two sensations. When the eye looks from the wafer to the white paper, the per- manent sensation of the accidental colour remains, and we see a green image. The duration of the primitive impression is only a fraction of a second, as we have already shown ; but the duration of the harmonic im- pression continues for a time proportional to the strength of the impression. In order to apply these views to the second class of facts, we must have recourse to another principle ; namely, that .when the whole or a great part of the retina has the sensation of any primitive colour, a portion of the retina protected from the impression of the colour is actually thrown into that state which gives the accidental or harmonic colour. By the vibrations probably communicated from the surrounding portions, the influence of the direct or primitive colour is not pro- pagated to parts free from its action, excepting in the particular case of oblique vision formerly mentioned. When the eye, therefore, looks at the white spot of solar light seen in the middle of the red light of the * The term harmonic has been applied to accidental colours ; because the primitive and its accidental colour harmonise with each other in painting. CHAP. XLVIII. IMPRESSIONS ON THE RETINA. 43? curtain, the whole of the retina, except the portion oc- cupied by the image of the white spot, is in the state of seeing every thing green ; and as the vibrations which constitute this state spread over the portions of the re- tina upon which no red light falls, it will, of course, see the white circular spot green. M. Plateau, to whom we owe so many valuable optical observations and instru- ments, has published an ingenious theory of accidental colours, in some respects the same, as he himself admits, as that which I had previously explained, in so far at least as they both ascribe the accidental colour to an impression of a peculiar nature spontaneously generated in the seat of vision, and not to any relative insensibility to certain rays. To this undoubted truth, M. Plateau has added the following proposition, " that while the combination of real colours produces white, the com- bination of accidental colours produces the contrary to white, or black;" but I consider this proposition as a mere verbal illusion, and the physical fact which it ex- presses as long known, and as the necessary result of our previous knowledge. The blackness which is pro- duced by the union, as it were, of all the accidental colours, is merely the sum of the insensibilities to all the colours, or the inability to see any colour from the ex- haustion of the eye. It cannot, therefore, be called an union of colours. It is the successive deprivation of the power of seeing all the colours of the spectrum. The following is M. Plateau's account of his general theory. <( When the retina is submitted to the action of rays of any colour, it resists this action, and tends to resume its ordinary condition with a force more or less intense. If it is then suddenly withdrawn from the exciting cause, it returns to its ordinary condition by an oscillatory movement, the intensity of which is pro- portional to the duration of the previous action ; a movement in virtue of which the impression passes at first from the positive to the negative state, then con- tinues generally to oscillate in a manner more or less regular, while it becomes weaker and weaker." This F F 8 438 A TREATISE ON OPTICS. PART III. principle of a regular, or a tendency to a regular, oscil- latory movement, is not very consistent with the ob- literation of the accidental colour, temporarily or per- manently, by involuntary winking, by closing the eyes with different degrees of pressure, by distending the eyes, and by a blow upon the head.* (210.) A very remarkable phenomenon, in which the eye is not excited by any primitive colour, was observed by Mr. Smith, surgeon in Fochabers. If we hold a narrow strip of white paper vertically, about a foot from the eye, and fix both eyes upon an object at some distance beyond it, so as to see it double, then if we allow the light of the sun, or the light of a candle, to act strongly upon the right eye, without affecting the left, which may be easily protected from its influence, the left hand strip of paper will be seen of a bright green colour, and the right hand strip of a red colour. If the strip of paper is sufficiently broad to make the two images overlap each other, the overlapping parts will be perfectly white, and free from colour. When equally luminous candles are held near each eye, the two strips of paper will be white. If when the candle is held near the right eye, and the strips of paper are seen red and green, we bring the candle suddenly to the left eye, the left hand image of the paper will gradually hange to green, and the right hand image to red.\ (211.) A singular affection of the retina, in reference to colours, is shown in the inability of some eyes to distinguish certain colours of the spectrum, which may be called Colour Blindness. The persons who experience this defect have their eyes generally in a sound state, and are capable of performing all the most delicate functions of vision. Mr. Harris, a shoemaker at Allonby, was unable from his infancy to distinguish the cherries of a cherry tree from its leaves, in so far as colour was concerned. Two of his brothers were * See Plateau's Essai d'une Theorie generate, fyc., Bruxelles, 1834. ; Edin. Review, April, 18;i4; and Phil. Mag. December, 1839, vol. xv. p. 435. f See Land, and Edin. Phil. Mag. % 1832, vol. i. p. 171, ; No. 5. p. 249.; No. 9. p. 168. CHAP. XLVIII. ON COLOUR BLINDNESS. 439 equally defective in this respect, and always mistook orange for grass green, and light green for yellow. Harris himself could only distinguish black and white. Mr. Scott, who describes his own case in the Philosophical Transactions, mistook pink for a pale blue, and a full red for a full green. All kinds of yellows and blues, except sky blue, he could discern with great nicety. His father, his ma- ternal uncle, one of his sisters, and her two sons, had all the same defect. A tailor at Plymouth, whose case is described by Mr. Harvey, regarded the solar spectrum as consisting only of yellow and light blue; and he could distinguish with certainty only yellow, white, and green. He re- garded indigo and Prussian blue as black. Mr. R. Tucker describes the colours of the spectrum as follows: lscY4 \*u ' Red mistaken for Brown. Orange - Green. Yellow sometimes Orange. Green - Orange. Blue sometimes Pink. Indigo - Purple Violet - Purple. A gentleman in the prime of life, whose case I had occasion to examine, saw only two colours in the spec- trum, viz. yellow and blue. When the middle of the red space was absorbed by a blue glass, he saw the black space, with what he called the yellow, on each side of it. This defect in the perception of colour was experienced by the late Mr. Dugald Stewart, who could not perceive any difference between the colour of the scarlet fruit of the Siberian crab and that of its leaves. Mr. Dalton was unable to distinguish blue from pink by daylight, and in the solar spectrum the red was scarcely visible, the rest of it appearing to consist of two colours. Mr. Troughton had the same defect, and was capable of fully appreciating only blue and yellow colours ; and when he names colours, the names of blue and yellow correspond to the more and less refrangible rays, all 440 A TREATISE O1S 7 OPTICS. PART III, those which belong to the former exciting the sensation of blueness, and those which belong to the latter the sensation of yellowness. In almost all these cases, the different prismatic colours have the power of exciting the sensation of light; and giving a distinct vision of objects. In ex- amining the state of Mr. Dalton's vision, I found that he saw distinctly the red extremity of the spectrum. Mr. Dalton endeavoured to explain this peculiarity of vision by supposing that in his own case the vitreous humour was blue, and, therefore, absorbed a great por- tion of the red rays and other least refrangible rays ; but this opinion was not well founded.* Sir John Herschel attributes this state of vision to a defect in the sensorium, by which it is rendered incapable of appreciating exactly those differences between rays on which their colour depends. A very interesting memoir on this subject has been recently published by M. Wartmann, of Geneva, entitled Memoire sur le Daltonisms f, a name very improperly given to this affection of the eye by the late Professor Prevost. The following are the results of M. Wart, mann's researches. 1. Colour blindness has not been studied bv the ancients. 2. It has been found only in individuals of the white race. 3. Some of the colour blind see only black and white, and some have the affection so slightly as only to con- found approximating shades of blue and green in candle light. 4. There are more of the colour blind than is gene- rally believed. 5. The female sex furnishes a small proportion. 6. In some cases they may be known by external signs. * After the death of Mr. Dalton the vitreous humour of hi& eyes was found to be perfectly colourless, t Geneva, 1844. CHAP. XLVJII. ON COLOUR BLINDNESS. 441 7. There are as many of the colour blind with blue as with black eyes. 8. Colour blindness is not always hereditary. ^ 9. It does not always affect the males of the same family. -& [( v 10. It does not always commence at birth. 11. The colour blind do not judge as we do of com- plementary colours^ or of the contrast of colours. 12. Several of them are not sensible to the least re- frangible rays. . v x ffYt 13. They see the / lines in the spectrum. 1 4. Colour blindness does not arise from any diseased conformation of the eye, or any coloration of the hu- mours of the eye or of the retina. 15. We may alter the state of colour blindness by very simple means. 16. Colour blindness has its origin in the sensorium.* * See Phil. Mag., vol. xxv. p. 134. 442 A TREATISE ON OPTICS. PART IV. ON OPTICAL INSTRUMENTS. ALL the optical instruments now in use have been invented by modern philosophers and opticians. The principles upon which most of them have been con- structed have already been explained in the preceding chapters, and we shall therefore confine ourselves as much as possible to a general account of their construc- tion and properties. CHAP. XLIX. ON PLANE AND CURVED MIRRORS. (212.) ONE of the simplest optical instruments is the single plane mirror, or looking-glass, which consists of a plate of glass with parallel surfaces, one of which is covered with tinfoil and quicksilver. The glass per- forms no other part in this kind of plane mirror than that of holding and giving a polished surface to the thin bright film of metal which is extended over it. Jf the surfaces of the plate of glass are not parallel, we shall see two, three, and four images of all luminous objects seen obliquely ; but even when the surfaces are parallel, two images of an object are formed, one reflected from the first surface of glass, and the other from the posterior surface of metal ; and the distance of these images will increase with the thickness of the glass. The image reflected from the glass is, however, very faint compared with the other ; so that for ordinary purposes a plane glass CHAP. XLIX. ON THE KALEIDOSCOPE. 443 mirror is sufficiently accurate ; but when a plane mirror forms a part of an optical instrument where accuracy of vision is required, it must be made of steel, or silver, or of a mixture of copper and tin ; and in this case it is called a speculum. In order to choose a good plane mirror, we should place ourselves at a great distance from it, and examine the correctness of the image which it gives. The formation of images by mirrors and specula has been fully described in Chap. II. Kaleidoscope. (213.) When two plane mirrors are combined in a particular manner, and placed in a particular position re- lative to an object, or series of objects, and the eye, they constitute the Kaleidoscope, an instrument which 1 in- vented for creating and exhibiting beautiful forms. If AC, BC, for example, be sections of two plane mirrors, arid MN an object placed between them or in front of Fig. 197. eacn > the mirror AC will form behind it an image m n of the object M N, in the manner shown in fig. 16. In like manner, the mirror B C will form an image M'N' behind it. But, as we have formerly shown, these images may be considered as new objects, and therefore the mirror A C will form behind it an image, M"N", of the object or image M'N', and B C will form behind it an image, m'n', of the object or image mn. In like manner it will be found that m" n" will be the image of the object or image M"N", 'formed by B C, and of the object or image m'n', formed by A C. Hence m" n" will actually consist of two images overlapping each other and forming one, pro- vided the angle A C B is exactly 60, or the sixth part of a circumference of 360. In this case all the six images (two of the six forming only one, m"n",') will, along with the original object, M N, form a perfect equilateral triangle. The object M N is drawn per- 444 A TREATISE ON OPTICS. PART IV. pendicular to the mirror B C, in consequence of which M N and M'N 7 form one straight line; but if M N is' moved, all the images will move, and the figure of all the images comhined will form another figure of perfect regularity, and exhibiting the most beautiful variations, all of which may be drawn by the methods already described. In reference to the multiplication and arrangement of the images, this is the principle of the kaleidoscope ; but the principle of symmetry, which is essential to the instrument, depends on the position of the object and the eye. This principle will be under- stood from fig. 198., where ACE and B C E re- present the two mirrors inclined at an angle A C B, and having C E for their line of junction or common intersection. If the object is placed at a distance, as at M N, then there is no position of the eye at or above E which will give a symmetrical arrangement of the six images shown in fig. 1 97. ; for the corresponding parts of the one will never join the corresponding parts of the other. As the object is brought nearer and nearer, the symmetry increases, and is more complete when the ohject M N is quite close to A B C, the ends of the reflectors. But even here it will not be perfect, unless the eye is placed as near as possible to E, the line of junction of the reflectors. The following, there- fore, are the three conditions of symmetry in the kaleidoscope : 1. That the reflectors should be placed at an angle which is an even or an odd aliquot part of a circle, when the object is regular and similarly situated with respect CHAP. XLIX. ON THE KALEIDOSCOPE. 445 to both the mirrors ; or an even aliquot part of a circle, when the object is irregular. 2. That out of an infinite number of positions for the object Iboth within and without the reflectors, there is only one position where perfect symmetry can be obtained, namely, by placing the object in contact with the ends of the reflectors, or between them. 3. That out of an infinite number of positions for the situation of the eye, there is only one where the sym- metry is perfect, namely, as near as possible to the an- gular point, so that the whole of the circular field can be distinctly seen ; and this point is the only one at which the- uniformity of the reflected light is greatest. In order to give variety to the figures formed by the instrument, the objects, consisting of pieces of coloured glass, twisted glass 'of various curvatures, &c., are placed in a narrow cell between two circular pieces of glass, leaving them just room to tumble about, while this cell is turned round by the hand. The pictures thus pre- sented to the eye are beyond all description splendid and beautiful ; an endless variety of symmetrical combina- tions presenting themselves to view, and never again recurring with the same form and colour. For the purpose of extending the power of the in- strument, and introducing into symmetrical pictures ex- ternal objects, whether animate or inanimate, I applied a convex lens, L L, fig. 198., by means of which an inverted image of a distant object, MN, may be formed at the very extremity of the mirrors, and therefore brought into a position of greater symmetry than can be effected in any other way. In this construction the lens is placed in one tube and the reflectors in another ; so that by pulling out or pushing in the tube next the eye, the images of objects at any distance can be formed at the place of symmetry. In this way, flowers, trees, animals, pictures, busts, may be introduced into sym- metrical combinations. When the distance E B is less than that at which the eye sees objects distinctly, it is necessary to place a convex lens at to give distinct 446 A TREATISE ON OPTICS. PART IV. vision of the objects in the picture. See my Treatise on the Kaleidoscope. Plane burning Mirrors. (214.) A combination of plane burning mirrors forms a powerful burning instrument ; and it is highly probable that it was with such a combination that Archimedes destroyed the ships of Marcellus. Athanasius Kircher, who first proved the efficacy of a union of plane mirrors, went with his pupil Schemer to Syracuse, to examine the position of the hostile fleet; and they were both satisfied that the ships of Marcellus could not have been more than thirty paces distant from Archimedes. Buffon constructed a burning apparatus upon this principle, which may be easily explained. If we reflect the light of the sun upon one cheek by a small piece of plane looking-plass, we shall experience a sensation of heat less than if the direct light of the sun fell upon it. If with the other hand we reflect the sun's light upon the same cheek with another piece of mirror, the warmth will be increased, and so on, till with five or six re- flexions we can no longer endure the heat. Buffon combined 168 pieces of silvered glass 6 inches by 8, so that he could, by a little mechanism connected with each, cause them to reflect the light^of the sun upon one spot. Those pieces of glass were selected which gave the smallest image of the sun at 250 feet. The following were the effects produced by different numbers of these mirrors : No. of Distance ot Effects produced Mirrors. Object. 