GIFT OF Tof. E.P.I LOWER D ISIOH LIGHT A COURSE OF EXPERIMENTAL OPTICS LT /^ T T -^T7\ : i'.";' 1 ,'''* G Hi A COURSE OF EXPERIMENTAL OPTICS CHIEFLY WITH THE LANTERN BY LEWIS WRIGHT AUTHOR OF 'OPTICAL PROJECTION, A TREATISE ON THE USE OF THE LANTERN SECOND EDITION, REVISED AND ENLARGED llontion MACMILLAN AND CO. AND NEW YORK 1892 The Right of Translation and Reproduction i$ Reserved VJ "ASSUREDLY there is something in the phenomena of Light; in its universality ; in the high office it performs in Creation ; in the very hypotheses which have been advanced as to its nature ; which powerfully suggests the idea of \h& fundamental, the primeval, the antecedent in point of rank and conception to all other products or results of creative power in the physical world. It is LIGHT, and the free communication of it from the remotest regions of the Universe, which alone can give, and does fully give us, the assurance of a uniform and all-pervading Energy a MECHANISM almost beyond conception complex, minute, and powerful, by which that influence, or rather that movement, is propagated. Our evidence of the existence of gravitation fails us beyond the region of the double stars, or leaves us at best only a presumption amounting to moral conviction in its favour. JBut the argument for a unity of de-.ign and action afforded by Light, stands unweakened by distance, and is co-extensive with the Universe itself." SIR JOHN HERSCHEL. JJlsJMT First Edition, 1882. Second, 1892. PREFACE TO THE SECOND EDITION AT the Annual Meeting in 1882 of the Teachers' Training and Education Society, Professor Huxley remarked upon the great difference between two kinds of " what persons called know- ledge." " That which they had constantly to contend against in the teaching of science," he said, " was, that many teachers had no conception of that distinction ; for they thought it quite sufficient to be able to repeat a number of scientific pro- positions and to get their pupils to repeat them as accurately as they themselves did The teacher should be in- structed that his business in teaching was to convey clear and vivid impressions of the body of facts upon which the conclu- sions drawn from those facts were based." To do this in some degree for one branch of Physics was the original object of this unpretending little work ; which aimed rather at being a companion and supplement to the already existing text-books, than anything else. No " formulae " will be found in it ; but I have merely tried to place clearly before the mind of the reader, through something like a complete course of actual experiments, the physical realities which underlie the pheno- mena of Light and Colour. In regard to the experiments described, there are two things to be said. It would have been desirable, if possible, to have r; r; -7 K < * Q VI PREFACE stated ' the ' originator of every experiment ; but it was not possible. Some arrangements are, to the best of my belief, original ; but none are put forth as such except the few expressly stated, and it should be perfectly understood that no personal claim is implied regarding other experiments because no credit is given to some one else. The absence of such credit is simply due to the difficulty of obtaining information concerning these matters. The second remark is, that the order of the experiments differs considerably in some cases from that usually adopted. Such is the result of considerable reflection, and of a belief that the order chosen is, upon the whole, best adapted to the primary end of assisting vivid conception of the physical realities considered, and the relation of the phenomena to one another. The same may be said as to the brief references made to the connection between the phenomena of Light and the problems of Molecular Physics. Brief as they are, it is hoped that they may in some minds excite a real interest in those problems, and deepen that sense of the reality of the phenomena which is so desirable. In a course of experiments in Physical Optics, projection upon a screen is not only far superior in general effect to any other method of demonstration, besides having the advantage of exhibiting the phenomena to the whole of a class or audience at the same time, but has another recommendation of primary importance. The trained physicist w r ell understands the mean- ing of what is visible to him solely through his lens, prism, or other apparatus ; but the scholar new to the subject finds it difficult to interpret in terms of physical phenomena what thus appeals merely to his own visual impressions. When he looks through a prism, for instance, it is difficult for him to get rid of a vague notion that " something in the prism " colours what PREFACE vii he sees. But when the rays of light are projected through the prism, and the colours appear on the screen apart from himself, as it were, he cannot help understanding that what thus appears to others at the same moment as to him is a physical reality which he has to trace out, and must learn to understand in physical terms. What is meant will be readily understood by any science-teacher. Hence the method of experiment chiefly adopted here, for which all science-teachers and students are deeply indebted to Professor Tyndall, who carried lantern demonstration to an extent and perfection never before attained. The magnificent apparatus of the Royal Institution, however, appears to have created an impression that electric cameras and other very costly appliances are necessary for effective work of this class ; whereas the greater number of experiments can be shown satisfactorily to at least a science class with even a good #as burner ; while any good lantern can be made at small expense a very efficient piece of apparatus. To make this also clear, and thus induce many teachers to substitute the most perfect kind of demonstration for far less striking methods, or for mere diagrams, was a second object of these pages. At the same time I have not forgotten the solitary student, and have tried not only to give sufficient hints for him to make most of. the experiments without lantern or other bulky apparatus, but especially to find abundant manual work for him, more particularly in the fascinating domain of polariscope phenomena. What indeed led me first to hope that room might be found for such a work as this, was the recollection of how much my own delight in the experimental study of Optics had been due to the personal help and teaching of a few individuals. To the Rev. Philip R. Sleeman, F.R.A.S., F.R.M.S., I had in particular been indebted not .only before viii PREFACE the first edition of this little book was thought of, but have been since, for many references to foreign papers and memoirs, and many " detached " items of information which only his wide and general acquaintance with the Continental treatment of Physical Optics could have supplied. And to Mr. C. J. Fox, F.R.M.S., I owed my first practical introduction to that mica-film work, which I hope others may find as attractive as I have done, and which so admirably illustrates the phenomena of polarised light. But for these two friends, some of the most acceptable among the following pages would never have been written. Such were the aims with which the first edition of this work was prepared ; and it has been a great and unexpected gratifi- cation to find how considerably they have been realised, and how much such a course of Experimental Optics appears to have been really needed. Of the numerous letters received, a great many, from all sorts of readers, have been of a positively enthusiastic character which was a surprise to me, and is prob- ably not very common concerning books of any kind upon any branch of Physics. From University lecturers and graduates, to hard-worked science teachers and solitary students, have such letters been received ; and it has been a source of peculiar pleasure to learn that in some cases a clearer appre- ciation of beautiful physical phenomena, gathered from this work, has awakened an enthusiasm previously quite lacking concerning that mathematical treatment of them, from which its own pages have been sedulously kept free. The present edition is somewhat enlarged, and in some respects modified. Further consideration has led me to revise the method and order of treatment as regards some of the phenomena of Polarised Light ; and criticisms of value regard- ing other points of the subject, by Professors A. W. Reinold PREFACE ix and S. P. Thompson, have gladly had regard paid to them in the present work. Some attempt has been made, though briefly, to show the general relation and bearing of recent dis- coveries by Hertz, Lippmann, and others. Having also re- ceived many proofs of the delight and instruction afforded by the beautiful mica polarising preparations first devised by Mr. C. J. Fox, and having carried the designing and preparation of such illustrations very much farther since this work origi- nally appeared, I have added full details of everything of the kind devised to the present date, and of the practical manipu- lation of mica films. These paragraphs will constitute perhaps the principal additions in the following pages. But aim and method remain the same. This is not a text- book, or intended as such. In spite of pressing requests so to extend the treatment as to give it somewhat more of that character, I adhere for many reasons to its original idea, and confine the theoretical explanation to diagrams and familiar mechanical analogies, couched in language which it has been endeavoured to make most simple and clear. There are abundance of most excellent text-books, amongst which Preston's Theory of Light, published quite recently, may be specially mentioned for its elegance of treatment and simpli- city of arrangement. The aim of this little .book is simply and solely to give such a clear conceptual grasp of the chief facts in Physical Optics, as may make the text-books real. I only add a few words respecting the last chapter, concern- ing the propriety of which a great difference of opinion has been expressed. As observed in the former Preface, the irre- sistible propensity to go beneath the surface and search for the hidden essence of things, has been felt and manifested not only by all our leading physicists, but by all who have had any vivid impressions of the mysteries surrounding them. The x PREFACE extract from Sir John Herschel which prefaces the volume, shows this tendency very strongly. So have I also uttered my thoughts ; it is believed without dogmatism, while there is not the slightest danger that the name of the author will give, as in some instances, any factitious weight to them. For such utterance there is no need of apology. But it does seem worth while to note the curious fact, that while these thoughts of mine have, as I find, been read with interest and re- ceived with respect by many interested (some few even distinguished) in mathematics and physics, certain scornful sneers and expressions of condemnation which have also not been lacking, have so far been traceable in every instance known to me to the adherents of a certain school of biology ! It appears to me rather remarkable that this attitude of mind towards such thoughts should be specially developed in a class of students and teachers whose acquaintance with physics is not, as a rule, very great and who deal largely with hypo- theses and generalisations not capable as yet of very precise verification ; whilst men who really are conversant with the mathematically exact operation of definite physical law, feel as a rule no such antagonism. Without further remark, however, I here again leave both the chapter and the work itself to the judgment of the reader. A large number of the experiments here described appeared originally as a series of articles in The English Mechanic. I am indebted to the proprietors of that journal for their free permission not only to use the text of the articles in any way thought best, but also the diagrams by which they were illustrated. I am further indebted to Messrs. Longman & Co., for permission to use certain of the diagrams in my work upon Optical Projection, published by them. LONDON, April 18, 1892. CONTENTS CHAPTER I THE LANTERN AND ACCESSORY APPARATUS PAGE The Lantern The Optical Objective Pencil attachment Various Radiants Oxyhydrogen and Arc lights Centering the Radiant Mounting and manipulation of the Lantern Accessory Apparatus Screens Vertical Work Importance of Darkness I 22 CHAPTER II RAYS AND IMAGES. REFLECTION Rays of Light Rays form Images Inversion of Images Shadows Law of Intensity at various distances Law of Reflection Virtual and Multiple Images The Doubled Angle of Reflection Application of this in the Reflecting Mirror Reflection from Concave and Convex Mirrors Images produced by Concave Mirrors Scattered Reflection Light Invisible 23 46 CHAPTER III REFRACTION. TOTAL REFLECTION. PRISMS AND LENSES. The Refraction or Bending of Rays The Law of Sines Index of Re- fraction Total Reflection The Luminous Cascade Trans- parency Prisms Lenses Images produced by Lenses Focus of a Lens Virtual Images and Foci 47 61 xiv CONTENTS CHAPTER XI POLARISING APPARATUS PAGE The Nicol Prism Foucault's Prism Improved Prisms Large and Small Analysers Care of Prisms Nicol Prism Polariscope Glass Piles The ordinary "Elbow" Polariscope Direct Reflecting Polariscopes Rotating the Reflected Beam Simple Apparatus for Private Study Norrenberg's Doubler . . . 241 259 CHAPTER XII CHROMATIC PHENOMENA OF PLANE-POLARISED LIGHT. LIGHT AS AN ANALYSER OF MOLECULAR CONDITION Resolution of Vibrations Interference Colours Why Opposite Positions of the Analyser give Complementary Colours Coloured Designs in Mica and Selenite Demonstrations of Interference Crystallizations Mineral Sections Organic Films Effects of Strain or Tension Stress in Liquids Effects of Heat and of Sonorous Vibration . . 260288 APPENDIX TO CHAPTER XII Manipulation of Mica-Film Work 289 300 CHAPTER XIII CIRCULAR, ELLIPTIC, AND ROTARY POLARISATION Composition of Vibrations into Circular Orbits Quarter-wave Plates Other Methods Fresnel's Rhomb Plane and Elliptical Composition Rotational Colours Circularly Polarised Designs Waves of Colour Contrary Rotations Effect of Polarising and Analysing Circularly Spectrum of Rotational Colours Phenomena of Quartz Right- and Left-handed Quartz Quartz in circularly-polarised Light Use of a Bi-Quartz Rotation in Liquids The Saccharometer Other Rotatory Crystals Electro-Magnetic Rotation Optical Torque Rotation or Torque of Common Light Reusch's Artificial Quartz Rotation and Molecular Constitution Effects of a Revolving Analyser 301-335 CONTENTS CHAPTER X OPTICAL PHENOMENA OF CRYSTALS IN CONVERGENT POLARISED LIGHT PAGE Rings and Brushes in Uni-axial Crystals Cause of the Black Cross Apparatus for Projection or Observation Preparation of Crystals Artificial Crystals Anomalous Dispersion in Apo- phyllite Rings Quartz Bi-axial Crystals Apparatus for Wide- Angled Bi-axials Anomalous Dispersion in Bi-axials Fresnel's Theory of Bi-axials Deductions from it Mitscherlich's Experi- ment Conical and Cylindrical Refraction Relations of the Axes in Uni-axials and Bi-axials Composite, Irregular, and Hemitrope Crystals Mica and Selenite Combinations Crossed Crystals Norrenberg's Uni-axial Mica Combinations Airy's Spirals Savart's Bands Crystals in Circularly-polarised Light Result of Polarising and Analysing Circularly Quartz in Circularly-polarised Light Spiral Figures All the Phenomena due to Interferences of Waves 336 371 CHAPTER XV POLARISATION AND COLOUR OF THE SKY. POLARISATION BY SMALL PARTICLES Polarisation of the Sky Light Polarised by all Small Particles Blue Colour similarly Caused Polarisation by Black Surfaces Experimental Demonstration of the Phenomena Multi-coloured Quartz Images Identity of all Radiant Energy 372 378 CHAPTER XVI LIGHT AS A SYMBOL . . . 379384 INDEX 385 FULL-PAGE PLATES PLATE PAGE I. CONVERGENT POLARISED LIGHT IN CRYSTALS . Frontispiece II. THE SPECTRUM AND ITS TEACHINGS To face 64 III. INTERFERENCE ,, 160 . IV. INTERFERENCES OF POLARISED LIGHT .... ,, 272 V. MICA DESIGNS ,, 312 VI. RINGS AND BRUSHES IN CRYSTALS ,, 336 VII. CROSSED AND SUPERPOSED CRYSTALS .... ,, 356 VIII. CIRCULAR POLARISATION IN CRYSTALS .... ,, 360 IX. SPIRAL FIGURES ...... , . ,, 368 LIGHT CHAPTER I THE LANTERN AND ACCESSORY APPARATUS The Lantern The Optical Objective Pencil attachment Various Radiants Oxyhydrogen and Arc lights Centering the Radiant Mounting and manipulation of the Lantern Accessory Apparatus Screens Vertical Work Importance of Darkness. i. The Lantern. Any fairly good lantern will serve to perform the following experiments, provided the " front " is so made as to slide on and off a flange-nozzle. This is usual with the better brass fronts made with lengthening tubes, but not with fronts half brass and half tin ; and in the latter case the alteration should be made, so that either the ordinary objective, or the optical objective to be presently described, or any other apparatus, will slide on and off at pleasure. The ordinary objective will be occasionally wanted to exhibit diagrams, while the other will be placed on the nozzle for experiments : the lantern will also be available for all ordinary purposes. A bi-unial is exceedingly convenient, as the top lantern may be used for diagrams, while the lower nozzle carries the optical objective. Any of the usual forms of condensers will suffice. My own bi-unial is mounted on four short brass pillars, in order to introduce conveniently a Bunsen burner or other apparatus for coloured flames into the bottom lantern if required. FULL-PAGE PLATES PLATE PAGE I. CONVERGENT POLARISED LIGHT IN CRYSTALS . Frontispiece II. THE SPECTRUM AND ITS TEACHINGS To face 64 III. INTERFERENCE ,, 160 IV. INTERFERENCES OF POLARISED LIGHT .... ,, 272 V. MICA DESIGNS ,, 312 VI. RINGS AND BRUSHES IN CRYSTALS ,, 336 VII. CROSSED AND SUPERPOSED CRYSTALS , 356 VIII. CIRCULAR POLARISATION IN CRYSTALS .... ,, 360 IX. SPIRAL FIGURES ,, 368 LIGHT CHAPTER I THE LANTERN AND ACCESSORY APPARATUS The Lantern The Optical Objective Pencil attachment Various Radiants Oxyhydrogen and Arc lights Centering the Radiant Mounting and manipulation of the Lantern Accessory Apparatus Screens Vertical Work Importance of Darkness. i. The Lantern. Any fairly good lantern will serve to perform the following experiments, provided the " front " is so made as to slide on and off a flange-nozzle. This is usual with the better brass fronts made with lengthening tubes, but not with fronts half brass and half tin ; and in the latter case the alteration should be made, so that either the ordinary objective, or the optical objective to be presently described, or any other apparatus, will slide on and off at pleasure. The ordinary objective will be occasionally wanted to exhibit diagrams, while the other will be placed on the nozzle for experiments : the lantern will also be available for all ordinary purposes. A bi-unial is exceedingly convenient, as the top lantern may be used for diagrams, while the lower nozzle carries the optical objective. Any of the usual forms of condensers will suffice. My*own bi-unial is mounted on four short brass pillars, in order to introduce conveniently a Bunsen burner or other apparatus for coloured flames into the bottom lantern if required. '- V .V ::.*;./ LIGHT [CHAP. "> ? -Optical : (Objective. The ordinary objective used for exhibiting slides would suffice more or less perfectly for many experiments ; but a special optical objective is almost necessary for many, and preferable for nearly all. It is, moreover, absolutely necessary for the polariscope to be hereafter described; and, as the same lenses and fittings answer for both, and are of a very inexpensive character, it is more satisfactory to provide for efficiency at the outset. The ordinary slide-stage is also unduly large for the insertion of the necessary apertures, slits, or other apparatus, besides being inconveniently situated for manipulation ; and the large field is a great waste of light for many experiments which need all we can 'use. Supposing, for instance, a rather small aperture has to be diffracted, we can condense no light upon it in the ordinary slide-stage ; whereas by bringing it a few inches out in front, we can insert an additional convex lens, mounted in a wooden frame as a slide^ in the ordinary stage, and so condense a very large portion of the full beam upon the aperture. The arrangement recommended for the optical objective is shown in Fig. i. A B is a nozzle (of japanned tin or brass, according to the style of the lantern), which slides nicely on the lantern nozzle, and is kept from rotating by a slot and pin. We will suppose it 3^ inches diameter, for 3j-inch condensers. B c is a 3-inch brass tube 3 inches long, which should screw into a collar at B, as it will be required to unscrew from this into the polariscope elbow, to be hereafter described. Near the bottom or lantern end a square aperture, K, is cut through both sides to form a slide-stage, which should "take" slides an inch thick, and 2\ inches wide. The slides are kept down to the bottom end by a circular L-shaped collar, L, operated by studs working in longitudinal slits as usual, and forced against the slides by a spiral wire spring M, abutting against the collar at c, which screws into the other end of the tube, and has screwed into it the jacket D of the focusing tube, with its rack i] OPTICAL OBJECTIVE 3 and pinion E. The focusing or lens tube F will be about i\ inches in diameter, and has screwed into it at the back end the cell of the plano-convex lens G of 5 inches focus, with the plane side towards the slide-stage. At the other end screws on a collar in which is fixed the nozzle N, projecting outwards from the front flange or collar a clear half-inch, and about if inches in diameter. Into the back end of this screws the lens H of 8 inches focus, which may either be a plano-convex, FIG. i. Optical Objective. or of a slightly meniscus form, the whole being arranged so that the lenses are 2f inches apart. The focusing jacket should be so adjusted that when the tube is run right out the lenses will focus any slide in K at a short screen distance, and have a backward travel of about ij inches. It will be seen that the lenses are of a very inexpensive character ; but such an arrangement is as good as can be adopted, and loses little light. It is the proper arrangement for the polariscope, for which it answers admirably ; and it gives a fairly flat field with but little colour. A rack and pinion is by no means essential : indeed, if the sliding tubes are accurately circular and fit well, a plain sliding tube is preferable, in order that the lenses may be removed at pleasure and slits used with parallel light only, or other appliances (such as an adjustable slit or revolving diaphragm) slid into the tube. I have, however, found a really well-fitted plain " draw- tube " by no means so common among ordinary opticians, on this scale, as a fair rack movement. A polariscope with such LIGHT [CHAP. an objective as is here described can now be purchased for a very few guineas, complete, as described in a future chapter ; and in that case nothing more will be necessary than to provide the additional tin or brass nozzle A B, into which the objective of the polariscope, when unscrewed from its elbow, will fit, and constitute the objective for straight work. The equivalent focus of the two lenses is about 3^ inches, and this will give suitable discs for average screen distances. If the general working distance is long, say from 20 to 25 feet, or more, a somewhat longer focus may be preferable, making the back lens say 7 inches focal length, and giving -more space between the two lenses, and between the back lens and the stage. It is very convenient to have such a lower power as well as the other ; and with it, unscrewing when required the front lens H, four powers are at command, and all easily ad- justed by inserting at c, if necessary, a short screwed tube or "lengthening adapter." 3. Pencil Attachment. There is another front, not by any means necessary, but which I have myself found very useful in certain experiments wherein it is desirable, without the arc light, to obtain an approximately parallel pencil or beam of light of smaller diameter than the condensers, as brilliant as possible. This may be effected by a pair of lenses arranged as in Fig. 2, the convex lens contracting the rays, and the concave re-paral- lelising them. Fig. 2 is a small-sized system, on which the rays from the condensers are slightly converged to begin with, and parallelised into a pencil about f-inch diameter (the parallelism being how- ever only approximate). Such a pencil will add much effect to a Lissajous' figure, as in Fig. 29, or the projection from a FIG. 2. Pencil Attachment. i] GAS AND OIL LAMPS 5 Barton's button. A larger system, with the convex lens of full diameter, so adjusted that when the condensers give a parallel beam and the attachment is inserted, the beam is condensed into about 2 inches diameter, may be of service for polariscope projections. The arc light of course needs no such condensation. 4. Light. Sufficient effects for a class-room or moderate- sized drawing-room may be obtained in nearly all the following experiments 1 from a good Argand gas-burner. A class or a few spectators do not need to see the phenomena on a large scale, and by employing a small disc at a screen distance of 5 or 6 feet, very good results may be got in this way. The lantern becomes hot with such a light ; but the convenience of being able to get it into work at a moment's notice, and without any apparatus, is very great. A good " Silber " or one of Sugg's best " London " patterns, may be employed, and either gives a very white light of from 22 to 28 candles. Such a burner costs about 6s. 6d. An Argand burner is best fixed in a lantern by having a slide-tray with an upright pin at the back end, as for the lime-light. Over this pin should slide a socket brazed oil a tube, with tap and nozzle on the back end as usual, while a plain elbow at the other end carries the burner. The lime-light, or plain gas, can then be used as convenient, gas sufficing to " work out " privately, at a minimum cost and trouble, almost any desired experiment, even when a more brilliant light is required for public repetition of it. The greater part of the experimental work following has been thus " roughed out " in the first instance. The brilliant mineral oil lamps give better effects than gas, ranging in power from 50 to as high as 90 candles, that is, standard or "gas" candles, there being a looseness about some opticians' estimates (due to taking any candles as tests) which is not desirable. The triple forms of wick, of which there are several, are much to be preferred for optical work : the double 1 The exceptions are chiefly such as require a parallel beam, and are for ' the most part noted especially. 6 LIGHT [CHAP. wicks are apt to give a comparatively darkish streak up the centre of the screen. This is little observable in exhibiting painted slides ; but in optical experiments is just where we can least afford any deficiency. Four-wick lamps give as much as 1 20 candles; but the heat is excessive, and in most cases a three-wick lamp is preferable for optical work. 5. The Lime -light. The lime-light is, however, strongly to be preferred if possible, the effect being so infinitely superior, not only in brilliance, but in whiteness, or completeness in the spectral colours. It is not an expensive light either, after the first purchase of the apparatus. Potassic chlorate is now cheaper than formerly, and can be purchased in most large towns at from 7 r . , faces of the glass. At a great angle of incidence, the reflection from the first surface of the glass is as bright, or even brighter than that from the silver surface ; showing clearly that the comparative inten- sity or completeness of reflection from various substances, when polished, differs with the angle of incidence. If a piece of plain glass be used instead of looking-glass, we find also that reflection takes place, not only when rays encounter the polished surface of a denser medium, as glass ; but also at the second surface, where the rays which have entered the glass meet the rarer medium of the air. We shall hereafter find that this last kind of reflection is often the most brilliant of the two. n] MULTIPLE REFLECTION 31 In all cases, reflection is the more copious the greater the angle of incidence, except in this last kind of reflection. Repeated reflection sometimes produces most beautiful effects. When two mirrors are inclined together at an angle which is any aliquot part of a circle, or 360, and the rays from any object pass between them so as to be reflected, there must be as many images (including the object) as the angle is con- tained in 360. A glance at Fig. 25 will show how this occurs. Two such mirrors, or even plain rectangular oblong strips of plate glass, fixed in a tube, with a cap at one end made of two FIG. 25. Symmetrical multiple images. parallel transverse glasses, between which are loosely contained some coloured beads, or other transparent objects, and with a small hole in a cap at the other end of the tube, form the kaleidoscope of Sir David Brewster. In Barker's Lantern Kaleidoscope, the mirrors are of platinized glass, and are mounted with a convex lens at each end ; thus mounted the apparatus takes the place of the ordinary lantern objective, and 32 LIGHT [CHAP. will produce beautiful patterns upon the screen if a rotating slide containing the fragments of coloured glass is placed in the ordinary slide-stage. In using this instrument the angle between the mirrors must be placed downwards, and the light must be raised half an inch to an inch above the usual central position, being adjusted carefully till all the segments are as equally illuminated as possible. The light which reaches the screen is reflected down upon, and upwards from, the mirrors ; and the effect will resemble that in Fig. 26. More perfect ap- FIG. 26. Kaleidoscope. paratus has been constructed in which the angle between the mirrors in the Lantern Kaleidoscope is adjustable by a screw, so as to divide the circle into different aliquot parts at pleasure. 24. The Doubled Angle of Reflection. Another very important consequence follows from this law of equal angles. li] THE REFLECTING MIRROR 33 It is obvious that in changing the position of the mirror, the reflecting surface itself moves through the same angular dis- tance as the index or normal. Hence it follows that any angular movement of the mirror is doubled by the angular movement of the reflected ray ; and this fact makes the " reflecting mirror " an invaluable method of demonstrating minute motions. We are familiar with the lever-index, moving from a centre ; but in practice we are fettered in this means of multiplying a small motion, by the weight and other mechanical imperfections of an index-pointer of great length. In the reflected ray of light we not only double the angle to start with, but we have a pointer we can make of any length, which is absolutely straight, but which weighs nothing at all. Hence the "reflecting FIG. 27. mirror " has constant applications, of which the following will serve as experimental examples. 25. The Reflecting Mirror. By keen sight, in the right light, the motion of the pulse may just be discerned, though it is almost imperceptible. But cut a piece of looking- glass an inch square, and paste on its face a bit of black paper with a circular hole \ inch in diameter. 1 To the back attach in a triangle three pellets of wax, or anything that will stick to the skin, and stick the little mirror on the wrist, with one of the pellets just on the pulse. In the slide-stage place a zinc-plate or card with a \ inch circular hole, and focus the reflected 1 Still better for such experiments as these are silvered pieces of micro- cover glass, which can now be procured of many opticians. D 34 LIGHT [CHAP. image of the aperture. Hold the wrist in the beam, so that the incidence is about 45, as in Fig. 27. At once the motion of the pulse is made visible to all by a motion of the reflected spot of light on the ceiling amounting to several inches. This is a very pretty and striking experiment, though simple. In preparing for it, it is well to find the exact spot on the wrist at leisure, and to mark it by a dot of ink. In the same way we may demonstrate the rapid and minute motions produced by heat. Upon the table we adjust a Trevelyan rocker, A, with its block of lead, L, and fulcrum- knob as usual. Having heated it, we fix on its face, by any cement that will bear the heat, a small mirror B, like that just used, and by our glass reflector, c, direct the beam of light from a small aperture down upon it at any angle, so as to be reflected to the ceiling or the screen, where the spot should be focused sharply. The whole arrangement is shown in Fig. 28, What would be a stationary spot of light if the rocker were cold, is by the small rocking mo- ti n at once P ro " longed (by the per- sistence of impres- sions on the retina) into a bright line of light, and by gra- dually raising with the hand the block D bearing the ful- crum end, this is converted into a beautiful wavy line E F, which makes every separate motion visible. The rocker should be judiciously chosen by experiment as to its period of vibration. The elegant experiment of M. Lissajous may easily be illus- FlG. 28. II] THE REFLECTING MIRROR 35 trated with the lantern and such a tuning-fork as may be bought for 5-r. On the outside of the end of one prong must be strongly cemented a small bit of silvered [glass, and on the other a bit of metal or glass to balance it. We then mount the fork in a heavy block of lead, place a slide with a small hole in the slide-stage, and arrange the whole with the plane reflector in the vertical socket, as in Fig. 29, so that the light from the lantern may be re- flected back from -= N the mirror on the fork A to that on the pillar-stand B, and thence to the screen, where it produces a spot, which must be focused. 1 The card screen should also be placed between the fork and screen, with its blackened side towards the lantern, so that none of the incident beam may pass and interfere with the effect. On now exciting the fork by a violin bow, the spot is expanded by the angular 1 Note on Parallel Beams and Pencils, It may be well to allude briefly to various methods of producing parallel beams and pencils. For merely parallel beams, the radiant is pushed up into the principal focus of the condenser.-, so as to make the whole beam parallel, and an aperture of the required size and shape is placed on the open end of the nozzle. With a gas-burner this will however scatter considerably, but may be sharpened by inserting in the ordinary slide-stage, or anywhere some inches farther back, a similar aperture rather larger. Such merely parallel beams are sufficient for such experiments as those in refraction, Fig. 39, 42, 43. But it is an improvement even with such experiments to focus the aperture, either with the loose lens, or by the optical front with the aperture in its stage ; and for figures described by a bright spot on the screen this is essential. The beam should however not be focussed anyhow, but first parallelised as far as possi- ble. For circular pencils the attachment shown in Fig. 2 is of great service, increasing the brilliance materially. FIG 29. 36 LIGHT [CHAP. motion of its mirror into a bright vertical line ; and by slightly turning the reflector B in its vertical socket, this is developed, as before, into a beautiful undulatory form c D, showing each vibration of the fork. We may, as is well known, substitute a second fork fixed horizontally for the mirror B, and thus get beautiful compounded curves ; but this belongs rather to an- other subject, and a pair of really accurate forks are expensive. The optical effects may be simply obtained by fixing the end of a springy steel rod in a piece of cork, cementing a small mirror on that, and fixing the other end firmly by a screw into a mass of metal sliding on one of the pillars. This is presented " end on " to the nozzle of the lantern, in the position of the fork- mirror A in Fig. 29, but the reflecting mirror B is not moved. On now drawing aside the rod, and releasing it, or striking it, or bowing it, beautiful curves will be produced, of which Fig. 30 may serve as specimens. This is a simple screen adaptation FIG. 30. The Kaleidophone. of Sir Charles Wheatstone's Kaleidophone. Mr. Ladd invented a modification, in which the rod is made of two steel slips of different lengths joined together so as to give transverse sections ; when, by bringing more or less out of a screw socket, almost any of Lissajous' combinations can be produced. 1 1 Forks that perform very well optically, may be bent up of steel about I x \ inch. The arms should be about a foot long, and each arm furnished THE REFLECTING MIRROR Get a large and thin claret or champagne glass the larger the better say 3 inches diameter, and fill to the brim with alum-water. Adjust this on the table as in Fig. 31, the reflector A throwing the full light from the nozzle N at a slight angle down on the glass, and the lens B focusing the sur- face on the ceiling. 1 On now ringing the glass by the edge of a knife, circular waves of light and shade will be seen : and on dipping the finger in the alum-water and holding the stem firmly down rubbing the edge till the well-known sound is produced, small ripples will cover the surface in exquisite patterns, and follow the finger round, all being reproduced above on the ceiling. A violin-bow, besides being in the way, produces somewhat too strong vibrations. with a metal socket sliding easily on it, and fixed by a screw at any point. By these movable sockets we have much control over the periods of vibration. Such forks need not be polished. By far the most effective apparatus for projecting Lissajous' figures is one of reeds mounted with mirrors, which I have described elsewhere, and which can be procured with a complete octave of notes for about seven guineas. It will also project beats and other scroll figures. 1 If an Argand burner is used, we want all the light, and the reflector and glass must be so brought up near the nozzle, that all is collected just into the circumference of the water. All scattered light must also be care- fully stopped ; seeing no light escapes anywhere, and standing the glass itself on a piece of black cloth, that no light may be reflected from the table surface , to the ceiling. In working with a low illumination much depends on these precautions, and with them this beautiful experiment will show very fairly on a ceiling 9 or 10 feet high ; a reflector in the lantern is also of service. With the lime-light we need not be so particular, or the glass may be placed in the phoneidoscope described in 108. LIGHT [CHAP. The vibrations due to sound may be shown by the reflecting mirror in yet another way, due originally to Professor Dolbear. Procure a tube of any material about i J inches diameter, and say a foot long paste-board will do, or metal. Over one end of it stretch any thin membrane part of a child's india-rubber balloon will answer excellently, or even a piece of paper gummed on. In the centre of this fix by a little gum or other cement a small bit of thin silvered micro-glass, not exceeding J inch diameter. The whole is to be arranged in any kind of crutch or rest as in Fig. 32, reflecting a spot of light to the screen from FIG. 32. the small mirror and plane reflector. Then sing into the open end of the tube. Every note will produce a line or figure of some kind, the figures often taking symmetrical forms, as the membrane vibrates under the sonorous vibrations in the tube. This simple experiment is very interesting and beautiful. Still more beautiful methods of optically representing these sound- waves will come before us when we consider the colours of thin films. Meantime these experiments may suffice for the power of the reflecting mirror ; which finds its fullest development in the " rotating " cubical mirror of Sir Charles Wheatstone, by which the velocity of light itself was measured by Foucault with such marvellous accuracy. 26. Reflection from Curved Surfaces. Concave Mirrors. Further consequences follow from the law, or fact, CONCAVE MIRRORS 39 that the angles of incidence and reflection are equal. Let us suppose our reflecting surface, instead of being flat, is curved, as in a portion of a sphere, of which a section is shown in Fig. 33, the centre of the curve or sphere being at c. A drawing FIG. 33. Concave Mirror. upon a large scale will speedily show that a series of parallel lines, representing rays, leaving the mirror A at equal angles to those of incidence, must meet or converge nearly at the point F, midway between c and A. If we take a divergent pencil as in Fig. 34, we find still the same thing : here c is the centre of FIG. 34. Image formed by Concave Mirror. the mirror, from which all lines drawn to it are perpen- diculars to its surface. One such normal is shown by the dotted line, and simple inspection makes it evident that the 40 LIGHT [CHAP. lowest ray from s, reflected from the mirror at an equal angle on the other side of that dotted line, proceeds to j, and that every other ray from sis reflected to nearly the same point. The qualification " nearly " is necessary, because mathematical analysis proves that only a parabolic form will exactly converge parallel rays to one point, and that a spherical mirror only exactly converges rays emanating from the centre of the sphere. But for small surfaces the aberration is not great even with spherical mirrors ; and these are the correct figure for aiding the light in lanterns or electric cameras, the rays proceeding from the centre of curvature, and being reflected back through the same point, so as to reach the condensers at exactly the same angles as the direct light. Parabolic mirrors are often fitted by opticians to lanterns ; but a moment's reflection will show that such an arrangement is a mistake, as the condensers cannot deal properly at once with the divergent light from the radiant, and the parallel light from the mirror. On the other hand, when a strong parallel beam is required, as in lighthouses, the parabola is the correct form. The point where parallel rays converge is called the principal focus. 27. Images from Concave Mirrors. As the rays from one point are collected by a concave mirror to another point, as in Fig. 34, we must necessarily have an image ( 15). And because a wide cone of rays is thus collected and converged, this will be a brighter image than those previously obtained. We have supposed s to be a point in Fig. 34, but if we take an object A B (Fig. 35) and trace only two diverging pencils for the sake of clearness from its top and bottom points, we shall see that both rays from A converge to a, and both from B at the point /; ; parallel rays crossing at F, the principal focus of the mirror, and rays perpendicular to the surface at c, the centre of curvature. If a b is the object, then the enlarged image will appear at A B, owing to the principle of reversibility ( 21). Inspection will show that the image must be inverted. All this can be easily proved by experiment, a concave n] CONCAVE MIRRORS 41 silvered glass mirror 6 or 8 inches diameter being now pro- curable for a few shillings, and answering the purpose sufficiently, 1 the secondary image from the first surface of the glass being too faint to matter much in mere demonstration. We simply remove the objective from the lantern, deflect it about 90 from the screen, and place in the ordinary lantern slide-stage any diagram, or some simple lantern-slide. The concave mirror (of not less than 6 inches focus) can then FIG. 35. Inverted Image. easily be so held by hand as to throw a recognisable image of the slide in the lantern upon the screen. This, then, is one method of collecting sufficient rays from an object to form bright images ; which is practically utilised in the reflecting telescope* largely used for astronomical purposes. The rays to be collected being practically parallel, the figure of the mirror is parabolic ; and the collected rays may be brought to the eye in either of several methods, which need not be 1 For private experiment the phenomena of curved mirrors may be easily traced out by blacking the convex side of a watch-glass for the con- cave mirror, and the concave side of another for the convex mirror. 42 LICzHT [CHAP. described in a work dealing only with the physical phenomena of light. 1 If the pupil of the eye be, say Jth of an inch in diameter, and we " see " a star by the " light " which enters that small area, it will readily be understood how many thousand times the same quantity of light will be collected by a good speculum several feet in diameter, and how much magnification an image so produced will bear, without too much loss of brilliancy. 28. Convex Mirrors. Virtual Images. The images just considered are real images : that is, the rays diverging from all points of the object being actually converged to certain points, if a screen be adjusted at these points the image or picture will appear upon it. A few moments' consideration and a simple diagram 2 will show that if an object be placed in front of a convex mirror, the divergent rays from it must be re- flected still more divergent, and must, therefore, since the rays are " seen " in their last apparent direction, appear to proceed from a point behind the mirror, obtained by prolonging behind it the reflected ray-lines. Such an image appears smaller, and erect, and is a " virtual " image, having no real existence. If an object be placed nearer a concave mirror than its principal focus, a diagram will also show that no real image can be formed, but that a " virtual," erect, enlarged image will appear behind the mirror. 29. Scattered Reflection. Turn the lantern again towards the screen, throwing from it either a beam of parallel light, or the image of an aperture an inch diameter if a plain burner is employed, stopping the beam with the black card screen at the end of the table. With the plane mirror throw the beam back, and rather towards the ceiling, to any point not 1 These and other optical instruments are fully explained and illustrated in Guillemin's Applications of Physical Forces, published by Macmillan and Co. - The student is strongly advised to construct such diagrams for himself, solely by the method of drawing ray-lines at equal angles of incidence and reflection. n] SCATTERED REFLECTION 43 very white or light-coloured. Nearly the whole of the light will be reflected, but the mirror itself will be little illuminated, and the room itself will remain nearly dark. Now take the card screen, and turning round its white side, use that in place of the mirror. The beam of light is no longer reflected as be- fore (in the form of a bright beam) to the ceiling ; but the card is brightly illuminated, and a very considerable amount of light is diffused throughout the room. Hence the light appears at first sight to be reflected according to different laws in the two cases. But it is not really so ; and this simple experiment, with what we have already discovered about forming images by collecting and converging diverging cones of rays, explains to us how things become visible, or send light to us, though that light be only borrowed or reflected. We can understand in a moment that a perfectly polished surface, if such were possible, can only reflect to us or converge for us, the diverging rays from other and luminous objects, without altering them other- wise. It must itself, therefore, be utterly invisible ! Such a perfect polish is unattainable, but our nearest approaches to it prove the truth of this. It is not uncommon for a large mirror occupying the whole of one end of an apartment, or the side of a landing, to be unperceived ; a and Colonel Stodare's " Sphinx," which made some sensation years ago, depended upon the space between the legs of an apparently three-legged table being glazed with brilliant looking-glass. The stage- being kept in a rather subdued light, and the carpet and hangings carefully arranged of uniform colour, with no "pattern," to all appearance there were only three legs under the table and box which supported a living head ; whereas the man's body was -comfortably accommodated behind the two silvered mirrors, placed with their angle of junction towards the spectator. With surfaces not perfectly polished, or which means the - f I once actually walked up against a large mirror placed at the corner of a club staircase, and occupying the entire wall at the corner. 