12 20 feet Small combustibles inflamed. 21 20 Beech plank burned. 40 66 Tarred beech plank inflamed. 45 20 Pewter flask 6lb. weight melted. 98 126 Tarred and sulphured plank set on fire. 112 138 Plank covered with wool set on fire. 1 j 7 20 Some thin pieces of silver melted. 128 150 Tarred fir plank set on fire. 148 0I Beech plank sulphured inflamed violently. CHAP. XLIX. CONVEX AND CONCAVE MIRRORS. 447 No. of Distance of Mirrors. Object. Effects produced. 154 150 feet Tarred plank smoked violently 1 54 9sn 5 Chips of fir deal sulphured and mixed I with charcoal set on fire. 224 40 Plates of silver melted. As it is difficult to adjust the mirrors while the sun changes his place, M. Peyrard proposes to produce great effects by mounting each mirror in a separate frame, carrying a telescope, by means of which one person can direct the reflected rays to the object which is to be burnt. He conceives that with 5QO glasses, about 20 inches in diameter, he could reduce a fleet to ashes at the distance of a quarter of a league, and with glasses of double that size at the distance of half a league. Plane glass mirrors have been combined permanently into a parabolic form, for the purpose of burning objects placed in the focus of the parabola, by the sun's rays ; and the same combination has been used, and is still in use, for lighthouse reflectors, the light being placed in the focus of the parabola. Convex and Concave Mirrors. (21-5.) The general properties of convex and con- cave mirrors have been already described in Chap. II. Convex mirrors are used principally as household orna- ments, and are characterised by their property of forming erect and diminished images of all objects placed before them. These images appear to be situated behind the mirror. Concave mirrors are distinguished by their property of forming in front of them, and in the air, inverted images of erect objects, or erect images of inverted ob- jects, placed at some distance beyond their principal focus. If a fine transparent cloud of blue smoke is raised, by means of a chafing dish, around the focus of a large concave mirror, the image of any highly illuminated object will be depicted, in the middle of it, with great beauty. A skull concealed from the observer is some- 448 A TREATISE ON OPTICS. PART IV. times used, to surprise the ignorant ; and when a dish of fruit has been depicted in a similar manner, a spectator, stretching out his hand to seize it, is met with the image of a drawn dagger, which has been quickly suhstituted for the fruit at the other conjugate focus of the mirror. Concave mirrors have been used as lighthouse re- flectors, and as burning instruments. When used in lighthouses, they are formed of plates of copper plated with silver, and they are hammered into a parabolic form, and then polished with the hand. A lamp placed in the focus of the parabola will have its divergent light thrown, after reflexion, into something like a parallel beam, which will retain its intensity at a great distance. When ccncave mirrors are used for burning, they are generally made spherical, and regularly ground and polished upon a tool, like the specula used in telescopes. The most celebrated of these were made by M Villele, of Lyons, who executed five large ones. One of the best of them, which consisted of copper and tin, was very nearly four feet in diameter, and its focal length thirty - eight inches. It melted a piece of Pompey's pillar in fifty seconds, a silver sixpence in seven seconds and a half, a halfpenny in sixteen seconds, cast-iron in sixteen seconds, slate in three seconds, and thin tile in four seconds. Cylindrical Mirrors. (216.) All objects seen by reflexion in a cylindrical mirror are necessarily distorted. If an observer looks into such a mirror with its axis standing vertically, he will see the image of his head of the same length as the original, because the surface of the mirror is a straight line in a vertical direction. The breadth of the face will be greatly contracted in a horizontal direction, because the surface is very convex in that direction, and in inter- mediate directions the head will have intermediate breadths. If the axis of the mirror is held horizontally, the face will be as broad as life, and exceedingly short. If a picture or portrait M N is laid down horizontally CHAP. L. SINGLE AND COMPOUND LENSES. 449 before the mirror AJ$,fig. 199-? the reflected image of it will be highly distorted; but the picture may be drawn distorted according to regular laws, so that its image as seen in the mirror shall have the most correct proportions. Cylindrical mirrors, which are now very uncommon, used to be made for this purpose, and were accompanied with a series of distorted figures, which, when seen by the eye, have neither shape nor meaning, but when laid down before a cylindrical mirror, the reflected image of them has the most perfect proportions. This effect is shown in fig. 199? where MN is a distorted figure, Fig. 199. M whose image in the mirror A B has the appearance of a regular portrait. CHAP. L. ON SINGLE AND COMPOUND LENSES. (217.) SPECTACLES and reading glasses are among the simplest and most useful of optical instruments. In G G 450 A TREATISE ON OPTICS. PART IV. order to enable a person to see small objects distinctly, when they are very near the eye, such as small manu- script, or a small type, a convex lens of very short focus must be used both by those who are long and short sighted. When a short-sighted person, who cannot see well at a distance, wishes to have distinct vision at any particular distance, he must use a concave lens whose focal length will be found thus, Multiply the distance at which he sees objects most distinctly by the distance at which he wishes to see them distinctly with a concave lens, and divide this product by the difference of the above dis- tances. A long-sighted person, who cannot see near objects distinctly, must use a convex lens, whose focal length is found by the preceding rule. In choosing spectacles, however, the best way is to select, out of a number, those which are found to answer best the purposes for which they are particularly intended. Dr. Wollaston introduced a new kind of spectacles, called periscopic, from their property of giving a wider field of distinct vision than the common ones. The lenses used for this purpose, as shown at H and I fig. 19-, are meniscuses, in which the convexity predo- minates for long-sighted persons, and concavo-convex lenses, in which the concavity predominates, for short- sighted persons. Periscopic spectacles decidedly give more imperfect vision than common spectacles, because they increase both the aberration of figure and of colour; but they may be of use to those who wear spectacles in a crowded city, in warning them of the oblique approach of objects. \ Burning and Illuminating Lenses. (218.) Convex lenses possess peculiar advantages for concentrating the sun's rays, and for conveying to an immense distance a condensed and parallel beam of light. M. Buffon found that a convex lens, with a great focal CHAP. L. ON BURNING LENSES. 451 length, was preferable to one of a small focal length for fusing metals by the concentration of the sun's rays. A lens, for example, 32 inches in diameter and 6 inches in focal length, with the diameter of its focus 8 lines, melted copper in less than a minute ; while a small lens 32 lines in diameter, with a focal length of 6 lines, and its focus | of a line, was scarcely capable of heating copper. The most perfect burning lens ever constructed was executed by Mr. Parker, of Fleet Street, at an expense of 700J. It was made of flint glass, was three feet in dia- meter and weighed 212 pounds. It was 3^ inches thick" at the centre ; the focal distance was 6 feet 8 inches, and the diameter of the image of the sun in its focus one inch. The rays refracted by the lens were received on a second lens, in whose focus the objects to be fused were placed. This second lens had an exposed diameter of 13 inches; its central thickness was 1-g of an inch; the length of its focus was 29 inches. The diameter of the focal image was -| of an inch. Its weight was 21 pounds. The combined focal length of the two lenses was 5 feet 3 inches, and the diameter-of the focal image 1 an inch. By means of this powerful burning lens, platina, gold, silver, copper, tin, quartz, agate, jasper, flint, topaz, garnet, asbestos, &c. were melted in a few seconds. Various causes have prevented philosophers from con- structing burning lenses of greater magnitude than that made by Mr. Parker. The impossibility of procuring pure flint glass tolerably free of veins and impurities for a large solid lens ; the trouble and expense of casting it into a lenticular form without flaws and impurities ; the great increase of central thickness which becomes neces- sary by increasing the diameter of the lens ; the enor- mous obstruction that is thus opposed to the transmission of the solar rays, and the increased aberration which dissipates the rays at the focal point, are insuperable ob- stacles to the construction of solid lenses of any consider- able size. 452 A TREATISE ON OPTICS. PART IV. fig. 200. (219.) In order to improve a solid lens formed of one piece of glass, whose section is Amp"BET> A, Buffon proposed to cut out all I the glass left white in the figure, viz. the por- tions between m p, fig. 200., and n o, and be- tween no and the left hand surface of D E. JE A lens thus constructed would be incomparably superior to the solid one A mp B E D A ; but such a process we conceive to be impracticable on a large scale, from the extreme difficulty of polishing the surfaces Am, Bjo, C n, F o, and the left hand surface of D fi ; and even if it were practicable, the greatest imperfections in the glass might happen to occur in the parts which are left. In order to remove these imperfections, and to con- struct lenses of any size, 1 proposed, in 181 1, to build them up of separate zones or rings, each of which rings was again to be composed of separate segments, as shown in the front view of the lens in fig. 201. This lens is composed of one central lens, A B C D, corresponding with its section D E in fig. 200., of -;T a middle ring G E L I corre- sponding to C D E F in fig. 200., and consisting of five segments ; and another ring, N PR' T, cor- responding to A C F B, and consisting of eight segments. The preceding construction obviously puts it in our power to execute these compound lenses, to which I have given the name of polyzonal lenses, of pure flint glass free from veins ; but it possesses another great advan- tage, namely, that of enabling us to correct, very nearly, the spherical aberration, by making the foci of each zone coincide. One of these lenses was constructed, under my direc- tion, for the Commissioners of Northern Lighthouses, by Messrs. W. and P. Gilbert. It was made of flint X3HAP. LI. ON PRISMATIC LENSES. 453 glass, was three feet in diameter, and consisted of many zones and segments. Lenses of this kind have been made in France of crown glass, and have been intro- duced into the principal French lighthouses ; a purpose to which they are infinitely better adapted than the best constructed parabolic reflectors made of metal. After nearly fifteen years' exertions I succeeded in getting them introduced into the Scottish lighthouses. CHAP. LT. ON SIMPLE AND COMPOUND PRISMS. Prismatic Lenses. (220.) THE general properties of the prism in refracting and decomposing light have already been explained ; but its application as an optical instrument, or as an important part of optical instruments, remains to be described. A rectangular prism, ABC, fig. 202., was first ap- plied by Sir Isaac Newton as a plane mirror for reflect- ing to a side the rays which form the image in re- flecting telescopes. The angles, B A C, B C A, being each 45, and B a right angle, rays falling on the face G G 3 454 A TREATISE ON OPTICS. PART IV. AB will be reflected by tbe back surface B C as if it were a plane metallic mirror ; for whatever be the re- fraction which they suffer at their entrance into the face A B, they will suffer an equal and opposite one at the face B C. The great value of such a mirror is, that as the incident rays fall upon A C at an angle greater than that at which total reflexion commences, they will all suffer total reflexion, and not a ray will be lost ; whereas in the best metallic speculum nearly half the light is lost. A portion of light, however, is lost by reflexion at the two surfaces, AB, BC, and a small portion by the absorption of the glass itself. Sir Isaac Newton also proposed the convex prism, shown at DBF, the faces DF, FE being ground convex. An analogous prism, called the meniscus prism, and shown at G H I, has been used by M. Chevallier, of Paris, for the camera obscura. It differs only from Newton's in the second face, I H, being concave in place of convex. On account of the difficult execution of these prisms, I have proposed to use a hemispherical lens, L M N, the two convex surfaces of which are ground at the same time. When a longer focus is required, a concave lens, RQ, of a longer focus than the hemisphere PRQ, may be placed or cemented on its lower surface, and if the concave lens is formed out of a substance of a different dispersive power, it may be made to correct the colour of the convex lens. A single prism is used with peculiar advantage for inverting pencils of light, or for obtaining an erect image from pencils that would give an inverted one. This effect is shown in fig. 203. 3 where A B C is CHAP. LI. ON PRISMATIC LENSES. 455 a rectangular prism, and R R' R" a parallel pencil of light, which, after being refracted at the points 1, 2, 3, of the face A B, and reflected at the points a, b, c, of the base B C, will be again refracted at the points 1, 2, 3, of the face AC, and move on in parallel lines, S r", 2 r f , Ir; the ray R 1, that was uppermost, being now undermost, as at Ir. A very useful prism for fluids is shown in the an- nexed figure, where MNO is a prismatic vessel with a Fig. 204. bottom N O of highly polished metal or even glass. A ray Rr incident on the fluid surface at ris refracted at r and reflected at A B, so as to give the spectrum at C D. We thus get rid altogether of the influence of the glass plate employed in prisms for fluids. Compound and Variable Prisms. (221.) The great difficulty of obtaining glass suf- ficiently pure for a prism of any size, has rendered it extremely difficult to procure good ones ; and they have therefore not been introduced, as they would otherwise have been, into optical instruments. The principle upon which polyzonal lenses are constructed is equally applicable to prisms. A prism constructed like A D, fig. 205., if properly executed, would have exactly the same properties as ABC, and would be incomparably superior to it, from the light passing through such a small thickness of glass. It would obviously be difficult to execute such a prism as A D out of a single piece of glass, though it is quite practicable; but there is no G G 4i 456 A TREATISE ON OPTICS. PART it. difficulty in combining six small prisms all cut out of one prismatic rod, and therefore necessarily similar. The summit of the rod should have a flat narrow face parallel to its base, which would be easily done if the prismatic rod were cut out of a plate of thick parallel glass. The separate prisms being cemented to one another, as in the figure, will form a compound prism, which will be superior to the common prism for all purposes in which it acts solely by refraction, (222.) A compound prism of a different kind, and having a variable angle, was proposed by Boscovich, as shown in fig. 206., where A B C is a hemispherical con- vex lens, moving in a concave lens, DEC, of the same curvature. By turning one of the lenses round upon the other, the inclination of the faces A B, D E,, Fig. 206. or A B, C E, may be made to vary from to above 90. (223.) As this apparatus is both troublesome to exe- cute and difficult to use, I have employed an entirely CHAP. LI. NEW APPLICATION OP THE PRISM. 457 different principle for the construction of a variable prism, and have used it to a great extent in numerous experiments on the dispersive powers of bodies. If we produce a vertical line of light by nearly closing the window shutters, and view the line with a flint glass prism whose refracting angle is 60, the edge of the refracting angle being held vertical, or parallel to the line of light, the luminous line will be seen as a brightly coloured spectrum, and any small portion of it will resemble almost exactly the solar spectrum. If we now turn the prism in the plane of one of its refracting faces, so that the inclination of the edge to the line of light increases gradually from up to 90 when it is perpendicular to the line of light, the spec- trum will gradually grow less and less coloured, exactly as if it were formed by a prism of a less and less re- fracting angle, till at an inclination of 90 not a trace of colour is left. By this simple process, therefore, namely, by using a line of light instead of a circular disc, we have produced the very same effect as if the refracting angle of the prism had been varied from 90 down to 0. (224.) Let it now be required to determine the rela- tive dispersive powers of flint glass and crown glass. Place the crown glass prism so as to produce the largest spectrum from the line of white light, and let the refracting angle of the prism be 40. Then place the flint glass prism between it and the eye, and turn it round, as before described, till it corrects the colour produced by the crown glass prism, or till the line of light is perfectly colourless. The inclination of the edge of the flint glass prism to the line of light being known, we can easily find by a simple formula the angle of a prism of flint glass which corrects the colour of a prism of crown glass with a refracting angle of 40. See my Treatise on New Philosophical Instru- ments, p. 291. 