44 LIGHT [CHAP. FIG. 36. Reflection from Unpolished Surfaces. same thing not perfectly smooth, it is very different. Let Fig. 36 represent such a surface, with its inequalities highly magnified. The rays from the left hand, say of a sun-beam, strike upon it all parallel. But even the few which for the sake of clear- ness are drawn, are reflected in all direc- tions, owing to the furrows and protube- rances of all sorts, which make the angle of incidence variable for almost every one. It can be seen that every reflected line in the diagram is drawn at the proper angle ; yet how different these reflected directions are ! In reality the variety of directions is countless ; and thus from every sensible portion of the surface comes, not the original parallel pencil of rays, but a cone of divergent rays. The body itself thus behaves like a candle, or has become luminous, though only by reflected light : and so it is that if we collect and converge these new cones of rays, either by the eye, or by any other methods, we form an image. 30. Light Invisible. We push our experiments on scattered reflection a step further, for it bears upon a very important matter. Already we cannot help asking ourselves, what is this Light, which obeys rigidly such simple laws, and yet produces such various effects by them ? The equal angles of reflection and incidence almost irresistibly suggest to us a ball rebounding from a wall, or a billiard-ball from a cushion. It is natural to conceive of Light as consisting of infinitely small and highly elastic particles, propelled from the original luminous source. Such a hypothesis would account for most of what we have found, if not all, and is very simple, and easily n] LIGHT ITSELF INVISIBLE 45 understood. But besides far greater difficulties we must grapple with later on, this hypothesis has one obvious difficulty that encounters us even now. Light ought, if it were so, to be visible. And indeed we are apt to picture it as possessing intrinsic brilliance of its own ; and we have even appeared in many of the previous experiments to *" see " the course of the rays the very " rays " themselves in our darkened room. Nevertheless it is not so, as a careful consideration of our last experiment soon leads us to perceive. This Light we are studying is not itself a Thing, but a Revealer of things. It is itself, and by itself, absolutely invisible. It makes visible to us, luminous objects or sources, rays from which actually reach our eyes ; but if we look " sideways " at rays alone from the most dazzling light, we cannot see them. Space is black. If we appear in previous experiments to have " seen " the course of the rays in our darkened room, that is only because of the little motes in the air ; and Professor Tyndall has shown that, destroying these by heat, and keeping fresh intruders out of a glass tube thus cleared, the space traversed by the full beam of an electric lamp is dark as night. We demonstrate it less perfectly, but sufficiently, as in Fig. 37. Place on the table a confectioner's glass jar, A, 6 inches in diameter, cover it with a glass plate, B, and drop into it a bit of smoking touch-paper, which soon fills the jar with smoke. Adjust the plane reflector, c, to throw the whole beam down as parallel as possible, when the jar is at once filled with a peculiar lambent light. Take off the plate and let the smoke out ; and, as it disappears, dark spaces appear where there are no particles to reflect the light, till all is dark. The Light itself is there alike at all times ; but where there are no solid particles to reflect it actually to the eye, we see nothing at all. The Light that illuminated the jar, is itself invisible. Once more : clear the jar and fill it with clean water. Again it is almost invisible, except where the rays may be reflected from some point of the glass direct to the eye ; and it would 46 LIGHT [CHAP. u. be quite invisible were the clearness of the water and polish of the glass perfect, as we have seen ( 29). But now pour in one or two spoonfuls of milk and stir it up. At once a splendid opal light fills the jar, and a pleasant radiance the room. Many students, and even teachers, too much despise these more simple experiments ; but they are not only of great beauty, they are pregnant with meaning. We have here not only a difficulty in the " emission '' theory which we must not FIG. 37. Scattered Reflection. forget, but we have had another striking example of scattered reflection that kind of reflection by which bodies are seen. In white light, more or less of such scattered light is always white. Therefore " coloured " bodies reflect white light as well as coloured ; and more white light will be reflected from a black hat in the light, than from a shirt-front in the shade. Smoke is soot, and we all know soot is black ; but in our last experiment but one, the light we got reflected from our particles of smoke, when diffused, was white. CHAPTER III REFRACTION. TOTAL REFLECTION. PRISMS AND LENSES. The Refraction or Bending of Rays The Law of Sines Index of Re- fraction Total Reflection The Luminous Cascade Transparency Prisms Lenses Images produced by Lenses Focus of a Lens Virtual Images and Foci. 31. Refraction. Provide a rectangular tank about two inches between the sides, one of which, to serve as the front, is a piece of glass a foot square, or a little more ; let one end also be of glass, and the top open. Paint over the face with black varnish all but a circle, on which paint a horizontal and vertical diameter, as in Fig 38. Provide also a strip of thin zinc or copper blackened, c D, rather wider than the tank, and about three inches longer, in which cut two slits ^ inch wide, and nearly the whole width of the strip (or depth from front to back of the tank) in length, in such positions that when the strip rests vertically against the glass end, the slit E shall be about ^ inch above the horizontal line, and the slit F make an angle of 40 degrees from the centre of the circle with the horizontal line. FIG. 38. 4 8 LIGHT [CHAP. Fill the tank exactly to the horizontal line with water mixed with two or three drops only of milk, or a grain of eosin, uranine, or any other fluorescent substance ; place the metal strip over the top with both slits towards the lantern, and ar- range the reflector as in Fig. 39, placing in the optical stage the slit used in our first experiment in reflec- tion, horizontally, or using the parallel beam. First of all direct the light through the slit E (Fig. 38), only a little off the vertical, covering over the other slit. It will be seen that the ray is bent or refracted on entering the water. Cover up this slit and uncover the slit F (Fig. 39), near the end of the tank, and blow in a very little smoke from a bit of touch-paper to show the course of the ray. (If too much is used the light will be scattered, as in 30.) We now see more clearly all that takes place. First of all, the ray is much more bent than before ; and secondly, a consider- able part is reflected according to the law found in our former experiments. 32. The Law of Refraction. We have found that in passing from the air into the water the ray of light is wrenched or bent down towards the vertical, or refracted, as it is called. The greater the original angle with the vertical, the greater also is this bending ; and we naturally inquire if there is any law which governs these variable angles of deflection. The law is simple enough when known, but not very obvious to mere ob- servation. It eluded even Kepler's special investigation, and was only discovered about 1620-25, by Willebrod Snell. It is FIG. 39. Refraction and Reflection. Ill] LAW OF REFRACTION 49 FIG. 40. The Law of Sines. called the "law of sines." Taking a circle, as drawn on the face of our tank, described round the point where the ray enters the denser or more refractive l medium, and drawing the per- pendicular or normal, A B (Fig. 40), which in the case of water is of course vertical, we may take any incident ray, A D c, and its refracted ray, c d. From the points at which these cut our circle we let fall D s and d s perpendicularly upon the normal A B. Then D s is the "sine " of the arc subtending the angle of incidence, and d s that subtending the angle of refraction, and the two lines will have a certain proportion ; in the case of air and water here supposed, it is almost precisely as 4:3. Now take any other angle of incidence, E c, and its refracted ray, c e, and drawing the sines as before, they will have precisely the same proportion. All the sines have the same invariable ratio. 33. Index of Refraction. When this proportion of the sines is put into the form of a fraction generally a decimal fraction it is called the " index of refraction." Unless other- wise specified, figures so given are understood with reference to air as unity. In the case of air and water we have seen that this ratio is nearly | ; and when put into decimals, 1*335 ' ls tne " index of refraction " for water. It follows, that the greater the refractive power the higher the index must be. 34. Refraction into a Rarer Medium. We have 1 A heavier fluid may have less refractive power, or optical density, than a lighter one. Oil of turpentine floats on water, but has much more refractive power. LIGHT [CHAP. proved that a ray passing obliquely from air into water is bent towards the vertical, or downwards ; and yet if we look at a stick standing in clear water it appears to be bent upwards- Fig. 41 explains this. The dotted lines represent the real posi- tion of the bottom part of the stick, and those dotted from its lowest point show the course of the rays which reach the eye from that point. On reaching the surface they are bent from the vertical, and the bottom of the stick is " seen '' in the direc- tion from which the rays actually enter the eye. We thus see that the course of the re- fracted ray, like that of a reflected ray, is exactly reversible. If the bottom of our tank is made of glass, and it is raised up from the table and a ray sent up through the water, it can be shown experimentally that at sufficient angles the ray is refracted from the vertical on leaving the water : or the ray may enter the top of the tank as before, and after first being refracted downwards, will, on passing through the glass bottom, be again refracted away from the normal. 35. Total Reflection. But there is a curious limit to this. Seeing that as the angle of incidence increases, the re- fracted ray is more and more bent towards the vertical,' we cover the top of the tank with a bit of plain board, and place the metal strip upright against the end of the tank, in the position of Fig. 42. Gently canting our lantern a little, we pass the beam direct through the slit E (Fig. 42), so as to enter the water almost horizontally. We find the ray bent down FIG. 41. Ill] TOTAL REFLECTION FIG. 42. a great deal, at about an angle of 45, as shown by the thin white line c D. Now we have ascertained that if we throw the ray first by our reflector up through the water, in this case the path is exactly reversed. It occurs to us at once, that if we sent our beam at a slightly greater angle (never forget that all angles measure from the normal) through the water, there is no path in the air it can assume : it would appear that it cannot get out of the water at all. We try it, as in Fig. 43, sending our beam up through the lower slit by a bit of look- ing-glass, so as to strike the centre at an angle of 50 from the normal. 1 It does not get out not a sign of it. It is totally reflected ; and be- cause this reflection is total, it has a bril- liance not possessed by that from even the best silvered mir- rors. It will be readily seen that the angle of total reflec- tion must decrease* as FIG. 43. Total Reflection. the index of refrac- tion increases; but this will be shown by a beautiful experiment when we come to study the subject of colour ( 47). 1 The limiting angle is about 48, but we keep on the safe side. 2 The phenomena of total reflection may be observed by the private student by looking at the under-surface of the water in a tumbles held rather above the level of the head and of a candle, or by immersing the LIGHT [CHAP. FIG. 44. 36. A Luminous Cascade. There is another very beautiful method in which total reflection may be illustrated by the lantern, called the " luminous cascade," or "fountain of fire," which may be arranged so as to be very effective by simple means. Get a two-necked glass receiver (Fig. 44) about 4j inches diameter, with as large necks as possible, and in each neck fix by corks glass tubes of similar size, as large as possible, not less than f inch clear bore, and \ inch is better. 1 Black- varnish all outside, except a circle, c, three inches diameter, opposite the neck meant to be horizontal ; and ad- just this as at A (Fig. 45) close against and projecting into the lantern nozzle (the flange nozzle, with the objective removed), on any stand, filling with water first, and corking the tube in the hori- zontal neck till all is arranged. Several feet higher, fix some sort of supply tank (a bucket will do) with a bit of tube fixed by a cork in the bottom, and connect with the top neck by a flexible tube, B, the whole arrangement being shown in Fig. 45. Finally adjust the light at such distance from the condensers that the greatest possible amount is concentrated into the space occupied by the emission-nozzle. Having ad- lower end of a test-tube slantwise in water. Whatever is placed in the dry. tube will be invisible, and the tube will appear brighter than silver ; but on pouring in water the brightness disappears and the contents of the tube become visible. 1 There is sometimes difficulty in procuring a receiver with both necks large enough, on a small globe. In that case, insert as large a tube as it will take in the largest neck, for the emission opening, and strain the flexible supply tube over the other neck alone, which will give plenty of aperture for the supply. A fair-sized stream must be obtained ; otherwise there is not enough light, and it breaks up too soon into drops. Since this work was published, several opticians supply at my suggestion a cheap metal closed tank with a flat glass side and an opposite nozzle, on purpose or the experiment. Ill] LUMINOUS CASCADE S3 justed all this, ancU filled the tank, remove the cork from the tube, and let the water stream out in a gentle curve into a bucket on the floor. The effect is beautiful even on this small scale. The jet is like a stream of living fire ; and if we have some coloured glasses and slip them in turn into the ordinary slide-stage of the lantern, we get blood-red, blue, or what colour we desire. All this is owing to " total reflection." If FIG. 45. Luminous Cascade. the water did not issue, and we replaced the cork by a ground- glass stopper with flat polished ends, we know the light from the lantern would be thrown horizontally into the room. But it meets the stream of water on every side at much more than the angle of total reflection ; and so it cannot get out, but is reflected from side to side all down the stream, making it brilliantly luminous by the small motes in the water. Place the hand in the jet, and it is bathed in light that light 54 LIGHT [CHAP. FIG. 46. Deflection. which cannot get out of the stream except where we thus break it up. 37. Deflected Rays. We must, however, follow refraction a little farther. We have seen that the path of a refracted ray is re- versible, and that, on leaving the denser medium, it is bent/*w the perpendicular. We easily see (Fig. 46) that if a ray, s, passes from and into air through a denser medium with parallel surfaces, as a thick piece of plate glass, it must be deflected somewhat, but finally resume a direction pa- rallel to the original, as if proceeding from s 1 . We may demonstrate this with the lantern, by placing in the ordinary stage with objective removed, and focusing on the screen with the loose lens, a blackened glass slide with one or more perpendicular lines, or other figures, scratched in white through the varnish. Now hold across the slide a strip of plate glass \ inch thick, so as only to cover a por- tion of the figure. When this is held parallel to the slide, there is of course no perceptible refraction ; but when the plate glass is held obliquely, so that one end is farther from the slide than the other, the lines as far as covered are perceptibly deflected or broken. (Fig. 47.) 38. Transparency. It appears very readily that the pro- FIG. 47. Deflected Image. in] TRANSPARENCY 55 perty of transparency must depend upon homogeneous struc- ture and uniformity of refractive index, and is reciprocal with irregular reflections and refractions. Arrange a screen of blotting paper between two lanterns if available, or if not between two gas-burners, so that it may be visible by reflected light from one source, or by transmitted light from the other. Oil or damp a small portion in the middle. By the oil or water the difference in refractive index between the fibres of the paper and the intervening pores is largely diminished, water or oil being denser than air ; and this portion will therefore ap- pear darker by reflected light, but brighter by the transmitted light. If thin ordinary paper with a grease spot be used, with the lantern on one side and a burner on the other, altering the distances till the paper appears equally bright all over, we have in a rough form Bun sen's photometer. But we can demonstrate the same thing by a far more beauti- ful experiment. Provide a bottle cemented like a prism-bottle, but with two parallel sides of plate glass about half an inch apart ; or even one of the cheap scent- bottles ground to two flat sides will answer less perfectly. Prepare also some pounded glass, from any fairly homogeneous piece in the first case, but for a common scent-bottle one or two similar bottles should be pounded up, heating the glass and throwing it into water. Common powdered glass, as sold, rarely answers, being usually a mixture of all sorts, and not of the same index. The bottle is filled with this, and the irregular refractions and reflections of the particles are so great, that the mass is perfectly opaque. By mixing in proper proportion benzol (less dense than glass) and carbon bisulphide (more dense) prepare a fluid of the same refractive density as the pounded glass, and pour it in. The fluid is easily mixed by " trial and error," in a bottle con- taining a few fragments of the glass. The bottle is now trans- parent, and will allow the rays of the lantern to reach the screen. A further refinement of this instructive experiment will occur later on ( 60). 56 LIGHT [CHAP. 39. Prisms. If the two surfaces of a piece of glass through which a ray of light is sent are inclined to each other, the ray must be permanently deflected into a new direction. Any re- fracting body with faces so inclined is called a prism. Fig. 48 shows a section of such a prism, and it is clear that a ray, s i, imping- ing on the first surface at the angle s i N with the normal N, will be re- fracted in the path i E towards the perpendicu- lar. But E N' is the nor- FIG. 4 8.-Pri sm . mal to the second sur ' face, and on emerging the ray must be refracted from that, in the direction E R, widely different from that of the incident ray. It is equally clear that the deviation must depend not only on the density, but on the angle of the refracting surfaces of the prism. It also, however, depends on the position of the" prism ( 40). All this is easily demonstrated ; but to avoid much colour phenomena, which must be studied separately, it is best to take a water-prism of rather a small angle ; or if of glass a very thin one indeed, usually called a wedge-prism, costing about 35. 6d. A water-prism is readily constructed by shaping a smooth wedge of beech about 3 inches square, one inch thick at one side, and tapering to an edge at the other. Bore centrally through, from face to face, a circular hole 2 inches diameter ; paint the inside of the hole with sealing-wax varnish ; and then, heating two clean pieces of plate glass 3 inches square, cement them with hot sealing-wax or shellac on the flat sides. By a small hole bored from one end of the wedge this prism may be filled with water, or the hole may be entirely opened out to one end so as to form a small open trough. Placing a small aperture in the optical stage, and focusing on Ill] PRISMS AND LENSES 57 I the screen, stand the water-prism on one end on the table-stand (Fig. n) and adjust in the path of the rays. It will at once be seen how the image is deflected. If a multi- plying glass, which can be bought for a shilling, is held in front of the nozzle, a number of re- f r a c t e d images will appear on the screen. 40. P o s i t i o n of Minimum Devia- tion. It will soon be found that the deflection varies as the prism is turned round upon its axis into different posi- tions. It will also be found that the deflection or refraction is least when the prism is placed as in Fig. 48, so that the incident and refracted rays make equal angles with their respec- tive surfaces. This posi- tion is known as that of " minimum deviation," and is carefully arranged for in all accurate prism work, such as spectrum analysis. 41. Lenses. Let us now consider a number of prisms of gradually increasing angles, arranged round an axis. Fig. 49 may represent such a combination of prisms in section. A glance at the diagram shows that the outer parallel rays, from the left hand, meeting prisms at greater obliquities, are more deflected than those nearer the centre ; and that if the ob- FIG. 49. Nature of a Lens. 58 LIGHT [CHAP. liquities are properly adjusted, all the rays might be made to converge in one point. If the obliquities are infinite in number, it is obvious that we get curved surfaces, and such form a lens. Lenses may either be convex or concave on either or both sur- faces, or flat on one, and convex or concave on the other. It is plain that whatever the figure may be, if they are thicker in the middle than at the circumference they will be converg- ing lenses ; if thickest at the circumference, diverging lenses. 1 42. Images formed by Lenses. Since parallel rays, falling on the double-convex lens A (Fig. 50) converge to the FIG. 50. Lens and Focus. point F, which (as in the case of a converging mirror) is the principal focus ; and since the path of the rays is reversible, and rays from the point F after traversing the lens become parallel ; a moment's consideration will make clear that if the rays diverge from any point beyond the principal focus, they must converge to some other point and form an image. Fig. 51 shows this. Parallel rays from A B traversing the lens o would converge at the principal focus F ; but if rays diverge from the points A and B of an object (only pairs of rays are shown 1 A lens formed by two equal convex surfaces is called a double convex lens, and if the two convex surfaces are of different curves, a "crossed" lens ; lenses with two concave surfaces are double-concave lenses ; those with one side flat, plano-convex or plano-concave ; a lens with one side convex and one concave, a meniscus. in] LENSES AND IMAGES 59 for the sake of clearness) they converge to the points a b and form an image. It is also clear how the respective distances of image and object govern their respective sizes, so that if a b is the object, A B will be its image. Also that the image thus formed must be inverted. Thus we have a second method of forming brilliant images, the lens taking up a large cone of rays from each point of the object. But it is very important to realize clearly that this image is formed by the rays of light proceeding from each point, pre- cisely as in 15, and that all the lens does is to converge (upon the same point in the image) large bundles of rays. Re- peat the lantern experiment in 15, removing all the lenses, FIG. 51. Image formed by Lens. covering the flange-nozzle with foil, and pricking a hole in the middle, and say four other holes equally spaced half an inch outwards from it. We get from the bare rays alone, as in 15, an image of the radiant in the centre of the screen, and four other images ranged round it, which represent diverging rays. Now take a large lens of somewhat longer focus than the dis- tance of the radiant from the tinfoil, and hold it in the hand close to the foil. It will be instantly seen that the four outer images are bent in more or less towards the middle one ; and a position is soon found, in which they are just so much bent in as to fall upon and coincide with it. That is "focusing" 60 LIGHT [CHAP. the lens, and the one image is now necessarily five times as bright as either of them was before. When the lens is in this position, we may go on pricking more holes, or take away the tinfoil altogether ; and there is still but one image, though much brighter still, because so many rays are now converged to the same point. It should be observed that, as in the case of mirrors, the spherical surfaces which are most easily ground do not truly converge the rays to a point, the figure necessary to do this being elliptic or parabolic. Such lenses have been ground, though with great difficulty. There are however other errors also to be corrected ; and it is easier and more convenient to correct all these errors by methods presently described, or to stop off some of the most erroneous marginal rays. FIG. 52. Lens and Virtual Image. 43- Virtual Images and Foci. A mere inspection of Fig. 52 will show that if the object or luminous point be nearer the convex lens than its principal focus F, the rays cannot form an image, but simply become less divergent. If the emergent ray-lines are produced back to s', that will be the "virtual" focus. There we have a virtual, magnified, erect image, as in the ordinary way of using a magnifying glass. 1 1 The student is again strongly urged to work out for himself diagrams of this and other cases ; not here described in detail, as unsuitable to the experimental character of this work. in] USES OF LENSES 61 44. Concave Lenses. A double concave or other di- verging lens either converts parallel rays into divergent, as in Fig. 53, or convergent rays into less convergent ones, which may be parallel, or still remain convergent. Such lenses can only have a " virtual " principal focus, F, obtained by producing back the divergent ray-lines into which they refract parallel rays. A whole host of optical instruments, which cannot here be described, 1 are based upon these properties of lenses ; especi- ally microscopes, telescopes, and such lanterns as we employ FIG. 53. Concave Lens. in our experiments or for exhibiting views. In most micro- scopes and telescopes, a magnified image is further magnified by an eye-piece. In the lantern, the " condenser*' lenses are employed to make the diverging rays from the radiant parallel or nearly so ; while the objective, or our loose focusing lens, forms a magnified inverted image upon the screen of some ob- ject powerfully illuminated. Except as regards details necessary for correcting aberrations, the phenomena of refraction explain them all ; and every curve of every lens has to be calculated for the special work which that lens has to do, according to its index of refraction and the law of sines. 1 See Guillemin's Applications of Physical Forces. Macmillan & Co. CHAPTER IV. DISPERSION AND THE SPECTRUM. DIFFERENT COLOURS HAVE DIFFERENT REFRANGIBILITY. The Spectrum Different Colours differently Refracted and each Colour has its own Angle of Total Reflection Position of the Prism and its Effect Correction of Aberrations by Variations in Position White Light a Compound of Various Colours Colour can be analyzed Suppression of Colour produces Colour Artificial Composition of White Light A Narrow Slit necessaiy for a Pure Spectrum The Rain- bow Refraction and Dispersion not Proportional Achromatic Prisms and Lenses Direct Vision Prisms Anomalous Dispersion. 45. The Spectrum. With the water-prism before de- scribed, or a wedge-prism with faces of small obliquity, nothing more may have been noticed than the refraction described in the last chapter ; though even with these instruments attentive observation will generally discover a slight fringe of colour at .the edges of^the refracted images. We must now, however, employ a prism of more density and greater angle either the glass prism (Fig. 9), or the prism bottle filled with carbon bisulphide. Place in the optical slide-stage a perpendicular slit f inch deep and inch wide, and arrange either the flint- glass prism, or the fluid prism on the stand, as in Fig. 54, first focusing the slit upon the screen ; and, as we expect the rays to be now very seriously deflected, turning the lantern off at a considerable angle before interposing the prism. 1 What a 1 With a gas-burner the screen distance should not exceed about six feet. The arrangement in Fig. 10 is very convenient for these lantern deflections. An arrangement for considerably increasing the brilliance of the spectrum is described at the beginning of Chapter VI. CH. IV] THE SPECTRUM FIG. 54. Production of the Spectrum. spectacle we have ! There stands the glorious rainbow-band, as first revealed to Newton's enraptured eyes ; and which is to introduce us to a new and magnifi- cent field that of colour. Of all the people who have experimentally studied Optics, and who of course have performed this ex- p e r i m e n t scores and scores of times, never one yet but has felt that it never loses its fascination ; the same feeling of delight ever comes upon us, as that SPECTRUM appears on the screen (Plate II. A), which is to go with us, and be more or less our guide, through great part of our future experiments. 46. Different Colours differently Refracted. It is at once noticed, that while all the colours are bent aside, the red end of the spectrum is much less bent than the blue. Newton deduced from this and other experiments with the spectrum, that each colour of light had its own degree of re- frangibility, and that white light was compounded of various colours. \ We demonstrate the first point as. follows. Arrange as before, but with a short as well as narrow slit in the optical stage let it be, say, an aperture \ inch square and let its long narrow spectrum be projected by the bisulphide prism. We may per- haps think that the effect of the prism is merely, of itself, to spread or open the colours. To see if this is the case or not, we adjust behind the first prism (i.e. between it and the screen) our glass prism in a horizontal position, with the refracting edge 64 LIGHT [CHAP. downward. If it were so, our spectrum would now be generally widened as well as refracted upwards. It is not, however ; the violet end is refracted up far more than the red end, and the spectrum appears on the screen askew, or slanting. The spectrum may be perhaps a little thickened or widened, but that is all (it will not be so if it is a long or well-dispersed one, such as is produced by employing two bisulphide prisms). Each colour, proceeding from the red end, simply appears more and more bent up. Hence the "dispersion," or opening out of the beam of white light into a spectrum of various colours, is accounted for by the hypothesis of a different refrangibility for each colour ; supposing only we find, on ex- periment, that such a combination of colours will compose white light. 47. Each Colour has its own Angle of Total Re- flection. Newton proved the special refrangibility of each colour by another still more beautiful experiment ; one of the most elegant ever devised. It depends on the fact already noticed, that the angle of total reflection must vary with the index of refraction ( 35) ; the violet rays being totally reflected (because more refracted), at an angle which would allow the red rays to leave the denser medium. Newton therefore ar- ranged an experiment as in Fig. 55, except that he employed the parallel rays of the sun instead of those from the lantern. A perpendicular slit N is placed in the optical stage with the objective removed, or on the nozzle of the lantern if an ad- justable slit is at command, and the parallel beam is sent through it (see Fig. 55, which shows all the arrangements in plan). As close to the slit as convenient, on a table-stand, simply " stood up " on their ends, are two similar right-angled glass reflecting prisms, p and P2, with their reflecting sides to- gether, kept together by an elastic band passed round near each end ; they must not, however, be in optical contact, and may, if necessary, be kept apart by a narrow slip of tissue paper. In the direct path of the rays from the slit, is a focus- PI.Z. THE SPECTRUM AND ITS TEACHINGS A. 5. tYide> C. D F. ts &pecrizms; shotting' tv-Titte, centra 2>rMv anaZyjeeZ of th& sun;. E .Absorption/ of C7dorvp7u/U. IV] NEWTON'S EXPERIMENTS ing lens, F, and beyond that, on another table-stand, is placed a bisulphide prism-bottle, B, in the usual position for throwing a spectrum on the screen, s s. In the path of the rays totally reflected from the film of air between p and P2, is another focusing lens, F, and beyond that, on a third table-stand, a second bisulphide prism-bottle, B2, which throws its spectrum on the screen, s s, adjusted at right angles to the other screen ; FIG. 55. Newton's Experiment or the screen s s will receive both spectra if the refracting angle of the prism B is turned the other way. All being thus arranged, the double prisms, p and P2, can be turned round their common perpendicular axis from right to left in the figure, till nearly all the rays from the slit pass through both, and the prism B throws a spectrum on the screen as usual. Except for a little loss by reflection and absorption, all F 66 LIGHT [CHAP. is just as if p and P2 were not there, the refraction of one being exactly neutralised by the other, and the rays passing as if through one square bar of glass. Let now the double prism be very carefully and slowly turned round in the direction of the hands of a watch. At one certain point of revolution, just when the film of air meets the rays from the slit at the critical angle for violet, the violet leaves the spectrum on the screen s s, and, being totally reflected, appears on the screen s s. 1 Con- tinuing very slowly to turn the double prism, all the colours in succession leave the spectrum on s s to appear simultaneously on the screen s s, so that if we letter the screens with the con- ventional names, at the point where one screen has only left on it the colours Y o R, the other screen presents the missing colours, v i b g, which are " totally reflected." 2 This beautiful experiment, then, shows that each colour has in addition to its own proper index of refraction for the same medium, and in consequence of it, its own proper angle of total reflection. 48. Position of the Prism. Notice next that, as with the water-prism, on turning a dispersion prism round its vertical axis (it may here be observed that the best place for a prism is nearly or a little beyond where the rays from the lantern appear to cross ; in this position all the light easily gets through it), a position is soon found in which the beam is least deflected. But still further observe that, on rotating the prism on its axis 1 The effect is less visible on this screen, enough light being always reflected from the air surface to give a little spectrum. But it can be seen that the violet is strengthened. 2 Only the sun, or the small radiant point of the electric light, will give the phenomena perfectly in these details. A large gas-burner will not answer for the experiment at all. A " mixed " jet will perform it fairly if the condenser will throw nearly parallel rays. The ' ' blow-through " form gives too large a radiant for a good parallel beam ; but even with that, it is at least easily shown, by taking both prism-fo/// away, and leaving the rest of the arrangement, that at a particular angle the direct image of the slit is reddish, and the reflected one bluish. IV] COMBINATIONS OF LENSES in one direction from this position, the ray is not only more re- fracted, but more dispersed : the spectrum is lengthened, par- ticularly at the violet end. Rotating in the other direction, while the refraction also increases, the spectrum is shortened. 49. Chromatic Aberrations. This fact has an im- portant application. If the prism refracts the blue rays more than the red, then a lens must do the same, and will bring blue rays to a focus nearer the lens than the focus for red rays. By placing in the slide-stage two apertures pretty close together in a black card, one covered with red gelatine and the other with blue, and focusing them on the screen with the large loose lens, it can readily be shown that this is the case ; and thus, besides the " spherical aberration," already alluded to ( 42), we have what is called " chromatic aberration," due to the fact that a single lens will not unite all colours accurately in the same focus. 50. Correction of Aberrations. But we have here found a means whereby different combinations of even single non-achromatic lenses may be arranged so as A B C to correct, to a con- siderable extent, both these aberrations. In detail, this must of j course be worked out \ mathematically ; but a simple illustration of a point which often puzzles students is worth while. We have just found that the effects of three prisms A, B, c (Fig. 56), of equal angles, variously inclined to horizontal rays coming, say, from the left hand, will be very different, not only in refraction but also in dispersion ; and therefore these effects may be made largely to counteract each other. But such F 2 FIG. 56. Effects of Position in Lenses. 68 LIGHT [CHAP. prisms may, as before shown, be regarded as portions of simple plano-convex and bi-convex lenses. The arrangement adopted for our optical objective (Fig. i) is one thus planned, to correct a great deal of chromatic and spherical aberration by very simple means. 51. White Light Compounded of the various Prismatic Colours. Taking the different colours, as they leave our prism independently for the screen, or exist other- wise, we can show in many ways that when mixed together in proper proportions they produce white. First of all, arrange a second prism B as in Fig. 57, so as to intercept the dispersed rays, and bend them back again, but leaving an interval of half 35, FIG. 57. Recomposition of White Light. an inch or so between the prisms. We at once restore the image of our slit on the screen, and it is white. 52. Suppression of Colour, the Chief Cause of Colour. Now interpose gradually a black card, c, between the tw-o prisms, so as to suppress part of the spectrum produced by the first prism. We still get a sharp image of our slit, and not a spectrum; what are left of the coloured rays are ac- curately brought together again ; but it is now a coloured image. This teaches an important lesson that holds good through nearly all future experiments. It is, that we almost invariably get colour by, in some way, taking away or suppress- ing colour. If, instead of the black card, we interpose the edge of a slightly wedge-shaped prism, the colour taken away appears separately, and is always "complementary" to the other that is, together they make white light. ( 76.) iv] COMPOUNDING COLOURS 69 53. Colour can be Analysed. The experiment further teaches a fact of transcendent importance in countless physical investigations. It is, that prism or spectrum analysis will always give us the exact actual composition of whatever light there is passing through the prism. If any colours be there, the dispersed spectrum will display them ; if any be absent, their absence will be betrayed it may be by immense gaps, or it may be by the narrowest lines. The truth of the analysis is only affected by the fact, that certain rays may be absorbed and so suppressed by the material of the prism itself. Such absorption has of course to be investigated and allowed for. 54. Experiments in Compounding Colours. Aeon- vex lens will also compress the colours together into a white image ; and a cylindrical lens will do the same. The latter may be extemporised successfully by using a confectioner's glass jar 6 inches in diameter filled with water. 1 Properly ad- justed between the prism and the screen, this will compound out of the spectral rays a white, though not perhaps very sharp, image of the slit ; and stopping off part of the spectrum will, as before, produce colour. If a cylindrical lens is used, it should be from 10 to 15 inches in focus, and will give quite a sharp white image. Another beautiful and striking method is shown in Figs. 58 and 59. Get seven bits of looking-glass } inch wide by 2 inches long. From a round wooden rod an inch in diameter cut discs, say J inch thick, as stands : to the top of each of these attach a bit of soft wax, and in this stick the end of a mirror, so as to stand vertically as Fig. 58. Arrange as shown in Fig. 59, standing the mirrors on a piece of blackened board, A, on a table-stand. First adjust the stand at such a distance that the rays from the prism p about cover the breadth occupied by all the mirrors to- gether, and then take off all but one at the end, and adjust 1 In cold weather the water should be slightly warmed, else condensation of moisture upon the jar will interpose tedious hindrances to getting a good image. 70 LIGHT [CHAP. that so that it may reflect its colour to a central spot on the screen, s. Put on the second, and turn that till its reflection occupies the same spot ; so of the third and the rest. Note the changes of colour as we add colour after colour ; till at last we have white. But take away suppress any one colour, and again we get colour. Our next method depends on the persistence of visual im- pressions. We " see " things nearly a second after the exciting FIG. 58. FIG. 59. The Colours Recompounded. cause is gone a long time, considering the apparently in- stantaneous character of all other light phenomena. Hold a slip of card in the diverging cone of light from the lantern ; it is a mere strip of bright white. Cut rapidly through the cone as with a sword ; it appears a white disc the size of the cone at the point of section. 1 Take, then, a white card circle, 12 inches 1 I first saw this simple illustration employed by Professor Tyndnll. Another familiar example is found in the circles of light produced by whirling round a lighted stick. Many toys of the "wheel of life " class depend on the same fact ; and slides can be procured from any optician by which the same phenomena can be excellently shown with the lantern. They are known as Eidotrope slides. Mr. Eric Stuart Bruce has introduced a very elegant demonstration. A long thin lath painted grey is rotated round its centre several times in a second. On this an ordinary lantern slide can be projected, appearing as a mysterious-looking phantom in the air. iv] NEWTON'S COLOUR-DISC 71 diameter (Fig. 60), and divide into four quarters. On each of these paint in clear water-colours, as nearly as possible in the proportions of the spectrum, the spectral colours. We may not get them very correct at first, and it may be best to pur- chase the " Newton's disc," as it is called, of an optician ; but some of such are too dark in the blue division. This disc is to be mounted so as to be rotated by a cord and simple multiplying arrangement, and then adjusted facing the lantern, so that all the light may be just about concentrated upon its face when the focusing lens is run fully out. If the disc of light is too large, place a circular aperture, cut in a black card, which will sufficiently reduce it, in the optical stage. This is important, for this fine experi- ment often fails because carried out by the general gas-light of the lecture-room, which gives very poor effect ; whereas the full beam from the lantern brought on the face of the disc in a dark room appears quite differently. Now rotate the disc rapidly, and we get white > more or less bright, or greyish, according to the correctness of the proportions, Newton's disc can also be purchased as a glass slide for the ordinary stage of the lantern, and shows very perfectly in this way, but it is inferior to the painted card for the next experi- ment. We see, either way, that the presentation of a proper assortment of the colours to the eye, anyhow, so as practically to mix them, produces white. It is true, that white produced in this latter way is, by com- parison, greyish ; and hence some of those who pride them- selves upon being " practical " colourists, and despise the scientific investigations of those they term "theorisers," have denied that white can be really thus compounded. It was recently stated in print by an " artist " that the experiment only succeeds at all with "pale washes," and only produces a 72 LIGHT [CHAP. poor grey then ; and this was stated with sufficient assurance to pass for knowledge. But it was simply due to ignorance of two points. In the first place, so far from requiring pale washes, the more vivid the colours are the better, if in correct proportion ; with some few discs I have seen a really good white produced. And in the second place, a grey is the necessary and simple consequence of a deficiency of light ; as can readily be proved by gradually diminishing the light thrown upon a really white disc of card it gradually becomes grey- Now assuming that the spectrum may roughly be divided into seven colours, and that our white is produced by the successive presentation of these to the eye, a moment's thought will make it evident that, at the very most, only one-seventh of the light that a white disc would reflect, can be reflected by the coloured disc. In reality, owing to absorptions explained later on, it is very much less ; and hence our white must be more or less of a grey, if contrasted with a really white card. Carry the last experiment a step further. Cut out from a circle of blackened paper, the size of the disc, radial sectors so arranged as to cover the same colours in each quadrant say> the violets and blues and fix them on the disc by a drawing pin at the end of each. We thus suppress colour ; and as before, we get colour. Again, prepare a disc of stiff, blackened card, as in Fig. 61, with two. radial slots each 2\ inches long and about \ inch wide. Run a drawing-pin through the centre into the end of a stick, so that it can be rotated by the finger like a child's windmill, and hold the affair, or fix the stick in the Bursen clamp, so that each slot in Rotating will cross the nozzle of the lantern, and so let a flash of light through. The nozzle itself must be covered with a cap in which is a similar slot, so as to make the flashes as nearly as IV] THE RAINBOW 75 single drop, we can trace what happens. This beautiful ex- periment was first performed with a sunbeam, by Antonio de Dominis, Archbishop of Spalatro, about 1600 A.D., though Descartes seems to have usurped the credit of his investigations, as he also attempted to do with the law of sines discovered by Snell. We take a small glass bulb ij inch diameter, blown on a small tube, and fill it with water : or we may use filtered FIG. 63. Rainbow Experiment. salt and water, for the reason that it not only increases the dispersion ( 57), but diminishes the angle of deviation. The lantern must be turned towards the spectator, and placed farther back ; the objective removed, and a blackened cardboard or other cap with an aperture the size of the glass bulb, placed on the flange nozzle ; round which, or on which, by a hole cut in the centre, is placed a screen, s, of white paper or cardboard. 76 LIGHT [CHAP. Instead of a card cap, a revolving diaphragm with various holes may of course be used. Adjust the lime-light to throw a parallel beam on the bulb B, between which and the spectators place the blackened card screen (p. 18) to intercept the direct light. The bulb will be held in the clamp, c, by the stem, and both bulb and fluid must be brilliantly clear. We at once see a miniature "rainbow" reflected back upon the screen round the lantern nozzle, provided the bulb be not farther from the nozzle than about the radius of the screen. 1 It hardly need be said that this rainbow is the real rainbow reversed ; any spot on the screen where red appears, means that an eye there would see red in the glass bulb ; and each other colour, unless the eye was moved, would need another bulb in the proper relative position : but the experiment does show correctly the emergence of a nearly parallel chromatic bundle of rays at one certain angle. That such must be the case at one certain angle (about 40 for water) can be proved mathematically from the " law of sines," applied to the spherical bulb ; and the demonstration of this is really due to Descartes. He showed that at one angle alone the rays, which at other angles of incidence emerged di- vergent and scattered, emerged as a nearly parallel beam, and thus produced conspicuous phenomena of some sort ; the pro- duction of colour being afterwards explained by Newton's dispersion experiments with the prism. Fig. 64 shows in out- line the course of the blue and red rays in both the inner and outer bow. The parallel rays, s s, from the sun, falling on the drop b at the proper angle, are refracted twice and reflected once, so as to transmit red light to the eye ; and from the drop a (the angle a o b making about 2), the blue rays being more refracted, also reach the eye ; a b is therefore the apparent breadth of the bow. Other solar rays, s' s', by two internal total reflections and two refractions, also transmit coloured 1 This experiment will not succeed with a plain gas-burner, a strong parallel beam being necessary. IV] REFRACTION AND DISPERSION 77 rays, but of course fainter ; and these form the outer bow. An inspection of the figure will show that the order of colours in the outer bow must be inverted. Theoretically several secondary bows are possible, and with a very bright sun three are occasionally seen ; but as a rule only the primary and the FIG. 64. first outer and inner secondary are sufficiently brilliant to be visible. 57. Refraction and Dispersion not Proportional. Make a water prism as in Fig. 65, by cementing with marine glue two slips of glass 6 or 7 inches long and 2 inches wide into a V trough with angle of 60 with two partitions as well as two ends. If any difficulty about these, wooden partitions will do, cemented with black sealing-wax varnish. Fill one division with water, the next with saturated salt and water, the third LIGHT [CHAP. with saturated sugar of lead in water. Place the horizontal slit in the optical objective, or on the flange nozzle, and focus on the screen ; then pass the three fluids in succession across the beam. Observe that the water refracts and disperses it some- what ; the brine more ; the lead most of all. The natural and first conclusion would be that the two effects are always pro- portionate : that dispersion goes with refraction in due pro- portion. Newton so concluded, misled probably by the frequent use of lead in his water prisms, which masked the very low dispersive power of water. At all events, he made an experiment he thought decisive, immersing a glass prism in a water prism of variable angle, with their refracting angles opposite. When the angle of the water prism was so ad- justed that there was no deviation or re- fraction, he found no colour ; and hence concluded that the dispersion of the glass and water were proportionate to their refractive powers. It is difficult to account for his result in any other way than that supposed ; for when Dollond repeated this very experiment with glass and water, the result was exactly the opposite : viz., when the re- fraction was exactly counteracted, colour or dispersion remained ; and when colour was banished a considerable deviation remained ; a discovery that led at once to the construction of achromatic lenses. In fact, different media vary widely in the proportion of their dispersive and refractive powers. For its refracting or bending power, the dispersive (or spectrum-lengthening) power of carbon bi-sulphide is enormous ; and if a prism bottle be filled with a solution of the double iodide of mercury and potassium, FIG. 65. IV] ACHROMATISM 79 as described by Dr. Liveing, prepared of the utmost density, while the blue end of the spectrum will be absorbed by the pale yellow solution, the green and red are dispersed nearly twice as much as by the bi-sulphide. Flint glass, again, refracts light little more than crown glass, but disperses it nearly twice as much for the same angle. 58. Achromatic Lenses. Here, then, we have the power of correcting or destroying chromatic aberration. Dealing with prisms as the simplest case of the problem to be solved, a flint glass prism of little more than half the angle (in fact, the proportion depends entirely on the density of the flint) will counteract nearly all the dispersion of crown, but leave a con- siderable amount of refraction. Such a double prism can be bought for $s. Focus a slit on the screen as before, and on a small table-stand place on end the crown glass prism. We get as usual refraction and a spectrum ; in this case rather a poor one, owing to the little dispersion of the crown glass. Now place next it, in contact, the flint prism, with its angle the reverse way : we still have the beam bent aside, but the colour is practically gone, and it is a white image of the slit, and not a spectrum, which appears on the screen. It is not necessary to explain in detail how this fact enables us to construct achromatic lenses. 59. Direct Vision Prisms. Conversely, a prism of flint glass of about 52 (for average density), will counteract the whole refraction of a crown glass prism of 60, but will so much more than counteract its dispersion, that there will be a con- siderable reversed spectrum. Hence we have the power of constructing " direct " prisms which give a spectrum without refracting the beam of light. Direct vision prisms composed of from three to five prisms of glass, are largely used in direct vision spectroscopes. For lantern work such prisms are very expensive when of large size, but Mr. C. D. Ahrens has introduced a prism as in Fig. 66, which answers our purposes at a very moderate price. G G are prisms of light glass, So LIGHT [CHAP. enclosing between them carbon bi-sulphide, or phenyl-thio- carbimide as suggested by Mr. H. G. Madan, or cinnamic ether, B. One made for me gives a dispersion equal to a prism- bottle of 60 without any deflection, and is not only very handy to work with, as obviating any turning of the lantern aside, but more light passes through, and the spectrum is not at all curved. 1 Mr. Ahrens also constructs a prism made as in Fig. 67. Here G is one equilateral prism of glass, projecting into the cell of fluid B B. There being only one ordinary glass prism here, this is the cheapest large compound prism that can be made. It gives enormous dispersion about 50 per cent. FIG. 66. FIG. 67. more than that of a prism-bottle with very little, if any, more than ordinary deflection, and can be supplied unmounted for about 405. Much more light traverses this prism than can get through the two prism-bottles generally used when great dispersion is required. A small direct prism of glass so mounted as to go into the nozzle of the optical objective, where the rays appear to cross, is very handy for many experiments, saving in some cases much adjustment of apparatus. 60. Anomalous Dispersion. We have not even yet got to the bottom of this matter, however. We may obviously construct prisms of different substances, such as water or crown glass, and flint glass, of such angles that their respective spectra 1 With a single prism there is a perceptible curvature in the transverse lines or edges of a spectrum projected on a screen, owing to the conver- gence, and consequent various angles, of the rays traversing it. To get rid of this curvature in spectroscopes, is one object of the collimating lens. This brings to parallelism the diverging rays from the slit adjusted at its focus, which then traverse the prism at the same angle. IV] ANOMALOUS DISPERSION Si shall be of equal length. But if we do so we find the two spectra do not agree. There is more dispersion in one region than in another, as produced by one substance compared with the other ; and hence perfect achromatism is almost impossible with only two prisms or two lenses. Such variation in dispersive power may be elegantly illustrated by a modification of the transparency experiment described in 38. Take the bottle-cell filled with powdered glass, rendered transparent in the way there described. Owing to the variations here considered, the refractive index of the fluid can only be brought exactly the same as that of the powdered glass, for some one colour of the spectrum ; and the contents are not perfectly transparent for the other colours. Place therefore an aperture on the nozzle of the lantern, and focus it upon the screen with the loose lens ; then interpose the cell filled with glass and fluid. The image will be still focussed fairly " sharp," of the colour formed by the small range of the spectrum which is corrected ; perhaps a greenish image may appear ; the other rays will be scattered, and form a nebulous halo round it of the com- plementary colour. In some cases these differences in dispersion are very great, and Fig. 68 shows another form of direct prism for projection, FIG. 68. Wernicke's Prism. constructed by Messrs. R. and J. Beck for Prof. S. P. Thompson, on a plan suggested by Wernicke, and founded upon this " irra- tionality,"as it is called. Cinnamic ether has the same mean refractive index as one of the new Jena glasses, but is widely different for the blue and red ends of the spectrum. A prism is therefore constructed by placing a very wide-angled prism F G 82 LIGHT [CHAP. of the glass, in a cell of cinnamic ether c c, closed by rectangular glass plates. The yellow ray is undeflected, but the red rays, R, and violet rays, v, are dispersed by the second face of the prism F as well as by the first, as shown in the diagram. This prism gives very great dispersion, and much better definition than carbon bi-sulphide, while the rectangular ends are an advantage. The cost of one not quite 4 inches long is about 5/. i os. But still stranger phenomena await us, to project which with the lime-light is rather difficult (it cannot be done with less ; with the arc-light there is no difficulty), but can be accomplished by cementing into a deep glass trough, such as microscopists use for examining polyzoa, two thin glass plates A c, B c (Fig. 69) carefully made fluid- tight at the bottom and all the angles, but so that no sur- plus cement impairs the "knife-edges "of FIG. 69. Plan of Trough. . * the two side com- partments at c. Down the cell at c a strip should be carefully blackened so as exactly to cover the space occupied by the cemented edges of the plates, up to these fine edges and no farther. All the compartments are filled with alcohol ; a slit is placed on the nozzle of the lantern and a parallel beam sent through it, focused on the screen by the loose lens ; and just where the rays are most condensed the trough is placed, with the side c turned towards the lens, one end cell shaded with card, and letting the rays pass through the other cell up to its extreme edge. Now with a pipette drop into this end cell, drop by drop, a little saturated solution in the same alcohol, of the purplish-red aniline dye called Fuchsine. This arrangement is necessary to obtain the dispersion of the Fuchsine separately ; as it will be seen that the alcohol cell A c B exactly neutralizes the refraction and dispersion of the iv] ANOMALOUS DISPERSION 83 alcohol in the two end cells. If we used a prism-bottle alone, filled with the dye, with a strong solution only red rays would get through ; while with dilute solution its dispersion would be overpowered by the more normal dispersion of the alcohol. As the dye is added in this way, the colours separate from the image of the slit, as we expect ; but if things are properly managed, 1 the red occurs, not at one end of the spectrum, but between the blue and the yellow, green being absent. Other substances give similar phenomena in various degree. Though startling, however, these appearances are not really more wonderful, when we attentively ponder them, than that dispersive power should, compared with refractive power, differ at all'm various substances. Our experiment with the Fuchsine simply shows us in a more exaggerated and startling form, the very same fact whatever it is which makes the dispersion of flint differ from that of crown glass. All alike reveal the " anomalous dispersion " of light. We can no longer maintain that the colours have even an invariable order of refrangibility. This is generally the case ; but we have now found that some- times they have not. And at this stage we must pause to collect our ideas. We 1 If the dye in the end cell is made too strong only red passes : if too dilute there is no visible dispersion. The use of the double cell is, that if the first be made too saturated, the other may be tried ; and for the same reason it is well so to adjust the glass partitions, as shown in the figure, which is the actual size, that the two may be of somewhat different angles, as 25 and 35. The most brilliant jet should be employed, in order to work through as much as possible of the Fuchsine. Often the effect can be coaxed out of an apparent failure, by simply covering up, not only the other cell, but the thicker part of the one employed, so as to diminish the pre- ponderance of red light which passes through, and may drown the much fainter blue and yellow. For private observation only, two small slips of glass may be inclined at an angle of say 10 by a strip of wood placed between them at one edge, and a drop of strong Fuchsine solution placed between them. Through this prism a brilliantly-lighted slit may be ob- served from a good distance ; and through such a small thickness even a solution strong enough to overpower the dispersion of the alcohol will allow sufficient of the colours to pass. 84 LIGHT [CHAP, iv might account for reflection by a rough working hypothesis, which for years was more or less accepted, and was known as the Emission or Corpuscular Theory of Light. But even then we found difficulties in it. These are now vastly increased in many ways ; and we find ourselves once more, by the mental constitution bestowed upon us, bound to ask the question : What is Light ? We must frame some intelligible hypothesis by which we may string together the foregoing facts ; and which if possible, may also account for such phenomena as we may yet further discover. This, then, will be the subject of the following chapter. CHAPTER V WHAT IS LIGHT? VELOCITY OF LIGHT. THE UNDULATORY THEORY Light has a velocity Velocity implies Motion of some sort The Emission Theory Transmission or Motion of a State of Things Transmission of Wave Motion Illustrations Wave-motion and Vision Analysis of Wave Propagation The Ether Refraction according to the Wave Theory Total Reflection, Dispersion, and Anomalous Dispersion Mechanical Illustrations. 6 1. Light has a Velocity. If a man strikes a bright light, say ten miles off, we see it so instantaneously, that it is very difficult at first not to believe that we are, in some mysterious way, conscious of it the very instant it happens that time has nothing to do with the matter. And that was probably the most ancient idea of the manner in which we " see " things. But this idea was necessarily abandoned for ever, after a discovery made by Roemer in 1676. He found that, taking the calculated time for the eclipses of Jupiter's satellites, they always took place eight minutes earlier when the earth was nearest to them, and eight minutes later when it was farthest away ; whilst if the earth was at either of the mid-points, they happened at the average time. He very soon drew the una- voidable conclusion, that light required about a quarter of an hour to cross the earth's orbit. This was soon after confirmed by Bradley ; who calculated the very same velocity independ- 86 LIGHT [CHAP. ently, as nearly as could be, from the apparent " aberration " of the fixed stars. At a later period the velocity was actually measured in- strumentally ; first by Fizeau and Foucault, later by Cornu, since then by Professors Young and Forbes in Scotland, and Professors Michelson and Newcomb in America. The methods have been chiefly two. In Fizeau' s method a ray of light is sent between the teeth of a toothed wheel to a distance of a few miles : and thence reflected back in the same path. If the wheel is rotated with a sufficient velocity, it is plain that while the ray has been journeying and returning a tooth instead of a space will have come to occupy its re- turn path, and produce eclipse of the reflected ray. This FIG. 70. Fizeau's Experiment. effect must be gradual as the velocity is increased, as in Fig. 70, till total eclipse is produced ; after this, if the velocity is further increased, the light will gradually reappear, to be again eclipsed ; and the velocities of the wheel being known, the various eclipses will mutually check each other. Professors Young and Forbes thought that their experiments revealed the extraordinary fact that in air the velocity of red light appeared considerably less perhaps one per cent, less fhan that of blue, which if correct would involve the possession by our atmosphere of an extraordinary amount of anomalous dis- persion ; but Michelson and Newcomb, using a slit half covered with red glass, could not discover any such phenomena. v] VELOCITY OF LIGHT $7 In Foucault's method, a ray of light, after passing cross- wires to serve as an image-point, proceeds any convenient distance to a mirror very swiftly rotated. It is thence reflected to a concave spherical mirror whose centre of curvature is the axis of rotation of the revolving mirror at the point struck by the ray. The ray is therefore reflected back in its own path to the rotating mirror ; and if this is at rest or rotated slowly, it is again reflected in its original path of incidence, centrally upon the cross-wires. But when the velocity is sufficient, the mirror has rotated through a small angle while the ray has travelled to the concave mirror and back ; and the return ray is there- fore deflected to one side of the cross-wires through an angle double that of the rotation of the mirror ( 24). This apparatus is so sensitive as to be applicable to distances of only a few feet ; and hence, by interposing a tube filled with water between the two mirrors, Foucault was able to prove absolutely that the velocity of light was considerably less in water than in air. All these methods give the very same velocity for light within quite a small percentage, much less than might have been expected in measuring such enormous velocities. The determination by Professors Young and Forbes is 187,200 miles per second, by Professor Michelson in 1882, 186,278 miles, and most recently of all by Professor Newcomb in 1884, 186,282 miles, the probable error not exceeding twenty miles. 62. Light must be Motion. The velocity of light once proved, involves another point. Observe the absolute necessity of the case. At the moment one of Jupiter's satellites emerges from behind the planet it sends out, some, how, a ray of light whatever that may be. At a given moment that ray from the planet P has reached the nearest point A of the earth's orbit. A quarter of an hour later it has reached the farthest point B. In the interval, something or other has passed from A to B. That passage of something from one point to another is obviously motion ; and the con- 88 LIGHT [CHAP. elusion that Light is Motion of some sort is an absolute intellectual necessity : there is no possible escape from it. It FIG. 71. Light necessarily Motion. only remains to discover what the motion consists of, or what it is that is moved. 63. The Theory of Emission. The emission of very fine particles from the luminous body was, as we have said, the most natural idea ; and it may be made to account for reflec- tion, though encompassed even at that point with considerable difficulties. One of these we have considered already ( 30) ; but it might be supposed that the luminous particles, to be seen, must actually enter the eye, and impinge upon the sensi- tive retina. But we have another and a greater difficulty, in the enormous momentum even the smallest particles must have, travelling at such enormous velocities as have been proved in the case of light. The weight of one grain would be equal in momentum to a large cannon ball as shot from the muzzle of a gun. Further still, what must be the expulsive force to produce such a velocity? And lastly, it is impossible to conceive of this expulsive force, and the velocity imparted, being the same for the largest and the smallest of all sorts of bodies, as is found to be the case. The feeblest candle-flame emits light at the same velocity as the enormous sun. These difficulties might be partially evaded by supposing that the particles are so infinitely small, or otherwise so utterly different from common matter, as jto have no relations of v] CORPUSCULAR HYPOTHESIS 89 attraction with it ; and, indeed, otherwise the propulsive or luminous body would, by its own attraction, gradually destroy the velocity, just as the earth gradually draws back a stone thrown up from it. But when Newton, who provisionally adopted this as a working hypothesis, though often leaning towards another next to be 'considered, sought to account on such a basis for some rays being refracted while others were reflected, the only way he could do so was to suppose that some particles reached the reflecting surface in a repulsive " fit," others being attracted. He was confirmed in this by the "law of sines." Versed in the mathematical laws offerees, so that at times he almost thought in mathematical terms, his keen eye saw at once that this peculiar law was a law of velocity ; and he suggested, therefore, that the refracted ray was dragged down or attracted by the glass or water, and had its velocity augmented in the proportion of the " index of refraction." As is rather general in algebra, this proportion, equally with the reverse, accurately works out many optical problems. But it would follow that the particles are attracted by matter ; and how, then, they can be projected with a velocity that never diminishes over stellar distances, is simply inconceivable. Finally, as we have seen, it has been proved rigidly, that the velocity of light is less instead of greater in the water than in the air. In absolutely proving this fact, Foucault and Fizeau absolutely overthrew the Corpuscular Theory, and that idea of the " motion " of light. We have therefore to explain in some better way why light is refracted ; why at certain angles it cannot get out into a rarer medium, but is totally reflected ( 35) ; and finally the strange phenomena totally unknown to Newton of anomalous dispersion ( 60.) 64. A State of Things may be Transmitted. Let us consider now another idea. 1 In Railway and Post Office we 1 For the idea of this paragraph, the simplest and most effective I have met with for illustrating what follows, I ought to acknowledge my indebted- ness to Mr. J. Norman Lockyer, F.R.S. 90 LIGHT [CHAP. have a very familiar example of actual Things being sent from one place to another, or from a sender to a receiver, at a given measurable speed. That may answer in many respects to the old Emission Theory of Light ; and it is to be remembered that even in this case we must have some road or channel along which the sent Thing may pass, if it is not to be projected like a cannon ball. But let us think for a moment about a telegraph message. To quote Mr. Lockyer, here also " two instruments may be seen, one the receiving instrument, the other the sender. Between the office in which we may be, and the office with which the communication is being made, there is a wire. We know that a Thing is not sent bodily along that wire, as the goods train carries the parcel. We have there, in fact, a condition of motion with which science at present is not absolutely familiar : but we picture what happens by supposing that we have a state of things which travels. The wire must be there to carry the message ; and yet the wire does not carry the message in the same way as a train carries the parcel. It is further remarkable that the wire carries the state of things along, very much quicker than the train can move in fact, with a velocity commensurate with that Light itself." 65. Wave-motion and its Transmission. Let us examine experimentally, then, another kind of actual motion. Make a large groove in a piece of board, or a light trough like Fig. 72 about a yard long, in which some elastic balls may roll ; glass balls, or ivory bagatelle balls, will answer. First roll one slowly along: we can measure the considerable time it FIG. 72. takes to go from one end to the other. Now place in the trough a set of 1 8 balls in contact ; and drawing back one for some inches, roll it up to the rest at the same slow speed as before. Observe the difference. Instantly^ to all appearance, the farthest ball now starts off as the first one strikes the row. It is not really so, for the v] WAVE MOTION time can be measured by proper appliances ; but the eye cannot discern any interval. Now this is wave-motion, of one sort. The first ball struck is compressed, and then expands, so passing on the com- pression ; and thus to the last. Each ball executes or has impressed on it small periodic movements exactly like those of its preceding neighbour, but a very little later in time. That is the entire essence of wave-motion ; which may be of many forms, but with this property common to them all. In the lantern we may illustrate this as in Fig. 73. Between two glass plates the size of the ordinary lantern slides, are cemented pieces of wood shaped to gentle curves as in the figure, of a thickness to just allow small balls of glass or ivory (or small steel balls from bicycle bearings will answer very well) to roll easily in the channels for them. In one, let a row of these balls rest, leaving the other clear. From the top of each slope let roll one of the balls. The one screen : the motion in FIG. 73 Slide or Rolling Balls. will be seen travelling across the the other case will appear to be transferred instantaneously to the last ball in the series. In a pond of still water, or in the middle of a circular sponge-bath filled with water, drop some small body, and study the beautiful phenomena. The spot into which the object fell is surrounded by a circular wave of water, which travels quickly outwards. This apparent motion is again very much quicker than any actual motion we could impart to the mass of water itself. It looks, too, as if the water were really proceeding outwards being poured out as it were from the central point. But if we drop one or two bits of paper on the water, we find 92 LIGHT [CHAP. it is not so : the paper only moves up and down. It has a very slight horizontal motion also it is true, but this too is not continuously outwards, but to and fro. In reality the paper at any point moves in an elliptic orbit ; but each particle moves in a similar orbit to its predecessor, a little later in time. Any one particle does not travel outwards, but sets in similar motion the next particle, and thus the state of things we call the wave is propagated. .It can be seen immediately, that if the motion of light be anything of this kind, we have got rid at once of our greatest difficulty, that of the enormous velocity ; for wave-motion is always much quicker" than actual translatory motion. Across a deep open sea like the Indian Ocean, the great tidal wave moves at the rate of 1,000 miles per hour, though the water itself could move at nothing like it. In fact, if we can only find the idea otherwise fits the phenomena, we have got rid of nearly all our difficulties at a step. We therefore trace the matter further. If the balls just now referred to were tied together by elastic threads, we should have a return wave from the last ball, since it would be sharply pulled back in its effort to escape. We have all seen this in an engine run up against a train, when each carriage or truck vibrates several times to and fro, giving us a picture of such waves in any elastic medium, such as sound- waves in air. These last give us our best example of this form of wave. In this case every particle of air moves to and fro in the direction of the wave, but otherwise keeps its own place ; and still the wave only, and not any particle of air bodily, moves onward. The fundamental property which characterises all true wave-motion is in this case difficult to picture clearly in the mind : but it is so important to do so, that we again have recourse to our lantern, which will place it before our very eyes. Get a circular glass plate, 13 or 14 inches diameter, mounted on an axle which can be turned. Exactly in the centre of the axle-hole describe a circle inch diameter v] CROVA'S DISC 93 and divide it. into 12 portions, as in Fig. 74. (It is near enough to divide off into six by the radius, and bisect each division by the eye.) Arrange all firmly on a table, and having blackened the disc all over, take a foot-rule divided into eighths as a standard, and with a 3-inch radius strike or scratch a circle from say the top division. Extend the compasses exactly |th inch and strike another from the next division ; then FIG. 74. FIG. 75. Crova's Disc. another th inch, and so from the next division in the same direction, and so on, till we have gone twice round the divisions and struck 24 circles, giving us a band of scratches 3 inches across, with a little margin outside. (See Fig. 75.) Remove the objective and place on the flange-nozzle of the lantern a cap with a fine horizontal slit A B, 3 inches long, or a glass cap with a line scratched in black ; and arrange the disc 1 in front of this, so that the band of circles crosses the slit as in Fig. 75. In front of all adjust the loose focusing lens, and focus on the 1 It is known as Crova's wave-motion disc. 94 LIGHT CHAP. screen. On now revolving the disc we see a " wave " of alternate compression and expansion beautifully delineated in actual motion : and by keeping the eye on any one bright dot, the precise nature of the motion will be understood better than by all the description in the world. 1 For reasons future experiments will make clear, the vibra- tions which constitute light are, however, to be considered as in one respect like those of water-waves, i.e. across the path of FIG. 76. FIG. 77. Wave Slide. the wave, not in it. A disc with a wave-line round it like Fig. 76, will give a moving image of this if revolved across a black- ened glass cap scratched with perpendicular lines all over ; but a better way is to make a " slide " as in Fig. 77, consisting of a fixed blackened glass, A, in front of which are open grooves, B B, the whole length, for a panoramic glass, 18 inches long, to slide freely. The slide is kept together by a slab of wood, c, in which is an aperture for the blackened glass. On the blackened glass scratch perpendicular lines ~ of an inch apart. On the long glass, also blackened, a single wave-line may be 1 The private student may draw the lines pretty thickly in black on a white card, and revolve the card under a slit cut in another card. v] A WAVE-SLIDE 95 scratched ; but in order to show the interference of waves at a later stage, it is better for the sliding-glass to be in three widths, kept edge to edge by a thin brass binding at each end, and \vitl\f0ur sets of waves as in Fig. 78, one pair twice as long as the other. The centre strip has a wave of each length ; then by drawing it along through the binding the length of the short wave, it can be shown as drawn below, how the same given retardation brings the short wave a whole vibration, and the long one half a vibration, behind their fellow waves. It will be evident that when the whole arrangement is placed in the FIG. 78. Movable part of Wave Slide. ordinary lantern-stage and focused, and the sliding part moved along, we shall have moving waves of white spots. 1 Now it is to be again carefully noticed, that here also no spot advances at all. Every spot simply moves up and down, while the wave-form only advances across the screen, being due, as before, to the fact that each spot, representing an atom of ether, moves a little later than its predecessor in a similar path. Thus we see that, by this kind of mechanism (actually proved to exist in the case of the ivory balls, sound, and 1 This slide was the result of much consideration ; and after trying both, I consider it much superior in effect to the disc usually employed, besides being much more easily made and adjusted. 96 LIGHT [CHAP. countless other motions), motion imparted at one end of a line of transmission is yielded up with enormous rapidity at the other, not only without any inconceivable motion between? but whilst things generally between the two ends, as in the case of our ivory balls, may almost seem to be in a state of rest. 66. Wave Motion and Vision. It is not difficult to conceive how such wave-motion as that shown by our slide may affect the eye. We can easily imagine how longitudinal pulses of air beat on the drum of the ear D, as in Fig. 79 ; and if we imagine the retina to be furnished, as at R, with perpendicular rods standing up like a cat's whiskers, we can readily conceive how the transverse motion i of the last particles in the ^^* wave should excite these. Those who are so happy as '^55^ to possess whiskers, can 1 1 II llllll 11 Mill easil y P rove b y experiment csk^zzizzzaR that a brush across them FIG. 79 . Sound Waves and Light Waves. yields more sensation than perpendicular pressure. Now it is remarkable that microscopical researches do show the retina to be studded closely with fine rods ; and it appears pro- bable that this is the true method of vision, or at least, that by which the optical image on the retina is transformed to con- sciousness in the brain, upon which our " seeing " Light as Light obviously depends. Several future experiments will lend much strength to this view ; and another weighty confirmation of it is found in the well-known fact, that pressure on the eye- ball produces the sensation of light. 67. Analysis of Wave Propagation. We have not solved all the problem, however. If light consisted of particles emitted, or if even wave-motion were only propagated in radial lines from each centre (and this is how some people quite erroneously understand the Undulatory Theory), it will be ANALYSIS OF WAVES 97 obvious that as the distance increases, the radii must separate as in Fig. 80, and we should have spaces between them with no wave-motion. Yet we see an unbroken circle of waves in our pond; how is this? Figs. 81 and 82 supply the answer. In Fig. 8 1 let us consider a wave direc- tion, A B, from the luminous centre A, and suppose the wave arrived at the particle B, The next particle in the same line to receive the motion will be c. But c only re- ceives it because it is the next particle ; and obviously the next particles D and E are just as near, and in the very same kind of con- tact ; they ought also to receive the motion. They do, and the consequence is that every vibrating particle over the whole sphere surrounding the wave-centre be- comes a new centre like B for another sphere F G. In Fig. 82 let us consider the waves from the centre L to have reached the circle M N. Every point in this circle sends out fresh circles of waves, shown on the curve o P. Analysis, how- ever, shows that all these secondary waves destroy each other by mutual interference (see Chap. IX.) ex- cept in the grand circle o P, where they reinforce each other ; and thus the curve o P remains, as in a pond, the grand " front " of a collective or main wave. If, however, we interpose a screen, at o o' P P', which stops this main wave, then the sub- sidiary waves which go to make it up are only partially H FIG. ST. New Centres of Wave-Motion. 98 LIGHT [CHAP. destroyed by interference, and appear at R s, as in the diffrac- tion fringes hereafter to be seen ( 113). Most of the diffi- culties found in comprehending the wave-theory are entirely owing to not understanding this "construction " of the waves ; and it is hardly too much to say that while, on the one hand, any apparent objection that can be brought against the Undulatory Theory applies with equal or more force to any other theory; on the other hand, any rays, when isolated and studied by themselves in detail, be- . 82. have exactly as the theory would lead us to expect. The correct analysis of these details of wave-propagation is originally due to Huygens. 68. The Ether. If, however, waves are sent from distant stars to our eyes, and elsewhere, there must, as in all the pre- ceding cases, be some medium through which they are pro- pagated. We know by experiment on other wave-propagations, such as those of sound, the general properties such a medium must have ; since it is found that the velocity of propagation is directly proportional to the square root of the elasticity of a medium, and inversely as the square root of its density. This has been proved by rigid experiments in many gases ; so that, for instance, the velocity in hydrogen, a rare gas, is much greater than in air. The enormous velocity of light-waves, therefore, is only possible in a medium which is almost in- finitely elastic, and at the same time almost infinitely rare ; and yet which is not quite so (or time would not enter into the question of distance at all) but has a definite proportion between these two functions. It cannot be attenuated air, but must be something far more rare ; since we can keep air out of a glass vessel, while light passes through glass and many bodies, and v] THE ETHER 99 through the best vacuum we can form ; moreover we know that air absorbs or stops light considerably, and hence light could never reach us, through the rarest atmosphere, from the enormous distances of the stars. Still further, attenuated air could not give us those definite velocities with which we have to deal, but must give a widely different one from that in denser air ; nor finally, is the proportion of its elasticity to its density anything like great enough. We have therefore to conceive of some still more rare and subtle medium which fills all space, and which is called the Ether. We shall hereafter see that we are obliged to attribute to it other physical properties quite different from those of an atmosphere. 1 But though this ether easily permeates all we call matter, it is easy to conceive of its particles, and those of matter, hinder- ing and otherwise acting on each other, or communicating motion to each other. Wind passes freely through a hedge of trees ; but still the trees hinder or " slow " it, while yet again the wind moves the trees ; and conversely, if we could shake the trees, we should cause a wind. Such, in brief, is the conception or hypothesis of the ether as held by physicists. 69. Explanation of Refraction. Refraction now is easily explained. Any beam of light, as we have seen, has a main wave-front across if, and it is obvious that in meeting any refracting surface obliquely, one part of this wave-front will meet it before another. Conceive, then, that while the ether permeates the open structure of all matter, it is still hindered in its motions by it, as the wind is hindered, but not stopped, by the trees. Then trace a beam A B (Fig. 83) to the refracting surface c D, marking off any assumed length of its waves by the transverse lines. The front will be retarded at E before it is retarded at F, and we will assume the retardation to be such 1 Some attempts have lately been made to dispute the existence of an ether (see Phil. Mag. April 1879, and July, 1881). The objectors have not borne in mind the essential physical necessities of the case. H 2 ioo LIGHT [CHAP. that the wave from E in the denser medium is only propagated to any shorter distance G, while in the rarer medium it travels from F to H. It is plain the beam must swing round ; but when the side F also reaches the denser me- dium, the whole will be retarded alike, and the -i D beam will proceed as be- fore, only slower and in a different direction. The theory so far exactly fits the phenomena ; and when FIG. 83. Refraction. we come to polarisation it will be easily seen why the beam is divided, and part reflected while part is refracted ( 129). 70. Total Reflection Explained. Total reflection can be explained by mathematical analysis, and is so explained by Airy, while it is impossible to explain it by any other theory that has ever yet been framed. Airy shows that, beyond a certain angle, no main w r ave can emerge, while the small secondary waves perish immediately by interference (Chap. IX.). 71. Dispersion Explained. The different refrangibility of different colours is easily accounted for. According to both Emission and Undulatory theories the measurements agree ; and those who believed the Emission theory, had to consider the red particles as larger or stronger than violet ones, as we have to consider violet waves only half the length of red ones. But as all colours of light seem to move with equal velocity in ether, violet waves must make two vibrations for each one of red. If, then, the vibrations are retarded at all in a refracting medium, on the face of things those which occur twuce as often will (as a rule) be hindered most ; they have more of the hindered motion to perform, and, therefore, must be more re- fracted, provided there be nothing so peculiar in the arrange- v] ANOMALOUS DISPERSION -ci ments of the molecules which retard them, as to affect them otherwise. 72. Anomalous Dispersion Explained. But there may be relations in the retarding molecules of matter which do affect the ether-motions peculiarly, and so cause " anomalous " dispersion. We cannot suppose that the lengths of the waves for each colour preserve under all circumstances a uniform proportion ; for we have not only seen they do not, but our very theory of refraction is based on the supposition, that the wave-lengths are shortened by retardation in a refracting medium. The only supposition possible is, therefore, that the number of vibrations per second, or their time period, is the determining constituent of colour, as it is of musical notes ( 81). Now we shall find strong presumptive proofs hereafter ( 84) that the mole- cules of different bodies, like small pendulums of given lengths, have in fact their fixed and proper time-periods of vibration. And we can thus very easily conceive how certain relations of these respective periods to each other, or of the lengths of the waves to the distances between the molecules, should cause molecules of matter to hinder or assist in very various degrees, the differing periods of vibration in the ether-waves. Cauchy has even shown mathematically, that dispersion at all, or the fact of different colours being differently refracted, can only be explained if the distance from molecule to molecule be fairly comparable with the length of the waves. (See 121.) An analogy may make this clearer. Imagine a line of soldiers marching across a hard common. On reaching a piece of heavy ploughed ground, their steps (representing wave-lengths) would be retarded and shortened. Imagine also a line of little children it is easy to understand that on the hard ground they might keep up with the men easily. On reaching the heavy ground they too would be retarded, and probably retarded more than the soldiers, their shorter and feebler steps thus representing the greater retardation in most substances of the shorter waves of light. But when at the sea-side some ,C2 LIGHT [CHAP. years ago, I happened to notice that on a particular piece of shingly beach my little boy was actually retarded or hindered in his pace less than I was there was something in that piece of beach which somehow hindered less the period and weight of his steps. Just so the molecules of some substances may be of such sizes or at such distances, that they are specially favourable or unfavourable to waves of certain character, as in anomalous dispersion. 73. Mechanical Illustrations. We may illustrate prac- tically many of these points by mechanical means, due to German ingenuity. 1 Though not "lantern" experiments, they are easily seen by a whole class, and vividly illustrate the subject. We are dealing with motions^ supposed FIG. 8 4 . to be in free ether equal at any two points of a wave-front exactly trans- verse to the direction of the ray. It is obvious this is a purely mechanical problem, and that we may mechanically represent it with fair accuracy by two equal wheels revolving freely on two ends of an axle, and left to roll down a slightly inclined board. Let Fig. 84 represent such a pair of wheels, the axle being made of |-inch iron, turned down at the ends to about J inch, on which revolve freely but accu- rately boxwood wheels about 2 inches diameter, with rounded rims. These dimensions were found best by Mr. Tylor. It is obvious that while rolled along the smooth board such an apparatus will preserve one 1 Described by Mr. Tylor in Nature, Jan. I, 1874. \\ \\ i 1 \ c l\ \ \ \ FIG. 85. MECHANICAL MODELS 103 direction. But referring now to Fig. 85, let there be glued on the board a rectangular and a triangular piece of the thick pile plush called "imitation sealskin." If this is presented to the wheel-track the right way of the pile, it will retard the motion considerably, and when the track A B is oblique, the wheel that first meets the plush being first hindered, the track will swing round to the direction B c, and on leaving the plush resume the track c D, exactly pic- turing the course of a ray of light through ^,. a thick piece of glass. The triangular piece in the same way represents a prism, the track E F being refracted to F G, and thence to G H. Nay, even dispersion may be thus pictured by having a second pair of wheels, s (Fig. 86), of smaller diameter, to represent shorter waves say ij inches to i J inches. These wheels will be found perceptibly more deflected fronTS F to the track F K. The wheels may either roll freely down a slight incline, or may be held back by a thread at the centre of the axle. Finally, total reflec- tion may be illustrated as in Fig. 87, for it will be found that if the track A B leaves the edge E F of the velvet at a certain angle, the wheel c, which first emerges, gains so much on the one still upon the velvet, that the axle swings right round and proceeds on the track B D. These illustrations will sufficiently enable us to grasp the main points of the wave theory. Some other points will arise later on ; but we shall now resume the experimental study of colour. CHAPTER VI COLOUR Absorption of Colours What it means Absorbed, Reflected, and Trans- mitted Colours Complementary Colours The Eye cannot judge of Colour Waves Mixtures of Lights and Pigments, and their Difference Primary Colour Sensations Not the same thing as Primary Colours Colour as we see it only a Sensation Experiments showing merely sensational Colour Doppler's Principle. WE have now cleared the way for another class of experi- ments, for which, to work with comfort, we must somewhat alter our arrangements by removing the objective, and placing on the flange-nozzle of the lantern a black card or other cap with a perpendicular slit cut in it rather longer than we have hitherto worked with say J inch to -f$ inch wide by i^ inches long. 1 A long slit, owing to the convergence of rays by the lens, gives a perceptible curvature across the spectrum band ; but this need not matter to us. Arrange the loose focusing lens F (the one of longest focus if there are two) so as to focus the slit on the screen. The lantern must then be deflected, as for all prism work (unless a compound " direct " prism is used) and adjust the prism p otherwise as before. The whole arrange- ment is shown in Fig. 88, and its object is simply to produce on the screen the spectrum of a slit upon which we can more readily make various experiments. We require throughout the experiments in this and the next 1 A brass cap with adjustable slit is, of course, much more convenient. CH. VI] SPECTRUM ARRANGEMENTS 105 chapter to have the most brilliant spectrum we can get, especially whenever a narrow slit is necessary. To secure this we converge light upon the slit, by arranging the latter at the focal point of either a cylindrical or spherical lens. This can be mounted in a wooden frame, so as to go in either the ordinary slide stage, or the stage of the optical front when that is used, choosing a focus which will converge the parallel or already slightly convergent rays from the condenser, upon the slit. The converged rays will of course diverge again after passing the slit ; but the focusing lens will collect them. Such an arrangement is not absolutely needed, but greatly adds to the brightness of the spectrum. 