458 A TREATISE ON OPTICS. PART IV. Multiplying Glass. (225.) This lens is more amusing than useful, and is intended to give a number of images of the same object. Though it has the circular form of a lens, it is nothing more than a number of prisms formed by grinding various flat faces on the convex surface of a plano-convex glass, as shown in^r. 207., where A B is Fig. 207. the section of a multiplying glass in which only three of the planes are seen. A direct image of the object C will be seen through the face G H, by the eye at E ; another image will be seen at D, by the refraction of the face HB, and a third at F, by the refraction of the face AG, an image being seen through every plane face that is cut upon the lens. The image at C will be colourless, and all those formed by planes inclined to AB will be coloured in proportion to the angles which the planes form with AB. Natural multiplying glasses may be found among transparent minerals which are crossed with veins op- positely crystallised, even though they are ground into plates with parallel faces. In some specimens of Ice- land spar, more than a hundred finely coloured images may be seen at once. The theory of such multiplying glasses has already been explained in Chap. XXXIX., 170. CHAP. LII. ON THE CAMERA OBSCURA. 459 CHAP. LII. ON THE CAMERA OBSCURA, MAGIC LANTERN, AND CAMERA LUCIDA. (226.) THE camera obscura, or dark chamber, is the name of an amusing and useful optical instrument, in- vented by the celebrated Baptista Porta. In its original state it is nothing more than a dark room with an open- ing in the window shutter, in which is placed a convex lens of one or more feet focal length. If a sheet of white paper is held perpendicularly behind the lens, and passing through its focus, there will be painted upon it an accurate picture of all the objects seen from the win- dow, in which the trees and clouds will appear to move in the wind, and all living objects to display the same movements and gestures which they exhibit to the eye. The perfect resemblance of this picture to nature asto- nishes and delights every person, however often they may have seen it. The image is of course inverted, but if we look over the top of the paper it will be seen as if it were erect. The ground on which the picture is re- ceived should be hollow, and part of a sphere whose radius is the focal distance of the convex lens. It is customary, therefore, to make it of the whitest plaster of Paris, or of ground glass when it is plane, with as smooth and accurate a surface as possible. In order to exhibit the picture to several spectators at once, and to enable any person to copy it, it is desirable that the image should be formed upon a horizontal table. This may be done by means of a metallic mirror, placed at an angle of 45 to the refracted rays, which will re- flect the picture upon the white ground lying horizon- tally ; or, as in the portable camera obscura, it may be reflected upwards by the mirror, and received on the lower side of a plate of ground glass, with its rough side uppermost, upon which the picture may be copied with a fine sharp-pointed pencil. Fig. 208. ~ 4&0 A TREATISE ON OPTICS* PART IV. A very convenient portable camera obscura for draw- ing landscapes or other objects is shown in fig. 208., where A B is a meniscus lens, with its concave side upper- most, the radius of its convex surface being to the radius of its concave surface as 5 to 8, and CD a plane metallic speculum inclined at an angle of 45 to the horizon, so as to reflect the landscape down- wards through the lens AB. The draughtsman introduces his head through an opening in one side, and his hand with the pencil through an- other opening, made in such a manner as to allow no light to fall upon the picture which is exhibited on the paper at E F. The tube containing the mirror and lens can be turned round by a rod within, and the inclination of the mirror changed, so as to introduce objects in any part of the horizon. When the camera is intended for public exhibition, it consists of the same parts similarly arranged ; but they are in this case placed on the top of a building, and the rotation of the mirror, and its motion in a ver- tical plane, are effected by turning two rods within the reach of the spectator, so that he can introduce any ob- ject into the picture from all points of the compass, and at all distances. The picture is received on a table, whose surface is made of stucco, and of the same radius as the lens, and this surface is made to rise and fall to accommodate it to the change of focus produced by ob- jects at different distances. A camera obscura which throws the image down upon a horizontal surface may be made without any mirror, by using any of the len- ticular prisms D E F, G H I, M L N, when the objects are extremely near, and P R Q, fig. 202. The convex surfaces of these prisms converge the rays which are CHAP. MI. ON THE MAGIC LANTERN. 46l reflected to their focus by the flat faces D E, G H, L N, and P Q ; and the prisms may be formed by ce- menting plano-convex or concave lenses on the faces A B, B C of the rectangular prism A B C, or the con- vex lens may be placed near to A B. If we wish to form an erect image on a vertical plane, the prism ABC, fig. 202., may be placed in front of the convex lens, or immediately behind it. The same effect might be produced by three reflexions from three mirrors or specula. I have found that a peculiarly brilliant effect is given to the images formed in the camera obscura when they are received upon the silvered back of a looking glass, smoothed by grinding it with a flat and soft hone. In the portable camera obscura I find that a film of skimmed milk, dried upon a plate of glass, is superior to ground glass for the reception of images. A modification of the camera obscura, called the me- gascope, is intended for taking magnified drawings of small objects placed near the lens. In this case, the distance of the image behind the lens is greater than the distance of the object before it. By altering the distance of the object, the size of the image may be reduced or enlarged. The hemispherical lens L M N, fig. 202., is particularly adapted for the megascope. The camera obscura has been brought to great per* fection from its application to photography. It is now generally constructed with two achromatic lenses. Magic Lantern. (227.) The magic lantern, an invention of Kircher, is shown in fig. 209., where L is a-lamp with a powerful Argand burner, placed in a dark lantern. On one side of the lantern is a concave mirror M N, the vertex of which is opposite to the centre of the flame, which is placed in its focus. In the opposite side of the lantern is fixed a tube A B, containing a hemispherical illumi- nating lens A, and a convex lens B ; and between A and B the diameter of the tube is increased for the purpose of 462 A TREATISE ON OPTICS. Fig. 209. PART IV. allowing sliders to be introduced through the slit C D. These sliders contain 4 or 5 pictures, each painted and highly coloured with transparent varnishes, and, by sliding them through C D, any of the subjects may be introduced into the axis of the tube and between the two lenses A, B. The light of the lamp L, increased by the light reflected from the mirror falling upon the lens A, is concentrated by it upon the picture in the slider ; and this picture, being in one of the conjugate foci of the lens B, an enlarged image of it will be painted on a white cloth, or on a screen of white paper, E, standing or suspended perpendicularly. The distance of the lens B from the object or the slider may be increased or dimi- nished by pulling out or pushing in the tube B, so that a distinct picture of the object may be formed of any size and at any distance from B, within moderate limits. If the screen E F is made of fine semitransparent silver paper, or fine muslin properly prepared, the image may be distinctly seen by a spectator on the other side of the screen. (228.) The Phantasmagoria is nothing more than a magic lantern, in which the images are received on a transparent screen, which is fixed in view of the spectator. The magic lantern, mounted upon wheels, is made to recede from or approach to the screen ; the consequence of which is, that the picture on the screen expands to a gigantic size, or contracts into an invisible object or small luminous spot. The lens B is made to recede CHAP. LII. ON THE CAMERA LUCID'A. 463 from the slider in C D when the lantern approaches the screen, and to approach to it when the lantern recedes from the screen, in order that the picture upon the screen may always be distinct. This may be accom- plished, according to Dr. Young, by jointed rods or levers, connected with the screen, which pull out or push in the tube B ; but we are of opinion that the required effect may be much more elegantly and efficaciously produced by the simplest piece of mechanism connected with the wheels. Camera Lucida. (229.) This instrument, invented by Dr. Wollaston in 1807, has come into very general use for drawing landscapes, delineating objects of natural history, and copying and reducing drawings. Dr. Wollaston's form of the instrument is shown in fig. 210., where A B C D is a glass prism, the angle BAD being 90, A D C 67i, and D C B 135. The rays proceeding from any object, M N, after being Fig. 210. reflected by the faces D C, C B to the eye, E, placed above the angle B, the observer will see an image m n of the object M N projected upon a piece of paper at m n. If the eye is now brought down close to the angle B, so that it at the same time sees into the prism with one half of the pupil, and past the angle B with the other half, it will obtain distinct vision of the image m n, and also see the paper and the point of the pencil. The draughtsman has, therefore, only to trace the out- 464 A TREATISE ON OPTICS. line of the image upon the paper, the image being seen with half of the pupil, and the paper and pencil with the other half. Many persons have acquired the art of using this in- strument with great facility, while others have entirely failed. In examining the causes of this failure, Professor Amici, of Modena, succeeded in removing them, and has proposed various forms of the instrument free from the defects of Dr. Wollaston's.* The one which M. Amici thinks the best is shown in fig. 211., where A B C D is a piece of thick parallel glass, F G H C a me- tallic mirror, whose face, F G, is highly polished, and inclined 45 to B C. Rays from an object, M N, after passing through the glass A B C D, are reflected from F G, and afterwards from the face B C of the glass plate to the eye at E, by which the object, M N, is seen at m n, where the paper is placed. The pencil and the paper are readily seen through the plane glass A B C D. In order to make the two faces of the glass, AD, B C, perfectly parallel, M. Amici forms a triangular prism of glass, and cuts it through the middle ; he then joins the * An account of these various forms will be found in the Edinburgh Journal of Science, No. V. p. 157. CHAP. LIII. ON SINGLE MICROSCOPES. 465 two prisms or halves, A D C, C A B, so as to form a parallel plate, and by slightly turning round the prisms, he can easily find the position in which the two faces are perfectly parallel. >^? OP CHAP. ON MICROSCOPES. A MICROSCOPE is an optical instrument for magnifying and examining minute objects. Jansen and Drebell are supposed to have separately invented the single mi- croscope, and Fontana and Galileo seem to have been the first who constructed the instrument in its com- pound form. Single Microscope. (230.) The single microscope is nothing more than a lens or sphere of any transparent substance, in the focus of which minute objects are placed. The rays which issue from each point of the objects are refracted by the lens into parallel rays, which, entering the eye placed immediately behind the lens, affords distinct vision of the object. The magnifying power of all such mi- croscopes is equal to the distance at which we could examine the object most distinctly, divided by the focal length of the lens or sphere. If this distance is 5 inches, which it does not exceed in good eyes when they examine minute objects, then the magnifying power of each lens will be as follows : Focal length in Linear magnifying Superficial magnifying inches. power. power. 5 1 1 15 25 -fo 50 2500 Tfo 500 250000 The linear magnifying power is the number of times an object is magnified in length, and the superficial 466 A TREATISE ON OPTICS. PART IV. magnifying power is the number of times that it is mag- nified in surface. If the object is a small square, then a lens of one inch focus will magnify the side of the square 5 times, and its area or surface 25 times. The best single microscopes are minute lenses ground and polished on a concave tool ; but as the perfect exe- cution of these requires considerable skill,, small spheres have been often constructed as a substitute. Dr. Hook executed these spheres in the following manner : Having drawn out a thin strip of window glass into threads by the flame of a lamp, he held one of these threads with its extremity in or near the flame, till it run into a globule. The globule was then cut off and placed above a small aperture, so that none of the rays which it trans- mitted passed through the part where it was joined to the thread of glass. He sometimes ground off the end of the thread, and polished that part of the sphere. Father di Torre of Naples improved these globules by placing them in small cavities in a piece of calcined tripoli, and remelting them with the blowpipe ; the consequence of which was, that they assumed a perfectly spherical form. Mr. Butterfield executed similar spheres by taking upon the wetted point of a needle some fine pounded glass, and melting it by a spirit lamp into a globule. If the part next the needle was not melted, the globule was removed from the needle and taken up with the wetted needle on its round side, and again presented to the flame till it was a perfect sphere. M. Sivright, of Meggetland, has made lenses by putting pieces of glass in small round apertures between the 10th and 20th of an inch, made in platinum leaf. They were then melted by the blow- pipe, so that the lenses were made and set at the same time. Mr. Stephen Gray made globules for microscopes by inserting drops of water in small apertures. I have made them in the same way with oils and varnishes ; but the finest of all single microscopes may be executed by forming minute plano-convex lenses upon or beneath glass either with plane, convex, or concave surfaces, CHAP. LIII. ON SINGLE MICROSCOPES. 46? with different fluids, separate or combined. When the fluid is suspended below the glass, it takes a form ap- proaching to the hyperbola, and its form varies ac- cording as the surface is plane, convex, or concave. A drop of fluid flattened by its weight, and resting upon plane glass, may be combined with a lens beneath and made hyperbolic by suspension. I have formed fluid doublets and triplets, either simple or achromatic, by the same means, and have succeeded in combining two im- miscible fluids with a glass lens, namely, castor oil and treacle or pure honey. A hyperbolic figure may be formed by suspending within the fluid lens a convex lens of glass which weighs it down ; and it may be made achromatic by suspending a concave lens. These various forms of fluid microscopes, or of fluid and solid lenses combined, may be made perfect by a simple method which I have adopted, of making the axes of the combined lenses perfectly coincident. I have made lenses of Canada Balsam of the 50th of an inch in focal length, and preserved it for many years.* I have also formed excellent microscopes by using the spherical crystalline lenses of minnows and other small fish, and taking care that the axis of the lens is the axis of vision, or that the observer looks through the lens in the same manner that the fish did.t The most perfect single microscopes ever executed of solid substances are those made of the gems, such as garnet, ruby, sapphire, and diamond. The advantages of such lenses I first pointed out in my Treatise on Phi- losophical Instruments; and two lenses, one of ruby and another of garnet, were executed for me by Mr. Peter Hill, optician in Edinburgh. These lenses performed admirably, in consequence of their producing, with sur- faces of inferior curvature, the same magnifying power as a glass lens ; and the distinctness of the image was increased by their absorbing the extreme blue rays of the spectrum. Mr. Pritchard, of London, has carried * See Treatise on the Microscope, p. f See Edinburgh Journal of Science, No. III. p. 98. H H 2 468 A TREATISE ON OPTICS. PART IV. this branch of the art to the highest perfection, and has executed lenses of sapphire and diamond of great power and perfection of workmanship. When the diamond can be procured perfectly homoge- neous and free from double refraction, it may be wrought into a lens of the highest excellence ; but the sapphire, which has double refraction, is less fitted for this purpose. Garnet is decidedly the best material for single lenses, as it has no double refraction, and may be procured, with a little attention, perfectly pure and homogeneous. I have now in my possession two garnet microscopes, executed by Mr. Adie, which far surpass every solid lens I have seen. Their focal length is between the 30th and the 50th of an inch. Mr. Veitch, of Inchbonny, has likewise executed some admirable garnet lenses out of a Greenland specimen of that mineral given to me by Sir Charles Giesecke. The late Mr. Blaikie, of Edinburgh, made some admirable lenses of diamond, garnet, sapphire, and at my request has executed both doublets and trip- lets with lenses made of gems, which are equal, if not superior, to any single microscope I have seen. (231.) A single microscope, which occurred tome some years ago, is shown in fig. 2 12., and consists in a new me- thod of using a hemispherical lens so as to obtain from it twice the magnifying power which it possesses when used in the common way. If A B C is a hemispherical lens, rays issuing from my object, R, will be refracted at the first CHAP. L1TI. ON SINGLE MICROSCOPES. 