74. Absorption of Colours. Providing now some coloured glasses, or some strips of coloured gelatine between FIG. 88. Spectrum Work. glass plates, we make some experiments which teach us a very important lesson. We are apt to think that the sunlight which comes through a red glass window is all turned into red made red. Well, there is the spectrum of our complete or white light on the screen, drawn out into its constituent colours. Over half the slit hold a bit of the red glass; if the light, or io6 LIGHT [CHAP. most of it, is really "reddened," all the spectrum ought to be turned into red. It is no such thing, however. There is no colour in the spectrum of the glass, where that colour does not exist in the ordinary spectrum ; the sole effect is that certain colours are cut out, or absent. We get the colour, as so often before, by suppressing colour. If the glass is a pretty pure red, only red, and a little orange, A B, is seen in the spectrum of the half slit covered by the glass ; all the rest is cut away. So of all the other gelatines or glasses, but we soon find it is very difficult to find a pure colour ; generally there are left, at least, two well-marked colours ; and if we unite just those portions of the ordinary spectrum, by employing proper slits in proper places, and uniting the colour passing through them by our con- fectioner's jar, or a cylindrical lens ( 54) we get the same colour as the coloured glass. We see, therefore, that in passing through a transparent body, its molecules take up or absorb the waves of certain periods, and the remainder passing through give the colour of the body. This is not at all difficult to understand. We have supposed every matter-molecule to have its own period of vibration (see next chapter) ; or perhaps more often several periods, as it seems probable most molecules are complex. These molecules can freely communicate any vibrations to the ether-atoms, but conversely it must be different : the matter- molecules can only take up synchronous vibrations. That one tuning-fork will communicate its vibrations to another of the same note we know ; and we also find that when thus giving up its motion to the second, it loses its own more quickly than a fork that does not. A fork mounted on a unisonal reson- ance-case sounds louder, but stops sooner, than one un- mounted : it has been imparting its motion to the unisonal column of air, and in so doing exhausts its energy. See then what must happen. If waves which produce red sensations require vibrations of 450 million millions of times in a second, and such rays pass with others through matter whose molecules VJ] ABSORPTION 107 vibrate at that rate if set in motion, these molecules must take up or absorb those particular vibrations from the ether, and the rest passing through give a colour due to the residual rays in this case green. We shall examine tests of this theory presently ; but mean- time, however absorption is produced, many other experiments will show that the colour of our glass is produced simply by the absorption of certain colours. Throw a good long spectrum on the screen through two prisms if the light is powerful enough and provide some large squares of the coloured glass or gelatine. Say we have a red one. Walk up near to the screen and hold the square in the hand by one corner in the red rays ; it stops these very little, or is " transparent " to red rays, which it permits to reach the screen. Move the glass along in the spectrum, however, and gradually we find it casts more and more shadow, till at last the shadow is black ; the glass is absolutely opaque to such colours of the spectrum ; it absorbs them all. We soon find also, that as absorption increases, not only the shade, but what we call the " colour " itself, often changes, more and more of the spectrum being cut out ; as indeed we should expect. With marine glue cement together a few glass troughs, of plates about 4 inches square, and tapering from % inch to 2 inches apart. Make solutions of chlorophyll (green leaves in alcohol, pretty fresh), permanganate of potash, picric acid, ammoniated sulphate of copper, oxide of copper in ammonia, and bichromate of potash. Try first the chlorophyll. The thin end cuts out all the blue half and some bands in the red end ; pass to the thick end of the same, and the light transmitted is probably only the extreme red. A very few experiments of this kind with other solutions will show how wonderful are the powers of this "spectrum analysis," for such it is, and how complex are most of the colours of natural bodies ; and will prepare us for the further details of the next chapter. 108 LIGHT [CHAP. 75. Absorbed, Reflected, and Transmitted Colours. But meantime a further lesson of the same sort. We should expect from the foregoing that colour transmitted through bodies, would often differ considerably from colour reflected by them. A red glass, since it absorbs the green and blue and transmits the red, reflects hardly any, and appears by reflected light almost black, as do some other colours. In some cases the colours reflected and transmitted are nearly complementary ( 76), but seldom quite so ; because even reflected light has penetrated some distance among the mole- cules of a body, and thus been partially subject to their absorbing influence, or had certain vibrations taken up by them. Two very simple and pretty examples will sufficiently illustrate this. Place a single film of gold leaf smoothly between two glasses 2\ inches by 4 inches, and bind round the edges to save from injury ; or place it between two discs of glass mounted with putty in wooden frames that size. Deflect the lantern at right angles with the line to the centre of screen, throw the light on the gold leaf 1 at 45, and focus it with the loose lens on the screen ; we get the yellow reflected image. Now place it in the optical stage, direct the lantern to the screen, and focus : we get a transmitted green image. Take, again, a clear glass, and another blackened at the back ; and cover each with a film of any red ink which owes its colour to aniline dye. When dry, place in the optical stage the clear glass : it transmits a fine red image. The blackened one reflects (when treated like the gold leaf just now) a beautiful yellowish green image. And the clear glass illustrates the usually compound nature (i.e. partly transmitted through a portion of the substance and so partially absorbed, and partly reflected) of reflected light, by giving a reddish orange image. We can easily prove by experiment that the colours we see 1 In focusing such surfaces by reflected light, all the light from the nozzle should be concentrated on the surface, and some small mark, such as a black dot, sharply focused on the screen with the loose lens. vi] COMPLEMENTARY COLOURS 109 in natural objects are chiefly residuals left after this internal absorption, or are colours to which the bodies are transparent. Get any flower which shows a full green leaf, and rich red petals in largish masses, such as a tulip ; and we soon find we cannot " see " its colours, unless they are either placed in white light, or in the appropriate colours of the spectrum. Throw once more on the screen the prismatic band, and move along the tulip in its rays. In the red rays the red flower shines bright red, and the leaves possibly dull red (owing to the peculiar spectrum of chlorophyll, which transmits the extreme red as well as the green). But as we move it along the red becomes black, and the green changes also, precisely as the spectrum did when we cast upon it the shadows of our coloured glasses. Highly coloured chromo-lithographs, moved along in the spectrum, yield very instructive phenomena of the same kind. As mentioned presently, two superposed cells containing acid copper sulphate and potash bichromate, allow a pure green only to pass ; and by this light a drawing executed in red and yellow chalk appears black. 76. Complementary Colours. We have found that we make white light by compounding together all the colours of the spectrum ; but we have also found that we may produce white with much less ; for in the experiment with seven little mirrors ( 54), many of the prismatic rays were of necessity omitted. We carry this method of experiment further, and arrange our prism as before, with either a cylindrical lens (or the water-jar as such), or a large bi-convex lens J so focused as to re-form a white image on the screen. Now prepare two black cards with slits \ inch wide and \\ inches long, and insert them, as in Fig. 89, in a strip of blackened wood, with a saw-cut in it, so that we can slide and adjust the slits at variable distances : provide also two other pieces of card by 1 A lens 6 inches diameter and 14 or 15 inches in focus is excellently adapted for such experiments as this, covering with card or paper all but a horizontal band 2 inches wide across its face. no LIGHT [CHAP. which these half-inch slits can be narrowed to any less width required. Introduce this just at the back of the re-uniting apparatus, and, first covering up one slit, arrange the other so that only the blue rays pass through it, giving, of course, a blue image. Next, uncover the other slit, and carefully sliding the second card to and fro, we can find a position (somewhere in the yellow or orange-yellow) and a proportionate width of the two slits, which again makes the image white. Continuing these ex- periments with other colours, we find that for almost any colour near one end of the spectrum, there is another towards the other end which, with it, makes white, and is accordingly called its " complementary colour." And notice that we can do this with our really "pure " spectrum colours. It is not as in a former experiment ( 52), when we divided the whole spectrum by a wedge-prism into two coloured images ; for those two colours really were themselves compounded, and between them contained all the coloured rays. But here two single colours make white ; and hence we learn that we may have a white, undistinguishable by the eye from any other white, which will not, on prismatic analysis, yield more than two colours. We may, by continuing these experiments, find that a white may be compounded of three colours, or of more. We never get a white unless there are waves of more than one period ; but either white, or almost FIG. 89. Slits for Complementary Colours. vi] PIGMENTS in any colour, may be compounded out of various con- stituents. 1 77. The Eye unable to judge of Colour Waves. Now this is another cardinal, fundamental fact. It teaches us a wonderful truth, which still more remarkable experiments will confirm : viz. that colour and light, as we see them, are not only purely matters of sensation, or subjective consciousness ; but that this consciousness is easily deceived, and quite incapable of distinguishing between whites and colours very differently constituted. We cannot tell " by the eye " that the blue-yellow white differs from seven-colour white ; nor can we tell by the eye that a compound blue, containing nearly one-half the whole spectrum, is different from a pure spectrum blue, which may be of the same apparent shade. 78. Mixtures of Light and of Pigments. And there is another strange thing. The old artists always considered that blue and yellow and red were " primary " or simple colours, and that blue and yellow made green. But here are blue and yellow, and instead of making green, they make white ! How is it they ever make green ? To solve the question, we fill one of our glass cells with solution of picric acid apparently a pure yellow and hold it in front of half our slit, as in previous absorption experiments. It allows not only yellow to pass, but nearly as much green, absorbing all the other rays. We take a rich blue glass, and analyse that in the same way. This apparently pure blue allows blue, and as much green, to pass, absorbing nearly all the rest. This itself is strange enough that when we add green to both blue and yellow we should be unable to detect it by the eye. But it is obvious now that if we place both colours in the path of the beam, one after the other 1 A slit in the red, one rather wider in the green, and a broad band in the violet, will give a white of three colours. A rather narrow slit in the red, and one double the width in greenish-blue, will give a white of two colours. A narrow slit in orange-yellow (just the red side of the D line) and a rather broad band in full blue, also give white. ii2 LIGHT [CHAP. the yellow solution will stop the blue rays which get through the blue glass, and the blue glass will stop the yellow ; but both allow the green to pass, and the net result is therefore that colour. It is the same with powders and paints ; the light penetrates some little distance among their particles ( 75), and is absorbed in the same way ; and the green we get is the survival, or net result after the absorption by both, mixed with some white light reflected unchanged from the outer surface. But get another lantern, or use both nozzles of the biunial if such is employed, and place the ordinary objectives on both. Place in the ordinary slide-stage of each a black card, with an aperture which shows, say, a 2-feet disc on the screen ; arrange that the two discs partly overlap, and hold in front of each objective one of the same two colours, or the blue may be a cell of the sulphate of copper. In this way, it is obvious that instead of the light on the screen being the remainder of two successive subtractions or absorptions, where the discs overlap it is the light from both colours added. And the result now from these two same colours is not green, but white. 1 Analogous effects may be shown with a good grass-green glass, chosen by trial, and the beautiful purple solution of perman- ganate of potash. As some may still have difficulty in realising that successive absorptions are the real cause of our ordinarily getting green by combining blue with yellow, or orange-yellow, we may make another striking experiment, which would seem to be a crucial test. Our previous blue and yellow allowed green to pass through each, as shown by spectrum analysis, and therefore green was what may be called the sole " surviving " colour. But, by search, we may find solutions which will give very 1 It is possible to get a solution of ammoniated sulphate of copper so pure a blue as to transmit hardly any green, when the green half of the experiment, with^that particular solution, would naturally fail ; but get either solutions or glasses of a good blue, which transmit green as well as their blue and yellow, and the same materials will do for both. vi] SUPERPOSED PIGMENTS 113 similar colours to the eye, but of another prismatic character. Make a solution of oxide of copper in liquor of ammonia. 1 This, too, is blue, and its spectrum, A c (Fig. 90), shows that it allows to pass, beside blue, nearly all the green ; in fact, all the spectrum to the point B. Make another solution of bichromate of potash, which is a deep or orange-yellow. This allows the red and yellow end of the spectrum to pass, from the point E, with only a trace of green, if any ; and by a little dilution of one or other solution, or the use of a wedge-shaped glass cell for each, the amounts of these two colouring matters can with care be so adjusted that the spectrum of one begins about where the RED END BLUB END FIG. 90. Complementary Absorptions. other ends, and there is no sensible portion transmitted by both. Now here are a blue and a yellow very similar to the preceding ; and their discs, when overlapped, produce, like them, a fair white, or nearly white. But superpose these two cells across the nozzle of the same lantern, and we get no longer green as we did before, but black ; the two stop the light altogether. Similar effects may be produced by Chance's " signal-green " glass, and another coloured a good red by copper oxide. These experiments explain a fact familiar to painters in water-colours, which as a rule are more or less transparent colours, showing very largely by the white light of the paper reflected through them ; as may be seen by their colour on the 1 Acid solution of copper sulphate with the bichromate allows pure green to pass. I ii 4 LIGHT [CHAP. paper differing widely from that of the cake. Hence brilliance of colour can only be got by a single wash ; every successive wash stops out more and more of the white light ; and several washes, of the proper spectral colours, instead of producing white as in the Newton's disc ( 54), or as even a mixture of colours in one wash sometimes will, rather produces a muddy grey approaching black. The final result can only be the colour which is allowed to pass by all the washes, which is very little. As Sir John Herschel expresses it, the water-colour painter * really works chiefly by destroying colour, and therefore uses as few washes as he can. Even with pigments painted in water-colour on white paper, the same facts may be proved by proper arrangements. If we mix on the palette bright cobalt-blue and the lighter chrome- yellow, a wash with the mixture gives us a good green, by the double absorptions among the particles already described. But so long ago as 1839 Mile found, that if rather narrow and long stripes were painted contiguously of each alternate colour separately, and then blended on the retina by removing the eye to a proper distance, the result was not green, but either a white or rather yellowish-w r hite, according to the shades of yellow and blue. 2 Or the colours may be blended in larger patches by a double-image prism, 3 or in other ways. Any 1 What is here said applies far less to oil painting, which deals with more solid layers of pigment, unaided by a white background. 2 I have seen a statement by a "practical artist," who accompanied it with much hard language about " scientific theorizers," that such stripes when so blended gave green. All that can be said about such an assertion is, that as a general rule, with really good blues or yellows, it is simply not the fact : the statement is due to sheer lack of experimental investigation. Some blues and yellows are so saturated with green in addition to the blue and yellow, that after the two latter have combined into a white, the green heavily pre- dominates. Such will of course give green ; but approximately pure and bright blues and yellows cannot be made to do so ; and examination of the blue-greens which do, through a prism, will reveal at once the great preponderance of green which causes the exception. a 122. vi] COLOUR SENSATIONS 115 tolerably pure blue and yellow will always, when their coloured images are added, produce white or near it, and cannot anyhow when so added be made to produce green. 79. Primary Colour Sensations. Nevertheless it is considered probable that there really are three primary colour sensations, though different from the blue, yellow, and red of the old artists. Helmholtz and Maxwell believe the three primaries rather to be violet, green, and red, neither of which can be compounded by any mixtures of colours, but which in combination can be made to produce any of the others. A narrow slit in the green between the b and E lines (Plate II. D), and a broad band in the violet rather to that side of the G line, can in the way described in 76 be made to give a blue, which accounts for nearly the whole half of the spectrum from the blue end, when combined, appearing of that colour. Yellow appears to the eye such a "pure" colour, that it is difficult to believe it can really be compounded. We have seen already, however, that it will bear mixture with a very large quantity of green without the eye detecting that mixture ; and it is easy to show by experiment that red and green will produce it. One method is a very pretty one easily demonstrated by any double lantern. From one nozzle project a spectrum by any of the arrangements which have been described ; from the other focus on the screen the image of a perpendicular slit in a black card in the ordinary slide-stage, long enough for the image to project some obvious distance above and beneath the spectrum, when thrown upon it. Place in the stage with it a pretty pure red glass, and move the slit so that the red image may travel along the spectrum somewhere in the green we shall get a fair yellow. Again take a green glass selected by trial with the slit, and somewhere in the red we shall again get a yellow. A second method is to compound, in the way described in 76, a wide slit in the red, and a still wider slit in the green extending beyond\he b and E lines. This will give a yellow from the prismatic colours. I 2 ii6 LIGHT [CHAP. Another method is due to Lord Rayleigh. A film of blue gelatine stained with litmus is placed between two glasses ; pris- matic analysis, by methods already described, shows that it cuts out all the yellow and orange rays. A similar yellow film coloured with aurine cuts out all the blue and violet. Both together, it will be seen, stop out all but the red and green. Now take away the prism, and let the light from the lantern pass direct through both, and we get an orange-yellow ; so that here we actually have apparently blue and yellow glasses pro- ducing neither green, as in one previous experiment, nor white, as in another, nor black, as in another but by successive absorptions, orange-yellow ! And in all cases prismatic analysis of the glasses or other coloured substances separately, perfectly accounts for all the phenomena. A still better combination is a cell of litmus and one of potash bichromate, which gives purer residuals so pure that if a small aperture is focused on the screen through both cells, the prism will disperse the yellow image into two nearly sharp discs of red and green. But observe, we say three primary colour sensations, and not three primary colours. The distinction is very important. So far as the actual spectrum and spectral colours go, even Newton's seven do not represent the case ; every point in the spectrum differs somewhat in shade from its neighbours, and each one has its own distinct period of vibration, on which the colour (and other properties also) depends. No one is any more "pure" or "primary" than the other. But there are generally believed to be in the retina of an ordinary eye three main sets of nerves, or of the fine rods already referred to ( 66), or whatever else receives the impacts of the ether-waves and translates them into consciousness ; one responding mainly to violet, another to green, and another to red. But tuning-fork?, to take one obvious analogy, will also respond, though in a much less degree, to other than their own proper notes ; and so it is supposed these sets of nerves, rods, or other mechanism also respond in less degree to other wave periods than their vi] COLOUR A SENSATION 117 own. It is then conceivable that periods which give, let us say, a pure spectral yellow, should also act on the brain by partially exciting the red and the green rods ; and we should of course expect that if these red and green rods were simultaneously excited by their own proper colours, they would conversely produce the same sensation of yellow, or nearly so, as in the other case. The same reasoning would apply to other colours ; and will account for blue and yellow alone making white. For if the blue waves excite the violet, blue, and some of the green, while the yellow waves excite the green and the red, the two together set in motion to some extent the apparatus which responds to all the colours of the spectrum. However the exact details may be worked out, the remarkable phenomena of colour-blindness, and the fact that they are almost entirely confined to blue, green, and red colours, make it very probable, if not certain, that in the main this view is the true one. 80. Colour merely a Sensation. The obvious and striking consequence at once results from such a theory, that colour is merely a sensation. We have already made many experiments which confirm this view, and prove that our sensations are by no means trustworthy guides ; but we can now demonstrate that it is so by still more striking experiments, whose nature is easily understood. We have ( 66) supposed vision to be excited by motion communicated transversely to the ends of fine rods, with which the retina is studded, and so communicated through the nerves to the brain. Now, if we press a rather blunt pin-point on any part of the body, or excite sensation in any other way, we feel it at first very vividly ; but by degrees the feeling deadens, and we take no notice. The nerves which respond to that particular feeling are by exercise, for the time, fatigued tired out and can no longer do their work. That is the reason we wear our clothes without feeling them, and of many similar facts. Now if we suppose some of the rods to respond, like tuning-forks, to certain vibrations or colours, and other rods to others, we ought to expect, under n8 LIGHT [CHAP. similar circumstances, results of the same kind. Demonstration of this is the object of our next experiments. Two lanterns may be used, one to illuminate the screen the moment the other is shut off; but one is to be preferred, as more certain, for the first two experiments at least. Remove the objective, and prepare a black card 3 inches or 4 inches square, with a cir- cular hole in the centre, which, when held against the flange- nozzle, as at N, Fig. 91, and there focused on the screen, gives a disc of about 18 inches diameter, or 12 inches for a short screen distance. Arrange the loose focusing lens F in front, to focus it accordingly, as in Fig. 91, and of course when the card FIG. 91. Subjective Colours. is removed the whole screen is instantly illuminated. Have ready also a piece of good red glass, the size of the card, the picric acid cell, and a blue glass. First we hold the plain card over the nozzle, as shown in the figure, while we count twenty rather deliberately, fixing the eyes meantime intently on the same point in the bright disc. After twenty or twenty-five seconds remove the card suddenly, and where the disc was, we now see a dark circle on the illuminated screen. The exhausted nerves no longer respond to the stimulus of the white screen, as do those over the untired area ; and hence, though vi] SUBJECTIVE COLOURS 119 all the screen is equally white, where the bright disc was it appears dark. Repeat the experiment with the red glass held over the card, removing both together. Here the fibres or nerves which respond to red vibrations are alone fatigued ; the others are not. Hence when the glass and card are withdrawn, and the screen illuminated with white light, the red rays of that light can no longer excite in the tired nerves such vivid sensations as the other colours, which act upon fresh and rested nerves ; and so, after a second or two, the place where the disc was appears green, though no green light is really there, except as a component of the white. In the same way, hold the picric acid cell in front of the card for twenty seconds, and we get a spectral blue ; while the blue glass gives us a yellow. We " see " a colour which does not exist, except in our nervous sensations. There is a still more striking experiment of the same class that of projecting upon the screen the entire spectrum^ Arrange the bisulphide prism as for so many previous experiments, but using now for brilliance as wide a slit as will give fairly pure spectrum colours ; and arrange that a tolerably brilliant gas- light can be turned up instantaneously, at a given signal. Project the spectrum on the otherwise dark screen, but in this case count thirty; and be sure vision is fixed, by placing a small black mark to look at about the middle of the spectrum. At the word " thirty," cover the lantern-nozzle, while an assistant 1 I believe this beautiful experiment was first performed by Professor Tyndall at Glasgow. Seeing the expressions of misgiving with which he introduced it even with the electric lantern, I was somewhat surprised to find that with the lime-light the effect is all that can be desired ; and that with a screen distance of about 6 feet, and a good bisulphide prism (with a glass one the spectrum is not long enough), it can be satisfactorily shown even with an Argand gas-burner, on one condition that the screen is not too brilliantly illuminated afterwards. Hence the illumination of the screen by an ordinary gas-light during the second stage, instead of throwing upon it the full beam from the lantern. i2o LIGHT [CHAP. turns up the gas : and we see on the screen the complementary spectrum, solely due to fatigue of the organs of vision. 1 With the aid of contrast, a mere shadow will deceive sensation in the same way. Arrange a powerful gas-burner rather nearer the screen than the lantern, and considerably to one side. Throw on the screen a strong light from the lantern, with a strong red or blue glass in the stage or held over the nozzle. After a few seconds hold a card with pattern- apertures cut in it in the coloured rays, the gas-burner being turned up at the same instant. Where the shadows fall, the screen is free from coloured light, and is illuminated by fainter white light from the other source. But the shadows appear by contrast strongly tinged of the complementary colour. If further proof be needed of the distinction between the physical realities which underlie light and colour, and our purely sensational consciousness of them, it is at hand. Some people are more or less " colour-blind," while yet the perfect optical images must be formed on the retina. Some few have absolutely no sense but that of light and shade, though the physical reality is the same for them as for us. What the world appears to them, we may demonstrate by lighting our room with a Bunsen burner, in the flame of which dry carbonate of soda is held, or still better, a morsel of sodium in a spoon, or for a large hall a handful or two of tow saturated with salt dissolved in diluted spirit and with salt rubbed into it, may be ignited in a wire basket held for safety over a basin of water. All is mere light and shade ; and we can see, as we turn up the ordinary gas, what we should miss, without the colour-sense, from our beautiful world. Again, a large dose of the medicine santonine affects the colour- sense considerably, 1 There are a few with whom these experiments do not succeed. Some of these are colour-blind, while others seem persistently "unable" in all such matters ; and the whole nervous system of some is so vigorous, that the retina does not really become fatigued ; but nine-tenths of any average audience find no difficulty. vi] DOPPLER'S PRINCIPLE 121 and, besides distorting other colours, making nearly all persons incapable of perceiving violet and purple. This strange fact is easily accounted for if we conceive that the drug renders the rods of fibres attuned to the quicker vibrations so relaxed, that for the time they only respond to slower ones. 81. Doppler's Principle. Final illustration of this is given by the verification of a principle pointed out by Doppler in 1841, and which also demonstrates that it is solely period ( 7 2 5 93) which determines a spectrum-colour. If an observer, and any body originating waves (of any kind) are rapidly approaching, the wave-periods appear quickened ; in the reverse case lengthened. With sound-waves, such apparent changes in period affect pitch. Accordingly the whistle of a locomotive sounds very much sharper whilst an observer in another train approaches, than when the trains, having passed, are receding. And more directly, by causing a sounding tuning-fork to excite sympathetic vibrations in another at some distance, the rise in pitch when either fork is made to approach the other, can be directly demonstrated. In light, similar changes in wave-period affect colour ; and a swiftly-approaching coloured star would appear of a shade nearer the blue end of the spectrum. The eye is unable to judge directly of any such differences in shade ; but the " lines " in their spectra described in the next chapter ( 87) give, as it were, divisions of a micrometer- scale for measurement; and by these we are enabled to see that every part of a spectrum actually is displaced under such circumstances. This actual shifting of the "lines" enables us to measure the velocity of an uprushing solar flame; or to determine that a star is ap- proaching or receding from us at a given rate ; or to affirm that a star which in the telescope appears single, is really double, and that its component stars are revolving round each other with definite velocity. This important means of investigation has within the last few years opened up an entirely fresh depart- ment in astronomical science. CHAPTER VII SPECTRUM ANALYSIS Continuous Spectra Absorption Spectra Their use in Analysis The Solar Spectrum Line Spectra Reversed Lines Radiation and Absorption Reciprocal Fraunhofer's Lines Reversed Solar Lines Thickened Lines Solar, Stellar, and Planetary Chemistry. HOWEVER much we disperse the spectrum of our lime-light or gas-burner, from the narrowest slit, we fail to find any dark bands in it ; it is an unbroken band of colours, insensibly shading into one another (Plate II. A). Such is called a con- tinuous spectrum, and it is found that any body which can be heated to incandescence without being vapourised that is, which glows while retaining a solid or liquid form gives this kind of spectrum. If we heat a piece of iron, for instance, it gives out first only red light the longest and slowest waves. As we heat it more, yellow is added ; then gradually green and blue ; but the spectrum is always continuous as far as it goes. A gas flame does not give us by ordinary methods the spectrum of a vapour, but that of the solid particles of carbon in a state of incandescence : hence the continuous spectrum. This rule has been found universal. Many substances are volatilised before they can be made to give a complete spec- trum : but if whilst solid they can be heated so as to emit light at all, it is an unbroken spectrum so far as it extends, and it commences from the red end. Thus the body emits CH. vn] ABSORPTION SPECTRA 123 the slowest vibrations first, gradually acquiring the quicker ones ; which we recognise in popular language when we say it first becomes red-hot and then white-hot. A thermometer moved in the spectrum will show us that still longer and slower waves than the visible red waves extend beyond the red end, and are even hotter than the red. So that a body, heated, first acquires comparatively slow vibrations, which are too slow and long in their waves to excite vision ; gradually it adds quicker and quicker ones ; till at a certain point, different for each body, the motion of the molecules is so rapid as to over- come the attractive forces, and they fly apart in vapour. We have now to examine phenomena of another class. In all experiments to demonstrate lines or bands in the spectrum, care must be taken that the spectrum is focused on the screen all along its range. The phenomena cannot be displayed otherwise ; but it requires the careful adjustment of the focusing lens. The best means of securing this is roughly to adjust the focusing lens and prism so as to get the spectrum on the screen ; then to hold a fine wire across the slit, and finally adjust the lens in focus, and incline it to one side or the other, until the shadow of the wire appears as a black line equally in focus from one end of the spectrum to the other. 82. Absorption Spectra. Some of the experiments in the preceding chapter have really been experiments in spec- trum analysis, of precisely the same nature as are half of the experiments made by microscopists and chemists every day. A large part of their work consists in the examination of mere " absorption spectra " such as we have already seen upon our screen. We may demonstrate its nature by many homely and instructive experiments. Filling, for instance, our glass cells with known samples of genuine claret or other wine, we obtain, by the method already described, a spectrum with certain dark bands. Now we can easily obtain other solutions, compounded with more or less alcohol, and coloured with various substances, which, "to the eye," are of exactly the same colour. But the LIGHT [CHAP. imitative solution will not give the same absorption spectrum. It cannot be made to do so, inasmuch as the vibrations ab- sorbed depend on the synchronal vibrations of the very mole- cules themselves. It is needless to give more examples, or to explain how we have even in this method of analysis a powerful and delicate means of detecting adulteration, in any substance which admits of being presented as a coloured solution, or any other transparent form. We have only to ascertain the absorption spectrum of a sample of known purity ; and the spectrum of the sample to be tested will at once reveal if it be genuine or adulterated. FIG. 92. (i) Iodine Vapour. (2) Nitrous Gas. Again, if healthy blood be somewhat diluted with water, a characteristic absorption spectrum will be observed with all the blue end cut out, and two broad bands in the yellow and green, near the D and E lines to be presently explained. But if we now hold in front of the slit a trough filled with blood poisoned by almost anything say by carbonic oxide, or prussic acid we shall perceive a marked difference in the spectrum. Light will be a Revealer of the poisoning to which the blood has been subjected. Coloured gases or vapours contained in closed tubes will give very characteristic absorption spectra. A closed tube con- vn] THE SOLAR SPECTRUM 125 taining some iodine, vapourised over a lamp and held in front of the slit, gives a very beautiful spectrum ; as also does one filled with nitrous gas (Fig. 92). The latter gas can be easily produced by putting some copper-turnings in a test-tube and pouring on them some nitric acid. Carefully avoid inhaling the fumes. A small piece of glass containing didymium or erbium, or a small bottle filled with solution of didymium sulphate, can be hown to be nearly colourless ; but when held in front of the slits will give remarkably distinct and characteristic absorption bands. 83. The Solar Spectrum. We cannot show the solar spectrum in the lantern, but every student should see the leading phenomena for himself. Provide sufficient blaclt cards to go all across a window, as a black band about a foot high resting on the middle sash or bar ; they need not be fastened, as the only object is, for the width of that band, to stop out the light, and a little overlap of loose sheets will effect this. In one of the middle sheets cut a slit not more than about half an inch wide and five or six inches long ; and choosing a day when the sky is brilliantly lighted, and the slit standing out against it, or at least against a bright white cloud, take the bi- sulphide prism, and observe the slit through it from the other side of the room, or from a distance of not less than eight or ten feet. The spectrum will be plainly seen to be crossed by several well-marked dark lines, as represented in Plate II., Fig. D. By employing more prisms to increase the dispersion, and examining the image with a telescope, these lines are increased to hundreds ; but most of the few in the plate can be seen with the single prism-bottle and nothing else. 1 1 It does not seem generally known that the principal lines of the solar spectrum can be perfectly well seen by this simple means. Even with a "lustre " of pretty good flint glass, I have never failed to see the D line, and the chief line in the blue. For further del ail of spectroscopes and spectroscopic work, see T/ie Spectroscope, by J. N. Lockyer, F.R.S. (Nature Series). This chapter only deals with the physical outlines of the subject. 126 LIGHT [CHAP. Now we have the best of reasons to believe that the sun is incandescent : his amazing heat alone makes the supposition a necessity ; and his spectrum is moreover, to the eye alone, un- less widely dispersed, so very near to a continuous spectrum as to make it almost certain, upon that ground also, that the light emitted from him originally must be from incandescent liquid or solid. What, then, is the cause of these dark lines ? The probability would appear to be, from what we have seen already, that they are in some way due to absorption. 84. Line Spectra. We examine next the spectra of coloured flames, or flames which contain the vapour of solid bodies. The metal sodium is a convenient substance, being so easily volatilised, and the vapour so readily made incan- descent by a moderate temperature. A spirit-lamp with salt well rubbed into the wick will show the line fairly well ; but if more brilliance is required, slide back the burner or lime jet, and introduce at about the point it usually occupies, a short Bunsen burner. In the flame of this hold in a small platinum spoon a pellet of sodium. The spectrum arrangements being all ready as before, we see on the screen simply a bright yellow line the characteristic line of sodium, known as the D line or lines. All the rest is dark ; the sodium-vapour gives a pure yellow light. 1 (Plate II., Fig. F.) Now, it is found that all incandescent gases give such *' line " spectra ; as if, when their molecules of matter were so dissociated as to be able to behave independently, they had their own periods of vibration, like pendulums of a fixed length. Some give more lines than others sodium itself 1 In every experiment involving combustion of sodium or other substance in the optical lantern, care shouldf be taken to protect the face of the con- denser by a plate of thin annealed glass or a film of mica ; otherwise morsels of the substance in a state of fusion are apt to splutter on to the lens and inbed themselves in its surface. I have in Optical Projection described a simple kind of combustion lantern burning the substances close to the slit without any lens, which was devised by Professor Weinholcl of Leipzig. vn] LINE SPECTRA 127 gives an additional line with the more intense heat of the electric arc ; while with wide dispersion, the yellow line is seen to split into two lines close together. But incandescent gases give line spectra, and no gas or vapour gives the same lines as any other ; so that when Mr. Crookes some years ago found in the spectrum of some lead-refuse volatilised, a new green line which none of the known metals had yielded, he knew that he had something before him that had hitherto been unknown, and pursued his investigation till he had separated the new metal Thallium. As in previous instances, Light was to him a true Revealer of the unknown. Lithium and strontium are pretty easily volatilised in the shape of their chlorides, and a small quantity of these salts will show bright line spectra in a Bunsen burner, or even if placed on the wick of a spirit-lamp. For a combustion lantern, burning the substances in a metal capsule or spoon close be- hind the slit, Prof. Weinhold gives the following recipes, a little heap of the powder being placed in the capsule, in which heap is stuck a cotton wick soaked in lead chromate : this is lighted, and in a few moments the powder will flare up and give its line spectrum. For sodium lines : 3 parts sodium nitrate, i part potassium chlorate, i part shellac. For calcium : 2 parts chalk, 10 parts potassium chlorate, 3 parts shellac. For strontium : 3 parts strontium nitrate, i part potassic chlorate, i part shellac. For barium : 3 parts barium nitrate, i part potassium chlorate, i part shellac. The shellac to be powdered separately from the salts, which are also to be rubbed down to, powder, and the two mixed previous to use with a horn or wooden spoon. Good line spectra can be projected with the oxy-hydrogen flame by Professor Edelmann's method. A " blow-through " jet is arranged with a vertical nozzle, over which can be adjusted by a sliding ring hollow carbon cones. The inside surface of such a cone is covered with a paste, composed of the salt rubbed down in a mortar with picric acid, ammonia, and 128 LIGHT [CHAP. alcohol. The burner is adjusted at the focus of the condenser, and gives good bright spectra. With the arc light the positive carbon or crater must be reversed so as to form the bottom pole, and a cup is formed in it, in which a morsel of the metal is placed. The poles must stand vertically, and a Brockie lamp will therefore require a wedge- shaped piece of wood placed under its base. A hand rack- regulator is however most convenient for mere spectrum- work. 85. Reversed Lines. In 1859 Kirchh off cleared up the mystery of the solar spectrum, by ascertaining that when the FIG. 93. Reversed Sodium Line. vapour of sodium was interposed between the slit and its spectrum, the D line was still further darkened. We have seen the bright D line of sodium, as projected from the lantern. We now restore the lime cylinder to its place, and throw the continuous spectrum on the screen in the ordinary way, 1 with a good prism bottle. At the point where the rays from the slit are made to cross by the lens, adjust the Bunsen burner, and 1 Nothing less than the mixed jet is brilliant enough to show the reversed line on the screen. vn] REVERSED LINES 129 between the burner and the screen interpose a black card, so as to stop all direct light from the sodium from falling on the screen hence a direct prism is not well adapted for this experiment. A little in front of the flame the prism is placed. Thus the sodium flame is not concentrated or focused on the screen at all, while all its direct light is easily shaded. 1 Intro- ducing a pellet of sodium into the flame, it bursts into vivid combustion, and the light from the slit has to pass through the yellow flame. At once a dark band in the yellow appears on the screen (E, Plate II). It is not really black ; for we know that if the sodium flame alone were employed it would give the yellow band ; but it is comparatively dark : it stops the larger portion of the brilliant light from the lime cylinder. See also note to 89. With the arc-light we can show the two spectra together, and demonstrate that in this way we get an exact and absolute reversal of the sodium line. The arrangement is shown in Fig. 93. Everything but the condensers is removed from the lantern, and a few inches from the flange-nozzle, N, is adjusted a rather large black tin screen, s, in which the slit is cut, and which has side-guards (not shown) in order to stop as much as practicable scattered light. Behind the slit is arranged the Bunsen burner, B ; by this arrangement all the light has to pass through the sodium flame, while none but what passes the slit can reach the screen. On now holding the spoon with the pellet of sodium in the flame, the dark band appears in the spectrum ; and by holding another plate, T, between the Bunsen burner and the condensers, the arc-light may be cut off from the upper portion of the slit, leaving the light of the sodium flame alone. Two prism-bottles should be used, and the result will be as shown. One half of the spectrum will show the bright line on dark ground, giving the radiation 1 This arrangement, devised by Mr. E. Cleminshaw, is, as he states (Proc. Physical Soc. vii. 53) much easier than the one given by me in the first edition of this work, and superior in effect to it. K 130 LIGHT [CHAP. spectrum of sodium, R. The other half will show the dark line on the continuous spectrum, giving the absorption spec- trum, A. The mere dark-line spectrum is very readily shown with the arc-light, only needing a rather large and deep cup-carbon. 86. Radiation and Absorption Reciprocal. After all, this is what we should have expected. It simply shows us that, as we have found reason to suppose before, the molecules of matter really do take up or absorb those ether-vibrations which synchronize with their own vibration-periods. We form the conclusion, subject to experimental verification, that all vapours ought to absorb the very same colours which they radiate or emit when heated to incandescence. Experiment does verify the conclusion. In every case, where the vapour of a metal gives out bright lines, there, when interposed in the path of a brilliant continuous spectrum, that spectrum is crossed by dark lines. 87. Fraunhofer's Lines. We can now perfectly under- stand the solar spectrum (Plate II. D). The dark sodium or D lines show us, that between the incandescent body of the sun and ourselves is the vapour of sodium ; other lines demonstrate the presence of incandescent hydrogen ; other lines, again, those of iron. With greater dispersion the dark lines are, as already observed, multiplied to hundreds, and nearly a hundred of these are iron lines. Fraunhofer's lines are of great value in another way. They serve as land-marks in the spectrum. It is difficult or im- possible to determine light of a given wave-length by the colour alone ; but these lines have fixed places, and, being all carefully mapped, answer every purpose ( 81). Where no solar spectrum can be employed, still the ascertained lines of iron, or sodium, &c., answer the purpose, the chief lines being all lettered and numbered. 88. Reversed Solar Lines. All the preceding suppo- sitions can be actually verified in the case of the sun, and we Vll] THICKENED LINES are able to obtain, with proper instruments, just such reversed or complementary spectra as our lantern gave us of the sodium line. If the sun is surrounded by various incandescent vapours, and these could be isolated from his overpowering continuous spectrum, we must have the bright lines. This was first accomplished during total eclipses, when the incandescent atmosphere gave the bright lines of sodium, hydrogen, iron, and other substances, conspicuously enough. By wider disper- sion, which it will easily be understood weakens proportionately the continuous spectrum, while not able so to disperse the more definite vibrations of line spectra, spectroscopists are able to FIG. 94. Solar F Line Reversed. show in juxtaposition the spectrum of the sun himself, and of his outer envelope of luminous gas, or chromosphere. Fig. 94 shows a very small portion of the result, 1 and we see plainly the bright F line in the chromosphere, while below is the portion of the continuous spectrum, which shows the dark line exactly coincident, just like the two sodium spectra in Fig. 93 89. Thickened Lines. There is one more rather im- portant point. We have seen that solids or liquids, whose molecules are comparatively close, when those molecules are forced into violent vibration by heat, appear so hampered as 1 Taken from The Spectroscope (Nature Series). K 2 i 3 2 LIGHT [CHAP. to vibrate in all periods, thus giving the continuous spectrum. When the molecules are at last driven apart, and are compara- tively free, they vibrate in their own individual periods, and give lines at least this is our hypothesis regarding the pheno- mena. If it be well founded, we can test it ; for obviously more pressure, or compressing even gas particles closer together, ought to produce more or less approach towards a continuous spectrum. Experiment verifies this, and many gases have been so compressed as to give a very considerable spectrum. The easiest demonstration, however, is with our ever-useful sodium and its reciprocal absorption spectrum. Enclosing some fragments of sodium in an exhausted tube afterwards filled with hydrogen, and again exhausted before sealing (this is to prevent oxidation), we have the materials for a very elegant experiment. 1 We throw the line spectrum on the screen as before, and hold the tube over the slit there is no appearance of absorption. Applying heat, a thin dark line comes on the spectrum, which we know so well. Continu- ing to apply heat, we of course increase the density of the sodium vapour, and its pressure ; and as we do so the line thickens, till it occupies a rather conspicuous width. Removing the lamp, the phenomena are all reversed. Our theory, and the expectations formed from it, are verified to the minutest particular. Again, referring to Fig. 94, it will be seen that the bright F line of the sun's chromosphere is much thicker at the bottom than the top. We gather from this optical evidence, what we know must be the case on other grounds, that the pressure of the incandescent atmosphere is much greater near the sun's surface. 1 Due to Dr. Frankland. There is some little risk about this experiment, unless carefully prepared with strong and hard combustion- tube, which, should not exceed about | inch in diameter. Heated to a less extent, the tube will be found to cast a shadow in the orange rays of the spectrum, but not elsewhere. vii] STELLAR CHEMISTRY 133 90. Solar and Stellar Chemistry. Thus we see how the spectrum enables us to ascertain with wonderful accu- racy much about the actual components, and even actual physical condition, of the most distant heavenly bodies. It is interesting to find that, so far as we can trace them in our telescopes, these are constituted of precisely similar matter to what we are familiar with, governed by precisely the same laws. Diverse and inconceivably far apart far enough for even Light, with its enormous velocity, to occupy hundreds of years in traversing the distance all are yet one vast unity. We can trace their materials, and sort them out into groups according to their stages of development ; we can tell if they are solid, or gaseous, and whether they have a surrounding atmosphere or not. Though so distant that the most precise measurements fail us, if they are rapidly approaching or receding from us we can know the fact ( 81). The Light they send us is a true Revealer of all, and brings evidence of all these things in its beams. CHAPTER VIII PHOSPHORESCENCE. FLUORESCENCE. CALORESCENCE Effects of Absorbed Vibrations The Invisible Rays of the Spectrum Three Independent Spectra non-existent Phosphorescence Fluores- cence Calorescence Relation of Fluorescence to Phosphorescence. 91. Effects of Absorbed Vibrations. In previous chapters, we have been led to adopt as our hypothesis of ab- sorption, and of the cause of colour in coloured substances, that molecules of matter having certain periods of vibration, took up from ether-vibrations of all periods, such vibrations as synchronized with their own, with others in less degree. We are bound to ask, what becomes of these absorbed vibrations ? Energy cannot be annihilated ; and any motion apparently de- stroyed must produce certain effects. If molecules of matter take up vibrations from the ether, these molecules ought, in their turn, being set vibrating, to give out new light, or at least waves of their own. That this is so as regards heat and light, is beautifully shown by the allied phenomena of Fluorescence and Phosphorescence. It readily appears, on reflection, that when small particles (as of the Ether) act by their motions upon large particles (as of Matter), the more common effect must be the conversion of quicker motions into slower ones. To use and expand a dynamical analogy which has been employed by Professor Stokes, let us consider short and choppy waves acting upon a CHAP, vni] THE INVISIBLE SPECTRUM 135 large vessel anchored at sea. The quicker motions cause a slower pitching and rolling of the vessel ; and these, again, originate new and slower waves in the water. But the latter are less perceptible than the primary waves, and may even be un- noticed, unless the water should become suddenly calm ; when they would at once be conspicuous as long as the rolling con- tinued, a period which would depend on the stability of the vessel. In the same way, long slow waves may more rarely be converted into quicker motion, and thence into quicker second- ary waves. Regard the waves as motions of ether atoms, and the vessel as a molecule of matter, and the analogy is fairly complete. 92. Invisible Parts of the Spectrum. But before we can fairly investigate these matters, we must take into our view more than the spectrum we " see " upon the screen. That spectrum has no sharply-cut ends ; and we know well enough that it has other effects than visual ones. We can readily trace heat in it ; and experiment in even a very rough way with a good thermometer, soon shows us that the heat is much the greatest at the red end. If, on the other hand, we expose a photographic plate in the spectrum, we find very energetic chemical effects ; and as regards salts of silver and many other compounds, we find that the power of producing such chemical changes is much more energetic at the violet end. If we push pur experiments farther, with more delicate in- struments, we find that some of the most energetic heat rays are quite outside of the visible red end, in a dark space, repre- senting still slower vibrations than the slowest red waves. And we also find that some of the most energetic chemical effects are produced in an invisible region outside of the visible violet end. Moreover there are broad absorption bands and Fraun- hofer lines in these invisible regions; and there are bodies, alike in being perfectly clear and transparent to " visible " light, which differ widely in transparency as to these invisible rays. Clear rock-salt is the only body transparent to all the heat 136- LIGHT [CHAP. rays : and quartz is one of the most transparent to the chemical rays, which are largely absorbed by glass ; as the heat rays are almost totally stopped or absorbed by solid alum or water. 93. Three Independent Spectra non-existent. Hence diagrams have been constructed showing the compara- tive intensity or working power of what is called the Light spectrum, the Heat spectrum, and the Chemical or Actinic spectrum ; the energy of each in every region of the spectrum being shown by a curve, whose highest point is at the place in the spectrum where the effect is greatest. Thus, the high- est luminous intensity would be over the yellow. And it was once considered that there were in a beam say of sun-light rays of three distinct kinds, called heat rays, light rays, and actinic or chemical rays. But this is now known to be a mistake. All the rays are subject to the same laws, being reflected, refracted, diffracted, &c., exactly as the rays whose luminous phenomena we have investigated. They differ solely in their periods of vibration ; and their different effects are due simply to the fact that certain periods and lengths are best adapted to produce those effects. Just as with sounds, some persons can hear much graver sounds and others more acute sounds than others can, and probably insects can hear sounds inaudible to us ; so while the lengths of average visible light-waves range only from -^ 6 ^ o0 th to --^--j-th of an inch in air, some persons can. see rays at one end or the other, invisible to the majority. Again, it has been said that chemical effects are almost nil in the yellow of the spectrum ; and it is so as regards the salts of silver. But the action of light upon plants is also a distinctly chemical effect ; and this is perhaps, if anything, the most powerful in that same yellow region. Science knows no real distinction but periods and lengths, between any of the rays in the spectrum ; each period being more or less adapted, as a rate of Motion, to pro- duce certain effects upon the molecules of bodies, or upon our nerves. vni] PHOSPHORESCENCE 137 Now as respects such effects, we have a proof that the quickest motions act most powerfully in some respects upon the molecules of matter, in the effects of vibration upon wrought iron. Slow motions do not affect it ; but quicker vibrations rapidly produce a crystalline structure, showing that the molecules are shaken, or forced in some way, into new positions. We see practically the same thing in the chemical power of the quicker waves of light. It is almost certain that the atoms upon which they act, are literally shaken into new combinations, very much as in the crystalline iron ; and thus we can imagine why it is that the quickest vibrations are often most powerful in their effects. Actinism is thus, in itself, one of the strongest proofs of the vibratory theory of light. As the transference of motion we here suppose, is from the ether to the ponderable atoms of bodies, we should expect to find it in some respects most evident from the quickest waves. We thus see, in a general way, what becomes of light when it meets bodies opaque to any given periods of vibration. It can always be traced somewhere. It is largely converted into heat in the body, while many reflected vibrations which would be true visible waves as 'regards period, are simply too weak to be discerned. We should expect that the quicker motions would be, as a rule, most readily traced ; and again, as a general rule, converted into slower ones. And yet we ought to find some exceptions to this rule, and many proofs in one way or another of what we are supposing takes place. 94. Phosphorescence. It will thus be understood, that when we place a body in the sun for some time, and on re- moving it, find that for a considerable time it gives out percep- tible heat rays, we have a case of what has been here described. Some people's eyes are sensitive to light much more faint than others can perceive : and if a large iron ball is heated white- hot, and then gradually cooled, such individuals may see the red light after others have ceased to perceive any visual phe- nomena. Hence there can be little or no doubt, that in the 138 LIGHT [CHAP. case of a body merely " warmed " in the sun's rays, there are also vibrations of shorter, truly visual periods, but too feeble for our senses. But there are a number of substances which, when exposed to light for a time, continue for some time after withdrawal to give out luminous rays, and this phenomenon is called phosphorescence. Prominent amongst these substances are the sulphides of calcium, strontium, and barium ; but they require to be heated and hermetically sealed in glass tubes. The diamond and fluor spar are examples in the mineral world. The compound sold as Balmain's luminous paint is one of the cheapest and best-known substances. Diamond and fluor spar glow for a comparatively short time after exposure to a strong light ; but the sulphides, or Balmain's paint, will shine for many hours by the energetic vibrations set up in their molecules by the ether-waves. 1 It is found that these effects are produced mainly, if not solely, by the quicker and shorter waves. If a sheet of paper painted with Balmain's paint is made slightly luminous, and then exposed in the dark to a strong spectrum for a while, when it is taken into a dark room it is found the phosphores- cence is destroyed where the slower waves fell. Those waves have the property of destroying the vibrations set up by the quicker waves, converting them into slower, or heat waves. 95. Fluorescence. But there is another class of bodies which are acted upon in a somewhat similar and yet some- what different manner. The vibrations of the infinitely small ether-atoms set up in their heavier molecules slower vibrations, as in the case of our ship ( 91.) We have had one example of this when light-rays are absorbed and cause heat-rays to be emitted from the body ; but similarly, the very quick and short invisible violet rays may be converted into slower visible rays. Professor Stokes found that when he employed quartz lenses and prisms ( 92), the invisible spectrum at the violet end was 1 A set of phosphorescent tubes, which give various colours after exposure to light, can be obtained for a few shillings of any good optician. vin] FLUORESCENCE 139 six times as long as the whole visible spectrum. It is no wonder, therefore, that this should be the most common of all these allied phenomena. It is called Fluorescence, and has been specially investigated by Professor Stokes, and since by Lommel, Kundt, and others. The conversion of invisible rays into visible ones is not very well adapted for ordinary lantern arrangements, for two rea. sons : firstly, incandescent lime is not rich in the invisible violet waves; 1 and secondly, crown glass lenses, and still more bisulphide prisms, are powerful absorbents of them. The electric light is extremely rich in these rays, much more so than that of the sun. The most convenient light for ordinary lantern experiments is that of magnesium ribbon, also rich in violet rays ; and it may be used without any special expense, by adjusting a bit of brass tube and passing through it two or three ribbons ; one of the three will then keep the others alight, but the light must be watched through a bit of dark glass. The lantern itself and the spectrum are, however, only needed to show the creation or conversion of the invisible spectram into visible rays ; and this is easily done by adjusting a spec- ^ trum from a glass prism on the screen. We project the spectrum, stop off all the brighter portion, and pin over -the violet end and beyond it, a white card painted with several coats of a solution of sulphate of quinine in water acidulated with sulphuric acid. We see a very obvious brightening of the visible violet, and that a perceptible region, before invisible, becomes visible where painted with the quinine (Fig. 95, B c). Taking a glass tank or large cell of the quinine solution, and interposing it in the path of the lantern-beam, the screen shows that it is as clear and colourless as water. But holding the cell so that the light in the cell can be seen, it glows with a beautiful bluish shimmer. A beautiful cone of blue light will be seen if we allow a large lens to come to a focus in the body of the tank. 1 The best actinic effects are from a magnesia cylinder. 140 LIGHT [CHAP. With this cell we can show the perfect reciprocity between radiation and absorption which we have found before. We project from the lantern, with a flint-glass (in default of quartz) train, the ordinary spectrum, A, B (Fig. 95). Towards the violet end B, is attached the piece of white card painted with the acid solution of quinine, producing the brightening at B and extension to c. Now we interpose in front of the slit or lantern- nozzle the glass cell filled with quinine solution. The B c portion at once disappears, and the spectrum is brought back to its former dimensions and character. The demonstration is thus complete, that emission here also is reciprocal with ab- sorption. We further perceive the reason why, in examining cells or tubes of quinine, a weak solution is better. In strong FIG. 95. solutions the effect only penetrates to a small depth, because as the light penetrates, more and more of the effective rays are absorbed ; until, at last, the light that has got through a certain amount, though to all appearance as white and com- plete in various waves as ever, has utterly lost all power of exciting the same kind of fluorescence. The exciting rays have been taken up by the quinine, which emits them on its own fresh account ; and therefore they no longer exist to cause fluorescence in what quinine may be behind. This is, how- ever, only true of the same fluorescence. While the fluores- cence in a tank of quinine is quite stopped by another tank of quinine, if instead of the latter we interpose a tank of uranine or fluorescein, its green fluorescence does not stop the other, viu] FLUORESCENCE 141 but both tanks will still glow brightly with their characteristic phenomena. Having demonstrated the spectral relations of these or any other fluorescing rays, however, a more convenient plan is to burn magnesium in a small box with one side of violet glass. This glass, of course, has no operation beyond stopping off the more brilliant part of the spectrum, which might otherwise overpower the more feeble fluorescent effects. The private student may use sunlight admitted through a small square of blue or violet glass into a dark box. Or if an induction coil is at command, a vacuum-tube filled with rarefied nitrogen, or even air, gives a light feeble, but rich in actinic rays, which, if surrounded by a large tube in which fluid can be introduced, gives fine effects. The purply-blue light of burning sulphur is sufficient for many substances ; and sulphur burning in oxygen, or some potash pyrotechnic mixtures, give powerful effects. There are an immense number of fluorescing substances, amongst which many of the following were brought to my notice by Mr. Sidney Jewsbury of Manchester. The most powerful fluorescing colours in general appear to be green and greenish yellow, in either of which it is easy to prepare designs (best upon darkish blue paper or card) which will shine out brilliantly in light which has passed through blue glass even from the ordinary lantern, or in cells of solution will glow magnificently in the rays from even an oil lamp. Designs are executed in warm size made from gelatine, in which the dye is dissolved, and which is laid on thickly with a brush, so as to give an appreciable thickness on the paper of fluorescent material ; or sheets of gelatine may be soaked in the dye, and when dried, geometrical shapes may be cut out from it and caused to adhere to a card. Fluorescein fluoresces a brilliant bright green. Its sodium compound uranine is a magnificent lighter green. Fused with bromine it gives eosin, also green. Chrysoline is a very pure green. All the above are red or yellow 142 LIGHT [CHAP. in solution ; and besides the above treatment, if a clear glass jar of water containing a few drops of ammonia be placed in the path of the lantern beam, and about a grain in powder of either of the above be scattered on the surface, exquisitely beautiful arborescent streams of green reflected light will be visible. Almost any red ink, even, dropped from the tip of a pen-holder into water, will exhibit the same phenomena, most of these inks being made from eosin. Barium platino-cyanide is another brilliant substance fluores- cing a yellow-green, but is best rubbed up with gum water. The most brilliant of all is probably a substance extracted from petroleum residue by Professor Morton, and termed by him thallene. I have not been able to find any medium which dissolves it (water, alcohol, ether, benzol, were all tried in vain), and Professor Morton, in kindly sending me a sample, told me he preferred to rub it up like paint with thin dammar and benzol. It is found that many carbon compounds containing slight and unknown impurities possess a brilliant fluorescence, which they lose when purified ; and accidental samples now and then occur in this way which cannot be duplicated. Glass coloured with uranium oxide is another substance fluorescing a brilliant green, if cubes or vases made of it be placed in the lantern beam which has passed through blue glass. Powerful fluorescence of other colours can be obtained in a tank of solution, making the latter weak enough for the cone of light to be clearly marked ; but I have not found it possible as yet to get much effect from any of them as regards designs upon paper. For blue, quinine has already been mentioned. ^scul\n fluoresces a bright blue in slightly ammoniated water, and streams of fluorescent light will descend from even small bruised fragments of horse-chestnut bark thrown on the surface. Most petroleum oils fluoresce blue, and so do sodium compounds of the /? naphthol sulphonic acids. Cyanosine (or methyl-tetraiodo-fluorescein) fluoresces orange in alcohol; and so do some of the rhodomines (water), the solution being vin] FLUORESCENCE 143 crimson. Magdala-red fluoresces orange-red. Diazo-resorufin dissolved very sparingly in methylated alcohol slightly am- moniated, fluoresces a vermilion red, but is itself red in solution. The tetra-bromide of the same is however blue in solution, but also fluoresces red, though a more dull red than the other. A solution of chlorophyll (or extract of nettle, or almost any other green leaves in alcohol, ether, or benzol) is green in solution, and fluoresces a dull blood-red. If we place a cell of chlorophyll before a slit in the lantern, and throw its absorption spectrum on the screen (Plate II. G) we can trace again the reciprocity of radiation and absorption for taking a dark absorption band, we find the fluorescence is brighter in those particular rays. As illustrating the wide range of these phenomena, a simple experiment described by Professor Stokes, though only adapted for private performance, is very suggestive. Darken a chamber or box, except a small window of dark blue glass, such as trans- mits through a window, when analyzed by a prism, only the violet, blue, extreme red, and perhaps a little green, but the less green the better. In the fullest light of this blue window lay a white plate or tile ; of course, on laying over this a slit cut in blackened metal or card, we see the same spectrum, only fainter. But now again we lay on the white a bit of bright scarlet flannel or cloth, so that through half the slit we see the white plate, and through the other half the scarlet, and can thus compare the spectra on again looking through the prism. We naturally expect the blue and violet part of the cloth spectrum to be nearly black, as it is, in the violet light ; but what the student probably does not expect, but what we shall find with many samples of scarlet, is to see the spectrum of the cloth lengthened towards the red end, and altogether more brilliant in the red portions than that of the white plate. In the majority of fluorescent substances shorter waves pro- duce vibrations of slower period, or lower refrangibility, and 144 LIGHT [CHAP. hence the difficulty of exciting blue fluorescence especially, through lenses which powerfully absorb the ultra-violet rays. But such is not always the case. The orange-red fluorescence of naphthalin-red is excited more or less by nearly all the rays except the extreme red ; and fluorescein and its allies (eosin, uranine, &c.) shows its green fluorescence in nearly all the rays, shining even in gas-light. Here, therefore, we have a distinct proof of fluorescence being set up by waves shorter than those of the fluorescent colour produced. 96. Calorescence. Still further, as Professor Tyndall has shown, we can stop off all but the slowest waves all but the invisible heat-rays by passing the electric beam through a cell filled with iodine dissolved in carbon bisulphide. If now a large quantity of these invisible or slowest waves be condensed upon platinum foil, or other suitable substances, they will pro- duce either a red, or even a white heat, thus causing the sub- stance to give out also the quicker waves of the spectrum. 1 Here again is a rise, or exaltation of refrangibility, or the con- version of slow vibrations into quicker ones. This phenomenon Professor Tyndall has called Calorescence. It is the reverse of what occurs when absorbed light produces heat ( 93). Thus we have found all our expectations exactly fulfilled. As a rule, the quickest waves are most noticeable in their effects ; and, as a rule, the extra-violet and violet waves are converted into slower waves, the extra-violet becoming 1 Carbon bisulphide is dangerous to use ; but the experiment may be performed quite safely by substituting carbon tetra-chloride. The solution in this liquid is not absolutely opaque, but only a little violet struggles through, which is hardly perceptible. Using a mixed jet of T V inch bore with high pressure, the whole lime will become incandescent, and radiate great heat if of the hardest Nottingham kind. All lenses should be removed, and a thin spherical glass flask filled with the solution be placed about six inches from the lime. If a bright tinned or silvered tube to slide in the flange nozzle occupy the intervening space, it will still further con- centrate the heat upon the flask, which will act as a lens, in whose focus the paper or foil is to be placed. VIII] RELATION OF PHENOMENA 145 violet, or blue, or green, and the violet a brighter blue, and so on. And yet we have a few examples of the reverse in naphthalin red and a few other substances. And yet, again, we have in phosphorescent substances examples of matter- molecules set in vibration by the ether-atoms so vigorously, that they give out light for a considerable time. The prob- ability is that all or nearly all substances fluoresce and phos- phoresce, but that in most cases the vibrations are too feeble to excite in our eyes visual effects. 97. Relation of Fluorescence to Phosphorescence. It needs one more step to make the analogy complete. Phos- phorescence, as shown by Balmain's ____________ paint, ought to be clearly connected with fluorescence. This step was always felt to be necessary by Bec- querel, and it was he who accomplished it. To ordinary observation, the effects of fluorescence seem to cease imme- diately the exciting light is withdrawn, while phosphorescence lasts perhaps for hours. Becquerel, however, con- structed a "Phosphoroscope," by which the illuminated fluorescent substances could be rapidly removed from the light, and he thus found they retained luminosity for a calculable time. His instrument is rather complicated ; but Professor Tyndall, whose fertility as an experimenter is well known, in his lectures at the Royal Institution, used an apparatus much simpler and more elegant. A square iron lantern, A (shown in plan in Fig. 96), had on one side a slit B, through which alone the light could pass. Dr. Tyndall, of course, used the electric arc; but magnesium will do nearly as well anyway, we represent the light at c. Outside the slit, which is of course vertical and nearly the depth of the lantern, is mounted on a per- L FIG. 96. 146 LIGHT [CHAP, vm pendicular axis the cylinder, D, driven by a grooved pulley and cords, E E, from a double system of multiplying wheels, so as to give swift rotation. This cylinder is painted with uranium or canary-glass, powdered, and the powder laid on as paint with some transparent vehicle. Turning the slit and cylinder towards the observer, it will be obvious that if there were no duration of luminosity, or true " phosphorescence," in the case of the fluorescent cylinder, it must appear dark ; but on im- parting rotation, it shines brilliantly with the characteristic green light. Some of the powerful fluorescent dyes already mentioned give the same phenomena. Thus, then, fluorescence is linked on to phosphorescence ; and though all fluorescent sub- stances will not show this with ordinary experimental means, there can be little doubt that it is only a question of degree, and of powers of observation. Once again, therefore, Light has revealed to us the minute, invisible motions which its own ether-vibrations communicate to the molecules of bodies. Where we may have thought all was still, it shows us molecules in constant and rapid motion. Where we seem to have lost that motion, further reflection and experiment yield us but another and impressive proof of the great law of the Conservation of Energy. We see that no motion is destroyed ; but that every single movement does its work, and is converted into some other form. We thus get a very vivid idea of the intense reality of these motions, which seem hypothetical only because they elude the direct examination of our senses. That sense of their reality and definiteness will help us to understand the beautiful and new field of experiment, embracing the most splendid phenomena of physical optics, which we now have to investigate. CHAPTER IX INTERFERENCE Net Result of Two Different Forces Liquid and Tidal Waves Why Single Interferences are not Traceable in Light Interference of Sound Waves Thin Films of Turpentine, Transparent Oxide, Soap, Water, and Air Colour Dependent on Thickness of the Film Newton's Rings Proved to be Dependent also on Reflection from both Surfaces Spectrum Analysis of Films Phenomena of Thicker Films Soap- Films and Sound Vibrations Colours of Thick Plates Fresnel's Mirrors Fresnel's Prism Irregular Refraction Diffraction Grat- ings Telescopic Effects Other Simple Experiments in Diffraction Striated Surfaces Barton's Buttons The Diffraction Spectrum Measurement of Waves Change of Phase in Reflection from a Rarer Medium Photographic Demonstrations of Interference Hertz's Experiments The Size of Molecules of Matter Appendix on Diffrac- tion in the Microscope. 98. Net Result of Two Different Forces or Motions. We have now to study a class of experiments which most of all clearly demonstrate the wave character of the phenomena which constitute Light. We know that different separate motions can so act upon the same particle of matter, as either to combine and strengthen, or to neutralize and destroy each other ; because the actual motion of any particle must result from the net sum, difference, or other result of the forces which act upon it. Take a billiard ball travelling in a direction and at a rate resulting from some stroke of the cue L 2 148 LIGHT [CHAP. if we impart another impulse in the same direction the velocity will be increased ; while if the ball be met by a second force of the same amount, it is brought to a standstill. 99. Interference of Liquid Waves. The same must result in the case of any series of vibrations of equal amplitudes FIG. 97. Interference of Liquid Waves. and periods, such as constitute a wave. If we drop two stones at some distance apart into the same pond, the circular waves from one will cross those from the other. At some ix] INTERFERENCE OF WAVES 149 points the crests will coincide, and reinforce each other's upward movements ; at others the same particle of water is elevated by one wave and depressed by the other ; there it is at rest. The consequence is a beautiful pattern caused by the intersecting ripples. Fig. 97 shows such a pattern caused in an elliptical bath of mercury by a drop or point introduced at one of the foci. They can be shown by the vertical attachment ( 12) to the lantern, laying over the condenser a glass plate to which is cemented an elliptical tin wall, making a tank some 6 inches in diameter and an inch deep, with a glass bottom. On focusing the surface, and then exciting waves by the point of a rapidly vibrating wire, the intersections of the original and reflected waves will be depicted upon the screen. 100. Interference of Tidal Waves. The same thing is true of tidal waves, a remarkable example of which is found in the channel between England and Ireland. The flood-tide, sweeping round from the Atlantic to the north and south of Ireland, meets about a line which usually passes just across the south of the Isle of Man. There the two currents destroy one another, and there is practically none, while the rise and fall of the tide is greatest. But going back from this point to north and south, there are also two points (near Portrush, in Antrim, at the north of the Irish Channel ; and near Courtown, in Wexford, at the south) where the falling tide meets the next rising tide ; at these points, therefore, there is practically no rise or fall of tide whatever, while the current is at the maximum. The same is true of the vast tidal waves that sweep round the globe. At certain times the sun-wave coincides with the moon-wave, and then we have the greatest tidal motion ; at others the sun's wave opposes the moon's wave, and we have the least motion. 101. Single Interferences not Traceable in Light and Sound. But here we must make a very important dis- tinction, the want of which has caused many a student difficulty. In the foregoing cases we could trace the interferences of single 150 LIGHT [CHAP. waves, because their motions were large, occupied considerable time, and thus enabled us to trace them most clearly in the grand tidal waves, which are longest of all. The student is apt to fancy that, in a similar way, rays from any two points of light must be constantly destroying one another by interference, much as in Fig. 98, supposed to represent the rays from two lighthouses. And to some extent they undoubtedly do so. But they can only thus act on each other at the points where the undulations cross ; and in the case of light the vibrations are so enormously rapid and numerous, that FIG. 98. Two Lighthouses. the comparatively few extinctions of this kind are not sensibly missed. But if we bring a whole wave series to act upon another similar whole wave series, then any effect at one point in any waves of the series is repeated throughout the series, and the effect becomes visible. In the case of sound we can get similar wave series easily, by employing exact unisons ; and so it will be found, if a tuning fork be struck and held close to the ear, that on turning it round on the stem there is a position in which the sound is nearly or quite extinguished. This position differs, as it should do, with the key of the fork ; but is when the two prongs are at an angle of nearly 45 with the direction of the ear. If the fork is steadily rotated, the sound will be alternately extinguished and reinforced, according to the phases in which the waves from each prong encounter one another. IX] THIN FILM COLOURS 151 In the case of light, as a rule, we can only get the exact similarity necessary, by employing two portions of light from the same original point of emission, or very nearly so ; but if we can bring two such exactly similar series of waves again to- gether, or so close together that the ether-atoms set in motion by them can act upon each other, while the paths of the rays are sufficiently parallel for many successive undulations to come into the same relations, then we ought to get effects which shall be visible to us. There are several methods of effecting this object. 102. Colours of Thin Films. The simplest and one of the most striking is reflection from a " thin film." If a pencil of light A (Fig. 99) strikes any thin transparent film at B, we know that a large part is reflected at a similar angle to c. But the rest is refracted to D, where (unless at the angle of total reflection) a portion passes through and is lost to us, while another portion is reflected to E and thence refracted to F. It is evident the ray E F must be precisely similar to the ray B c in the periods of its waves, and also precisely parallel to it ; and, if the film be thin enough, it should also be near enough to it to cause interference. As to the phenomena we ought to expect, remembering that every colour has its own wave-length, and reverting to the wave-slide shown in Fig. 78, we see there how the retardation of the central section of that slide by a given distance brings the long waves into contrary phases, while the short waves of half the length, at the same time exactly coincide. A very little thought will teach us that with waves of all various lengths, only one length can be exactly coincident, and only one exactly contrary in phase, when one set is retarded a given distance ; all others being affected one way or the other in varying degrees. Applying this to colours, and remembering what we have found already as to the effect of suppressing any part of the spectrum, we therefore expect that colour will be produced. Now in Fig. 99 this state of things is what we have. The 152 LIGHT [CHAP. ray E F has had to traverse the film twice, from B to D and from D to E, before it can start on its journey parallel to B c. It has got by that distance behind B c, and as this retardation affects each length differently, and more or less suppresses FIG. 99. Reflections from a Film some lengths while it more or Uss strengthens others, we are prepared to expect colour, if the film is thin enough to allow the two to act upon each other at all. We can subject the matter to experiment in many ways, all of which give phe- nomena of great beauty. Take a small black tray or hand-waiter w, say 8 by 12 FIG. loo. Film of Turpentine. inches, lay it on the table, or on a block to raise it if needful, and fill it about half an inch deep with water. If it is a lime- light, cant up the back of the lantern, as in Fig. 100, so that ix] SOAP FILMS 153 the parallel (or rather slightly divergent) beam from the flange- nozzle with the objective removed may fall on the water at w, and be reflected to the screen s. If it is a gas-burner, the reflector must be used to bring the beam down ; and in some situations it will be best to focus the surface on the ceiling, as in some previous experiments ; but with the lime-light the plain beam is best. Having adjusted all, dip the end of a pen-holder or any pointed rod into a bottle of spirits of turpentine, and let a single drop fall on the water. It spreads out instantly, and the reflected light on the ceiling or screen is tinged with the most beautiful colours. Support a polished steel plate 3 or 4 inches square on a small tripod, and place a spirit-lamp or Bunsen flame underneath the centre (Fig. 101). Bring down the light from the lantern, and focus, as in Fig. 31 ; then light the lamp. As a film of transparent oxide forms on the steel, colour appears, which gradually takes the rough shape of variously coloured rings, though not very FIG. ioi. Film of Oxide, regular. This experiment is a little tedi- ous ; but it is a very interesting one. Oxidation may be hastened by covering the hot plate with a very thin film of paraffin-wax. 103. Soap-Films. Soap-films, however, offer the most splendid phenomena. A good solution is of great importance, and there are many recipes, the most generally known being Plateau's. For this dissolve i ounce oleate of soda, cut into thin slices, in two pints (40 ounces) distilled water, rather hot. Mix the solution with 30 fluid ounces of pure glycerine, and shake violently for several minutes, several times, with some hours interval between ; then leave for several days before use (as the solution " tempers " together for a certain time), and filter clear on a cold day. This recipe does well for warm weather ; but I think it toughens the solution to substitute for a portion 154 LIGHT [CHAP. of the pure oleate, which should be fresh-made and soft, some shavings of Marseilles soap. Warm this at convenient intervals on the hob, or otherwise, for several days, shaking it and leaving it to settle between. Finally, let it thoroughly cool, add a few drops of ammonia, and then filter it at about 50 through Swedish paper into stoppered bottles, which will filter out all precipitate and make it clear. If, however, the weather turns very cold, or after considerable time, it may become turbid and useless ; and it is necessary either to filter again, or (what does as well in the former case) to warm the solution before use, warming also the saucer and other apparatus. After all, the first solution thus made may not be thoroughly satis- factory. I then provide a number of such paraffined rings as are described presently, take small samples of the above " stock," and add to them separately (making memoranda) different quantities of soap solution, or glycerine, or water, well shaking and leaving them some hours to "temper"; then stretch a film of each on the rings, the ends of which are stuck into horizontal bradawl-holes in a long slip of wood. Notice is taken, comparing several trials, which lasts the longest ; and when that is ascertained, the whole solution is made up to that standard. By this tentative method tougher solutions may be got than by any one recipe that can be given for a variable climate, 1 and with the varying qualities of soap, glycerine, and 1 Two other recipes may however be useful. The following is that adopted and recommended by Professors Reinold and Riicker and C. V. Boys. Fill a stoppered bottle three-fourths full with distilled water, add one-fortieth by weight fresh oleate of soda, and leave for a day to dissolve. Nearly fill the bottle with Price's glycerine, and shake well (it will be noticed that this is considerably less glycerine than Plateau's). Leave the bottle a week in a dark place, then with a siphon draw off the clear liquid from under the scum into a clean bottle, add a drop or two of strong liquid ammonia to each pint, and keep carefully in the stoppered bottle in a dark place, filling a small working bottle from it when required, but keeping the stock bottle undisturbed, and never putting any back into it. They advise never to warm or filter the solution, and never to leave the stopper out or the liquid exposed to the air. Herr Dahne, of Dresden, has a handy IX] SOAP SOLUTIONS 155 even oleate. It is perfectly easy to place on the ring-stands shortly described, bubbles nearly a foot in diameter ; and I have several times blown in the usual way globes half a yard in diameter; but even a twelve-inch is a magnificent object. A solution must always be brilliantly clear to do good work, FIG. 102. Rings for Soap Solution. and if turbid, should be re-filtered through Swedish paper before any important experiments. The saucer used must also be perfectly clean. Make a few rings of 1-16 inch iron wire, like A (Fig. 102), 2^ inches diameter, and a few rather larger, say 3 inches : the method, which allows the solution to be mixed as required, even in a test- tube, from separate ingredients kept in stock. Keep in bottles (i) a satu- rated solution of soda oleate in distilled water, carefully neutralised and filtered clear in the cold. (2) Filtered distilled water. (3) Price's best glycerine, tested free from acid. Then mix as follows, according to the purpose in view : (a) For greatest toughness or lasting properties take one vol. oleate solution, one vol. glycerine, and two vols. distilled water, (b] For beautiful coloured bands, quickly developing : one vol. oleate, vol. glycerine, and four vols. water, (c) For rapid development of the black spot : one vol. oleate, five vols. water, and only a trace of glycerine. For a sudden emergency a simple solution of any good glycerine soap generally answers tolerably well. A solution may often be toughened for immediate use by a trace of gelatine ; but as the animal matter soon decomposes, such a solution cannot be preserved for any time. 156 LIGHT [CHAP. latter stick into woodervfeet as at B. Solder the joints, afterwards smoothing them off, and then dip the rings into melted paraffin, or warm them and smear very thinly with it, which keeps them from cutting the films. Arrange several of the B stands in a row, first dipping their paraffined rings in a saucer of solution and wetting them thoroughly with it ; then we can with a little practice blow large bubbles and place on the stands. Through the whole row throw the full lantern beam, which gives a fine effect. Or a large bubble may be blown on the saucer itself, first carefully soaping it to the very rim ; if this is placed in front of the lantern and the nozzle canted down towards it, fine reflections may be cast on the screen. We must avoid carefully all froth in the saucer, keeping as free as possible from all bubbles but the one we are blowing. By far the best instrument for blowing bubbles is one of the smallest glass funnels (an inch across), sold for filtering small quantities of fluid, on which is sprung half a yard of sufficiently small india-rubber tubing. But the finest experiment is with a flat film. Pinch one of the A rings (Fig. 102) as at c, in the clip, the ring standing above its stem, 1 and adjust it so that the plane of the ring is vertical, and stands the same height as the lantern nozzle. Turn off the lantern L (Fig. 103), parallel with the screen, then dip the ring in the saucer of solution, lift a film, and place it, as at A, at an angle of 45, with the whole light concentrated on it, which will be reflected to the screen, or a slightly con- vergent beam from the condensers will be better still. Turn the clip-stand till the reflected light is central on the screen, and then adjust the loose focusing lens F to form an image. A glorious image it is, as band after band of interference colours travels up the oval image of the wire (the bands really move down the film as it becomes thinner, but the image is of 1 The film lasts much longer thus than if the stem is uppermost, owing to the thinnest portion being dependent from the smooth and unbroken circular wire. IX] ROTATING SOAP-FILM 157 course inverted), while every motion of the film from the least breath of air is pictured plainly (Plate III. C). Simple as it is, there is no more beautiful experiment than this (unless perhaps the following modification of it), and with a good solution the film may last for an hour. The horizontal bands are obviously due to the gradual thinning of the film under the action of gravity ; and if we blow a large bubble on the saucer and place a glass shade over FIG. 103. Projection of a Flat Soap-Film. it, the bands will appear quite as regularly upon that. If we could make the thinning of a flat film, take place round a centre, we ought therefore to get circular rings ; and we can do this easily by a magnificent modification of the experiment, devised I believe by Lord Rayleigh. We only need a slight air-blast, which is best obtained from an acoustic bellows, but the breath may with care be made to suffice. The film being arranged as before, a small glass nozzle (for which one of the glass fillers sold with stylographic pens answers excellently) is 158 LIGHT [CHAP. connected by a tube with the bellows (or the mouth) and ad- justed in another Bunsen holder so as to direct a slight blast at a very small angle with the surface of the film. Adjusted as at A (Fig. 104), the whole is converted into one swiftly whirling A FIG. 104. Rotating Soap-Films. vortex, which exhibits gorgeous colours as the film gets thinner. Adjusted nearer the centre as at B, two vortices will be pro- duced, the chromatic effects being the same. The colours produced in this way are peculiarly vivid, but a tough solution is required, and a 2-inch ring will generally give better results than a larger size. Any surface (not too convex) of iridescent glass (which has a film on the surface whose refractive power has been altered by a chemical process) may be focused in the same way as the soap-film. Another beautiful experiment is with a film of moisture. Blacken a piece of glass on the back, rub a piece of soap over the surface, and clean off with a chamois leather. Pinch this in the clip, adjust it like the soap-film at 45, and focus ; but keep it cool by interposing a glass cell filled with water or alum solution, or the experiment will fail, as it depends on conden- sation of the breath by the cold surface. Then blow on the centre through an india-rubber tube of J-inch bore. As the breath condenses, roughly circular coloured rings will form, and gradually change as the moisture evaporates. Next we may take a film of air. Get two squares of plate ix] NEWTON'S RINGS 159 glass, say 3 inches square, and grind off the sharp edges to prevent scratching. Carefully clean them, and then carefully slide or grind them with moderate pressure smoothly together. We very soon see beautiful fringes of gorgeous colour. When satisfactory, pinch one lower corner of the double plate in the clip, and the three others with loose wooden spring letter-clips. Focus as before : all will be reproduced on the screen, and as we further pinch anywhere, even with the finger and thumb, changes and movements of the colours will demonstrate that the particular colour wholly depends upon the thickness of the film. 104. Thickness of the Film. Newton's Rings. We want to know, if possible, however, what that thickness is, and the last experiment probably suggested to Newton his famous " rings." He placed a convex lens of very slight con- vexity, as in Fig. 105, in contact with a flat glass, against which FIG. 105. Newton's Rings. it was pressed by screws. A simpler method sometimes em- ployed is to cut two circular y&z/ glasses (they must be a J-inch thick, or, at least, one must be so), and having carefully cleaned them, place a ring of thin tinfoil between them at their circumference. Mounted as in Fig. 106, pressure from the centre screw at the back produces, as in the other case, " New- ton's rings," which, in either case, are presented to the lantern and focused on the screen precisely in the manner of the soap- film (Fig. 103). This method is within the power of many who like to construct their own apparatus. It is clear that, knowing either the curve of the lens, or the thickness of the foil, we can calculate the thickness of the film 160 LIGHT [CHAP. of air at any given distance from the centre. Newton found that when he employed pure monochromatic light, he obtained recurring rings of coloured light, and of darkness, at once, twice, thrice, and other multiples of one definite small thick- ness. He soon discovered another beautiful fact, viz., that the rings were broader, or required a thicker film, in red light than in blue light ; and finally, by a movable prism, he threw the successive colours of the spec- trum on the rings, and found them gradually contract as he FIG. io6.