4$ surface A C, and, after total reflexion at the plane sur- face BC, will be again refracted at the second surface AB, and emerge in parallel directions def, exactly in the same manner as if they had not been reflected at the points a, 6, c, but had passed through the other half B A' C of a perfect sphere A B A' C. The object at R will therefore be magnified in the same manner, and will be seen with the same distinctness as if it had been seen through a sphere of glass ABA'C. We obtain, conse- quently, by this contrivance all the advantages of a sphe- rical lens, which we believe never has been executed by grinding. The periscopic principle, which will presently be mentioned, may be communicated to this catoptric lens, as it may be called, by merely grinding off the angles B, C, or rough grinding an annular space on the plane surface B C. The confusion arising from the oblique re- fractions will thus be prevented, and the pencils from every part of the object will fall symmetrically upon the lens, and be symmetrically refracted. Before I had thought of this lens, Dr. Wollaston had proposed a method of improving lenses, which is shown Fia 213 in./2gr. 213. He introduced between two plano-convex lenses of equal size and radius a plane of metal with a circular aperture equal to ^th of the focal length, and when the aperture was well centered, he found that the visible field was 20 in diameter. In this compound lens the oblique pencils pass, like the central ones, at right angles to the surface. If we compare this lens with the catoptric one above described, we shall see that the effect which is produced in the one case with two spherical and two plane surfaces, all ground separately, is produced in the other case by one spherical and one plane surface. (232.) The idea of Dr. Wollaston may, however, be improved in other ways, by filling up the central aperture with a cement of the same refractive power as the lenses, or, what is far better, by taking a sphere of glass and H H 3 470 A TREATISE OX OPTICS. PART IV. grinding away the equatorial parts, so as to limit the central aperture, as shown in^r. 214.*; a construction Fig. 214. which, when executed in garnet, and used in homo- geneous light, we conceive to be the most perfect of all lenses, either for single microscopes, or for the object lenses of compound ones. A lens of tbis kind, whether the surfaces have the same or a different radius, may be called a Concentric Lens, and has valuable properties. An Equivalent concentric lens may be made by com- bining two plano-convex lenses with their plane sides separate but next one another, the lenses having dif- ferent radii. The smaller lens may be either a hemi- sphere, or less or greater, and they may be so adjusted that the surface of the large lens may be in the focus of the combination, and consequently the place upon which the object is to be viewed. Single microscopes may be made by combining semi' lenses or quarters of tenses, or any number of portions of a given lens. tne Kejtexion ana, ttejraction oj L,ignt, puonsnea in j^y. mr. tjpacungton had probably got one made by some London optician, who had ignorantly supposed it to be new, and presumed to give it a name to which it was not Entitled. CHAP. LIU. Fig. 215. READING GLASSES. 471 In fig. 215. is represented a com- bination of two semi-lenses, ABC, DEF, cut from the same lens so as to make a lens of twice the magnify- ing power. If the one semi-lens A B has a greater power than the other, then we shall have in the same com- bination the highest power in the portion E B, another lower power through the portions m, o, and a still lower power through the portions n,p. A combination of quarters of lenses is shown in fig. 216., to which the preceding de- scription is applicable. The quarter lenses may be com- bined like the upper half of fig. 215. Several of these combinations may be united for optical purposes. The preceding method of combining divided lenses en- ables us to make two or more lenses, or microscopes, or telescopes, exactly of the same magnifying powers, an effect which cannot be obtained by any other process. Fig. 216. Reading Glasses. (233.) The reading glasses hitherto used are merely large convex lenses, which enable us to read with both eyes at the same time. In using reading glasses, we should always combine them with spectacles, when spec- tacles are required. Those who read much and require a reading glass, should have it so placed in a frame that it can rest on the book, and if the bottom of the tube is constructed H H 4 472 A TREATISE ON OPTICS. so as to allow only two or three lines to be seen at once, the eyes will be protected against the mass of light which falls upon them when one or two pages are exposed. An illuminating lens might be advantage- ously placed on the side of the tube, and the eyes en- tirely defended against the direct light of the lamp or candle. When a reading glass cannot be readily obtained, a temporary one may be made, as in the annexed figure, by crossing two bottles filled with water or any trans- parent fluid, and looking through the crossed portion. Two very small bottles, or two test tubes, crossed in the same manner, will form a good extempore microscope. When a single microscope is used for opaque objects, the lens is placed within a concave silver speculum, which concentrates parallel or converging rays upon the face of the object next the eye. Compound Microscopes. (234.) When a microscope consists of two or more lenses or specula, one of which forms an enlarged image of objects, while the rest magnify that image, it is called a compound microscope. The lenses, and the progress of the rays through them in such an instrument, are shown Fig. 218. gr, 218., where AB is the object glass, and CD the CHAP. LIII. COMPOUND MICROSCOPES. ?3 eye glass. An object, MN, placed a little farther from A B than its principal focus, will have an enlarged image of itself formed at m n in an inverted position. If this enlarged image is in the focus of another lens, CD, placed nearer the eye than in the figure, it will be again mag- nified, as if mn were an object. The magnifying effect of the lens AB is found by dividing the distance of the image m n from the lens A B by the distance of the ob- ject from the same lens; and the magnifying effect of the eye glass C D is found by the rule for single microscopes ; and these two numbers being multiplied together, will be the magnifying power of the compound microscope. Thus, if MA is ^th of an inch, and A n ^ an inch (mn being supposed in the focus of C D,) the effect of the lens AB will be 20, and that of C D 10, and the whole power 200. A larger lens than any of the other two, called the field glass, and shown at E F, is generally placed be- tween AB and the image mn, for the purpose of enlarg- ing the field of view. It has the effect of diminishing the magnifying power of the instrument by forming a smaller image at v u 9 which is magnified by C D. The com- pound microscope has been brought to great perfection by modern opticians. The instruments made by Ross, Powell, Smith, and Beck, with achromatic object- glasses varying from 1 inch to -pg-th of an inch, have not been surpassed by those of any other artists in the world. Fig. 219. The object glass consists sometimes of two, but generally three, double i achromatic lenses, as shown in the an- nexed figure, an arrangement first pro- s^ "\ posed by Mr. Joseph Lister. Mr. Ross p**- *^J * s we helieve, the only artist who has executed lenses of this kind with so small a focal length as T ^th of an inch ; and, without undervaluing the skill of other opticians, we venture to say that his microscopes are now unrivalled. A TREATISE ON OPTICS. PART IV. 474 Mr. Ross's microscope * had the following object glasses and angles of aperture (BAG): 1 inch focal length 2 ' 3 27 aperture. - H3 - 107 -135 M. Nachet, of Paris, who received a prize medal, ex- hibited an admirable microscope with an object glass T ^th of an inch in focal length and angle of aperture of 134. The eye-piece at present universally employed in the compound microscope is what is called the Huygenian eye-piece, and has no focus without the field lens. It is shown in fig. 220,, where AB is the field glass and Fig. 220. C D the eye glass, placed at a distance, B D, equal to half the sum of their focal lengths. Three of these eye-pieces are generally supplied to each microscope. In Mr. Ross's instrument the dif- ferent eye-pieces magnify in the ratio of 1, 1^, and 2^, and when a one-inch object glass is used, the powers will be 30, 45, and 75. The object which Huygens had in view in proposing this eye -piece was simply to correct the spherical aber- ration ; but it was shown by Boscovich that it has also the valuable property of correcting a large portion of the chromatic aberration, as the spherical aberra- *. This microscope gained the Council Medal at the Great Exhibition. CHAP. JJII. COMPOUND MICROSCOPES. 475 tion of the eye glass, C D, compensates the chromatic aberration of the field glass AB. As we have never found the chromatic aberration to be completely cor- rected, we would recommend the substitution of achro- matic for common lenses. The time indeed is not far distant when such lenses will be employed in all our optical instruments. In Ramsden's eye-piece, with its focus without the field lens, and with the convex sur- face of that lens towards the eye, neither of the aberra- tions are corrected, and hence the use of achromatic lenses is necessary to give it any real value. An improvement in the microscope, which we owe entirely to Mr. Ross, deserves our special notice and admiration. When the correction for spherical aber- ration is perfect, which it is when no refracting sur- face intervenes between the object and the object glass, an aberration is produced either if the object is im- mersed in a fluid, or placed between plates of glass or mica. This aberration is compensated by an opposite aberration, which Mr. Ross produces by making the lower achromatic lens in fig. 219- approach to the middle lens, an effect which is obtained either by making the tube containing the two lower lenses slide upon the tube containing the two upper ones, or by a screw collar, which moves the one tube upon the other with greater accuracy. We have not seen any of the stands of the micro- scope that are thoroughly adapted to scientific inves- tigation of an optical kind, and I have been obliged to provide additional pieces for a fine microscope by Ross, which I have long used. These pieces are, first, an addition to the stage, by which, when an object is in the centre of the field, we can turn the object round 360 and yet keep it in the centre; and, secondly, an ad- ditional piece above the stage, by which we can place between the surface of the polariser and the object a plate of sulphate of lime, or any other body, which can be moved round through a large arc in order to deter- mine the character of the polarisation of the object, or A TREATISE ON OPTICS. PART IV. of any part of it; and, thirdly, a very small prism with three different refracting angles, by which we can analyse the colours of objects seen in the microscope. This prism must be placed between the eye and the eye lens, so as to turn freely round its axis and be placed in every azimuth. A diaphragm with an ex- tremely narrow slit should also be provided, to be placed when necessary between the field and eye glasses. The ingenuity of philosophers and of artists has been nearly exhausted in devising the best forms of object glasses and of eye glasses for the compound microscope. Mr. Coddington has recommended four lenses to be em- ployed in the eye piece of compound microscopes, as shown in fig. 221. ; and along with these he uses, as an object glass, the sphere excavated at the equator, as in fig. 214*., for the purpose of reducing the aberration and Fig 221. dispersion. " With a sphere," says he, is inserted in a hole in the window-shutter, and the sun's light reflected into it by a long plane piece of looking-glass, which the observer can turn round to keep the light in the tube as the sun moves through the heavens. Living objects, or objects of natural history, are put upon a glass slider, or stuck on the point of a needle, and introduced into the opening C D, so as to be illu- minated by the sun's rays concentrated by the lens A. An enlarged and brilliant image of the object will then be formed on the screen E F. * See the article MICROSCOPE, Edinburgh Encyclopaedia, vol. xiv. p. 22fi, which has been published in a separate treatise. J I 482 A TREATISE ON OPTICS. PART IV. Those who wish to see the various external forms of microscopes of all kinds, and the different modes of fitting them up, are referred to the article MICROSCOPE, in the Edinburgh Encyclopedia, vol. xiv. p. 215 233. In the latest work on the microscope, viz. Mr. Pritchard and Dr. Goring' s Microscopical Illustrations, London, 1830 and 1845; in Mr. Quekett's admirable Prac- tical Treatise on the use of the Microscope, and in Mr. Ross's excellent article on the Microscope in the Penny Cyclopaedia, the English reader will find much valuable and interesting information. On the Illumination of Microscopic Objects. (240.) Various methods of illuminating microscopic objects have been in use ever since the invention of the microscope ; but, in so far as I know, no attempt was ever made to adopt a method of illumination in which the object should appear as if it shone by its own light. In every other method the light condensed upon the object radiates from one or more points before it falls upon the object, and thus produces the phenomena of diffraction, which, when high powers are used, are de- structive of all distinctness of vision. Dr. Wollaston's method of illumination, already de- scribed, does not, in the least degree, accomplish this object. His sole purpose was to get rid of unnecessary light which impeded vision, and not to remove the evils arising from diffraction. He never even mentions dif- fraction^ or any other cause but that of superfluous light, as the origin of the imperfect vision which arises from the usual modes of illumination. He throws the image of a perforation, and not the focal image of the illumi- nating body upon the object, so that the rays which fall upon the object actually diverge from a point between it and the illuminating lens, and produce a maximum degree of diffraction. But even if he had proposed to throw the real focal image upon the object, the method which he adopted CHAP. LIU. ILLUMINATION OF MICROSCOPIC OBJECTS. 4S3 proves that his purpose was to make the object appear as if it were self-luminous, or, what is the same thing, to make the light diverge from the point of the object under examination. To do this by a plano-convex lens or a properly crossed lens ^ths of an inch focus and T \ths of an inch in diameter, would be as absurd as to expect to see the satellites of Saturn through an opera glass ; and still more absurd would it be when the object is illuminated by rays whose conjugate focus is the centre of a perforation, within two or three inches of the lens, instead of being at a very great distance. The rays which emanate from the focus of such a lens diverge from an infinite number of foci depending on its chromatic and spherical aberration, and must there- fore, especially with strong lights and high powers, give indistinct vision. It is obvious^ therefore, from these observations, that the light which is thrown upon microscopic objects must be converged upon the point under examination, and radiate from that point; and this can be done only by having an illuminating appa- ratus as perfect as the magnifying apparatus. The object glass of the 12th of an inch should be the illu- minating glass when the object lens of the next lowest power is used, and so on with the other powers. But even this is not sufficient when difficult structures are to be developed. In such cases we do not desire to see the whole field illuminated, or to see any thing more than the single point under examination. We would therefore lay the object upon the plane side of a piano- s convex lens of diamond or garnet with a focal length of the 30th or 50th of an inch, and having sueh a thick- ness that the focus coincided nearly with the object or part of the object under examination. When a com- pound apparatus is used, it might be another microscope ; but whatever it be, it should be independent of the real microscope, and capable of having its minute pencil of light thrown readily upon the object. When every method of developing a structure fails, we must have recourse to homogeneous light, which may ii 2 484 A TREATISE ON OPTICS. PART IV. be obtained from the monochromatic lamp, from the absorption of coloured media, or from the prism.