-Newton^Rin gs with Fiat travelled towards the violet end. With most lanterns there is hardly light enough to employ this beautiful method ; but the phenomena may be shown as follows : Arrange the Newton's rings, and focus on the screen as before. Provide one of the movable slide-frames now r used by all lantern lecturers, and fit in it two half-size glasses, one blue and one red. Con- dense the light on the rings ; and as close to them as possible, between them and the nozzle, hold the coloured glasses; as these are moved from side to side, the rings will open or contract as the red or blue glass is interposed, and when they equally cover the rings, the two semicircular segments will be seen not to coincide, the red being larger in diameter than the blue. It is easy to ^understand, therefore, that if we employ white light, we must obtain rainbow-coloured circles. 105. Failure of the Emission Theory. Having to ac- count for these phenomena, and adopting for practical pur- poses the corpuscular theory ( 63) as his working hypothesis, 1 Newton accounted for his bright and dark rings recurring at 1 There is ample evidence in the last edition of his Optics, that Newton was latterly very strongly attracted towards the Undulatory Theory, but did not feel 'justified in adopting it, owing to difficulties he was unable to solve. PI. 3. INTERFERENCE Jfew ton's Jlinffs B 3pesfs~<*m' Soap Films D Spertrrttn rf Ditto. JperJrum; of LigTit reSlecfvd farm f>2m' Diffrcwtivn' Spectra ofufffr a Afobertj grating J)ito. oTxservec? ix] THE TWO THEORIES 161 every multiple of a given thickness of the transparent film, by supposing that the " particles " of light suffer alternate " fits " of transmission or reflection, at regularly recurring intervals or distances. Professor Tyndall supposes that he imagined a rotation during their progressive motion, and this is not im- probable ; but is only a supposition. If, then, light reaches the first surface of the film in a fit of transmission, it enters it and travels to the second surface ; and if the thickness is such that it is in the same fit or phase when arriving at the second sur- face, it is again transmitted, and so is lost to view by reflected light. There is at that point, therefore, a dark ring ; and ob- viously at every multiple of that thickness another dark ring. If, on the contrary, the particle is in the opposite or reflecting fit when it reaches the second surface, it is reflected and forms a bright ring. It will be plain how, on either hypothesis, the " particles " or the " waves "of red light are larger than those of blue. We can easily, however, test the two theories. Obviously all the light that has anything to do with the rings, according to the corpuscular theory, enters the first surface ; and the " fit :J in which it reaches the second has alone anything to do with them. On our wave hypothesis, it is the interference of waves reflected from both surfaces that causes them. We have not come to Polarisation yet; but it may be briefly stated that polarised light utterly refuses to be reflected from glass at a certain angle; and this polarised light we readily obtain by fitting a " Nicol prism " on to the nozzle of our optical objec- tive. 1 All our light is then polarised ; and when the long diameter is vertical and the Newton's lenses are adjusted at an angle of 55 to 56 with the beam from the lantern, none of it will be reflected from the top glass, or in other words, from the first surface of the film. And if two plain glasses were used, none would be reflected from the second surface either. But 1 For details and explanations on these points see Chaps. X. and XI. Only sufficient is stated here for the purposes of this experiment. II 1 62 LIGHT [CHAP. metal is subject to quite other laws, and does reflect light co- piously under such circumstances ; therefore, by substituting for the bottom glass one which has been silvered or platinised, we can still get reflection from the second surface of the film of air. On the corpuscular theory, we ought therefore still to get the rings. But we do not. There is light on the screen, but the rings have vanished, in the proper position of the Nicol ; to be restored again when this is so turned round as to restore reflection from the first surface also. Further yet ; if we next adjust the lenses so as to meet the light at a still greater angle (from the normal) than that of polarisation, and thus partially restore reflection from the first surface, on rotating the Nicol we get a complicated and beauti- ful phenomenon, first discovered by Arago ; viz., in one posi- tion the rings are of certain colours, and when the Nicol is rotated 90 they show complementary colours. Detailed ex- planation of this is here impossible ; but it can be understood how we thus prove absolutely that the rings are due to the mutual actions of the rays of light reflected from both surfaces of the film. We may prove this in "yet another way, by substi- tuting for the glass and metal surface, two glasses of widely different refractive powers, whose polarising angles are there- fore also different ( 130). We can then adjust the beam of light to either, and in either case, by destroying reflection from either surface of the film, we destroy the rings. This last method of demonstration is, however, only suitable for private experiment. 106. Spectrum Analysis of the Rings. We further in- vestigate the matter by bringing to bear our never-failing method of spectrum analysis. Cover the pair of Newton's lenses with a disc of black paper or card, having in it a slit, say, -^ of an inch wide, and reaching all across, exactly over the centre ; the slit then crosses all the bands at right angles, and the appearance, or image on the screen when focused there, is like one of the bands in Fig. 107. The whole arrangements IX] ANALYSIS OF THE RINGS 163 are shown in plan in Fig. 108. The lantern must be turned considerably away from the screen, so that the reflected beam may have a small angle of incidence ; or else, as the glasses are FIG. 107. so thick, the light from the film will not be able to emerge from the narrow slit by which it enters, and there will be only an image of a white slit as reflected from the upper surface of the top glass, and none of the portions of rings, which is what we FIG. 108. Spectrum Analysis of the Rings. want. The reflected slit is focused by the loose lens, F, at about the screen distance, but must be considerably divergent from the screen to allow for refraction by the prism, p, which gives the spectrum on the screen, s. The lenses are drawn much larger in proportion for the sake of clearness. Thus passing the image of the slice of rings from white light through the prism, and throwing its spectrum on the M 2 1 64 LIGHT [CHAP. screen, it is easy to see what we may expect if the wave theory be correct. Dr. Young saw it long ago, and in his " Lectures " he has drawn what he foresaw clearly with the eyes of his mind, though there is no record that he observed it in actual fact as we are about to do. Seeing that red light gives us bands of a certain width, as at R in Fig. 107, while blue light gives us narrower bands as at B, by drawing the imaginary lines as dotted, we can see what must occur when all the colours are dispersed into their several places in the spectrum. We must get, unless all our theory is wrong, the beautiful appearances shown in B, Plate III. ; the spectrum of the slit being crossed by parabolic dark lines, which will show exactly the waves cut out by interference at every thickness of the film. Such a spec- trum, with its parabolic interference bands, stands before us on our screen. l The flat soap-film may be analysed in precisely the same way. Arrange for a parallel beam, and place the cardboard or adjustable brass slit on the nozzle, as for previous spectrum- work. The slice of light from the nozzle will then sufficiently mark the slit whose spectrum is desired, and may impinge at any convenient angle. When all is adjusted, take up a fresh film ; and as it thins, the dark interference bands, showing the waves destroyed by interference, will travel across the spectrum steadily, as long as any colour is shown. The appearances of the flat soap-film and its spectrum are shown at C, D, Plate III. The student can observe these phenomena directly through any form of prism ; and nearly all the phenomena described in this chapter can also be seen privately, without any lantern or other expensive apparatus whatever. 107. Phenomena of Thicker Films. Towards the edges of a pair of Newton's lenses the rings of colour seen in white light disappear \ and some students realise with difficulty why 1 To the best of my belief this beautiful experiment was first publicly made with the lantern by Dr. Tyndall. ix] THICKER FILMS 165 tliis is so, when the films reach a certain thickness. There are two reasons. One is very much the same as the reason why we could not get a pure spectrum from a wide slit. ( 55.) Interferences are produced, up to a certain point ; but so many very narrow rings or fringes are mingled, so close upon one another, that the visual effect is white. Homogeneous light will show rings in much thicker films, and is one proof that this is so. Spectrum analysis of a film not so thin is another. With care, a film of mica can be split so thin that, while it appears to reflect perfect white light, if a slit of this light be analysed, by blacking the mica all but a narrow stripe, and then treating this stripe of reflected light like the slice of light from Newton's lenses, the spectrum will be seen crossed by numerous straight interference bands. Such a spectrum from a film of mica is shown at E, Plate III. But there is another reason. When the film reaches a still greater thickness, it will also be seen on consideration that the two reflected rays into which each original ray is divided, are so far separated by refraction, that they are no longer close enough to interfere with each other at all. Thin mica films may be employed in yet another way. Pro- ject a spectrum from a slit as usual, and across the path of the rays hold the film obliquely. A portion of the rays are then transmitted direct, while a portion are reflected within the film and then transmitted, after losing a certain distance as before. Again the spectrum will be crossed by beautiful in- terference bands, though hardly so distinct as by the preceding method. It is very clear that the thicknesses at which the light and dark rings occur, must give us definite information as to the wave-lengths of the different colours of lighL This point will, however, be better explained a little farther on ( 117). 108. Thin Films and Sound Vibrations. The most elegant application of the colours of thin films in physics is due to the researches of Mr. Sedley Taylor, and relates to the 1 66 LIGHT [CHAP. vibration of a telephone plate. It is well known that, by the variable attraction of a magnet under the influence of variable currents, and vibrations thus caused in a thin sheet of iron, the most complex sounds of the human voice, or other instru- ments, are reproduced by another sheet of iron at the other end of a telegraph wire ; but it is very difficult to realise how complicated speech can be reproduced by such simple means. By stretching a soap-film over an aperture in a plate laid over a resonator, and exciting the vibrations of the air contained in the latter, Mr. Taylor obtained most beautiful figures which elucidate the matter, by showing how complicated these vibra- FIG. 109. Principle of Lantern Phoneidoscope. tions are. Later on Mr. Tisley constructed the phoneidoscope, which, when sung into through an open mouthpiece on the end of a tube, shows the same phenomena in a film laid hori- zontally over the other end of the tube. The scale of this instrument is, however, too small for lantern work, and it is very difficult to avoid constant bursting of the film. After many trials an apparatus was constructed, which easily gives magnificent phenomena, and the essentials of which are shown in Fig. 109. A is any vessel open at both ends, 2 to 3 inches across at the top, and with a neck at the bottom large enough for an inch vulcanised india-rubber tube to stretch a little IX] LANTERN PHONEIDOSCOPE 167 tightly over an elbow, B, connected with it by a piece of rubber tube, c. A piece of a common bottle, cut round the body and neck, and ground flat at each end, would suffice, or a tin funnel with an elbow at the bottom and a flat ring soldered flush round the top will answer admirably. The whole can be fitted into any thin box, the funnel projecting through a hole cut in the top. The other end of the elastic tube is stretched over the neck of a kind of telephone mouthpiece, M, furnished with a membrane, F. A soap-film being laid over A, and used as presently described, can readily be focused on the ceiling or an overhead screen in the same way as the ripples in Fig 31. But I now use a more complete and convenient apparatus constructed for me by Mr. C. Darker, which works direct to the ordinary screen, and is shown in Fig. no. The diagram explains itself, the dotted line showing the course of a slightly converged beam from the condensers, and how the first mirror brings down the light upon the mouth of the funnel, and the second re- directs the rays reflected up from the film into a horizontal path ; the focus- ing lens (of rather long focus) focus- ing the image. The mirrors have some adjustment in two horizontal slots in the back-board. The funnel should have apertures or notches at the top to allow air to escape from under the film, and be so mounted that it can be withdrawn from the kind of open box in which it fits, when its place can be occupied by a vessel of water or mercury, or other apparatus. A black card will need to be adjusted against the side of the apparatus next the screen, high enough to prevent any stray direct light from the lantern, or other than the reflected rays, passing the apparatus. My first mouthpiece was made of wood, FIG. 1 68 LIGHT [CHAP. FIG. in. as in Fig. 109, with a vibrating diaphragm of thin mica at F; but this sometimes rattled, and I prefer it as in Fig. in, with a membrane of very thin india-rubber. A membrane of any kind, if thin enough, does not interfere with true sound vibra- tions, but prevents the film being prematurely ruptured by any direct blast of air, which might occur with an open mouthpiece. The india- rubber speaking-tube may be any convenient length, and it is more impressive if connected with a sufficient length of metal pipe to reach to the other end of the room. All being arranged, some plates must be pre- pared, of metal or very thick card, 3^ inches or 4 inches diameter, with openings in the centre of different shapes ; the best effects are from circular, square, and hexagonal apertures, which should be about if inches or 2 inches diameter. The apertures should be bevelled towards one side of the plate (this is done because the film will, by its contractile power, draw flat to the smallest side of the aper- ture), and if of card, well varnished to resist the moisture. Finally, they are blackened, and we are ready for work. The apparatus is adjusted so that one of the plates laid across the top of the funnel lies nearly level, and all is arranged so that the aperture is truly focused on the screen. Then we dip the end of a strip of card, rather wider than the apertures, in a saucer of soap solution, and drawing it carefully over the smallest side of an aperture, readily cover it with a film. (Use no more solution than necessary.) Several plates may be covered at once to avoid delays. Hold the plate at an incline, or upright, till interference colours begin to show ; then lay it centrally on the funnel, with the soap downwards, so that a dead black dry margin surrounds the film. If all is right, we have an image of the film on the screen. Be sure all is focused properly, and that all light possible is condensed upon the film. IX] PHONEIDOSCOPE EFFECTS 169 Then take the mouthpiece, or let some one else do so at the other end of the room, and sing into it. Not only every note, but every different vocal sound on the same note will be re- presented in different, complicated, and most beautiful kalei- doscopic patterns, very poor ideas of a few of which are shown in Fig. 112. At first we may get only shadowed figures, but with a little practice we soon get exquisite colour figures, with symmetrically-arranged whirling vortices ; and if we sing a song, every change of note will be optically repre- FIG. 112. Phoneidoscope Effects. sented on the screen by a corresponding figure. Employing a mouthpiece with a vibrating plate or membrane, there is little risk (as with Tisley's form of apparatus) of bursting the film, and a good tough one will sometimes last a quarter of an hour. If the film breaks too soon, it shows either that the solution is not good, or that the plates have ragged edges, or are too dry : metal ones, which are best, hold the film more smoothly if heated and smeared with a thin coat of melted paraffin. This is one of the most magnificent optical experiments, and 1 70 LIGHT [CHAP. very easily shown. With the apparatus in Fig. no interesting modifications can be made, by withdrawing the funnel and tube, and laying larger plates with apertures and films upon the box itself. If then a tuning-fork on a resonance-box be ex- cited, and the open end of the resonator be presented to the open side of the box under the film, strong stable vortex figures will be caused ; or a cornet blown whilst presented in the same w r ay will also excite most powerful vibrations. 109. Colours of Thick Plates. Thick plates of glass, ground and polished with sufficient accuracy, can be made to exhibit interference colours in several ways ; but only one or tw r o can be demonstrated in the lantern. Jamin showed that if a pencil of light was reflected at an angle of about 45 from a plate of thick glass, and the reflected pencil again received at the same angle on another plate, so as to be finally reflected in a direction parallel to that of the original pencil, provided the plates were of exactly equal thickness (which is secured by cutting both from the same piece of optically worked glass) interference was produced ; the pencil reflected from the first surface of the first plate and second of the second, interfering with that reflected from the second surface of the first and the first surface of the second. Accordingly, the very least devia- tion from parallelism between the two plates produces inter- ference fringes, until the divergence becomes too great. For projection the apparatus is arranged in the form known as Delezenne's analyser. In this instrument the two plates are arranged so close to each other in comparison with their area, \\ that the original pencil of light (here supposed to come from the top of the page) cannot pass the edges of both plates. Each plate is mounted on the inner flat surface of a circular cell resembling in shape the half of a collar-box, one being capable of rotation inside the other in the same way as that well-known article : in this case the flat lid and bottom of the box would be parallel to the lines of this page, and the axis of revolution parallel to the side of the page. Then by slightly rotating the ix] THICK PLATES 171 cell bearing one of the plates, beautiful interference fringes are produced, exactly resembling Savart's bands ( 201 and Fig. E, plate 7). The parts of the brass mount representing the lid and bottom of the collar-box are pierced with apertures, so adjusted as to prevent any light from passing the apparatus, except that which has been reflected from the two glass plates. These last may be either silvered on the back, or not. The individual student has only to look through Delezenne's analyser at a window, or sheet of white paper, or any fairly bright surface, to see the fringes. Newton's experiment with a thick glass concave mirror is also of great beauty and easily projected. The mirror should be of about three or four feet radius of curvature. The face is carefully cleaned, and then somewhat dulled all over by a film of weak milk and water laid on with a clean sponge : milk alone is far too opaque, and dusting with lycopodium powder, which I have seen done in alleged substitution, gives rise to rather different diffraction phenomena, as described in 114. The radiant must now be adjusted in the centre of curvature of the mirror, so that the reflected rays focus again at the same point. With a good jet or the arc light, a very good plan is to send all the converged light possible, from the lantern through a small aperture on the nozzle, the aperture thus be- coming the focal radiant ; and around the nozzle to adjust a screen of white card with an aperture in the centre for the nozzle to protrude, precisely as in the rainbow experiment figured on p. 75, except that here the parallel pencil is re- placed by a diverging one, collected and thrown back by the concave mirror. Brilliant circular iris-coloured rings will now appear on the white card screen, surrounding the aperture as a centre. If the mirror be slightly deflected so as to separate the focal image from the radiant centre, the rings will surround a centre midway between the two, and the appearances of this centre will vary remarkably with changes in its position. In this experiment, the interference is produced between pairs 172 LIGHT [CHAP. of rays or very small pencils irregularly scattered by the dulled surface of the mirror : the one ray, that scattered on entering the glass ; the other, that scattered on leaving it after reflection from the silvered back. Or the arrangements may be varied by using the naked jet and lime-cylinder quite out of the lantern, and adjusting it with the incandescent face towards the mirror. The lime itself will shield the light from the large projection screen behind ; or if the incandescence be too great for this, a small opaque screen should be arranged to do so, and a cylindrical case round the mirror stop stray light from the room. Then the rings will be projected in air in the focal plane of the lime-cylinder, and a large lens of long focus will produce a fair image of them upon the screen. A glass mirror for this experiment must be optically worked : the common cheap ones do not suffice. A student may, how- ever, perform it with a good piece of thick plane looking-glass alone. Dull the surface as before, and support the looking- glass piece at one side of the apartment. Taking a candle or other small flame in the hand, go to the other side, and hold the flame so that the image is seen in the centre of the dulled mirror when the eye is as near it as possible. Broad fringes will be seen in the mirror. no. Fresnel's Mirrors. There are many other ways of producing interference between two rays of light than the use of plates or films ; but not all of them are capable of em- ployment with the lantern, owing to the small amount of light which can be used not being sufficient to be visible when spread over a screen. Fresnel, for instance, letting a cone of light from a luminous point fall upon two mirrors very slightly inclined together from the same plane, formed interference fringes. The arrangement is shown in Fig. 113, where a pencil of rays from the sun is converged by the lens to the one point or line of emission we have already found necessary. A test- tube filled with water as a cylindrical lens answers perfectly ix] FRESNEL'S PRISM 173 well, or the line of light reflected in sunlight from such a tube filled with mercury will also answer. The diverging rays be- yond the focus are then received upon the two mirrors, M m, m N, and if the inner edges or junction line of these be very slightly depressed, it is manifest the reflected rays will some- what cross each other, and that light from both will appear on a portion of a piece of card held as a screen at s. On this portion will be found dark and light, or coloured stripes, due to the interference of the waves. Two pieces of the same glass blacked on the back and laid on a piece of cloth on a flat board, the inner edge of one being depressed a little by the end of any pointed tool, will enable the student to perform this instructive experiment. If the light from the lantern be made to diverge from an extremely narrow slit, and the mirrors be arranged at several feet distance from it, the dark fringes may be observed by the few who can gather round the apparatus ; but on the screen the fringes are too faint to be seen. in. Fresnel's Prism. Fresnel also caused two beams to interfere, by interposing in the diverging cone a double prism of very small obliquity, called an "interference prism," with the same result. Here, too, the light is very faint for a large screen, but some approximation to the effect is possible with a powerful jet, and still more with the arc light. The prism must be good, and ground with a very small angle ; when the bands are broadest. The lenses should be removed from the 174 LIGHT [CHAP. optical front, a slit placed on the nozzle, and a lens mounted in a wooden frame placed in the optical stage, so as to focus all possible light upon a short slit, the rays diverging from this. In the diverging rays the bi-prism is placed, not far off the slit, and carefully adjusted for parallelism with the slit. If the prism is a good one, and the jet powerful, most eyes will dis- cern perpendicular fringes on the screen in the brighter band where both sides of the prism unite their rays. Often they show more plainly by using a piece of very transparent red glass ; and they are generally improved by using an achromatic lens of several inches diameter and 6 or 8 inches focal length, to focus upon the screen, not the prism or any other actual object, but the fringes as they appear in the focal plane of the lens, a few inches in front of the prism. This is almost the only case in which an achromatic lens is really conspicuously better than a simple one for optical demonstration. 1 With a jet not capable of this experiment, something may yet be done in a rougher way. Prepare two or three sliders, the 4 x 2 J inch size, of blackened glass, and through the black, cut or scratch, over the field, vertical lines (Fig. 114) of uniform width and distance for each slide, but varying in these characters on different glasses, the medium width being about one-thirtieth of an inch. (Only one is really necessary, but it will be found that each screen distance shows the best pheno- mena with its own gauge of bright lines, which must be found 1 I have obtained the best screen effects with the - projection microscope. On the compound or table microscope the experiment is a very easy and beautiful one, a very small bi-prism sufficing. This is laid on the stage, fixed or mounted on the middle of a glass slip. An inch or more below, in the sub-stage, is adjusted a disc or piece of glass blackened all over, with one bold line scratched in the centre, on which is condensed as much light from the mirror as possible. The bi-prism has only to be got in line and in centre for the fringes to appear. They may either be looked at with the eye-piece alone, or a low-power objective may also be used, not to focus the prism, but a plane above it. Either the eye-piece or the objective focuses for vision the state of the fringes in its own focal plane. ix] MIXED PLATES 175 by trial.) Place in the optical stage and focus : then against the nozzle, N, hold, or fit in a tube which slides on it, the double prism, p, as in Fig. 115, which will give two images, whereof FIG. 114. one set of slits will, more or less, overlap the other. If the slits are the right gauge for the lenses and screen distance, we get colour ; and it can readily be shown, by covering one half FIG. 115. Fresnel's Prism. the prism, that nearly all this colour is due to the interference of the two sets of waves. 1 112. Irregular Refraction. Another means of causing interference is by irregular refraction, causing retardation of portions of the light. Such are the phenomena of what Dr: Young called " mixed " plates. Provide a few discs of plate glass about 2 inches diameter. Carefully clean two discs so that they show colour when pressed together, and then intro- 1 The private student will have no difficulty at all with this experiment. He has only to cut in a black card a set of slits, about one-sixteenth of an inch in width and distance, and hold this at arm's length against a bright sky or the opal globe of a lamp, with the slits perpendicular. On now holding the double prism close to the eye, with the centre line over the pupil, he will at once see conspicuous colours, Such prisms an inch square cost from 2s. 6d. to 5..?. each. 176 LIGHT [CHAP. duce between them a bit of butter or suet the size of a large pin's head, and some clean saliva or a drop of water ; or the froth of white of egg well beaten up will do ; or fine soap- lather. Work together with a circular movement, and gradually a film of mixed grease and water, or albumen and air, &c., will spread between the plates. Now it is plain that the light which passes through a molecule of the denser portion of this mixture is more retarded than that which passes through the other ; and hence we find, on looking through the film at a luminous point, there are beautiful halos of colour. Or if we place in the optical stage a black card in which a few small holes are made, on focusing the holes, covering the nozzle with another black card pierced with a |-inch hole, and holding a little in front of this (the exact distance must be found by trial) the " mixed plate," the images are surrounded by coloured halos, the colour of course depending upon the thickness of the film. To the same cause must probably be referred the curious phenomena seen when an equal mixture of glycerine and spirits of turpentine is shaken together. What is known as diffraction will not account for it, since there is no approach to a spectrum ; but it is completely accounted for by the unequal retardation of the light by the two media in small molecules, which only mix mechanically. On looking through the mixture at any illuminated objects, they will be seen fringed with colour, the colour changing as the liquids again settle, till only a coloured line is seen in the fluid itself where the two are in contact. I have only tried the experiment thus, but by making a small closed tank with parallel sides, there is not the slightest doubt some beautiful phenomena might be projected on the screen. 113. Diffraction. One of Newton's two great difficulties about the Undulatory Theory was, that if it were true, the ether- waves ought to bend round the edges of bodies into the shadow. It appears strange now, that even the few experiments he made in diffraction did not suggest to him that this is precisely what TX] DIFFRACTION 177 does happen. If we hold any opaque body, such as a black card, in the rays from a very small point or line of brilliant light, such as already described, we find there is no sharp shadow, but a series of coloured fringes due to interference, both within and without what should appear as the geometrical shadow. Dr.. Young, who first pointed out the true character of these fringes, supposed them due to the interference of the direct rays with those reflected at a great obliquity from the edges of the body. This has been shown to be incorrect ; and all the fringes have been proved to occur from the inter- ferences of the secondary waves shown in Fig. 80, when separated from the "grand wave" by the opaque body. They can be observed without any apparatus at all, by receiving on a card a shadow from the planet Venus at its brightest, in an otherwise dark room. But more beautiful phenomena are within our reach, the nature of one class of which is best seen from a simple experi- ment without the lantern, which should be made by every student. Cut a slit ^-inch wide in a black card, and hold it in front of a flame so as to be brightly illuminated. Blacken a bit of glass, and scratch with a needle a straight line on that. Hold the scratch close to the eye, and look through it at the slit, held at arm's length, both being vertical. We see the slit in the centre, and on each side of it are a series of spectra, and we thus prove conclusively that the waves of light do spread out laterally from the second slit, becoming visible under these circumstances partly because all stronger light is cut off, but chiefly because we stop off the greater part of the main wave. (See Fig. 80.) The spectra, of course, represent overlapping images of different colours, as we can see if we cover our first slit half with blue glass and half with red ; we then get a series of red images farther apart than the blue images, precisely as in previous experiments. The reason why we get the dark spaces between, and not one unbroken band of light, is that at certain intervals, which can be, and have been, exactly N i?8 LIGHT [CHAP. calculated, the waves from, say, one edge of the slit, interfere with the waves starting from the other edge, or some other point in it. From one edge the path to the eye is longer, and we have already learnt that retardation means extinction of certain colour- waves. (See 117.) 114. Gratings. The foregoing experiment theoretically ought to be shown by the lantern, and it has been stated that it can be; but I have never been able to do so, for the reason already given ; the light passing through the second slit is not sufficient. Undoubtedly the spectra must be on the screen ; but they are too faint to be perceived. We must get "more light," and we are helped in this by the fact, that if we arrange a number of slits exactly at equal distances, their various interferences and correspondences all fall at regular intervals, depending partly on the width of the slits, and partly on their distances apart. Such is what is termed a " grating," or series of very fine light and dark lines. If fine enough, such an assemblage of slits practically cuts out, at each point on the screen, all but one single wave-length, and so produces pure spectral colours only ; whereas the other interference colours we have seen are mixtures of residual colours. Nobert has ruled gratings with 3,000 and 6,000 lines to the inch, and photographic copies of the first of these are sold at a guinea, or less, and produce most beautiful phenomena. Placing a slit, say \ inch wide, in the optical stage, and focus- ing, we hold the grating in front of the nozzle, with its lines parallel to the slit. There are at once projected on the screen, on each side of the central image, a most beautiful series of diffraction spectra (see F, Plate III.). Two similar gratings crossed give beautiful spectra of a small hole about \ inch diameter, especially if the aperture be illuminated by the pencil attachment shown in Fig. 2, but without the front concave lens ; or the light may be condensed on the aperture by a lens in the optical stage as previously described. There are not only perpendicular and horizontal spectra, but also diagonal ix] GRATINGS 179 ones. The finest effects are, however, produced by placing in the optical stage a symmetrical pattern of several small holes in a thin metal plate say eight arranged in a square; but the pattern, size, and distance must be found by experiment and adapted to the gratings used and the screen distance. If pro- perly adjusted, and with sufficiently brilliant light, on rotating one grating, most beautiful diffracted patterns will appear on the screen. 1 A circular grating, two or three inches in diameter, scratched on glass, gives brilliant circular rainbows, when inter- posed in the path of the rays from a small aperture focused on the screen. Any kind of grating gives most brilliant effects if held close to the eye, and looked through towards any small naked flame at some distance, or still better towards an arc light. Another attractive method of observing diffraction phe- nomena is to cover the object-glass of any telescope one such as can be bought for is. 6d. will do with caps of black card, in each of which is pricked or cut one or more very small holes of various sizes, arranged in different patterns. Or the cap may be of blackened glass, on which is scratched very small any regular curve or figure, such as a tiny circle or square. On looking through the telescope thus furnished at a bright star, beautiful diffraction figures will be seen : or if the telescope be directed to a small hole in a plate close in front of a good limelight, the phenomena will be gorgeous beyond description. This is known as Brooks's apparatus. But such apparatus is not needed to show diffraction. Two simple slits have already been mentioned. Even the fingers will 1 Mr. C. J. Fox, F.R.M.S., first showed me this beautiful experiment in the microscope, to which he had adapted it, and in which the effects, owing to better illumination, are far superior. For that instrument the apertures r pricked in a blackened circle of paper, are focused by a low- power objective, and the gratings mounted over the eyepiece. With the lantern, the parallel beam from even the limelight needs to be condensed by an extra lens into the smallest area which will cover the apertures. N 2 i8o LIGHT [CHAP. show fringes if nearly closed and looked through at a distant candle. With care, any one may rule on smoked glass for him- self, with a sharp needle, a grating of 120 lines to an inch, and even this will give very perceptible spectra. Wire-gauze is obtainable 120 meshes to the inch, and sometimes 150 meshes ; and this will give perceptible phenomena, especially if gauze and lens be both five or six inches in diameter, greater number of lines increasing the brilliance and "resolution." So also will a selected bit of the very finest cambric ; but a good piece can only be found by experiment, when it should be mounted between two glass plates. Even more simple objects are at hand. Get a broad pheasant's body feather (some birds' are better still, but this is easily got ; most fowl feathers are too coarse), and mount it between two glass plates, blacking out all the space the feather does not cover. Focus on the screen a small hole in a black card, and interpose the feather ; or look through it at any naked gas-light ; again we get attrac- tive diffraction phenomena. A very familiar example is found on looking through almost any railway carriage window at night, at one of the lamps. The dripping of the rain and dust, and the process which goes by the name of cleaning, combine to form tolerably perpendicular lines on the glass, and these draw out the luminous point into a long band. Usually this is only vaguely luminous, the lines being irregular, various colours overlap and produce white but on one or two occasions in the course of several years I have seen colours. Halos are produced in a very similar way. If a small dis- tant flame be looked at through a glass dulled by the breath, colour will be seen : and if a piece of glass be dusted with lycopodium powder, very good halos will be seen through it. Satisfactory effects from such dusted glasses on the screen, will however depend upon the size of the dusted glass, greater size increasing the resolving power as with the gauze. If the dusted glass be six inches in diameter, and it be held close to a lens as large, so as to employ the whole surface, beautiful ix] PERFORATED PLATES 181 halos will be seen, even with lycopodium ; but there are still better spores of black or purple colour to be sometimes obtained, such as those of Elaphomyces granulatus. Most beautiful lantern projections may also be produced from perforated cards, such as can be bought for book-markers at a penny each. Several sizes are made, the smallest being about twenty-five holes to the inch ; purchase one or two of each size, and blacken all but the smallest, which would fill up or choke. 1 Cut circular discs to fit such standard wooden frames as already mentioned ; and fix in frames, by a spring circular wire, two specimens of each size. First place in the optical stage one such slide (generally a medium gauge does best for this ; but again, much depends on the screen distance). On focusing, we of course get images of the circular holes. Now gently run in the focu sing-tube a little farther, so that the focus is projected rather beyond\he screen. The pencil of light from each aperture now interferes with its neighbours, and we get a more or less decidedly coloured pattern, which varies as the lens is moved in or out of the focusing-tube ; at two or three feet away from the nozzle, the colours are pretty vivid. Much interest will be found in the various interference patterns given even by single cards in this way. But now add a second slide in front of the other. If the frames are -| of an inch thick, and the slides are inserted " the same way,'' the cards will be that distance apart, which, with a screen five feet off, is for most lenses a good distance ; if a little more or less inter- val is necessary, one slide may be reversed. The pencils of light from the posterior holes are now further diffracted by the second set. As a rule, I have found the best effects at four or five feet distance, the back card being focused somewhat short of the screen, and from medium gauge cards ; but fine effects are produced at that distance (which should not be 1 An alum-trough is desirable, or the black card may burn with the heat. Perforated zinc is not troublesome in this way, but cannot be got in the smaller gauges. i82 LIGHT [CHAP. exceeded with a lamp or burner) with most of the cards, or by a coarser one behind with a finer pattern in front. A little experiment will soon be repaid by most beautiful coloured tartan patterns, especially if the front card can be rotated in a frame such as is described later on for polariscope experiments ; all produced by the interferences and diffractions of the small pencils of light. With the limelight and a screen distance of ten or twelve feet, I have found the best effects from using both cards of the finest pattern, placed back to back, so as to be only J inch apart. As one card is rotated, beautiful effects will be produced when the right focus is got ; and in certain positions it will be found that a little alteration in focus only, appears to rotate large squares of the pattern in a most beautiful manner. But the arrangements are different with each objective and screen distance. The small white screen will be found very handy to show the varying effects at the shorter distances ; and any experiments intended for exhibition should be carefully worked out at exactly the distances that are to be employed, or the effect may be found quite different from that intended. Any experimenter, however, may depend upon finding great pleasure in this direction. The private student may hold one card close to the eye, and the other at a little distance. 115. Striated Surfaces. Lastly, light reflected from very narrow lines or grooves also gives us interference. Turn off the lantern parallel with the screen, and placing a perpendicu- lar slit in the optical stage, focus it as reflected from a bit of plane glass held close to the nozzle at an angle of 45. Then substitute for the plane glass a grating held in the same position ; the image of the slit is now flanked on each side by spectra, just as when transmitted light was used, only not quite so bright. If no grating be possessed, get a finely-coloured piece of flat polished mother-of-pearl, or one of those beauti- fully-coloured haliotis shells found in Jersey, which can be bought for one shilling almost anywhere, or a finely-coloured IX STRIATED SURFACES 183 pearl card-case will do ; the main thing is to select a richly- coloured specimen. There is really no colour in these shells whatever : it is entirely due to the interferences of rays reflected from the countless little grooves which cover their surface, as can be proved by taking a good impression of one of the best bits in black sealing-wax, when the indented wax will show the colours of the pearl. Adjust the shell or piece of pearl like the soap-film, condensing all the light on it at 45, and focusing with the loose lens. The coloured image shows a kind of glowing "transparency" on the screen, very beauti- ful ; but as we now gently turn the shell so as to change the angles, the colours change, showing that they are not fixed, but due to interference. Even a peacock's feather gives beautiful phenomena treated in the same way, but some of the colour appears to be more of the nature of that from a thin surface film. If we mount the end of one by two black ligatures sewn through a black card, and treat it like the pearl, we shall find that at different angles we get very different colours, passing from deep purple to brilliant green. This is a beautiful experiment, but requires the lime-light, at not too great a screen distance. For all these latter experi- ments, the handiest plan is to prepare a small blackened tablet like Fig. 1 1 6 ; a thin piece of blackened deal, D, being glued on a boss, B, into which is driven a tube, T, fitting in the sockets of our pillar-stands. The feather, or shell, or other article, can either be fastened direct to the tablet with two elastic bands, if solid and small enough, or the feather on the black card can be affixed by two blackened drawing-pins. The object can then be either rotated on a FIG. 1 16. Tablet for Objects. 184 LIGHT [CHAP. horizontal axis, or the angle of incidence and reflection rotated vertically by turning the pillar. The metal buttons engraved with very fine lines, formerly made by Sir John Barton, then Master of the Mint, and still known as " Barton's buttons," are amongst the most splendid examples of the interference of reflected light. They are very scarce now, none having been made for forty years ; but a few are treasured here and there, and when the polish is well pre- served, they glow with brilliant colours impossible to describe. 1 Any who possess one, in good condition, may produce an exquisite screen projection with the lime-light by taking out all the front lenses, placing a J-inch aperture in black card in the ordinary lantern-stage, and allowing the beam from this to be reflected from the button and focused on the screen. Or the naked lime-light, through a small aperture in a cap slipped over the empty condenser-cell, may be focused on the screen, which gives more light ; as will the pencil attachment, Fig. 2. Various small spectra will be seen arranged in a beautiful stellar pattern, depending on that of the button. I have seen also very good effects from the finest cut that can be produced in the lathe from a pointed tool on the flat surface of bright metal. 116. The Diffraction Spectrum. In all these ways we have produced colour, or dark fringes, by the interference of different series of waves. It will be manifest that, as before, we have got all our colours solely by suppressing or quenching colour that the colours are precisely of the same character as the dark fringes. It is equally manifest that since, as a rule, 1 By the great kindness of Mr. John Barton, grandson of the inventor, I was placed in possession of a fine set of these buttons or "Iris orna- ments." I learnt from him that the dividing engine, constructed for Sir John Barton by Messrs. Maudsley and Co., had been always in possession of the family since ; but that since his father's death, no one for a long while .could use it efficiently. After many trials, however, Mr. Robert Barton, in Australia, succeeded in producing good results, and some specimens of his workmanship were shown at the Melbourne Exhibition of 1880-81. ix] GRATING SPECTRA 185 only one particular wave-length can be completely extinguished at any given point, the colours we see are not pure, but com- pound residuals, or made up of the residue of the spectrum. The only exception is in the case of gratings, which, by the orderly sequence of successive extinctions, cut out all the colours except one wave-length at a given point. A little thought will lead to the conclusion that in these grating spectra we must therefore get the colours, or Fraunhofer lines which locate them, in the real order and proportion of their wave-lengths, and not as affected by the various or anomalous dispersions of refracting prisms. This is so ; and the fact makes grating spectra, though less brilliant than those given by a prism, owing to the large suppressions of light which produce them, especially valuable to the physicist. This difference in the spectra, and the uniformity of diffrac- tion spectra as compared with those produced by a prism, can easily be shown by experiment. Diffracting the pencil from a brilliant small aperture by a parallel grating, and further dif- racting the spectra thus produced by a second similar grating, held with its lines at right angles to those of the former, we have already seen ( 114) that we get a most beautiful series of diagonal spectra. This, of course, must follow from con- siderations already discussed, and the greater distances apart of the red images than the blue. All these diagonal spectra are perfectly straight. But if, instead of a second grating, we use a prism, with its refracting edge at right angles to the slit, it is not so. We still disperse the central pencil of white light, and refract each spectrum produced by the grating ; and, as before, the blue portions of the spectra are more deflected than the red. But the deflection is no longer proportional, but dependent on the special dispersion of the prism ; and hence the refracted spectra now appear as parabolic curves, represented at G, Plate III. 117. Measurement of Waves. We have, in the pheno- mena of interference, various means of measuring the lengths of 1 86 LIGHT [CHAP. the waves which produce any given colour. For many and obvious reasons such measurements are easiest taken with monochromatic light ; and the simplest case is that of the light from a slit or point passing through a second slit ( 113). Let A B be a highly magni- fied representation of the second card and c D of the slit in it. The rays which pass perpendicu- larly through c D will none of them be retarded ; and therefore produce on :///////// the retina or a screen an ordinary white image the t;. 117. Nature of Diffraction. J central white band. But as the card A B stops off the main wave-front ( 67), every particle of ether in motion all across the width of the slit produces new secondary waves spreading right and left of the perpendicular direction : let us take any given inclination, c E, D F. Then drawing c w perpendicular to the course of the ray, we see that the waves from D have farther to go than those from c by the distance D w. Assume that at this inclination D w is a wave-length of the colour employed, and number the supposed ether particles across the slit from unity onwards, then w r e see that from 4, the central particle, the waves are half a wave before those from D, and half a wave behind those from c. But still further, the rays from i will be half a wave before, or in complete discordance with, those from 5, 2 with 6, and so on : every single ray finds another in complete discordance with it somewhere in the slit : ob- viously therefore at this particular angle there must be a dark band. Farther to the right or left the relations will alter, and there will be a bright band, to be succeeded by other dark and bright bands. A general proof of the correctness of this rea- soning is found in the fact, that plainly, according to the IX] MEASURING WAVES 187 theory, the narrower the slit the greater must be the angular distance of any given band from the central image. This must be, because it will demand a greater obliquity to make the necessary difference of paths from the edges of a narrower slit. Experiment shows that this is the case. Upon this hypothesis we can measure exactly the length of a wave, as in the diagram, Fig. 118. Draw the line A B to FIG. nS. Measurement of Wave-length. represent the card as before, with c D, the slit in it, and c E, D F, the inclination for the first dark band from the centre of the field. With the radius c D describe a semicircle, and from c also draw c w as before, perpendicular to D F ; then D w is one wave-length, and x y is the angular value of the obliquity of the dark band. Inspection shows us that the angle x D y is necessarily equal to D c w ; and as D w is for such a small distance practically coincident with a segment of the semi- circle, we only have to take the proportion of 180 (the semi- circle) to the angle D c w (the obliquity), and the same propor- tion must exist between the linear length of the semicircle and that of the wave. Schwerd found that with a slit of 1-35 mm. the angle D c w was i' 38", the ratio of 180 to which is 648,000 to 98. The linear length of the semicircle is 4*248 mm. It follows that the length of the wave, of the colour employed in his experiment, is about the ^olhro of an inch- 1 1 The phenomena of gratings are too complex to enter into here ; they are admirably elucidated in Miiller-Pouillet's Lehrbuch der Physik. 1 88 LIGHT [CHAP. We may reason in the same way from thin films. The thickness of the film at the first bright ring in Newton's lenses, with the same colour employed by Schwerd in the above experiment, is found to be about yeVoo^ ^ an i ncri - This thickness we know has to be doubled to give the retardation, which gives us soihro f an i ncn f r a retardation that causes a bright ring. Here then is an apparent discrepancy ; for according to our calculation with the slit, goisinr f an mcn should only be half a wave, and the ring ought to be black. One or other of the reflected rays is half a wave ouf, or is in the contrary phase to what the mere retardation produces. 118. Change of Phase in Reflection from a Rarer Medium. But on careful consideration this apparent con- tradiction proves the truth of the theory : since we perceive it ought to be so. We have seen that waves involve periods and phases even more essentially than lengths ; and we have to consider what happens when a wave is reflected from a denser or a rarer medium respectively. Take for illustration, as simplest, our first example of wave motion, in a set of ivory balls. Let from A to B in Fig. 1 1 9 be large balls, and B to c much FIG. IIQ. Dense and Rare Media. smaller ones, and let them be united together by an elastic cord a c through the centre of all. Then if we roll a ball up against A, the wave of compression is transmitted to B. There it throws off the ball D, which in turn passes on the wave through the smaller balls. But the small balls are not enough to take up all the motion as the. large ones did ; they are driven off more freely, in strict analogy to a wave encountering a rarer medium. The last ball D has therefore motion to spare, and follows the first small ball ^, but slower and more feebly. In this it is however checked by the elastic cord, which instantly IX] REVERSAL OF PHASE 189 pulls it back, or is rather pulled by it ; and so the effect is really a pull upon the balls behind. In other words, the wave of compression is, in the very moment and in the act of reflection from the medium of less resistance, changed into a wave of extension. In other words again, it is converted into the opposite phase ; or yet again, is thrown half a wave-length out of phase. If, however, we reverse the process, rolling the loose ball against the smaller row, so as to impart the impulse to c, it is not so. The last small ball e finds a greater obstruction to its motion instead of a less, and cannot therefore have any tendency to fly off; the reflected wave remains a wave of compression, as it was at the moment of impact. Thus we see that when light is reflected from two surfaces of a film, one of which is the surface of a denser and the other of a rarer medium, the reflection which is of the latter character must be thrown half a wave-length, or half a phase, which is the same thing, out of its order. In a soap film it is the second surface ; in the film of air the first surface. The result is that the retardation which, judging by thickness alone, would have retarded the ray from the second surface half a wave- length, is altered another half wave-length forward or back (it does not matter which, the alteration to the opposite phase of vibration being the point), and the two rays are brought into accordance, or give the bright ring. This measurement, therefore, now gives the same wave-length as the other. The explanation can be easily subjected to experiment. If we use a top lens of very low density, and an under plate of great density, we can introduce between them a film of fluid of some intermediate density, as oil of sassafras. Both reflections then take place from a denser medium, and the retardation alone should come into play, without any other alteration of phase. Experiment fulfils this expectation to the letter. 1 1 This explanation is taken in substance from Sir John Herschel, his popular exposition of it being the best I am acquainted with. 190 LIGHT [CHAP. The apparent objection thus becomes a strong argument for the truth of the theory. 119. Photographic Demonstrations of Interfer- ence. A similar reversal of phase occurs in reflection from many metallic surfaces, so that the surface becomes a nodal point, and causes interferences at successive nodes (corre- sponding to half a wave-length) between the incident and reflected rays. Wiener demonstrated this by photography in 1889. Placing a very thin homogeneous photographic film in contact with a silver surface, but very slightly inclined to it, and causing the light to impinge at an angle instead of normally, the distances between the nodes were so magni- fied that he obtained conspicuous interference bands on the photographic film, parallel of course to the line of intersection of the planes of the film and reflecting surface. But still more striking confirmation amounting in fact to absolute demonstration of the literal reality of these inter- ferences between waves, was furnished in 1891 by the beautiful photographic experiments of Professor Lippmann, of the Sor- bonne. Carefully preparing thicker photographic films of homogeneous or non-granular structure (since such a structure, by dispersing the rays, destroys or impairs the phenomena), he backed the film by a bright reflecting surface of mercury, the film on its glass plate forming the side of a mercury trough. He reasoned, like Wiener, that any wave of definite length, pass- ing through the film and then being reflected from the mercury, must occasion periodic interferences and reinforcements between the primary and reflected waves, at regular intervals correspond- ing with the half wave-length of the light employed. But with such an arrangement, reinforcement and extinction by inter- ference produce respectively photographic action and non- action : and hence there ought to be a deposition from the silver-salt in successively recurring and equi-diitant very thin layers, which should give by reflection the colour of the homo- geneous light employed. This is found to be the case when ix] HERTZ'S EXPERIMENTS 191 proper precautions are taken ; and many brilliant and nearly complete coloured photographs of the spectrum have been successfully produced in this manner, 1 forming thus an absolute demonstration of the wave-theory, and its phenomena of interferences. The experiment was entirely founded upon the theory, and has proved its truth to the letter. 120. Hertz's Experiments. The other phenomena of interference are similarly capable of calculation. And the most complicated phenomena have so far corresponded with calculation in the most minute particulars. Perhaps the most far-reaching proof of the general phenomena of the undulatory theory, has been given by the classical experiments in electrical radiation worked out by Professor Hertz of Vienna in 1889, which are not unlikely to prove the most epochal discoveries of the nineteenth century. They not only provide demonstra- tion of the undulatory hypothesis here considered, but equally so of all the fundamental features of the electro-magnetic theory of light formulated by the late lamented J. Clerk- Maxwell ; and hold out hopes of carrying us ultimately some way into the physics of the ether itself. The very briefest out- line of the nature of these experiments, so far as they bear upon our present subject, must however here suffice. We have spoken hitherto of waves. What is a wave ? We have referred to different kinds of waves to waves in water, in air, in a row of balls, &c., &c. The phenomena of these differ materially, but we saw that the essence of the matter in all 1 Though in a sense this is true "photography in colours," it is not so in the ordinary sense, and it by no means follows that coloured photography from Nature will ever be attained by it, though he would be a bold man who would affirm the contrary. We have seen how mixed nearly all natural colours are ; and it will easily be seen how the superposition of many different wave-lengths would destroy all the sharp precision of definite layers on which the photographic result depends, especially as all photographic action spreads a little in the plate itself. Also no sensitive salts have yet been found which respond equally to even the pure colours of the spectrum. 192 LIGHT [CHAP. cases was this : that each successive particle of the medium passed through operations exactly similar to those of the pre- ceding particle, a little later in time. That is the one point essential and common to all in other words, a wave is some disturbance or change of state periodic in space and time. What is the nature of the disturbance in the ether which constitutes the physical basis of light, we do not yet positively know ; but Clerk-Maxwell supposed it to be an electric disturbance, and found confirmation for his hypothesis in the fact, that the known velocity of propagation of an electric disturbance, and of light, were one and the same. It followed, however, that light ought to be stopped by conductors, which is the fact ; and that insulators should be transparent, which latter was supposed to be contradicted by fact. If this latter difficulty were cleared up, it was comparatively easy to conceive how a wave of electrical disturbance might be propagated. The ether must possess, in regard to electricity, two qualities answering to what we call elasticity and inertia. Then a state of electric stress would correspond to the bending aside and holding by a detent of a steel spring. An electric discharge would correspond to the release of that spring ; and the electric inertia of the ether would give the discharge such momentum as to carry it beyond the neutral point, and create a stress of the opposite kind ; which would again be discharged, so keeping up an alternating or oscillating discharge. Such an oscillating discharge might be propagated as Light. We know as a fact that there is this electric inertia, causing momentum, overplus, and recoil in discharges. If we cut a wire carrying a current round an electro-magnet, the momentum of the current carries a spark across the interval ; and it has long been known that the discharge of a Leyden jar consists of numerous oscillations, which Professor O. Lodge has, by in- creasing the " capacity " of the apparatus, rendered so slow as to be made visible by a rotating mirror. But while such discharges cause sparks, and these sparks in a sense give "light," of the ix] ELECTRICAL WAVES 193 propagation in space of the oscillation itself, as a wave identical r in character with light, there was till recently no proof. This proof was Hertz's great step, and was afforded by the simplest means, viz., by providing a second sparking apparatus whose period was synchronous with the primary oscillation. This is very readily done by adjusting the " capacity " ; then an apparatus so " tuned," as it were, acts as a " resonator " to the primary oscillation, and reproduces it, just as a tuning-fork in unison responds to another set in vibration. The next step was to increase the oscillations of the discharge in number and frequency, which was done by connecting the wires of an induction-coil to two small cylinders with sparking knobs set in line, and separated by a small interval. By this means oscillations were produced as rapid as 300 millions per second, which by calculation must produce (at the velocity of light) waves about a yard long. Such waves as these the shortest in length and period it is yet found possible to produce in this way are still, of course, far too long and slow to be visible. (The spark is of course visible, but that is not what we are concerned with ; what we want to get at is the propagation of the oscillatory discharge to a distance in space.) But by the " resonator " Hertz pro- vided an electrical eye, as it were, which perceives the state of things many yards away, and by this aid he has demonstrated that the oscillatory discharge is propagated, and that such electrical waves reproduce all the phenomena of light with the utmost exactness. They reach the " resonator " with the same velocity as light. They are reflected, and brought again to a focus by parabolic mirrors. Using a large prism of pitch, with faces a yard square, they were found to be refracted ; and pitch, wood, and other semi-insulators, opaque to visible light, are perfectly transparent to these longer waves, thus triumphantly verifying Clerk-Maxwell's hypothesis, and show- ing yet again that transparency and absorption are entirely questions of wave-length as compared with molecular con- o 194 LIGHT [CHAP. stitution ( 92). On the other hand, these electrical waves ar^ reflected by metals. Lastly, by reflecting them back fro^L sheets of metal,.- nodes of interference are produced (easily located by adjusting the resonator) which are precisely similar in all but the space between them (corresponding with the wave- length) to the nodes demonstrated by the photographic experi- ments of Professor Lippman (119). The rapidity already obtained in the oscillations of discharge, has been gained by the use of smaller and smaller oscillators. With these we have arrived at waves approximately three feet long ; but the longest visible waves are only about y^J^^ of an inch ! To get such, we must conceive still smaller and smaller oscillators ; but we should then find ourselves approaching in size the molecules of bodies. There is- reason to believe that such oscillation of discharges between molecules, is* just what happens when light is produced. 1 121. Size of Matter Molecules. I am not willing to conclude this. chapter, without some explanation of the manner in w r hich the dimensions of light-waves throw light upon the dimensions of the molecules of Matter itself. We are forced to conceive of Matter as consisting of detached molecules, or separate very small portions, on account of the enormous power of expansion which all matter possesses when heated. Moreover, while water and alcohol expand as one to three in the liquid form, for the same increase of temperature ; in vapour they expand in the same ratio? which we can only account for on the supposition that the molecules are now at enormously greater distances, so that their special action on one another has ceased, and they only obey the general laws of gases 1 Even as these pages are passing through the press, strong confirmation of this view has been given by the wonderful experiments of Nikola Tesla concerning the various effects of rapidly alternating currents of high poten- tial. These currents no longer give shocks, while some of their phenomena closely resemble flames. 2 About ^575- for each rise of i Fahrenheit. 1X ] SIZE OF MOLECULES IQ5 exposed to heat. We are therefore confronted with these Cached Molecules of Matter ; and some of the questions physicists are now investigating, are concerning the probable size and other properties and relations of these molecules. Now on the first of these questions the measurements we obtained of our light-waves throw very considerable light. First, the molecules must be considerably less than those waves in their dimensions, or they would be at least partially visible with the powerful microscopes we now possess. Nobert's test- lines of 112,000 to the inch half the dimensions of a blue wave were resolved in America by Dr. Woodward. More- over, in many transparent bodies at least, as the waves pass through amongst the molecules without being very sensibly destroyed or affected, this is another proof that such waves are large in proportion; since they plainly are not split up amongst them, but as it were surge grandly over them, with little resistance. And yet, secondly, the molecules cannot be infinitely \^ relatively-or, shall we say, tremendously less; because if they were, it is easy to see that a difference in the waves of one half (we may take red light as - 3 ^T) and vl a S .^l of an inch) could not so profoundly affect the phe- nomenal it does. To use an illustration I have seen some- where, sawdust would show no perceptible difference in effect upon water waves thirty feet and fifty feet apart; but logs of wood probably would. All this is indefinite, and yet it does give us a notion of what physicists call the class or order of magnitudes involved; and from some other considerations of this kind which cannot be given here, 1 it has been argued with very great probability that the average distance from moleci to molecule can hardly be more than a thousandth part, and hardly less than one ten-thousandth part, of the average 1 of a wave. , Very analogous deductions may be drawn from t i Many of them are discussed towards the end of Tail's Recent Advance in Physical Science (Macmillan and Co.). 196 LIGHT [CHAP. nomena of a soap film. With a good solution, if a film is stretched upon a ring as in Fig. 103, and carefully observed, after a while coloured bands cease to form, and a large white patch appears, answering to the first bright ring. This we know ( 1 1 8) to be a thickness of one-fourth of a wave-length. But after this comes a patch of very dark grey, often called black. 1 Now the peculiarity about this is, that the boundary edge is perfectly sharp, as if cut with scissors ! It is not so with Newtoris lenses, where the diminution of thickness is gradual ; and the only conclusion is, that in the soap-film there is some sudden change in the thickness, and therefore physical constitution of the film. As to the thickness, it cannot be nearly one-fourth of a wave-lengh, or a considerable portion of light would be reflected. It must be as compared with the wave-length practically nil, for either (i) the two reflecting surfaces are so close that the retardation is practically nothing, and discordance is produced solely by the half-wave difference of phase due to the denser medium ; or (2) the film is so thin that the air on both sides is in optical contact and there is no reflection at all. Obviously the first supposition must be the true one ; and it is very easy to see that if the film exceeded in thickness one-fortieth of a wave-length, we must have some traces of colour. We have here, then, apparently an abrupt transition from T ^^ 2 an ^ it is difficult 1 It is often stated that this grey only comes in patches, and that the film almost immediately bursts. With solutions made as described on page 154, I have had half the film remain of the dark grey for hours. 2 Three years before the above was written, Dr. Dewar had estimated the thickness of the grey at T.Trci.Tnnr f an inch. I think it best to repeat the reasoning which led me in 1882 to estimate the thickness at less than half that. Since then Professors Reinold and Riicker have proved, by most rigid experiments on two distinct lines which agree in their results by measuring the electrical resistance, and, secondly, the retardation caused in a ray of light by passing through a definite number of films that the thickness is in actual fact about ^.^^'trotr f an inch. ix] A SOAP FILM 197 not to believe that this must be due to some peculiar change in the physical plan, or constitution of the film ; which again must almost certainly be in some simple numerical relation with the size of the molecules, And as we know that the mechanical equivalent of the heat required to vaporise a grain of water would not be sufficient (according to the law of capillary attraction) to reduce it to a thickness of 6TnriTn ^ fTnnr of an inch, and therefore at that thickness the molecules could no longer hold together, but would separate in vapour, we seem to have here two outside limits between which the size of the molecules, or rather the distances between their centres, must lie. 1 Finally, however, we can hardly suppose that a film only one molecule thick would hold together at all. We must therefore multiply the lesser limit by some figure, and we shall be within the mark in estimating the molecules in the film's thickness at from 3 to 5. Even this low figure brings the limits of measure- ment for the molecules of this form of matter as something like ^.(jTj-J.o-oTj- of an inch for the greatest possible distance between the centres and ^STF.^^ <7o to TO o.olio.o o o (according to the multiplier we assume) for the least distance. It is remarkable that several other lines of investigation lead to similar conclusions ; but they need not be mentioned here. Only the merest outlines of the optical argument have been given ; but these will suffice to show how Light is still, in another sense, a Revealer of those minute elements which can never be seen by mortal eyes. 1 Sir William Thomson believes that the molecules of gas cannot exceed Tnr.infr.innr of an inch ; and Mr. Sorby estimates various molecules as probably from T^'info'innF to TTnr.-fru7r,7n)7r f an incn - 198 LIGHT [CHAP. APPENDIX TO CHAPTER IX. Diffraction in the Microscope. The phenomena of diffraction described in this chapter have a very important bearing upon microscopical investigation, and especially upon the advantage of increased angular "aperture " in microscopic objectives. That the increased angle ob- tainable by immersing object and objective in a fluid, instead of observing the object in air, gave marvellously increased powers of delineation, had long been known ; but so long as this was supposed to be due merely to greater illumination, or the collection of a larger pencil of light from the object, it could not be satisfactorily accounted for. At length Professor Abbe pointed out the true nature of the advantage gained, and the matter was soon demonstrated by ingenious experiments devised by himself, Mr. Stephenson, and Mr. Frank Crisp, a full account of which may be found in the Journal of the Royal Microscopical Society. The following brief explanation is condensed from Mr. Crisp's lucid summmary of the subject in that journal for April, 1881, to which I am also indebted for the diagrams by which it is illustrated. It will be understood, from the phenomena of "gratings" already investigated, that if between the reflecting mirror and the stage of the microscope we interpose a very small opening in a diaphragm, and on the stage lay a "grating" of ruled lines, on removing the eye-piece and look- ing down the tube we observe a series of images of the aperture like Fig. 120, cir- cular in homogeneous light, but the outer ones cons i stm g of spectra in white light. The small pencil admitted through the diaphragm is " diffracted," just as we have already found. We IX] MICROSCOPIC DIFFRACTION 199 next lay upon the stage a slide such as Fig. 121, consisting of both wide and narrow lines ruled on glass. Removing the eye-piece as before, we have of course, on looking down the tube, the appearance presented in Fig. 122, the coarse lines FIG FIG. 122. giving diffraction spectra twice as close and numerous as those caused by the fine lines. The reason for this we have already seen (117); the present point is, what influence these diffracted rays have upon the image, and it is here that the experiments referred to are so important and interesting. First of all, by a diaphragm at the back of the objective such as that in Fig. 123, let us cover up all the diffraction spectra, allowing only the direct, or central white pencil, to reach the conjugate focus, or image-point. On replacing the eye-piece, FIG. 123. FIG. 124. all the fine ruling has disappeared, leaving only the general outline of the object, as in Fig. 124. By suppressing the diffracted rays, therefore, fine detail or " structure " of an object is obliterated. 200 LIGHT [CHAP. Secondly, let us adjust behind the objective a diaphragm like Fig. 125, which allows all the lower spectra in Fig. 122 to pass to the image-point, but suppresses every alternate spectrum of the upper set, diffracted by the coarse lines. The image now appears as in Fig. 126, the upper set of lines to all appearance FIG. 125. FIG. 126. being identical with the lower set. Precisely in the same way, if we substitute a diaphragm like Fig. 127, stopping off yet another half of the alternate spectra, the lines are again apparently doubled, and we "see" Fig. 128, though the actual object remains the same. In these experiments therefore, I I FIG. 127 FIG. 128. while retaining the central pencil of light throughout, we have created apparent detail or structure in the object by suppressing certain of the spectra. Still further, however, let us take a slide which when magni- fied resembles Fig. 129, or a "crossed grating." We get with this, from the small aperture, rectangular spectra somewhat like IX] MICROSCOPIC DIFFRACTION 201 Fig. 130 ; but these also cause diagonal spectra by their mutual diffraction of one another, as described in 114, ir6. Constructing a diaphragm like Fig. 131, which allows FIG. 129. FIG. 130. only the central pencil and two of these diagonal spectra to pass, the vertical and horizontal lines of the object have vanished, to be replaced by Fig. 132. This experiment is FIG. 131. FIG. 132. troublesome, the diaphragm having to be prepared with extreme care ; but the results deduced from theory have been rigorously verified. Now the microscopic student knows that many objects, by their minute and regularly recurring " structure," cannot fail to give, and do give, strong diffractive effects. The well-known Pleurosigma angulatum will serve as an example of the practical effect of the foregoing considerations. It gives three sets of diffraction spectra arranged as in Fig. 133. As each set is produced by something resembling alternations of structure at right angles to it, the three sets of lines in the object must be 202 LIGHT [CHAP arranged mainly as in Fig. 134; but it will be obvious from what has gone before, that by selecting different sets of spectra, with or without the central beam, the apparent images will differ widely. It is also manifest that all these images cannot FIG. 133. FIG 134. represent the true structure. If, however, we have the character- istic spectra, and their position and relative intensity can be calculated, then the resultant image can also be calculated ; and so far as all the spectra are included, it will represent the real object. The general conclusion is, therefore, that we have no true image of an object whose structure is sufficiently fine to give strong diffractive effects, unless all the diffracted rays, or rather, perhaps, all the truly characteristic sets of spectra, are collected ; and the image will more or less resemble the object, in pro- portion as the spectra are all collected, or at least sufficient of these characteristic spectra. As we have found before ( 117) that the finer the grating, the more widely deflected are the diffracted spectra, we can readily understand how, as regards minute structure especially, collection of the widest possible angular field of rays from the object is a point of the utmost importance for correct delineation, quite irrespective of greater illumination ; and it is in this respect that immersion objectives have such an enormous advantage. Of course these considerations only apply to structure of a certain degree of minuteness. With more coarseness, all the diffracted spectra which are visible may be collected by a ix] MICROSCOPIC DIFFRACTION 203 moderate angle. But when we reach a certain fineness, it will be seen that the image in a microscope of small angular aperture can be no true representation of the object at all, but is due to peculiar selective conditions. This may be well shown by an experiment with Amphipleura pellurida. With a homogeneous-immersion objective of large aperture, focus the object under an illumination so oblique as to show up all the lines clearly. Then remove the eye-piece as in previous experiments ; and placing the eye near the conjugate focus or image-point of the objective, the direct beam will be seen to emerge obliquely as a bright spot ; while on the other side of the field, and close to its margin, will be seen more or less of the inner portion of the first diffraction spectrum. (Fig. 135.) Only a portion of one spectrum, observe ; and that so near the margin that it must be lost with any objective of much less angle. If now a small bit of paper be adjusted on the back lens of the objective FIG. 135. so as to stop this spectrum and no more, the illumination is diminished by an almost infinitesimal portion, and the diatom is still visible, apparently as brightly illuminated as before. But the characteristic striation, which caused, and was therefore imaged by, the diffracted light, is gone, just in the same manner as was demonstrated in Figs. 123 and 124. NOTE. I prefer still to represent the Abbe theory in its earlier, moderate, and demonstrably accurate form, rather than in the extreme and (as I consider) wholly inaccurate development which has been given to it since the first edition of this work appeared. It is in this earlier form that Professor Abbe's brilliant discoveries will remain, I believe, ever associated with his name ; that they pointed the way to marvellous advances in microscopic optics, which are also chiefly due to his hands; and that they still point the way, not illusively, but with well-grounded hope, to nearer and nearer approaches towards an ideal of perfection ; whilst his later and extreme 204 LIGHT [CHAP. views logically imply the worthlessness of the work he has himself done, and confront the optician with a dictum of blank despair. As \he. Journal of the R.M.S. has practically suppressed any further discussion of Professor Abbe's views, it may be well to add a few words respecting the distinctions to be drawn, in my opinion, between their earlier and later form, and the reasons (as they appear to me, from considerable study of diffraction phenomena) for making such marked discrimination between them. This seems the more advisable, because it has been repeatedly stated that the theory here questioned has "been demonstrated by mathematical analysis." As all physicists are aware, no theory of the kind can be demonstrated by mathematical analysis, which solely deals with quantities or relations or functions already postulated or proved by experiment. The theory itself must stand or fall by its consonance or otherwise with ascertained physical facts ; and the following remarks are made solely from this point of view. The different nature of Abbe's later theory is easily made clear. The reasoning and experiments briefly summarized in the text above, imply the great advantage, and as regards the image of minute periodic structure the necessity, of the microscopic object-glass embracing a wide-angled cone of rays from each point in the object ; and they further imply, that with a wide cone of rays (other things being equal) we may expect greater truth of image. But in a much more recent paper (Journal R.M.S., 1889, p. 723), Professor Abbe, if his argument be admitted, utterly de- molishes a large part of this fabric. The whole paper is directed against the value of wide-angled cones, on the alleged ground that every ray (or infinitely small pencil of rays) of which the illuminating cone consists, causes its -own "fan" of diffraction-spectra, owing to the different obli- quities of these original pencils. Of such fans he then alleges: "These various elementary diffraction -pencils, mingled together within the objective, produce images of the object quite separately. Every single elementary pencil gives rise to its own image, the rays of different elementary pencils being unable to co-operate" Hence he concludes : " The resulting image produced by means of a broad illuminating beam [by which he means, as he has explained, a wide-angled cone] is always a mixture of a multitude of partial images, which are more or less different, and dis- similar to the object itself. There is not the least rational ground, nor any experimental proof, for the expectation that this mixture should come nearer to a strictly correct projection of the object (be less dissimilar to the latter) than that image which is projected by means of a narrow axial illuminating pencil." As regards " experimental proof" space forbids discussion here ; but the converse of the above proposition in that respect has been absolutely demonstrated by Mr. E. M. Nelson, in the Journal of the Quekett Club for July, 1890. Ample experimental proof will be found there detailed^ that a wide cone does give true images where a narrow cone gives false ix] MICROSCOPIC DIFFRACTION 205 images, and that Abbe's earlier theory is practically correct, as against his later one. Here only a few remarks can be made in attempt to show that there is every "rational ground for the expectation" that such would be the case. We have seen already ( 15, 42) 'that a visible image is produced, when upon any point of a screen or other image-plane there are re-collected rays diverging from one point in an object, and when no other rays reach that point of the screen. In the microscope, the diverging pencils are thus re-converged by a lens, and the result is called a dioptric image in all other similar cases. Professor Abbe, however, laid down the proposition even in his earlier statements, that the images due to diffraction-spectra were not dioptrically formed, but due lo interferences of the diffracted rays. This proposition appears to me fundamentally erroneous, and to have naturally led ultimately to the further conclusions above. Consideration of the phenomena will, I think, make it clear that the diffraction image, so far as it is a real image at all, is dioptrically formed precisely as is the image formed by all other rays. The diffraction-spectra due to very fine striations in an object are them- selves due to periodic selective interferences, as we have seen in the text of this chapter. Not only so, but in simple fact all rays of light, in them- selves, are phenomena resulting from interferences precisely analogous to diffraction, as very briefly explained in 67. Confining ourselves how- ever to the apparently simpler phenomena of diffraction, and taking the experiment with P. angulatum above (Fig. 133), every stria in the object sends to the same point on a screen its contribution to the effect, adding to the brilliance of the same band of light of any given wave-length ; whilst on the other hand interferences destroy the light in the dark bands. But in seeking a microscopic image, the arrangements differ radically from those described above. In place of a small aperture beneath the stage, we have a small source of light carefully focussed upon the diatom by the condenser. This focussing of the light itself implies that the luminous rays, diverging afresh from the condenser's focal point, are identical in path with the image-forming rays proceeding from the object as in 42. The object thus appears to emit the rays upon its own account. This is readily understood and admitted, as regards objects seen by scattered reflection, but seems to be practically forgotten as regards transparent objects seen through the microscope ; that it is equally true of them also, however, is well shown in "dark-ground illumination," where all direct light is excluded from the objective, and the object is seen brilliantly illuminated by the rays reflected or refracted or diffracted from the points of the object, and by these rays alone. This being so, however, it does not matter in the least, so far as the dioptric character of the image is concerned, how the rays of light are caused to diverge from any point in the object. Whether they scatter by 206 LIGHT [CHAP. reflection, or scatter by refraction, or scatter by diffraction, the fact remains that they diverge from the one point ; as such a diverging pencil of rays the lens collects them, and converges them again to the conjugate focus. At that focus there must be an image, and the only true image ; and that image is a dioptric image, though partly due to diffracted rays. The first passage quoted above is therefore contrary to fact in both sentences. The "various elementary diffraction-pencils " do not" produce images of the object quite separately " : they do not of themselves produce any images at all, and without the objective never would do so. The spectra diverge from the object, not from or in the lens ; and it is necessary for the lens to re-converge them to get an image, just as all other diverging rays are re- converged to the conjugate focal point. So far from being " unable to co-operate," an experiment properly carried out proves that they can and do co-operate ; and that a perfect lens, to the limit of its aperture, will bring every ray diverging from any point in the object, however caused so to diverge, to one and the same image, which is a dioptric image as regards every ray thus re-converged by a lens. This reasoning only holds good in its fulness, when the luminous point of emission, and the point of emission from the object itself, practically coincide. Hence coincidence of image-point for the direct and the diffracted rays must largely depend upon a small source of light being accurately focused upon the object ; and it will be limited to the aplanatic aperture or cone of the condenser. That these conditions are necessary to what is commonly called a " critical " image, is well known ; and the fact is a strong confirmation of the view here expressed. There is further a very simple optical principle which gives strong " rational ground for the expectation " that, as Professor Abbe formerly taught, the image will be a true image so far as all its elements are grasped by the lens. It is the simple optical principle of reversibility the fact that if we consider the image as an object, rays traced from it backwards must give us an image exactly resembling the object. Why it is, that if a striation causes diffraction-fans, we must utilize these fans of rays if we are to truly image the striation, we do not fully know : yet it seems reasonable to suppose that, in face of the fundamental connection between minute striation and such separation of the rays into diffraction-fans, it should be so. One reason may be, that wherever striation is uniform or periodic, every element in it combines to intensify the phenomena the light that images a single line in a grating, is contributed by rays from every other line, and intense in proportion to their number ; the bearing of which upon the question of visibility is readily seen. Apart from any lens or question of aperture, the greater the number of lines in a grating the greater its power of "resolution ; " and the same law holds good as regards the mere thick- ness of glass traversed by the rays through a dispersive prism. That such is the whole truth, is not however suggested. All here insisted upon is ix] MICROSCOPIC DIFFRACTION 207 the simple fact for it is a fact that every ray diverging from a point of the object is converged dioptrically (so far as the lens is perfectly corrected and embraces the pencil) to the conjugate focus, and that here alone can be a true image. The student who has experimented with perforated cards in the manner described in 114, will not be at a loss to understand Professor Abbe's disbelief in the truth of any results from diffraction pencils. He will have learnt from those experiments how interferences of pencils from the nume- rous apertures, do also produce the most surprising changes of pattern and appearance, as the focus of the objective is altered. Such patterns are readily thrown upon the screen ; and if a single card or plate be used, the phenomena will very closely resemble those of a diatom in the microscope. But these are mere interference fringes, not images in any sense. There is still one true image to be got, and one only ; and it is in the plane where the diverging diffraction-fans are truly focused by the lens. One has only to consider how subtle a thing, compared with this rough focusing, is the focusing of a diatom of 50,000 striations per inch under high power, to understand all the baffling microscopic phenomena. But there are further the imperfections of the microscopic objective and con- denser to consider, and especially in the one point which Professor Abbe has himself, in the celebrated lenses constructed on his formulae, most markedly disregarded. That point is flatness of fleld. It is generally held that this quality, and that of definition, are to some extent incompatible. Practically it has heretofore been considered so, with large apertures ; and Professor Abbe's own lenses have accordingly sacrificed the one point largely to the other. But it is easy to see that flatness of field the requirement that an object in one plane should be truly imaged in one plane is of vital importance as regards diffraction pencils caused by minute periodic struc- ture. The very few elements in the centre of the field may be truly focused, and so far all seems favourable to a true image. We shall indeed get such of a minute bacterium or flagelfam, and probably even of a small portion broken off separately, containing only two or three elements of a diatom structure. But with an entire diatom containing many elements the rays diffracted from more circumferential elements of the striation, are not focused by a lens whose field is concave instead of plane. Now with periodic structures, rays from these outer striations which are not in focus, not only go to form their own image, (which we may be willing to neglect) but also go to impair by interference the image of the centre striations also. They are not in true focus there either ; and so we may get a false interference "pattern" instead of a true image. Different zones in the area of the lens may also have different foci, and very often have such. Though very difficult to remedy, this latter fault is however well under- stood ; but the necessity, so far as avoiding unfocused interference "patterns" and getting one true dioptric "image " is concerned, of the 208 LIGHT [CHAP, ix outer elements being in true focus, even to secure the inner elements them- selves being only formed by truly-focused rays, does not seem to have been acknowledged, and is a point in which the optician has to learn from the physicist. The condenser also plays a most important part in the result, and Professor Abbe's old chromatic form, which has been so largely used in problems of high aperture, is about the least capable of giving any true image at all, that could possibly be constructed. It is highly chromatic, and is incapable of any true aplanatic focus. But every ray from the lamp-flame not truly focused upon the striated structure, cannot be truly converged to an image, and by false "crossing" must produce interferences with other rays. To come to a practical conclusion : the task thus set before the micro- scopic optician is doubtless one of tremendous difficulty. If he is to attain a true image of a minute periodic structure, he must combine perfect flatness of field in his lens with perfect corrections in other respects, and he must produce a perfectly aplanatic condenser. This perfect ideal may be unattainable, though Professor Abbe has himself done so much that we may reasonably hope for much more. But so far as attained, an unmistak- able image, which alone can be beyond doubt accurately focused, will assuredly be obtained with it, true in proportion as all the elements are gathered in. That very much advance may be made in this direction, is shown by the recent beautiful apochromatic lenses of Powell and Lealand, which, without the slightest loss in definition, have attained a much greater degree than formerly of flatness in field. This fact I myself proved by ex- haustive screen tests ; and it is noteworthy that Dr. Dallinger, many months afterwards, from tests entirely different in character of the very same power (\ inch) so tested by me, pronounced it a lens to which he had seen, from his own practical working point of view, "no successful rival." In any dozen lenses, there are moreover some much flatter in field than others, without being at all defective in other respects. There are ample proofs that, with the aid of fluorite and its wonderfully low figures of refraction and dispersion, the real importance of this factor has only to be adequately recognised, instead of being ignored, for great advances in performance to be made. The optician may at least work on, with all the hopes first aroused by Abbe's classical discoveries ; not checked by the negation to all his efforts implied in the paper above cited. CHAPTER X DOUBLE REFRACTION AND POLARISATION Double Refraction Huygens's Experiment of Reduplicating Images Polarisation Polarisers, Analysers, and Polariscopes Phenomena of Tourmalines Polarisation by Reflection and Refraction What Polarisation implies Analysis of Polarisation by Reflection and Refraction The Polarising Angle Direction of the Vibrations Ana- lysis of Polarisation by Double Refraction Principal Planes Extra- ordinary and Ordinary Wave-Shells in Doubly-Refracting Crystals Action of the Tourmalines Appendix : Vibrations of Common Light. IN dealing with light hitherto, we have found it reflected, or otherwise behaving according to certain uniform laws which were not affected by the position or direction of the ray. We have now to examine phenomena in which that is not the case. 122. Double Refraction. Place in the optical stage the smallest aperture that will show a bright spot upon the screen, and in front of the nozzle hold a piece three or four inches long of the clear mineral called Iceland spar, which crystallises in the form of a rhombohedron, as shown in Fig. 136. There appear perceptibly two images, separated by a slight interval ; and if the spar is turned round pretty equally, it is seen that one image rotates round the other. It is plain that the single p 210 LIGHT [CHAP. pencil from the lantern A B (Fig. 137) is, in passing through the spar, divided into two, P. c and P. n ; and equally clear that if one of these rays is refracted in the plane of incidence, and FIG. 136. Iceland Spar or Calcite. according to the law of sines, the other in some positions cannot be. It is also obvious that somehow or other the indices of refraction ( 33) must differ in the two' rays. Large pieces of spar are clumsy, however, and give little separation, as both rays resume parallelism (c E, D F) when FIG. 137. Double Refraction. they emerge from it. But as we have tw r o indices of refraction in certain positions, if we cut a prism of the spar, with its refracting edge in a proper position, the angular deviation will continue after the two rays emerge, and the separation increases with the distance. The dispersion of such a prism is easily x] HUYGENS'S EXPERIMENT 211 achromatised, or nearly so, with a reversed prism of glass, 1 and a small bit of spar thus treated gives us a wide separation. We shall suppose two such prisms, A and P, (Fig. 138), mounted in cork, and so fitted that the brass tube containing the first rotates on the nozzle at N, while the second, P,, rotates in the first, with a space, s, between them, through _ _ 1*10.138. Huygens s Apparatus for which, by slits in the sides of the the lantern, mounting tube, a- slide an inch wide can be inserted. Two double-image prisms thus fitted are usually called a " Huygens's apparatus." 