* On the Polarising Microscope. (241.) A polarising microscope is nothing more than the common microscope, simple or compound, in which polarised light is transmitted through the object, and the transmitted light subsequently analysed by any of the methods which are best adapted to the purpose. Such a microscope cannot properly be called an invention, although the invention of it has been claimed by several persons who certainly did not invent it. So early as J 815, 1 constantly used a quarter of an inch lens with a plate of tourmaline attached to it as a simple analyser, taking the polarised light from the nearest re- flecting surface ; and about the same time I fitted up a compound microscope as a polarising one, with which Mr. Lizars subsequently executed the beautiful coloured drawings of apophyllite, &c., which were communicated to the Royal Society of Edinburgh early in 1817, and with which Dr. Greville delineated the remarkable po- larising structure which I discovered in the Equisetum Hiemale.^ In constructing polarising microscopes the polariser may consist of a bundle of thin plates of glass refracting or transmitting the illuminating rays before they fall upon the object, or of a plate of tourmaline, or a rhomb of Iceland spar, or a Nicol's prism ; but whichever of these polarisers is used, it should have, what it has not in any of the best microscopes I have seen, the means of revolving in a plane perpendicular to the polarised ray or the axis of the microscope, and with a divided circle to measure its arcs of rotation. Between the polariser and the object there should be left, as we have had occasion previously to state, a free space for introducing * See the Encyclopaedia Britannica, art. MICROSCOPE, chap, iv., and Edin. Journal of Science, Jan. 1832. t Encycl. Brit., supra, chap.iv. I have no doubt that both M. Arago wd M. B:ot had occasion to use polarising microscopes in their researches. CHAP. LIU. ON THE POLARISING MICROSCOPE. 485 a film of sulphate of lime, or any other body whose polarising structure or influence we wish to combine with that of the body under examination. It would be desirable even that the observer should have various plates of sulphate of lime, from the thickness that po- larises the faintest blue of the first order to that which would polarise several of the higher orders of colours. These films should have their axes marked upon them, and should be placed in brass caps, so as to turn round in the opening of the stage. The other part of the polarising microscope, namely the analyser, may be any one of the pieces already mentioned as suited to be the polariser,* but the most convenient is either a Nicofs prism or a rhomb of Calcareous Spar. I greatly prefer the latter, for rea- sons which I have elsewhere given at great length. When the analyser is a rhomb or a Nicol's prism, it may be placed either within the microscope or without it, between the eye and the eye-glass, where it was al- ways placed till I suggested the idea of its being attached immediately within the object glass, an improvement which, I believe, is now universally adopted. In this position, however, it would be advisable to give it a motion of rotation, without disturbing the position of the object lens ; so that in a perfect polarising micro- scope, the polariser, the test plate of sulphate of lime, the object, and the analyser, should all have a motion of rotation round the axis of the microscope. The rotation of the analyser is particularly important when we are examining any object within a doubly re- fracting crystal. When this object is complex, its struc- ture is masked by the double image of its parts, and the readiest remedy for this is to extinguish one of the images by turning round the analyser. * I have used a plate of topaz with a fine cleavage plane for an analyser. It was made to revolve between the eye and the eye glass, with its surface inclined 31 26' to the axis of the microscope. ii 3 486 A TREATISE ON OPTICS. PART IV. The Microscopic Finder. (242.) The microscope requires a finder as much as a telescope, but so far as I know, no person has tried to give it one. We obviously cannot, with advantage, attach a smaller microscope to the larger one, as is done in the telescope, but the desideratum may be supplied by very simple means. In using very high powers to examine a single point of an object, or an individual object among a great number, it often requires much time and patience to rediscover it. In this case we are obliged to take off the high power (both the object lens and the eye piece), and after finding the object with a low power, we must place it in the centre of the field, remove the low powers, replace the high power, and readjust the microscope. We shall now find the object in the centre of the field. This labour is, however, in- tolerable. I propose, therefore, to slip upon the tube of the object lens a deep concave lens, which reduces the power, enlarges the field, and enables us at once to find the object. The concave lens is then removed, and the instrument readjusted. CHAP. LIV. ON REFRACTING AND REFLECTING TELESCOPES. Astronomical Telescope. (243.) THAT the telescope was invented in the thirteenth century, and perfectly known to Roger Bacon, and that it was used in England by Leonard and Thomas Digges before the time of Jansen or Galileo, can scarcely admit of a doubt. The principle of the refracting telescope, and the method of computing its magnifying power, have been already explained. We shall therefore pro- CHAP. LIV. ASTRONOMICAL TELESCOPE. ceed to describe the different forms which it successively assumed. The Astronomical Telescope is represented in fig. 224. Fig. 224. It consists of two convex lenses A B, CD, the former of which is called the Object glass, from being next the object M N, and the latter the Eye glass, from its being next the eye E. The object glass is a lens with a long focal distance ; and the eye glass is one of a short focal distance. An inverted image m n of any distant object M N is formed in the focus of the object glass A B ; and this image is magnified by the eye glass C D, in whose anterior focus it is placed. By tracing the rays through the two lenses, it will be seen that they enter the eye E parallel. If the object M N is near the observer, the image m n will be found a a greater distance from A B ; and the eye glass C D must be drawn out from A B to obtain distinct vision of the image m n. Hence it is usual to fix the object glass A B at the end of a tube longer than its focal distance, and to place the eye glass C D in a small tube, called the eye tube, which will slide out of, and into, the larger tube, for the purpose of adjusting it to objects at differ- ent distances. The magnifying power of this telescope is equal to the focal length of the object glass divided by the focal length of the eye glass. Telescopes of this construction were made by Cam- pani Divini and Huygens, of the enormous length of 120 and 136 feet; and it was with instruments 12 and 24 feet long that Huygens discovered the ring and the fourth satellite of Saturn. In order to use object glasses of such great focal lengths without the incumbrance of tubes, Huygens placed the object glass in a short tube i i 4 488 A TREATISE ON OPTICS. PART IV. at the top of a very long pole, so that the tube could be turned in every possible direction upon a ball and socket by means of a string, and brought into the same line with another short tube containing the eye glass, which he held in his hand. As these telescopes were liable to all the imperfections arising from the aberration of refrangibility and that of spherical figure, they could not show objects distinctly when the aperture of the object glass was great ; and on this account their magnifying power was limited. Huygens found that the following were the proper pro- portions : .Focal length of the Apprture of the Focal length of the Msumifvinimower object glass. object glass. eye glass. 1ft. 0-545 inches. 0-605 20 3 0-94 1-04 33^ 5 1-21 1-33 44 10 1*71 1-88 62 .50 3-84 4-20 140 100 5-40 5-95 197 120 5-90 6-52 216 In the astronomical telescope, the object, M N, is always seen inverted, as at m n. Terrestrial Telescope. (244.) In order to accommodate this telescope to land objects which require to be seen erect, the instrument is constructed as in fig. 225., which is the same as the preceding one, with the addition of two lenses E F, G H, which have the same focal length as C D, and are placed at distances equal to double their common focal length. If the focal lengths are not equal, the distance of any two of them must be equal to the sum CHAP. LIV. GREGORIAN REFLECTING TELESCOPE. 489 of their focal lengths. In this telescope the progress of the rays is exactly the same as in the astronomical one, as far as L, where the two pencils of parallel rays C L, D L cross in the anterior focus L of the second eye glass E F. These rays falling on E F form in its prin- cipal focus an erect image n' m f , which is seen erect by the third eye glass G H, as the rays diverging from m' and n' in the focus of G H enter the eye in parallel pencils at E. The magnifying power of this telescope is the same as that of the former when the glasses are equal. Galilean Telescope. (245.) This telescope, which is the one used by Ga- lileo, differs in nothing from the astronomical telescope, excepting in a concave eye glass C D, fig. 226., being Fig. 226. - substituted for the convex one. The concave lens C D is placed between the image m n and the object glass, so that the image is in the principal focus of the concave lens. The pencils of rays A B n, A B m fall upon C D, converging to its principal focus, and will therefore be refracted into parallel lines, which will enter the eye at E, and give distinct vision of the object. The magnifying power of this telescope is found by the same rule as that for the astronomical telescope : it gives a smaller and less agreeable field of view than the astronomical telescope, but it has the advantage of showing the object erect, and of giving more distinct vision of it. Gregorian Reflecting Telescope. (246.) Father Zucchius seems to have been the first 490 A TREATISE ON OPTICS. PART IV. person who magnified objects by means of a lens and a concave speculum ; but there is no evidence that he con- structed a reflecting telescope with a small speculum. James Gregory was the first who described the con- struction of this instrument, but he does not seem to have executed one ; and the honour of doing this with his own hands was reserved for Sir Isaac Newton. The Gregorian telescope is shown in fig. 227., Fiy. 227. where A B is a concave metallic speculum with a hole in its centre. For very remote objects the curve of the speculum should be a parabola. For nearer ones it should be an ellipse in whose farther focus is the object and in whose nearer focus is the image ; and in both these cases the speculum would be free from spherical aberration. But, as these curves cannot be communi- cated with certainty to specula, opticians are satisfied with giving to them a correct spherical figure. In front of the large speculum is placed a small concave one, C D, which can be moved nearer to and farther from the large speculum by means of the screw" W at the side of the tube. This speculum should have its curvature elliptical, though it is generally made spherical. An eye- piece consisting of two convex lenses, E, F, placed at a distance equal to half the sum of their focal lengths, is screwed into the tube immediately behind the great spe- culum AB, and permanently fixed in that position. If rays M A, N B, issuing nearly parallel from the extre- mities M and N, of a distant object, fall upon the speru- CHAP. LIV. GREGORIAN REFLECTING TELESCOPE. 491 lum A B, they will form an inverted image of it at m n as more distinctly shown in fig. 14. If this image m n is farther from the small speculum C D than its principal focus, an inverted image of it, m'n', or an erect image of the real object, since m n is itself an inverted one, will be formed somewhere between E and F, the rays passing through the opening in the speculum. This image m' n' might have been viewed and magnified by a convex eye glass at F, but it is pre- ferable to receive the converging rays upon a lens E called the field glass, which hastens their convergence, and forms the image ofmn in the focus of the lens F, by which they are magnified ; or, what is the same thing, the pencils diverging from the image m' n' are refracted by F, so as to enter the eye parallel, and give distinct vision of the image. If the object M N is brought nearer the speculum AB, the image of it, mn, will re- cede from AB and approach to CD; and, consequently, the other image m! n 1 in the conjugate focus of C D will recede from its place m 'n' ', and cease to be seen distinctly. In order to restore it to its place m 1 n'> we have only to turn the screw W, so as to remove C D farther from A B, and consequently farther from m n, which will cause the image m n to appear perfectly distinct as before. The magnifying power of this telescope may be found by the following rule : Multiply the focal distance of the great speculum by the distance of the small mirror from the image next the eye, as formed in the anterior focus of the convex eye glass, and multiply also the focal distance of the small speculum by the focal distance of the eye glass. The quotient arising from dividing the former product by the latter will be the magnifying power. This rule supposes the eye-piece to consist of a single lens. The following table, showing the focal length, aper- tures, powers, and prices of some of Short's telescopes, will exhibit the great superiority of reflecting telescopes to refracting ones : 492 A TREATISE ON OPTICS. PART IV. Focal lengths in feet. Aperture in inches. Magnifying powers. Price in guineas. 1 30 35 to 100 14 2 4-5 90 300 35 3 6-3 100 400 75 4 7-6 120 500 100 7 122 200 80O 3OO 12 18-0 300 1200 800 Cassegrainian Telescope. (247.) The Cassegrainian telescope, proposed by M. Cassegrain, a Frenchman, differs from the Gregorian only in having its small speculum CD, fig. 228., convex instead of concave. The speculum is therefore placed Fig. 228. before the image m n of the object M N, and an image of M' N will be formed at m' n between E and F as in the Gregorian instrument. The advantage of this form is, that the telescope is shorter than the Gregorian by more than twice the focal length of the small speculum ; and it is generally admitted that it gives more light, and a distincter image, in consequence of the convex speculum correcting the aberration of the concave one. Newtonian Telescope. (248.) The Newtonian telescope, which may be re- garded as an improvement upon the Gregorian one, is re- presented in fig. 229., where A B is a concave speculum, and mn the inverted image which it forms of the object from which the rays M, N proceed. As it is impossible to introduce the eye into the tube to view this image without obstructing the light which comes from the object, a small plane speculum C D, inclined 45 to the CHAP. LIV. Is 7 EWTONIAN TELESCOPE. 493 axis of the large speculum, and of an oval form, its axes being to one another as 7 to 5, is placed between the spe- Fig. 229. A culum and the image mn, in order to reflect it to a side at m' n', so that we can magnify it with an eye glass E, which causes the rays to enter the eye parallel. The small mirror is fixed upon a slender arm, connected with a slide, by which the mirror may be made to approach to or recede from the large speculum A B, according as the image m n approaches to or recedes from it. This ad- justment might also be effected by moving the eye lens E to or from the small speculum. The magnifying power of this telescope is equal to the focal length of the great speculum divided by that of the eye glass. As about half of the light is lost in metallic reflexions, Sir Isaac Newton proposed to substitute, in place of the metallic speculum, a rectangular prism A B C,fig. 202., in which the light suffers total reflexion. For this pur- pose, however, the glass required to be perfectly colour- less and free from veins, and hence such a prism has seldom ever been used. Sir Isaac also proposed to make the two faces of the prism convex, as D $ F, fig. 202., and by placing it between the image m n and the object, he not only erected the image, but was enabled to vary the magnifying power of the telescope. The original telescope, constructed by Sir Isaac's own hands, is preserved in the library of the Royal Society. The following table shows the dimensions of New- tonian telescopes, which we have com-puted by taking a fine telescope made by Hawksbee as a standard; -r- 494* A TREATISE ON OPTICS. PART IV. 'Focal length of great Aperture of Focal length of Magnifying speculum. speculum. eye glass. power. 1ft. 2 -23 inches. 0-1 29 inches. 93 2 3-79 O 152 158 3 5*14 0-168 214 4 6-36 0'181 265 6 8-64 0-200 360 12 14-50 0-238 604 24 24-41 0283 1017 (249.) On account of the great loss of light in metal- lic reflexions, which, according to the accurate experi- ments of Mr. R. Potter, amounts to 45 rays in every 100, at an incidence of 45 *, and the imperfections of re- flexion, which even with perfect surfaces makes the rays stray five or six times more than the same imperfections in refracting surfaces, I have proposed to construct the Newtonian telescope, as shown in fig. 230., where A B is the concave speculum, m n the image of the object, M N and C D an achromatic prism, which refracts the Fig. 230. image m n into an oblique position, so that it can be viewed by the eye at E through a magnifying lens. Nothing more is required from the prism than to turn the rays as much aside as will enable the observer to see the image without obstructing the rays from the object MN. As the prisms of crown and flint glass which compose the achromatic prism may be cemented by a substance of intermediate refractive power, no more light will be lost than what is reflected at the two sur- faces. In place of setting the small speculum, C D, of the Newtonian telescope,^. 229-;, at an angle of 45 to the * Edinburgh Journal of Science, No. VI,, new series, p. 283. CHAP. LIV. SIR w. HERSCHEL'S TELESCOPE. 495 incident rays, I have proposed to place it much more obliquely, so as to reflect the image m n, fig. 230., out of the way of the observer, and no further. This would of course require a plane speculum, C D, of much greater length ; but the greater obliquity of the reflexion would more than compensate for this inconvenience. It might be advisable, indeed, to use a small speculum of dark glass, of a high refractive power, which at great inci- dences reflects as much light as metals, and which is capable of being brought to a much finer surface. The fine surfaces of some crystals, such as ruby silver, oxide of tin, or diamond, might be used. A Newtonian reflector, without an eye glass, may be made by using a reflecting glass prism, with one or both of its surfaces concave, when the prism is placed between the image m n and the great speculum, so as to reflect the rays parallel to the eye. The magnifying power will be equal to the focal length of the great speculum, divided by the radius of the concave surface of the prism, if both the surfaces are concave, and of equal concavity, or by twice the radius, if only one surface is concave. Sir William Herschel's Telescope. (250.) The fine Gregorian telescopes executed by Short were so superior to any other reflectors, that the Newtonian form of the instrument fell into disuse. It was revived, however, by Sir W. Herschel, whose labours form the most brilliant epoch in optical science. With an ardour never before exhibited, he constructed no fewer than 200 seven feet Newtonian reflectors, 150 ten feet, and 80 twenty feet in focal length. But his zeal did not stop here. Under the magnificent patron- age of George III., he began, in 1785, to construct a telescope forty feet long, and on the 27th of August, 1789, the day on which it was completed, he discovered with it the sixth satellite of Saturn. The great speculum had a diameter of 49J inches, but its concave surface was only 48 inches. Its thick- 496 A TREATISE ON OPTICS, PART IV. ness was about 3^ inches, and its weight when cast was 21181bs. Its focal length was 40 feet, and the length of the sheet iron tube which contained it was 39 feet 6' inches, and its breadth 4 feet 10 inches. By using small convex lenses, Sir W. Herschel was enabled to apply a power of 6450 to the fixed stars, but a very much lower power was in general used. In this telescope the observer sat at the mouth of the tube, and observed by what is called the front view, with his back to the object, without using a plane spe- culum, the eye lens being applied directly to magnify the image formed by the great speculum. In order to pre- vent the head, &c., from obstructing too much of the incident light, the image was formed out of the axis of the speculum, and must, therefore, have been slightly distorted. As the frame of this instrument was exposed to the weather, it had greatly decayed. It was, therefore, taken down, and another telescope, of 20 feet focus, with a speculum 18 inches in diameter, was erected in its place, in 1852, by Sir John Herschel, with which many important observations have been made. It was with this instrument that he discovered 525 new nebulae and clusters of stars, and took the places of be- tween 3000 and 4000 double stars. This instrument, with three mirrors, he carried to the Cape, and with it he made the valuable observations which are recorded in his work on that subject. Mr. Ramage's Reflecting Telescope. (251.) The late Mr. Ramage, of Aberdeen, con- structed various Newtonian telescopes, of great lengths and high powers. The largest instrument at present in use was constructed by him, and erected at the Royal Observatory of Greenwich in 1820. The great specu- lum has a focal length of 25 feet, and a diameter of 1 5 inches. The image is formed out of the axis of the speculum, which is inclined so as to throw it just .to the CHAP. LIV. LORD ROSSE*S TELESCOPE. 497 side of the tube, where the observer can view it without obstructing the incident rays. The tube is a 12-sided prism of deal, and when the instrument is not in use it is lowered into a box, and covered with canvas. The apparatus for moving and directing the telescope is ex- tremely simple, and displays much ingenuity. Lord Rosses Telescopes. (252.) After many interesting experiments on the cast- ing, grinding, and polishing of specula for reflecting tele- scopes, the Earl of Rosse completed a Newtonian tele- scope with a speculum three feet in diameter and 26 feet in focal length. By means of this instrument, which Dr. Robinson, who made many observations with it, characterised as the most powerful that was ever exe- cuted, many important discoveries were made in the re- solution of nebulae into stars, and in the delineation of their true forms. This noble instrument had scarcely had a fair trial of its powers before Lord Rosse resolved to construct a still greater telescope with a speculum six feet in dia- meter and a focal length of fifty feet. It was cast on the 13th April, 1842, and was composed of 32 parts of copper and 14'91 of tin. In 1843, the speculum was ground, and various parts of its mounting completed, and the construction of the tubes and piers occupied the rest of the year. In the early part of 1 844, a partial polish was given to the speculum in order to ascer- tain its focal length, which was found to be exactly fifty-four feet; and early in February, 1845, the instru- ment was so far completed as to allow Dr. Robinson and Sir James South, who had been invited on purpose, to make the first trial of its powers. The speculum weighs four tons, arid with its sup- ports is seven times as heavy as Herschel's four feet speculum. The base of the actual mounting is a mas- sive joint of cast-iron, like that of a pair of com- passes, moving round a pin in order to give the K K A TREATISE ON OPTICS. PART iVi 498 transverse motion for following the star in right ascen- sion. This pin is fixed to the centre piece between two trunnions like those of an enormous mortar, lying east and west, and upon which the telescope has its motion in altitude. On this massive joint is firmly bolted a large cubical wooden box about 8 feet wide, into which the speculum is introduced by an opening in one of its sides. To this box is fastened the tube, about 50 feet long, 8 feet in diameter in the middle, but tapering to 7 at the extremities, and furnished with in- ternal diaphragms 6^ feet in aperture. It is made of deal staves an inch thick, hooped with strong iron clamp rings. It carries at its upper end the small oval spe- culum A, 6 inches in its lesser diameter. Fig. 231. It is moved in altitude by a strong chain cable B attached to its top ; and, passing over a pulley down to a windlass in the ground, it is wrought by two assistants. East and west, near the top of the lofty castellated piers between which the telescope is established, are fixed* CHAP. LIV. LORD ROSSE's TELESCOPE. 4Q9 large iron pulleys C moving freely in azimuth, and over which pass to the sides of the tube chains D,D sus- pending the counter-weights E. The eastern pier, which, like the western, is 60 feet high, carries a strong semicircle of cast-iron, about 85 feet in diameter, bolted to the pier. The telescope being connected with this circle by a strong racked bar with friction rollers attached to the tube by wheel- work, so that the observer with a handle near the eye- piece can move it on either side of the meridian to the distance of half-an-hour for an equatorial star. The western pier supports the stairs and galleries for the use of the observers. An altitude of 42 is com- manded by the first gallery, which is a strong and light prismatic framing H H, sliding between two ladders L L, attached to the southern face of the piers. It is coun- terpoised and raised to any required position by a wind- lass K. Its upper plane affords support for a railway, on which the observing gallery L moves about 24 feet east and west, two of its wheels being turned by a winch M near the observer. Other three galleries N, O, P, in succession reach to 5 below the pole, and are each carried by two beams Q, Q, which run between pairs of grooved wheels R, R, and are drawn forward when they are turned by a singularly elegant piece of mechanism. These galleries hold twelve persons, who are a little startled when they find themselves suspended over a chasm 60 feet deep. I have enjoyed the great privilege of seeing this noble instrument, one of the most wonderful combinations of art and science that the world has yet seen. I have in the morning walked again and again, and ever with new delight, along its mystic tube, and in the evening with its distinguished inventor pondered over the marvellous sights which it discloses, the satellites and belts and rings of Saturn the old and new ring which is ad- vancing with its crest of waters to the body of the planet the rocks and mountains and valleys and extinct vol. canoes of the Moon the crescent of Venus with its K K 2 500 A TREATIE ON OPTICS. PART IV. mountainous outline the systems of double and triple stars the nebula? and clusters of stars of every variety of shape, and those spiral nebular formations which baffle human comprehension, and constitute the greatest achievement in modern discovery. Mr. Lassells' Telescope. (253.) While Lord Rosse's telescope has been chiefly occupied with the phenomena of the stars far beyond the limits of our system, our countryman, Mr. Lassells, has with a smaller instrument of his own construction been making important discoveries within the limits of the Solar system. The speculum of Mr. Lassells' reflector is fully 2 feet in diameter, with a focal length of 20 feet. It is composed of copper and grain tin in the same pro- portion as Lord Rosse's, with the addition of a small quantity of white arsenic. Mr. Lassells' tube is of sheet iron. The smaller diameter of his small speculum is two inches, and he sometimes uses the total reflection of a glass prism. The deposition of dew upon this prism is prevented by attaching to it a case containing a small piece of heated lead. The telescope is protected by a revolving cupola 30 feet in diameter, which carries a stage for the observer. With this fine instrument, constructed in all its parts by himself, Mr. Lassells has discovered four new satellites, two to Uranus, one to Saturn, and one to Neptune. A few months ago Mr. Lassells transplanted his 20 feet telescope to Valetta in Malta, where he is at this mo- ment (February llth, 1853), directing it with great success to the heavens. He has already discovered the transparency of the new ring of Saturn, and we may soon hope to hear of other and more important discoveries. Mr. Nasmyth's Telescope. (254.) This instrument, invented by Mr. James Na- smyth, is a combination of the Cassegrainian and the CHAP. LIV. MB. NASMYTHS TELESCOPE. 501 Newtonian telescope, for the purpose of bringing the image to the eye through two hollow trunnions, upon Fig. 232. which it moves in altitude. The advantages of this construction are very great. The observer, without changing his place, can direct the instrument to any part of the heavens, and, seated in a small observatory with a party of his friends, he may carry on his observations with an economy of time and patience which cannot be obtained from any other form of the instrument. The motions of the telescope shown in the annexed figure, are effected in the following manner. The motion in altitude round the trunnions is obtained by means of the usual tangent screw and wheel, shown in front of the observer, and the motion in azimuth by means of the turn-table E. such as is used on railways. In order to obtain this construction for the stand, a Newtonian speculum throws the image upon a convex speculum, which reflects it back along the axis to the place where the trunnions are required. The image K K 3 502 A TREATISE ON OPTICS. PART IV. is then thrown to the side of the tube, and through the hollow trunnion, hy means of a totally reflecting prism, or a small plane speculum, and is magnified in the usual manner by an eyepiece placed at the end of the trunnion. The observer, as shown in the figure, sits in extreme comfort, and with his own hands and by machinery within his reach, he directs his instrument to any part of the heavens. CHAP. LV. ON ACHROMATIC TELESCOPES. (255.) THE principle of the achromatic telescope has been briefly explained in Chap. VII., and we have there shown how a convex lens, combined with a concave lens of a longer focus, and having a higher refractive and dispersive power, may produce refraction without colour, and consequently form an image free from the primary prismatic colours. It has been demonstrated mathema- tically, and the reader may convince himself of its truth by actually tracing the rays through the lenses, that a convex and a concave lens will form an achromatic com- bination, or will give a colourless image, when their focal lengths are in the same proportion as their dis- persive powers. That is, if the dispersive power of crown and flint glass are as 0*60 to 1, or 6 to 10 ; then an achromatic object glass could be formed by com- bining a convex crown glass lens of 6, or 60, or 600 inches with a concave flint glass lens of 10, or 100, or 1000 inches in focal length. But though such a combination would form an image free of colour, it would not be free of spherical aberration, which can only be removed by giving a proper propor- tion to the curvature of the first and last surface, or the two outer surfaces of the compound lens. Sir John Her- schel has found that a double object glass will be nearly CHAP. LV. ON ACHROMATIC TELESCOPES. 503 free from aberration, provided the radius of the exterior surface of the crown lens be 6'?2, and of the flint 14-20, the focal length of the combination being 10*00, and the radii of the interior surfaces being computed from these data by the formulae given in elementary works on optics, so as to make the focal lengths of the two glasses iu the direct ratio of their dispersive power. This combination is shown in fig. 233., where A B is Fig. 233. the convex lens of crown glass, placed on the outside towards the object, and C D the con- cavo-convex lens of flint glass placed towards the eye. The two inside surfaces that come in contact are so nearly of the same curvature that they may be ground on the same tool, and united together by a cement to prevent the loss of light at the two surfaces. In the double achromatic object glasses constructed previous to the publication of Sir John Herschers investigations, the surface of the concave lens next the eye was, we believe, B D always concave. Triple achromatic object glasses consist of three lenses Fig.234. A B > c D, E F, fig. 234., A B and E F being convex lenses of crown glass, and C D a double concave lens of flint glass. The object of using three lenses was to obtain a better correction of the spherical aberration ; but the greater complexity of their construction, the greater risk of im- perfect centering, or of the axes of the three lenses not being in the same straight line, together with the loss of light at six sur- faces, have been considered as more than compensating their advantages; and they have accordingly fallen into disuse. The following were the radii of two triple achromatic object glasses, as constructed by Dollond : /U\ 504 A TREATISE ON OPTICS. PART IV. A B, or first Crown Lens. FIRST OBJECT GLASS. SECOND OBJECT GLASS. Radii of first surface, - 28 inches - . 28 second surface, 40 35*5 C D, or Flint Lens. Radii of first surface, - 20'9 - - - 21-1 second surface, 28 ... 25 '75 E F, or second Crown Lens. Radii of first surface, - 28 -4 - - 28 second surface - 28*4 28 Focal length of the compound lens 46 inches - - 46 '3 In consequence of the great difficulty of obtaining flint glass free of veins and imperfections, the largest achromatic object glasses constructed in England did not greatly exceed 4 or 5 inches in diameter. The neglect into which this important branch of our national manu- factures was allowed to fall by the ignorance and supine- ness of the British government, stimulated foreigners to rival us in the manufacture of achromatic telescopes. M. Guinand of Brenetz, in Switzerland, and M. Fraun- hofer, of Munich, successively devoted their minds to the subject of making large lenses of flint glass, and both of them succeeded. Before his death, M. Fraunhofer executed two telescopes with achromatic object glasses of 9-nr inches, and 12 inches in diameter; and he in- formed me that he would undertake to execute one 18 inches in diameter. The first of these object glasses was for the magnificent achromatic telescope ordered by the Emperor of Russia for the observatory at Dorpat. The object glass was a double one, and its focal length was 25 feet ; it was mounted on a metallic stand which weighed 5000 Russian pounds. The telescope could be moved by the slightest force in any direction, all the moveable parts being balanced by counter weights. It had four eye glasses, the lowest of which magnified 175, and the highest 700 times. Its price was 1300/., but CHAP. LV. ON ACHROMATIC TELESCOPES. 505 it was liberally given at prime cost, or 950/. The ob- ject glass, 12 inches in diameter, was made for the King of Bavaria, at the price of 2720/. ; but as it was not perfectly complete at the time of Fraunhofer's death, we do not know that it is at present in use. In the hands of that able observer, Professor Struve, the telescope of Dorpat has already made many important discoveries in astronomy. A French optician, we believe, M. Lerebours, has more recently executed two achromatic object glasses of glass made by Guinand. One of them is nearly 12 inches in diameter, and another 13*2 inches. The first of these object glasses was mounted as a telescope at the Royal Observatory at Paris ; and the French go- vernment had expended 500/. in the purchase of a stand for it, but had not the liberality to purchase the object glass itself. Sir James South, our liberal and active countryman, saw the value of the two object glasses : he acquired one of them for his observatory at Kensing- ton ; and the other was purchased by Mr. Cooper for his observatory at Markree Castle, in Ireland. The Northumberland telescope in the Cambridge Observatory contains an achromatic object glass 12 inches in diameter, made, we believe, in Paris with Guinand's glass. A remarkable telescope with an object glass of rock crystal, which has a very small dispersive power, 4'2 inches in diameter and 6 feet 3 inches in focal length, was placed in the Great Exhibition by M. Burin, of Paris. Mr. Glaisher, in his report, states that (t it was found to be good in every respect." The lens was cut out of the prism of quartz perpendicular to its axis, and the double refraction was therefore so small as not to produce any injurious effect. If there had been a double image, the evil might have been remedied, but at the expense of half the light, by the use of an analyser. The great difficulty which has been so long ex- perienced in procuring large discs of flint glass for 506 A TREATISE ON OPTICS. PART IV. achromatic telescopes has been entirely removed by the ingenuity of M. Bontemps, who, during the French revolution in 1848, came to England on the invitation of Messrs. Chance, Brothers, and Company, of the Smethwick Glass Works, to unite with them in the attempt to improve the quality, and extend the utility of this important branch of manufacture. They have produced a disc of 29 inches in diameter, weighing 2 cwt., which, after being carefully examined by the jury of Class X., was found to be entitled to the Council Medal. It is now found to be more difficult to make large discs of crown than of flint glass. At the Smethwick works they have executed such discs 20 inches in diameter. The Rev. Mr. Craig s Achromatic Telescope. (256.) This telescope is the largest achromatic tele- scope that was ever executed. The achromatic object glass is composed of two lenses, one of flint glass from Messrs. Chance's works at Smethwick, 24 inches in diameter, with a negative focal length 49 feet 10 inches, and a refractive index of 1'608, and the other of plate glass, with a positive focal length of 30 feet H inch, and a refractive index of 1*503. When these lenses are combined, their focal length for parallel rays is 76 feet. The mode of fitting up the instrument is shown in the annexed figure. The central tower, which is of brick, is 64 feet high, 75 feet in diameter, and weighs 220 tons. The tele- scope is suspended on the side of this tower. The length of the main tube is 76 feet, and with the eye- piece at one end and the dew cap at the other, its total length is 85 feet. The tube, which is externally of bright metal, is 13 feet wide at a point 24 feet from the object glass. It was executed by Messrs. Rennie, under the direction of Mr. Gravett, F. R. S., and is a CHAP. LV. MB. CRAIG'S ACHROMATIC TELESCOPE. 507 beautiful specimen of art. The optical work of the instrument was executed by Mr. F. Slater, of Somers Fi. 235. Place West, Euston Square. The tube rests upon a light wooden framework with iron wheels attached, and is fitted to a circular iron railway at the distance of 52 feet from the centre of the tower. The chains by which it is lowered is capable of sustaining a weight of fifteen tons, though the weight of the tube is only three tons. We understand that this telescope exhibits very satis- factorily the new ring of Saturn, which Mr. Lassell and Mr. Dawes have found to be transparent, as the body of Saturn is seen through it ; but that the correction for 508 A TREATISE ON OPTICS. PART IV. spherical aberration is not perfect, and that it is neces- sary to stop out the central part of the object glass. ON ACHROMATIC EYEPIECES. (257.) Achromatic eyepieces when one lens only is wanted, may be composed of two or three lenses exactly on the same principles as object glasses. Such eyepieces, however, have been seldom used, because it was supposed that the colour could be corrected in a superior manner, by a proper arrangement of single lenses of the same kind of glass. This arrangement is shown in fig. 236., where A B and C D are two plano- Fig. 236. B convex lenses, A B being the one next the object glass, and CD the one next the eye, a ray of white light RA, proceeding from the achromatic object glass, will be refracted by A B at A, so that the red ray A r crosses the axis at r, and the violet ray A v at v. But these rays being intercepted by the second lens C D at the points m, n, at different distances from the axis, will suffer different degrees of refraction. The red ray m r suffering a greater refraction than the violet one n v, notwithstanding its inferior refrangibility, so that the two rays will emerge parallel from the lens C D (and therefore be colourless) as shown at m /, m v'. When these two lenses are made of crown glass, they must be placed at a distance equal to half the sum of their focal lengths, or, what is more accurate, their dis- tance must be equal to half the sum of the focal distance of the eye glass C D, and the distance at which the field glass A B would form an image of the object glass of the telescope. This eyepiece, which we have already CHAP. LV. ON ACHROMATIC TELESCOPES. 5Q9 mentioned, is called the Huygenian negative eyepiece. The stop or diaphragm must be placed half way be. tween the two lenses. The focal length of an equivalent lens, or one that has the same magnifying power as the eyepiece, is equal to twice the product of the focal ! lengths of the two lenses divided by the sum of the same numbers. An eyepiece nearly achromatic, called Ramsden's i Positive Eyepiece, and much used in transit instru- ; ments and telescopes with micrometers, is shown in fig. 237. & 2S 7- where A B, C D, are two plano-convex lenses with their convex sides in- wards. They have the same focal length, and are placed at a distance from each other, equal to two- thirds of the focal length of either. The focal length of an equivalent lens is equal to three- fourths the focal length of either lens. The use of this eyepiece is to give a flat field, or a distinct view of a system of wires placed at MN. This eyepiece is not quite achromatic, and it might be rendered more so by increasing the distance of the lenses ; but as this would require the wires at M N to be brought nearer A B, any particles of dust or imperfections in the lens AB would be seen magnified by the lens CD. The erecting achromatic eyepiece now in universal use in all achromatic telescopes for land objects is shown Fig. 238. in fig. 238. It consists of four lenses A, C, D, B, placed as in the figure. Mr. Coddington has shown, that if 510 A TREATISE ON OPTICS. PART IV. the focal lengths, reckoning from A, are as the numbers 3, 4, 4 and 3, and the distances between them on the same scale 4, 6, and 5, 2, the radii, reckoning from the outer surface of A, should be thus : A C First surface 27 7 , , A | Second surface 1 J nearl y P la -'nvex. C [ Srona^urface 4 } a meniscus - D \ rst * urf T <>} \ nearly plano-convex. I Second surface 21 \ -n ( First surface 1 1 , . , B | Second surface 24 j double convex ' The magnifying power of this eyepiece, as usually made, differs little from what would be produced by using the first or fourth lens alone. I have shown, that the magnifying power of this eyepiece may be increased or diminished by varying the distance between C and D, which even in common eyepieces of this kind may be done, as A and C are placed in one tube A C, and D and B in another tube D B, so that the latter can be drawn out of the general tube. In fig. 238. I have shown the eyepiece constructed in this way, and ca- pable of having its two parts separated by a screw nut E, and rack. This contrivance for obtaining a variable magnifying power, and consequently for separating op- tically a pair of wires fixed before the eye glass, I com- municated to Mr. Carey in 1805, and had one of the instruments constructed by Mr. Adie in 1806. It is fully described in my Treatise on Philosophical Instru- ments) and has been more recently brought out as a new invention by Dr. Kitchener, under the name of the Pancratic Eye Tube. The subject of eyepieces is one of the most important in practical optics, and in practical astronomy, and it is upon their construction and improvement that the per- formance of reflecting and refracting telescopes depends. It is in vain that Lord Rosse's great speculum forms in the axis of its tube a perfect image, colourless and CHAP. LV. ACHROMATIC EYEPIECES. 511 free from spherical aberration, unless we can bring that image uninjured to the side of the tube, and magnify it without chromatic and spherical aberration. As the extent of the field of view is generally of no importance, we would recommend the use of an aplanatic concave eye lens, or one in which the secondary colours of the spec- trum are corrected, by the use of fluids when necessary, as in Dr. Blair's combinations. There can be no doubt that a single concave aplanatic eye glass is superior to a single convex aplanatic one, and that for two reasons, namely, that there is no interference or collision of the rays till they fall upon the retina, and that the greater thinness of the glass exposes the transmitted pencils to less injury from any unequal density or want of homo- geneity in the glass.* As a very considerable power can be obtained from the combination of prisms as described in the following section, we cannot doubt, from their having neither chromatic nor spherical aberration, that they might be advantageously used as eyepieces. There are cases also in which, from the purity and homogeneity of their substance, we might use fluid lenses made achromatic by processes which I have elsewhere described, as the temporary eye lenses for large telescopes, I say temporary, because, when an observer fails in defining an object with his instrument, he should have recourse to every method by which there is any probability of effecting his purpose. The subject of achromatic eyepieces has been re- cently treated with great ability by M. Biot, in an ela- borate and admirable memoir published in 1843.f In the following table I have given the general result of his investigations for an eyepiece of four lenses. The following are the dimensions of the object glass for which the calculations of the eyepiece were made. compensation. f Memoires de VInstttut, torn, xix, p. 1310. 512 A TREATISE ON OPTICS. PART IV. Millimetres. Principal focal length - - 565-000 Efficacious aperture - - 50* Magnifying power - - + 24 The principal focal lengths of the four lenses, reckon- ing from the eye next the object, and their distances, are as follows : Millimetres. 1st eye lens A 48-707 2nd A' -59-361 3rd A" -59-300 4th - A'" - 29*949 Distance of object glass from A - + 584*483 image from A - - +19*483 of A from the diaphragm behind it - - - 53*135 Radius of this diaphragm from the radius of the lens A - +2-273 Distance of A from A' - - - +72-451 Distance of A' from A" - - +94-785 Distance of A" from A"' - - +54-508 Radius of the diaphragm in the focus of A"' 8-000 Distance of centre of pupil from A' fr 19 -937 Total length of the eyepiece - - 221-744 Radius of the apparent field - - 38' 16" -79 With these dimensions M. Rossin executed two eye- pieces, one of the whitest crown glass and the other of rock crystal. Each of them, when applied to the object glass, gave as achromatic an image as could be desired. Straight lines placed at the margin of the field had no sensible curvature ; and both of them were fully equal, if not sometimes superior, to the best eyepieces of the same size with which they were compared. The rock crystal eyepiece was found by Biot to be " undoubtedly superior to those made of crown glass/' the double refraction being too small to interfere with the distinctness of the image. In eyepieces with only two lenses, such as those shown in figs. 236. and 237., it would be dangerous to construct them with doubly refracting materials, not only because the curvature CHAP. LV. PRISM TELESCOPES. 513 of the lenses would require to be deeper, but because the double refraction woulcfrbe increased twofold in con- sequence of the rays passing through both lenses on the same side of the axis. As the loss of light is in many cases of little import- ance, we would recommend the employment of achro- matic lenses for eyepieces of all kinds, whether single, double, triple, or quadruple, special attention being paid to the correction of the secondary spectrum. Prism Telescope. (258.) In 1812, I showed that colourless refraction may be produced by combining two prisms of the same substance, and the experiments which led to this result were published in my Treatise on New Philosophical Instruments in 1813. The practical purposes to which this singular principle seemed to be applicable were the construction of an achromatic telescope with lenses of the same glass, and the construction of a Teinoscope, for extending or altering the lineal proportions of objects. If we take a prism, and hold its refracting edge downwards and horizontal, so as to see through it one of the panes of glass in a window, there will be found a position, namely, that in which the rays enter the prism and emerge from it at equal angles, as in fig. 20., where the square pane of glass is of its natural size. If we turn the refracting edge towards the window, the pane will be extended or magnified in its length or vertical direction, while its breadth remains the same. If we now take the same prism and hold its refracting edge vertically, we shall find, by the same process, that the pane of glass is extended or magnified in breadth. If two such prisms, therefore, are combined in these positions, so as to magnify the same both in length and breadth, we have a telescope composed of two prisms, but unfortunately the objects are all highly fringed with the prismatic colours. We may correct these colours in 514 A TREATISE ON OPTICS. PART IV. three ways : 1st, We may make the prisms of a kind of glass which obstructs all the rays but those of one homogeneous colour ; or, we may use a piece of the same glass to absorb the other rays when two common glass prisms are used : 2d, We may use achromatic prisms in place of common prisms : or, 3d, What is best of all for common purposes, we may place other two prisms exactly similar, but in reverse positions, or they may be placed as shown in fig. 23$., which repre- sents the prism telescope ; A B and A C being two prisms of the same kind of glass, and of the same re- fracting angles, with their planes of refraction vertical, and ED, E F, other two perfectly similar prisms, simi- larly placed, but with their planes of refraction hori- zontal. A ray of light, Ma, from an object, M, enters the first prism, EF, at a, emerges from the second prism, ED, at 6, enters the third prism, AC, at c, emerges from the fourth prism, AB, at d, and enters the eye at O. The object, M, is extended or magnified horizontally by each of the two prisms, EF, ED, and vertically by each of the two prisms, AB, AC; so that objects are magnified by looking through the prisms in the direction O M. This instrument was made in Scotland by the writer of this Treatise, under the name of a Teinoscope, and also by Dr. Blair, before it was proposed or executed by Professor Amici of Modena. Dr. Blair's model is now before me, being composed of four prisms of plate glass with refracting angles of about 15. It was presented to me several years ago by his son ; but as no account of CHAP. LV. ACHROMATIC OPERA GLASSES. 515 it was ever published, Mr. Blair could not determine the date of its construction.* In constructing this instrument, the perfect equality of the four prisms is not necessary. It will be suf- ficient if AB and DE are equal, and AC and EF, as the colour of the one prism can be made to correct that of the other by a change in its position. For the same reason it is not necessary that they be all made of the same kind of glass. Achromatic Opera Glasses with Single Lenses. (259.) M. d'Alembert has long ago shown that an achromatic telescope may be constructed with a single object glass and a single eye glass of different refractive and dispersive powers. To effect this, the eye glass must be concave, and be made of glass of a much higher dispersive power than that of which the object glass is made ; but the proposal was quite Utopian at the time it was suggested, as substances with a suf- ficient difference of dispersive power were not then known. Even now, the principle can be applied only to opera glasses. If we use an object glass of very low dispersive power, the refraction of the violet rays may be cor- rected by a concave eye lens of a high dispersive power, as will be seen by the following table. Object glass Eye glass Magnifying made of made of power. Crown glass Flint glass 1 Water Oil of cassia 2 Rock crystal Flint glass 2 Rock crystal Oil of aniseseed Crown glass Oil of cassia 3 Rock crystal Oil of cassia 6 Although all the rays are made to enter the eye * It is probable that Dr. Blair, who had read my description of the Teinoscope, had applied it in this modeL L L 2 516 A TREATISE ON OPTICS. PART IV. parallel in these combinations., yet the correction of colour is not satisfactory. Mr. Barlow's Achromatic Telescope. (260.) In the year 18131 discovered the remarkable dispersive power of sulphuret of carbon, having found that it " exceeds all fluid bodies in refractive power, surpassing even flint glass, topaz, and tourmaline ; and that in dispersive power it exceeds every fluid substance except oil of cassia, holding an intermediate place be- tween phosphorus and balsam of tolu. * * * Although oil of cassia surpasses the sulphuret of carbon in its power of dispersion, yet, from the yellow colour with which it is tinged, it is greatly inferior to the latter as an optical fluid, unless in cases where a very thin con- cave lens is required. The extreme volatility of the sulphuret is undoubtedly a disadvantage ; but as this volatility may be restrained, we have no hesitation in considering the sulphuret of carbon as a fluid of great value in optical researches, and which may be of incal- culable service in the construction of optical instru- ments." * This anticipation has been realised by Mr. Barlow, who has employed sulphuret of carbon as a substitute for flint glass, in correcting the dispersion of the convex lens. It had been proposed, and the ex- periment even tried, to place the concave lens between the convex one and its focus, for the purpose of correct- ing the dispersion of the convex lens, with a lens of less diameter, but Mr. Barlow has the merit of having first carried this into effect. The telescope which he has made on this principle, consists of a single object lens of plate glass, 7' 8 inches in clear aperture, with a focal length of 78 inches. At the distance of 40 inches from this lens was placed a concave lens of sulphuret of carbon, with a focal length of 59'8 inches, so that parallel rays falling on * On the Optical Properties of Sulphuret of Carbon, in Edinburgh Trans, vol. viii. p. 285., Feb. 7. 1814. CHAP. LV. ROCERS'S ACHROMATIC TELESCOPE. 517 the convex plate lens, and converging to its focus, would, when refracted by the fluid concave lens, have their focus at the distance of 104 inches from the fluid lens, and 144 inches, or 15 feet, from the plate glass lens. The fluid is contained between two meniscus cheeks, and a glass ring, so that the radius of the concave fluid lenS is 144 inches towards the eye, and 56-4 towards the object lens. The fluid is put in at a high temper- ature, and the contraction which it experiences in cooling is said to keep every thing perfectly tight. No decom- position of the fluid has yet been observed. The great secondary spectrum which I found to exist in sulphuret of carbon is approximately corrected by the distance of the fluid lens from the object glass ; but we are persuaded that the telescope is not free from secondary colour. Mr. Coddington remarks, that the general course of an oblique pencil is bent outward by the fluid lens, and the violet rays more than the red, so as to produce in- distinctness ; but we are not aware that this defect was observed in the instrument. The tube of the telescope is 11 feet, and the eyepieces one foot. " The tele- scope/' says Mr, Barlow, te bears a power of 700 on the closest double stars in South's and Herschel's cata- logue, although the field is not then so bright as I could desire. Venus is beautifully white and well de- fined with a power of 120, but shows some colour with 360. Saturn, with the 120 power, is a very brilliant object, the double rings and belts being well and satis- factorily defined, and with the S60 power it is still very fine." Mr. Barlow remarks, also, that the telescope is not so competent to the opening of the close stars, as it is powerful in bringing to light the more minute luminous points.* Mr. Rogers s Achromatic Telescope. (261.) In April, 1828, Mr. Rogers communicated to the Astronomical Society an account of a new form * See Edinburgh Journal tf Science, No. xiv M p. 335., No. xv. p. 93., and No. xviiL p. 220. LL 3 518 A TREATISE ON OPTICS. PART IV. of the achromatic telescope,, in which the colour of an object lens of crown or plate glass is corrected by a compound lens of crown and flint glass acting as a plane glass on the mean refrangible ray, and placed be- tween the object lens and its focus. This compound lens will produce no alteration in the focus for the mean rays, but will lengthen the focus for violet, and shorten it for red rays, which is what is wanted to cor- rect colour. If the colour is not corrected for the position assumed for it, we have only to move it along the axis of the tube till the achromatism is complete. It is not necessary that the connecting lens should act as a plane lens ; all that is required is, that it should have a shorter focus for the red than for violet rays. In order to correct the colour of a lens of crown and plate glass of 9 inches aperture and 14 feet in focal length by a disc of flint glass three inches in diamete^ the focus of either lens of the correcting lens must be nine inches ; if by a glass of four inches, the focal length of each must be sixteen inches. Mr. Rogers states that by a proper adaptation of the distance, foci, c. of the lenses, we might hope to destroy the secondary spectrum ; but it is obvious that this cannot be done unless by means of two kinds of glass, in which the coloured spaces have the same ratio to one another. It may, however, be corrected by a combination of smaller lenses upon the principle at first adopted by Dr. Blair.* Achromatic Solar Telescopes with single Lenses. (262.) An achromatic telescope for viewing the sun or any highly luminous object may be constructed by using a single object glass of plate glass ; and by making any one of the eye glasses out of a piece of glass which transmits only homogeneous light ; or the same thing may be effected by a piece of plane-glass of the same colour ; but this introduces the errors of other two sur- * See Edinburgh Journal of Science, No. xvii. p. 126, and Chap. IX. CHAP. LV. ACHROMATIC SOLAR TELESCOPES. 519 faces. In such a construction it would be preferable to absorb all tbe rays but the red ; and there are various substances by which this may be readily effected. The object glass of this telescope, though thus rendered monochromatic, will still be liable to spherical aberration. But if the radii of the lens are properly adjusted, the excess of solar light will permit us to diminish the aper- ture, so as to render the spherical aberration almost imperceptible. Such a telescope, when made of a great length, would, we are persuaded, be equal to any in- strument that has yet been directed to the sun. If we could obtain a solid or a fluid which would absorb all the other rays of the spectrum but the yellow, with as little loss as there is in red glasses, a telescope of the preceding construction would answer for day objects, and for all the purposes of astronomy. If the art of giving lenses a hyperbolic form shall be brought to per- fection, which we have no doubt will yet be done, the spherical aberration would disappear ; and a telescope upon this principle would be the most perfect of all instruments. The spherical aberration might be cor- rected by two object lenses of plate glass with the radii determined by Sir John Herschel, a construction which has been adopted in the telescope which was made for me by Dollond, at the expense of the Royal Society, for examining the fixed lines in the solar spectrum. Even by using red light only, a great improvement might be effected in the common telescopes for day ob- jects and for astronomical purposes. If the red rays, for example, form T ^th of white light, we have only to increase the area of the aperture 10 times to make up completely for this defect of light. The spherical aber- ration is, no doubt, greatly increased also : but if we consider that, when compared to the aberration of colour, it is only as 1 to 1200, we can afford to increase it in order to gain so great an advantage. Common tele- scopes, indeed, may be considerably improved by apply- ing coloured glasses, which absorb only the extreme rays L L 4 520 A TREATISE ON OPTICS. PART IV. of the spectrum, even though they do not produce an achromatic or homogeneous image. These observations are made for the benefit of those who cannot afford expensive instruments, but who may yet wish to devote themselves to astronomical observ- ations with the ordinary instruments which they may happen to possess. On the Improvement of imperfectly Achromatic Telescopes. (263.) There are many achromatic telescopes of con- siderable size, in which the flint lens either over corrects or under corrects the colours of the crown glass lens. This defect may be easily removed by altering slightly the curvature of one or other of the lenses. But all achromatic telescopes whatever, when made of crown and flint glass, exhibit the secondary colours, viz. the wine-colour and the green fringes. These colours are not very strong ; and in many, if not in all, cases we may destroy them by absorption through glasses that will not weaken greatly the intensity of the light. The glasses requisite for this purpose must be found by actual experiment; as the secondary tints, though ge^ nerally of the colours we have mentioned, are variously composed, according to the nature of the glass of which the two lenses are made. 521 APPENDIX. TABLE I. (Referred to from Page 25.) Table of the Refractive Powers of Solid and Fluid Bodies. Index of Refraction Index of Refraction. Greenockite 2-688 Plate glass, from 1 Realgar artificial 2-549 1-514 to - J" 1*542 Octohedrite 2-500 Crown glass, froml Diamond 2-439 1-525 to - J 5 Nitrite of lead 2-322 Oil of cloves - 1-535 Blende - 2-260 Balsam of capivi 1-528 Phosphorus 2 224 Gum arabic 1-502 Sulphur melted 2-148 Oil of beech nut 1-500 Zircon ... 1-961 Castor oil 1-490 Glass lead 2 parts, "1 flint 1 part - J 1-830 Cajeput oil Oil of turpentine 1-483 1-475 Garnet - 1-815 Oil of olives 1-470 Ruby ~ 1-779 Alum ... 1-457 Glass lead 3 parts, 7 O./AOQ Fluor spar 1-434 flint 1 part - J z \)o Sulphuric acid 1-434 Sapphire 1794 Nitric acid 1-410 Spinelle - 1764 Muriatic acid - 1-410 Cinnamon stone 1-759 Alcohol - 1-372 Sulphuret of carbon 1-678 Cryolite ... 1-349 Oil of cassia - 1-641 Water - 1-336 Balsam of Tolu 1 -628 Ice ... 1-309 Guiacum 1-619 Fluids in minerals 7 Oil of aniseseed 1-601 1 294 to - J 1-131 Quartz - 1-548 Tabasheer 1-111 Rock salt Sugar melted - 1-557 1-554 Ether expanded to~1 thrice its volume J 1-057 Canada balsam 1-549 Air - - 1-000294 Amber ... 1-547 * S*>e my Treatise on New Philosophical Instruments, p. 253, 264, 283 ; and Encyclopedia rttannica, vol. xvi. p. 384. 522 A TREATISE ON OPTICS. Table of the Refractive Power of Gases* Index Vapour of sul- ~\ phuret of carbon J Phosgene gas Cyanogen * Chlorine Olefiant gas Sulphurous acid Sulphuretted hy-~) drogen - J Nitrous oxide Hydrocyanic acid Muriatic acid of Refraction. 1-001530 1-001159 1 -000834 1 -000772 1 -000678 1 -000665 1-000644 1 -000503 1-000451 1 -000449 Index Carbonic acid Carburetted hy- drogen Ammonia Carbonic oxide - Nitrous gas Azote Atmospheric air Oxygen - Hydrogen Vacuum of Refraction. 1 -000449 1 -000443 1 -000385 1 -00034O 1 -000303 1 -000300 1 -000294 1 -000272 1 -0001 38 i-oooooa TABLE II. (Referred to from Page 26.) Table of the Absolute Refractive Powers of Bodies. Index of Refraction. Index of Refraction. Tabasheer 0-0976 Nitre - 0-7079 Cryolite 0-2742 Rain water 0-7845 Fluor spar 0-3426 Flint glass 0-7986 Oxygen 0-3799 Cyanogen 0-8021 Sulphate of barytes 0-3829 Sulphuretted hy- 1 0*841 9 Sulphurous acid gas 0-4455 drogen - J Nitrous gas - 0-4491 Vapour of sulphuret "] - 0-8743 Air 0-4528 of carbon - J Carbonic acid 4537 Ammonia 1-0032 Azote - 0-4734 Alcohol rectified 1-0121 Chlorine 0-4813 Camphor 1-2551 Nitrous oxide 0-5078 Olive oil 2607 Phosgene 0-5188 Amber 3654 Selenite 0-5386 Octohedrite - 3816 Carbonic oxide 0-5387 Sulphuret of carbon 420O Quartz 0-5415 Diamond 4566 Glass 0-5436 Realgar 6669 Muriatic acid 0-5514 Ambergris 7000 Sulphuric acid 0-6124 Oil of cassia* 1-7634 Calcareous spar 0-6424 Sulphur 2-2000 Alum - 0-6570 Phosphorus - 2-8857 Borax - 0-6716 Hydrogen 3-0953 * See Edinburgh Journal of Science, No. XX. a 308. TABLE OF DISPERSIVE POWERS. 523 No. I. (Referred to from Page 83.) In order to convey to the reader some idea of the variety of dispersive powers which exist in solid and fluid bodies, I have given the following table, selected from a much larger one, founded on observations which I made in 1811 and 1812.* The first column contains the difference of the indices of refraction for the extreme red and violet rays, or the part of the whole refraction to which the dispersion is equal ; and the second column contains the dispersive power. Table of the Dispersive Powers of Bodies. Diff. of Indices Dispersive of Refraction Power. f or extreme Rays* Oil of cassia - 0-139 0-089 Sulphur after fusion - 0-130 0-149 Phosphorus . 0-128 0-156 Sulphuret of carbon - 0-115 0-077 Balsam of Tolu - - 0-103 0-065 Balsam of Peru - . 0-093 0-058 Barbadoes aloes - 0-085 0-058 Oil of bitter almonds - . 0-079 0-048 Oil of anise seed ,. 0-077 0-044 Acetate of lead melted * 0-069 0-04O Balsam of styrax . 0-067 0-039 Guaiacum - - 0-066 0-041 Oil of cumin - 0-065 0-033 Oil of tobacco ... . 0-064 0-035 Gum ammoniac . 0-063 0-037 Oil of Barbadoes tar - - 0-062 0-032 Oil of cloves . 0-062 0-033 Oil of sassafras . - - - 0-060 0-032 T? - 0-057 0-032 Oil of sweet fennel seeds - 0-055 0-028 Oil of spearmint - 0-054 0-026 Rock salt - - 0-053 0-029 Caoutchouc - - 0-052 0-028 Oil of pimento - - 0-052 0-020 - 0-052 0-026 Oil of angelica ... - 0-051 - 0*050 0-025 0-024 Oil of caraway seeds - 0-049 0-024 Flint glass - - . - 0-048 0-029 * See my Treatise on New Philosophical Instruments, p. 315. ; and Encyclopedia Britannica, art. OPTICS, vol. xvi. p. 409, 410. 524 A TREATISE ON OPTICS. DifT. of Indices Dispersive of Refraction Power. for extreme Rays . Gum thus ... - 0-048 0-028 Oil of juniper ... Nitric acid - - 0-047 - 0-045 0-022 0-019 Canada balsam . - - - 0-045 0-021 Cajeput oil - Oil of rhodium ... . 0-044 . 0-044 ' 0-021 0-022 Oil of poppy ... Zircon, greatest ref. Muriatic acid - . 0-044 - 0-044 - 0-043 0-022 0-045 0-016 Gum copal - - 0-043 0-024 Nut oil - - 0-043 0-022 Oil of turpentine ... - 0-042 0-020 Felspar - - 0-042 0-022 Balsam of capivi . - - - 0-041 0-021 Amber - - 0-041 0-023 Calcareous spar greatest - 0-040 0-027 Oil of rape-seed - - 0-040 0-019 Diamond - - 0-038 0-056 Oil of olives - 0-038 0-018 f t" - 0-038 0-022 Oil of rue ... > 0-037 0-016 0*037 0-022 Ether . . - - . 0-037 0-012 C 1 *4- 0-020 Alum . - - - - 0-036 0-017 Castor oil - - 0-036 0-018 Crown glass, green . 0-036 0-020 Gum arabic - - 0-036 0-018 Water .... - 0-035 0-012 Citric acid - - 0-035 0-019 Glass of borax - . 0-034 0-018 g-^ 0-034 0-018 Chrysolite ... . 0-033 0-022 0-033 0-018 Oil of wine ... - 0-032 0-012 Glass of phosphorus - 0-031 0-017 Plate glass . - - - 0-032 0-017 Sulphuric acid ... . 0-031 0-014 Tartaric acid - - 0-030 0-016 Nitre, least ref. . - - - 0-030 0-009 Borax .... - 0-030 0-014 Alcohol .... . 0-029 0-011 Sulphate of baryta - OO29 0-011 Rock crystal - 0-026 0-014 Borax glass 1. bor. 2, silex - 0-026 0-014 TABLE OF TRANSPARENT BODIES. Blue sapphire Bluish topaz Chrysoberyl Blue topaz Sulphate of strontia Prussic acid Fluor spar Cryolite Dispersive Power. 0-026 0-025 0-025 0-024 0-024 0-027 0-022 0-022 0-021 0-016 0-019 0-016 0-015 0-008 0-010 0-007 No. II. (Referred to from Page 85.) The following table contains the results of several experi- ments which I made in the manner described in p. 84, 85- The bodies at the top of the table have the least action upon green light, and those at the bottom of it the greatest. The relative position of some of the substances is empirical ; but, by referring to the original experiments in my Treatise on New Philosophical Instruments, p. 354., it will be seen whether or not the relative action of any two bodies upon green light has been determined. Table of Transparent Bodies, in the order in which they exercise the least action upon Green Light. OIL OF CASSIA. Sulphur. Sulphuret of carbon. Balsam of Tolu. Oil of bitter almonds. Oil of anise seeds. Oil of cumin. Oil of sassafras. Oil of sweet fennel seeds. Oil of cloves. Canada balsam. Oil of turpentine. Oil of poppy. Oil of spearmint. Oil of caraway seeds. Oil of nutmeg. Oil of peppermint. Oil of castor. Gum copal. Diamond. Nitrate of potash. Nut oil. Balsam of capivi. Oil of rhodium. FLINT GLASS. Zircon. Oil of olives. Calcareous spar. Rock salt. Gum juniper. Oil of almonds. CROWN GLASS. Gum arabic. Alcohol. Ether. Glass of borax. 526 A TREATISE ON OPTICS. Table of Transparent Bodies, $c. continued. Selenite. Beryl. Topaz. Fluor spar. Citric acid. Acetic acid. Muriatic acid. Nitric acid. Rock crystal. Ice. WATER. Phosphorous acid* SULPHURIC ACID. No. III. (Referred to from Page 96.) Table of the Indices of Refraction of several Glasses and Fluids. Refracting Media. Spec. Grar. Indices of Refraction for the Seven Rays in the Spectrum marked in Jig. 55. with the following Letters. B Red ray. c Red ray. D Orange. E Green. F Blue. G Indigo. H Violet. Water . - 1-000 1-330935 1-331712 1-333577 1-335851 1-337818 1-341293 1-344177 Solution of 7 Potash j 1-416 1-399629 1-400515 1-402805 1-405632 1-408082 1-412579 1-416368 OilofTur-7 pentine J 0-885 1-470496 1-471530 1-474434 1-478353 1-481736 1-488198 1-493874 Crown Glass 2-535 1-525832 1-526849 1-529587 1-533005 1-536052 1-54165-7 1-546566 Crown Glass 2756 1-554774 1-555933 1-559075 i -563150 1-566741 1-573535 1-579470 Flint Glass - 3723 1-627749 1-629681 1-635036 1-642024 1-648266 1-660285 1-671062 Flint Glass - 3-512 1-602042 1-603800 1-608494 1-614532 1-620042 1-630772 1-640373 LONDON : SPOTTISWOODES and SHAW, New-street-Square. U.C.BERKELEY LIBRARIES 14 DA^ CObl3bS7Sb RETURN TO DESK FROM WHICH BORROWED LOAN DfcPARTMENT This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. n tfl MflBZ? 73 <* PMQ9 BSCO V: NON-REN