123. Huygens's Experiment. We can now use a larger aperture. Place one, \ inch in diameter, in the optical stage, and focus the image ; on placing one prism on the nozzle and rotating it, one image is seen to revolve round the other, but no difference in brightness or otherwise is observed. Let A (Fig. 139) represent these two original images. Add -the A B C D E F FIG. 139. Huygens's Experiment. second prism in front of the first, however ; and keeping the first immovable (say with its two images vertically disposed), rotate the other in front of 'it. Starting with both prisms in the same position, two images still appear, only at double the distance, B, showing that each ray from the first prism suffers no further division, but is only further bent in passing through 1 A better plan is to make both prisms of spar, cut in two directions at right angles with each other, on a plan devised by Dr. Wollaston. This gives better chromatic correction, and doubles the separation of the images. P 2 212 LIGHT [CHAP. the second. But directly the front prism is rotated in the least degree, four images appear ; each pair being of unequal bright- ness, however, until one-eighth of a revolution has been made, or the second prism is at an angle of 45 with the first ; all four are then equal, as at c. Proceeding, what were the faintest images ' become the brightest, and vice versa, until when a quarter of a revolution is reached there are again but two equal images, this time, however, placed at an angle of 45 from the perpendicular on the screen, D. Still proceeding, the same stages are gone through reversed ; but on reaching the half revolution, if both prisms are of equal separating power, there is but one image, F, into which all four have merged. The successive phenomena are represented in Fig. 139, and are of course reversed through a further half revolution back to the first position.- The student will do well to examine these phenomena more in detail, if possible, which he can easily do without any other apparatus than two small rhombs the size of Fig. 140, if he does not possess two such prisms as described. They can either be laid on a sheet of. paper with one round black spot, or held against the window over a pin-hole pricked in a black card. Let the under rhomb be kept in the same position as shown by the white figure, and the other rotated over it as shown by the shaded figure. It will first of all be seen that with the single rhomb, if so cut that the sides are of equal length, the line joining the two images is always parallel to the short diagonal. The same will also be noticed of the reduplication of the images ; and the details of the diagram will enable the successive modifications to be accurately traced, and show all that takes place. (The white spots represent a total extinction of the image.) 124. Polarisation of Light. It is manifest that the pencils of light which have passed through the first piece or prism of Iceland spar, differ remarkably in some way from common light ; and that the difference essentially consists in x] POLARISER AND ANALYSER 213 this : that they behave differently according to which of their sides are presented to certain sides of the second prism. We have here an obvious analogy to the "polarity" of magnets and currents of electricity, which, though not strictly accurate, is sufficient to justify the term of " polarised " light. 125. Polariser and Analyser. And the analogy goes farther. As we cannot detect magnetic polarity until we bring FIG. 140. Analysis of Huygens's Experiment. to our presumed magnet some other magnetic or diamagnetic substance, by whose attraction or repulsion we detect the magnetism ; so here, we could not detect any "polarisation " in our two pencils of light, until we subjected them to a second process similar to the first. This law holds good throughout the subject. A great deal of reflected and other light around- us is, as we shall immediately find, really polarised ; but we cannot detect it to be so without subjecting it to some second 214 LIGHT [CHAP. process, which of itself would polarise it were it not polarised already. If it is, such a further process at once reveals the already existing polarisation, and the apparatus so used is then called an "analyser." A polariser and analyser together form a "polariscope." Any one of the methods which are capable of polarising light, may be used equally to analyse light when polarised ; whether it be the same process as polarised it or not, being a matter of complete indifference beyond the convenience of the operator. These methods are several, and we have now further to experiment with them. 126. Phenomena of Tourmalines. There is another doubly refracting crystal called tourmaline, some specimens of which, when cut in slices parallel with the axis, have the property of rapidly absorbing, or being almost opaque to, one of the two pencils produced. Hence we greatly simplify the phenomena. 1 As one ray only passes through, which is the colour of the crystal, if we focus the slice upon the screen, we see nothing remarkable about it. Obtain, however, two slices of tourmaline, of such sizes and shapes that one can- be seen distinctly over the other. Let one be mounted in one of the 4 x 2-J inches wooden frames, and the other on a loose disc of glass, which can be secured in a metal circle by a spring, and rotated by a pinion and circular rack. 2 Place both in the optical stage, parallel with each other, and focus ; then rotate the front one : the successive appearances are as in Fig 141, 1 Two mistaken statements are often made about tourmalines. One is, that green ones are good polarisers. Some few are, but many are not, and far the best colours are the various shades of browns, or some which are a very pure purplish grey, and very little change the colour of objects seen through them. The other error is that tourmalines ' ' polarise by absorp- tion." All that the absorption does is to take up or stop one of the already-polarised rays due to double refraction ; for if a very thin wedge be ground, at the thinnest edge both images can be distinguished. 2 Such rotating frames, of the standard 4 inches by 2\ inches size, can be purchased for a few shillings of any good London optician, and at least one is indispensable for many experiments. x] TOURMALINES 215 When parallel, A, there is simply a rather deeper colour from the double thickness ; when the movable one is rotated 45, as at B, a considerable portion of light is stopped where both are FIG. 141. Two Tourmalines. superposed ; when at right angles, c, no light whatever can get through the screen there is black. It is plain we have here the same phenomena as before, only simplified by the absorption of one of the two rays. To prove it, we remove the fixed tourmaline, leaving only the rotating one in the stage, and placing with it a circular aperture in a plate or card, just large enough to encircle the tourmaline. On the nozzle of the objective we place one only of the double-image prisms, which if of wide angle will quite separate the two circles of light with the tourmaline image in the centre ; if the separation is not sufficient for this, remove the second lens from the objective, and insert at c, Fig. i, alength- FIG. 142. Tourmaline and Double-Image Prism. ening tube or adapter, about 2 J inches long, which by reducing the size of the discs, but not their distance apart, will " clear " them on the screen. Adjust the prism so that the images stand horizontally, while the tourmaline stands vertically. One image transmits the light, the other is completely black (A, Fig. 142). Now rotate the tourmaline till it stands horizon- 216 LIGHT CHAP. tally ; the light image gradually becomes black, and vice versa, (B) whilst in passing through the angle of 45, both are alike and semi-opaque. Rotating next the prism, while the tourma- line is stationary, the same alternations are repeated. It is perfectly clear that the tourmaline gives us in a single pencil, precisely what the Iceland spar gave us in two pencils. 127. Polarisation by Reflection and Refraction. In 1808 it was discovered by Malus that reflection from glass at certain angles gives the very same " polar " phenomena ; and a few years later it was discovered that the refracted ray which passed through the glass had the same property. On a piece of board, B D (Fig. 143), as base, glue or screw two triangular side pieces, BCD, and fix between the hypothenuse edges of these, B c, ten or twelve plates of thin crown or plate glass, so that the angle A B c, is about 56. It is evident that when laid on a table stand in front of the objective, a beam, E F, from the lantern will be partly 'reflected towards the ceiling as F G, and partly refracted and transmitted to the screen as F H. Adjust it thus : remove the double-image prism but leave the rotating tourmaline in the stage. On rotating the tourmaline, it will be found that when this is horizontal, the reflected image on the ceiling is bright, and when the tourmaline is vertical, black ; and on looking at the screen we see that these effects, by the transmitted ray, are precisely reversed. And if we place an aperture in the stage without the tourmaline, and on the nozzle the double-image prism, we of course find on screen and ceiling reciprocally light and dark images of the x] NATURE OF POLARISATION 217 aperture, which change to the opposite character as the prism is rotated. Next lay the apparatus on its triangular side, and every image is precisely reversed. All through we have found similar phenomena; and if we use the pile of glass first (either as reflector or transmitter) and another pile of glass, or any of the other apparatus, after it, it is still the same ; the beam of light when "polarised " by any one of these methods, behaves in opposite ways when " analysed " by any one of the methods, in positions at right angles with each other round the axis of the beam. A single plate of glass is sufficient, when adjusted at the exact polarising angle, to polarise all the light that is reflected ; and an equal quantity of polarised light is also transmitted through the plate. But this quantity being small, and in the case of the transmitted beam overpowered by the larger quantity of common light also transmitted, it is usual to employ a pile of at least a dozen plates. Even this does not polarise all transmitted light, but sufficiently increases the quantity of reflected light. Owing to inequalities in plates of glass, for accurate experiments it is sometimes necessary, when reflected light is employed, to employ only one plate of perfectly flat glass blackened at the back. At other than the angle of complete polarisation, a somewhat less quantity of light is polarised. 128. Nature of Polarisation. The phenomena of double refraction and polarisation puzzled Huygens and Newton, for opposite reasons. Newton's notion of alternate " fits " could be- made to account in some measure for polarisation, but not for double refraction. Huygens could not account for polarisation, but easily accounted for double refraction on the Undulatory Theory, even as then understood, when it was supposed the ether vibrations resembled those of sound-waves, or were propagated in the direction of the ray. We have seen that the retardation which causes refraction is most probably caused by greater density or less elasticity in the ether within the re- 218 LIGHT [CHAP. fracting body : and Huygens had only to suppose a doubly- refracting crystal was less elastic in some directions than in others, to account for it, provided only the ether vibrations also were affected by these differences in the structure of matter. This, we have found from numerous experiments, is probable. But the theory as then understood failed to account for polarisation, which finally occasioned Young and Fresnel's great conception of transverse vibrations, by which everything is simply and perfectly accounted for. 1 Let it be supposed that common light consists of vibrations in all azimuths, but all perpendicular to the path of the ray, as at A, Fig 144. Whether vibration takes place in different azimuths simultane- ously, or in succession, does not affect the reasoning. 2 Such a ray must behave indifferently as to its sides, whatever it meets with in its path. But let all these azimuths of vibration be " re- solved " into two planes at right angles to each other, as at u, Familiar as the conception is to us now, it is difficult to realise what a profound and tremendous revolution in scientific opinion it was, when first promulgated by Young and Fresnel in 1816 and 1817. To endow such a rare and subtle fluid as the ether with the most distinguishing property of a solid, was such a stupendous overturn of all previous notions about the Undulatory Theory, that Arago, who had up to that time shared and endorsed Fresnel's previous memoirs, shrank from such a step, and left Fresnel to bear the brunt of it alone. Fresnel related in 1821, that he himself hesitated to adopt it for a while, and states (see Whewell's History of the Inductive Sciences, vol. ii.,p. 417) how "Mr. Young, more bold in his conjectures, and less confiding in the views of geometers, published it before me, though perhaps he thought it after me." Whewell goes on to relate, from information given him personally by Arago, how when Fresnel had pointed out that transverse vibration was the only possible way. of translating the facts of polarisation into the Undulatory Theory, the elder Frenchman "protested that he had not courage to publish such a concep- tion, and accordingly the second part of the Memoir was published in Fresnel's name alone." And yet, when Arago thus shrank from the new theory, he had received also a letter from Dr. Young, dated January 12, 1817, in which the same idea was suggested for the same reasons ! Facts like these should not be lost sight of, for the sake of the instruction they convey to the student of science. - See Appendix to this chapter. x] ANALYSIS OF POLARISATION 219 where the top and bottom quadrants of A are supposed to be mainly resolved into c D, 1 and the others into E F ; and suppose we can obtain either plane separately ; for instance, the spar separates them somewhat as at c. Very plainly, such a FIG. 144. Nature of Polarisation. fixed plane of vibration, on meeting reflecting and refracting surfaces, must behave very differently according as the ends or whole course of each path of vibration come in contact with the reflecting or refracting surface. 129. Analysis of Polarisation by Reflection and Refraction. It is even easy to see that reflection and refraction, of themselves, must tend towards this state of things. For tracing a ray whose transverse vibrations are in all azimuths, to an inclined surface, it is natural to suppose those vibrations which come in contact with that surface, or "kiss " it as it were, along their whole path, should be reflected in their integrity, while others must be seriously affected. .A simple experiment confirms this supposition. It is supposed throughout the Undulatory Theory that we are dealing with actual physical realities with actual physical atoms of some kind, vibrating with inconceivable rapidity in definite paths. Now, any solid small body thus moving in an orbit, with sufficient rapidity, produces on our sense of touch and in many 1 It results from very elementary principles of mechanics that if C D and E F are the only possible directions of vibration in a body, all vibrations in any other azimuth than one of the two must be resolved into both in varying proportions according to the angles. Near c D nearly all the motion is resolved into C D, and only a small portion into E F ; while the vibrations in azimuths of 45 will be resolved equally into C D and E F. (See Fig. 170.) 220 LIGHT [CHAP. other mechanical respects (and we are dealing with strictly mechanical effects here) the same effect as a solid occupying the dimensions of its path. If, for instance, the driver-stud in the driver-chuck of a lathe can be rotated with sufficient rapidity, it is in many respects mechanically equivalent to a solid cylinder bounded by the circumference of its circle of revolution. In the same way, a small sphere vibrating rapidly enough in a path perfectly straight, would produce effects similar to those of a small rod, equal to it in diameter and of length equal to its path. We may thus conceive of the front of a ray of light, supposing there are transverse rectilinear vibrations in all azimuths, as equivalent to a number of rods crossing the axis of the ray in all azimuths, as A, Fig. 144. Now let us consider these various rods, preserving their rectangular relation to the ray, obliquely projected against the surface of some retarding medium, such as we have considered refracting media to be. We can predict the result theoretically ; but we can, as regards single rods, representing single azimuths of vibration, FIG. 145. Catapult. subject the matter to experiment by the simple instrument shown in Fig. 145. Let there be hinged on a base-board, B A, at a pivot, a light frame c, pulled towards B by a strong spiral spring, s. On pulling it back and releasing it, the part c will x] EXPERIMENTAL ANALYSIS 221 act as a kind of catapult, and project objects laid upon it with considerable velocity at any inclination with the horizon, determined by a stop or obstacle, o. Provide a few smooth rods of wood, as accurately circular as possible, of different diameters and weights (because the best rods for each project- ing apparatus must be found by trial : as a rule rather heavy wood is best), and placing the instrument in front of a shallow bath of water, project the rods obliquely against the water. Let a horizontal rod be first so projected, so that the whole length strikes the water at the same moment. With a little practice it will be found that when the rod is projected pretty accurately, it is reflected from the water, as in Fig. 146, as boys FIG. 146. Reflected Rod. play "ducks and drakes," or as a shot ricochets on the surface of the sea. 1 Now let A (Fig. 14?) be the wave-lengths in a ray of light, the rod R will represent those vibrations which reach the retarding medium as at B ; and they are reflected 'to c. Lay next a rod vertically on the face of the catapult, so that the end strikes the surface of the water first, as at E (Fig. 147). Such a rod represents mechanically the vibration at right angles to the former ; and it will be found it is no longer reflected, but swung round in some such direction as F. But this is not all ; for attentive observation, even with this 1 The rods must strike the surface of the water at a considerably less angle than in Fig. 146. 222 LIGHT [CHAP. rough and simple apparatus, will show that, in rods placed in intermediate positions, there is a sensible, visible tendency on meeting the water to swing round into one or other of the two positions we have examined. It follows that if we could project such a rod, without losing its energy, against surface FIG. 147. Refracted Rod. after surface, it would gradually be brought into either one or other of these two rectangular positions. And this precisely accounts for what was long a difficulty, viz., the gradually increasing body of polarised light, as common light is reflected from, or transmitted through, a greater number of successive plates of glass. 130. The Polarising Angle. Lastly, a very elementary knowledge of geometrical mechanics necessitates the clear perception that, according to this purely mechanical method of analysis, the amount of reflected and refracted light polarised in two rectangular planes, assuming the original beam to contain equal proportions of all azimuths, must be equal ; and further, that the most favourable position for the operative surface, or that which must give from any surface the largest quantity of each kind of light, must be at an angle of 45, at which angle alone an equal number of azimuths are affected in x] POLARISING ANGLE 223 each of the two directions, and at which alone the transmitted ray is at right angles to the reflected ray. Now, at first sight, this seems to be contradicted by the fact that the polarising angle of glass is not 45, but about 56, and that it varies with every transparent substance. But when examined this difficulty disappears ; for Sir David Brewster discovered in 1815 the beautiful law shown in Fig. 148. Reference to the diagram of FIG. 148. Angle of Polarisation. sines (Fig. 40) will show on mere inspection, that there must be a given angle of incidence, at which the ray, i R (Fig. 148), reflected from the refracting surface, at the same angle with the normal, N, as the incident ray, s, is at right angles with the refracted ray i r. That angle in every case is the angle of polarisation. With glass it is about 56 35', but must of course depend upon the refractive index of the glass. 1 1 Sir David Brewster long ago (Phil. Tr. 1815) advanced various argu- ments to show that the incident rays were probably subjected to the refractive influence of the reflecting body before reflection. This conclusion in itself, quite apart from Brewster's reasons, has received strong confirmation from phenomena since discovered. That plane-polarised rays are rotated when 224 LIGHT [CHAP. It follows that, as the refractive index of glass or any other medium differs for different colours, polarisation by reflection can- never be quite perfect for all the colours of white light at any one angle. The imperfection is, however, so small, that it may be neglected for all but very highly refractive substances, or very delicate experiments. 131. Direction of the Vibrations. The question whether the actual vibrations which constitute the wave in a ray of plane-polarised light, are in the plane called the plane of polarisation (the plane of reflection when polarised by that method) or at right angles to that plane, has often been treated as an open one. The mechanical considerations above cited in favour of the second hypothesis, appeared to myself to leave no doubt about the matter even when the first edition of this work was published ; and Stokes's experiment on the effects of a fine diffraction-grating upon the plane of polarisation 1 was also of great weight. But actual demonstration has since been afforded. Wiener's photographs of the fringes caused by interference of waves reflected from a plate of silver with the inci- dent waves, have already been referred to ( 119). Now when plane-polarised light was employed at an incidence of 45, the interference bands were produced when the plane of polarisa- tion was the same as the plane of incidence, but none when at right angles to it, showing that the actual vibrations were parallel to the reflecting surface. And finally, in Hertz's rays of electrical radiation ( 120) we know the plane of electric reflected from the pole of a magnet in Kerr's experiment ( 177) seems to show, as Dr. Lodge points out, that the wave is influenced by a layer of iron of a certain depth before reflection. And Drude ( Wied. Ann. xliii. 158) has very lately ascertained that the thin black portion of a soap-film (see 121 ) has a polarising angle differing from that of the much thicker coloured part of the film, the difference amounting to as much as seventeen minutes of arc. Lord Rayleigh has also proved that surface impurities affect the phenomena ; which likewise implies that a certain thickness of film has an effect upon them. 1 Sec Cambridge Trans. 1850. x] 4 ELASTICITY IN CRYSTALS 225 oscillation ; and using sheets of metal as reflectors, Trouton has shown that the rays are reflected at all incidences when the vibrations are parallel to the reflecting surface or perpendicular to the plane of polarisation, but at a certain angle are not reflected when the vibrations are in the plane of incidence. 132. Polarisation by Double Refraction. Having determined the direction of the vibrations in a " plane of polarisation," we can now consider the phenomena of a doubly- refracting crystal. ^ It has been assumed that double refraction is due to an inequality of elasticity in different directions within the crystal. Is there then this inequality ? Experiment shows us not only that there is, but that the physical properties of a crystal in this respect stand in fixed and invariable relation to its optical properties as tested by experiment ; and that both these again have a fixed relation to its form. Some crystals are symmetrical in all directions, as the cube ; if heated, these conduct heat equally in all directions ; and with variations in temperature they expand equally in each direction. Such crystals may be assumed to be equally elastic in all directions, and accordingly, in a free or natural condition they have no double refraction. But if now we take a crystal of quartz, which crystallises in six-sided prisms with pyramidal ends, it is manifest on inspection that it is not geometrically symmetrical in all direc- tions, but only round one axis, that of the prism. Take a slice cut parallel to this axis, A (Fig. 149), and pierce it with a hole into which we can introduce a wire heated by an electric current or otherwise. Coat the plate with a film of wax, and introduce the heated wire : the wax FIG I49 ._ Quartz P i ate s. will gradually melt around it, and it will soon be seen that the melted surface is an ellipse ; in other words, the heat is conducted more rapidly along the Q 226 LIGHT [CHAP. crystallographic axis than across it. Doing the same with a slice cut across the axis, E, the melted area is now a circle : showing that conduction is equal in all radial directions round the axis. 1 It has further been determined by experiment, especially by Professor Mitscherlich, that when a crystal of this description is heated or cooled, it expands or contracts unequally in different directions. Almost if not quite invariably, a moderate heat expands the shorter axis of the perfect crystal more than the others, or brings the crystal nearer to the form of a cube, or other shape, which in its most perfect and simple form can be inscribed in a sphere (this is the simplest general sign of the form of a non-doubly-refracting crystal). With this change comes a diminution of the inequality in elasticities, which, at a certain temperature, may even altogether disappear, as we shall hereafter demonstrate by a beautiful experiment, due also to Professor Mitscherlich ( 193). The various faces of such crystals also show very different powers of cohesion ; and even different resistances to the disintegrating action of chemical re-agents. Finally, it has been shown directly by Savart, who strewed fine dust upon plates of doubly-refracting crystals cut in various directions, and then excited sonorous vibrations in the plates, that there are such differences in actual elasticity as we should expect. If now we take a rhomb of Iceland spar or calcite, and reduce one or the other of its faces till all the edges are of equal length the true form of the crystal we find it resembles quartz in being symmetrical around one axis A A (Fig. 150), and no other. It is as if we took the skeleton outline of a cube made with wires, jointed at each corner of the cube, and placing one corner on the table, pressed down the opposite one. In the longer rhomb, also depicted in Fig. 150, the direction A A parallel to the other is still the true crystallo- 1 This experiment is due to Senarmont, x] OPTIC AXIS OF A CRYSTAL 227 graphic axis, round which the crystalline molecules are sym- metrically built. 1 If we cut a plate with artificial faces per- pendicular to this axis, and melt wax from a heated centre, as with the quartz, the melted area is circular. Take now a ray passing along this axis. The vibrations, being perpendicular to the ray, are therefore perpendicular to the axis, and in all these perpendiculars the elasticities are equal. There ought, therefore, to be no double refraction. If the FIG. 150. Axis of Iceland Spar. crystal is so cut that a ray can be thus transmitted, we find it is so ; there is no double refraction ; and the axis is therefore in this case the optic axis of the crystal. But now let the ray pass through the crystal at a right angle with this axis. The elasticities being equal all round the axis, that in the direction of the axis itself must be either greatest or least in the calcite it is greatest The axis itself, in such a case, is a plane of vibration at right angles to the ray (and therefore such as luminous vibrations require) in which the ether vibrates most freely ; and at right angles to this is another plane in which vibration is most retarded. According to the 1 The axis is a mere direction, which at any point in the crystal, if it were split so that there was produced an obtuse solid angle at that point, would be an axis to that angle. Q 2 228 LIGHT [CHAP. simplest mechanical principles, all the azimuths of vibration in the ray must be resolved into these two, and the ray be thus divided into two, differently refracted, and oppositely polarised. Take next an intermediate position ; for instance, lay the rhomb on a flat table over a black spot ; the ray sent perpen- dicularly in the direction A B (Fig. 151) to an eye over the spot, is neither parallel to, nor at a right angle to the axis. But its vibrations, being necessarily at right angles to itself, may be represented by lines drawn on a piece of card laid on the top horizontal face of the calcite. Draw two such lines at right FIG. 151. Direction of Vibrations in the Spar. angles to each other, to represent planes of polarised vibration, a by c d. The card can easily be turned round so that there is a position in which a b is perpendicular to the axis, the direc- tion of least elasticity ; and the other line, c d, is that of the greatest elasticity possible in the front of a wave travelling in this direction, and must obviously lie in the same plane as the axis. Into these two directions, therefore, will such vibrations be resolved ; arid the two images will always be in the line c d, which is in the same plane as the optic axis. 133. Principal Planes or Sections. The plane thus passing thro ughYMifr!ili a 53* H I I .u O" 0. --' 1-5 , Ji i - i-ii* 1-1 C tf.^ tl n-1 Ti -*.^J .i | JHfi I f/'.rM "^2i ^ ||| flljl | Sl 4=4= ."2 "Z5" ^7 *5^ - o w "7* fl W 1-2 i35 -n'-jid^^"' " l'iiyll'8 I * 2 *s 2 c 9.S4j i.'2Ss^:2&n : |< a, 254 LIGHT [CHAP. The greatest fault of such a pile so used, however, is that it usually gives a perceptible green colour, owing to the thickness of glass. The " ten or twelve plates " often mentioned, do not polarise the whole beam by a great deal. 144. Direct Reflecting Polariscopes. Of late there has been an absolute famine of Iceland spar, and this has turned attention to the improvement of reflecting projection polariscopes by the abolition 01 the angular deflection, as sug- FIG. 163.. FIG. 164. gested long ago by Uelezenne. His idea was to bring the rays back into a direction parallel to their original incidence, by an additional reflection ; and this is done by modern opticians in two ways. Mr. Ahrens constructs a Delezenne polariser as in Fig 163. Here the parallel beam from the lantern is first deflected by a massive totally-reflecting prism of glass, T R, whose end faces are normal to the incident and emergent rays ; then the rays fall at the proper angle upon the polariser, P, either a plate of black glass> or two or three thin plates with a blackened one at the bottom. This construction is however costly, so massive a glass prism being expensive ; while the absorption of light is also serious, xi] DIRECT REFLECTING POLARISCOPE 255 The Rev. P. R. Sleeman prefers the construction in Fig 164, which is much cheaper, more easily adjusted, and on the whole better in my opinion. Here the silvered glass mirror, s, re- places the reflecting prism, and P is a " pile " with a blackened glass at the bottom. This can be made in a very cheap form, and of any size desired. In the first instruments made upon this plan the optical beam, which is necessarily deflected several inches from the axis of the flange-nozzle, though re- FIG. 165. Direct Reflecting Polariscope. stored to parallelism with it, was brought down below that axis as by Fig 164. This made the apparatus high and awkward-looking, however ; to obviate which a side deviation was next tried. That also, however, did not look well, and necessitated a large case. To obviate these objections I reversed the polariser so as to deflect the beam upwards, and Messrs. Newton and Co, the principal makers of this class of appa- ratus, now construct the instrument on that model, as shown in Fig 165. It will be seen that it is thus made as compact as the Nicol construction. All except the polariser is precisely the same as shown in section in Fig. 161. Like the "elbow" form of polariscope, the Delezenne polar- iser cannot of itself rotate the polarised beam ; but this opera- tion, so desirable for many experiments in rotary polarisation, is easily effected in a manner suggested by Professor S. P. 256 LIGHT [CHAP. Thompson. It will be seen later on that if the plane-polarised beam is passed through a mica quarter-wave film properly adjusted, it becomes circularly polarised ; and if in front of this film we place another which can be rotated, the beam becomes again plane-polarised, in a plane depending upon the position of the second film, Such an arrangement of two films can either be mounted permanently next the polariser, with the second plate in a divided circle and actuated by spokes, as usual with rotating polarisers, or the two micas can be mounted and used in an ordinary rotating frame. To get a per- fectly dark field, the second mica must be in the " crossed " posi- tion to represent that state of affairs. It is convenient to have at least a separate slot or slide-stage for the reception of the frame with its pair of micas, so that it can be handled quite inde- pendently of anything in the ordinary slide-stage. This method of rotating the polarised beam can of course be equally applied to the common " elbow " polariscope. 145. Analysers. Besides the Nicol or Prazmowski prism, it is well to have a glass analyser (Fig. 166) FIG. 166. Thin Glass Analyser. formed of eighteen or twenty pieces of microscopic cover-glass, G, placed at the proper angle in a tube which fits at N on the nozzle of the objective. An aperture, R, in the side of the tube, allows the reflected ray also to be used. For reasons already given, such an arrangement is not equal to a Nicol ; but it gives a large field, is very instructive and interesting in throwing complementary images of all phenomena on screen and ceiling, and will do thoroughly satisfactory work for all to whom 405-. or 60^. for a Nicol prism may be an object. In fact, a xi] TABLE APPARATUS 257 glass reflector and thin glass analyser are within the reach of any one who can work in brass. 1 A tourmaline is also useful ; and either a double-image prism, or a pair of these mounted in a Huygens's apparatus, will of course be provided. 146. Table Apparatus. For merely private study very cheap and simple apparatus will suffice. Make a shallow paste-board or wooden tray, A (Fig. 167), i inch deep, say A FIG. 167. Simple Table Polariscope. 7 inches by 4 inches. Drop into it thin glass plates to within | inch of the top, cleaning them well, and blacking the back of the bottom one. Cut two wooden or pasteboard side pieces, E, united across the top by another piece, D, and fill in the ends by a piece of gr0und-g\a.ss, B, 4 in. square, and another, c, of clear glass the same size. The light will fall on the ground glass as shown by the arrow, if it is turned towards a lamp or the window ; will be nicely softened and scattered, and polarised by the pile in the bottom ; and the objects can be laid on the clear glass at c to be examined by the small pile of microscopic glass, P, contained in a round or square card- board tube. The "elbow" polariscope already described also makes a capital " table " polariscope, if a disc of fine ground- glass, to soften the light, be fitted into the end, N (Fig. 162), which goes on the flange of the lantern. It will be found that the lenses pleasantly focus the objects in the slide-stage, which are examined by looking in through the analyser on the nozzle. 1 My own first glass analyser was fitted up by myself, and used, in a pasteboard tube. 2 5 8 LIGHT [CHAP. In fact, a small Nicol, or tourmaline, or pile of thin micro- glass fixed slantwise in a tube, as analyser, and the light reflected from any glass plate, or the top of a mahogany table, as polariser, will suffice for many experiments. 147. Ndrrenberg's " Doubler." There is a form of polarising apparatus to which I have ventured to give this name, and which is so useful if the student does any personal work with thin films, as to need special mention. As designed by Norrenberg, it is as in Fig. 168, where the ray of light shown by the arrow is reflected at the polarising angle from the single plate of glass, F, normally to the horizontal piece of looking-glass, H. It is thence reflected per- pendicularly upwards, passing this time through the polarising plate to be examined by the Nicol, or other analyser, at N. It will be obvious that if the object be laid on the stage at E, the phenomena are as usual. But if it be placed between the polariser and the looking-glass, at D, the polarised ray has to pass twice through the film or object to be examined, which is equivalent to doubling the film in thickness. The use of this " doubling " in ascer- taining the thickness of thin films, will appear in the next chapter ; and there are other peculiar uses of this form of apparatus. A very simple construction will answer all real pur- poses, however. Knock out the opposite sides F and B of an oblong box such as a cigar-box and on the remaining sides fix guides for the polarising plate, P, at the proper angle. On FIG. 168. Norrenberg's Doubler. XI] THE DOUBLER 259 one end, R, lay a piece of good looking-glass the size of the end ; and in the other end cut a hole in which the Nicol, N, or other analyser, can be rotated (Fig. 169). The object can be FIG. 169. Simple Doublet. held between p and R, or in the case of gauging films, laid "on the looking-glass itself. For most purposes of the " doubler " no focusing lenses will be required. I have even laid a piece of looking-glass on the table, and arranged over it a plate of clear glass at the proper angle by means of the Bunsen uni- versal holder (Fig. 17), holding the Nicol in my hand. But for ascertaining the polarising planes in films the box form is best. It should then be made with great accuracy : and the glass mirror R should be cut truly square, and be scratched with a diamond on the face along both diagonal and rectangular diameters, all passing through the centre of the plate. The use of these lines will be seen in the next chapter. s 2 CHAPTER XII CHROMATIC PHENOMENA OF PLANE -POLARISED LIGHT. LIGHT AS AN ANALYSER OF MOLECULAR CONDITION Resolution of Vibrations Interference Colours Why Opposite Positions of the Analyser give Complementary Colours Coloured Designs in Mica and Selenite Demonstrations of Interference Crystallizations Mineral Sections Organic Films Effects of Strain or Tension Stress in Liquids Effects of Heat and of Sonorous Vibration Appendix: Mica Film Work. 148. Resolution of Vibrations. We could have formed no conclusion as to the precise orbits of the molecules of ether in our polarised waves, apart from the phenomena ; but if we have rightly interpreted these, then any one acquainted with elementary mechanics and the " resolution of forces " will see that we can test such a theory by experiment. Dealing with motions whose direction we are supposed to know, if we are correct we can " resolve " those motions. Taking a vertical plane of vibration, for instance, and supposing ether-atoms moving freely in the plane orbit A B, B A (Fig. 170). if we interpose in the path of a wave consisting of such motions, a plate of crystal whose structure is of some such sort as shown in the figure, as only permits of vibrations being executed in the planes c D, E F, the motions in the vertical orbit A B must be resolved into the other two planes, which make angles of 45 with the original plane. CH. XIl] RESOLUTION OF MOTION 261 This strictly mechanical resolution of a plane of motion into two, when the wave-motion encounters a substance presenting rectangular planes of greatest and least resistance at any angles with the orbit of motion other than o and 90, will be readily understood from a strictly mechanical analogy. Let the sub- stance be a piece of very straight-grained board ; and the motion be that of a narrow saw-blade cutting through it. While the saw cuts either exactly "with the grain," or at right angles FIG. 170. Effect of a Crystalline Film. across it, there is no tendency towards deflection of the cut. But if an attempt be made to cut across the grain at an angle of 45, a strong tendency will be felt towards deflection on one side or the other, and a straight cut will be found almost im- possible. It is to meet this difficulty that cross-cut saws intended for miscellaneous straight work are made with a narrow " set " and thin blades. The saw-blade cannot divide itself into two cuts ; but the free ether-atoms are able to do so, and hence 262 LIGHT [CHAP. are " resolved " into both set of rectangular motions, into which the saw-cut tends to deviate. It would seem already that we have obtained this resolution of motions, from the duplication of our images when the two double-image prisms were placed at an angle of 45 with one another, and from the transmission of about half the light through two tourmalines superposed at the same angle. If we are right, the two oblique planes must both be also capable of resolution in their turn, by the analyser, into perpendicular and horizontal planes. When our polariser and analyser are crossed, and the " field," therefore, quite dark, if we interpose between them a tourmaline at 45 we ought to restore the light. Cross therefore the Nicol or other analyser till the screen is dark, and insert the rotating tourmaline. Truly enough, as we rotate it, though the tourmaline is really a brown tint, mounted on a clear glass, it appears, when in the position of B, Fig. 141, as a light image on thexdark field. We, have, however, learnt that the tourmaline stops one of the rays, and we wish to see beyond doubt if the original plane of polarisation really is resolved into two planes. We therefore want a slice of some crystal Which allows both halves of the doubly-refracted ray to pass. Either selenite 1 or mica is convenient, splitting easily into thin plates, which transmit the rays polarised in both planes of vibration. Let a thin plate of either crystal, mounted between glass discs, be placed in the rotating frame, and introduced into the stage when the analysing Nicol is crossed. On rotation, we find two positions in which no effect at all is produced ; but in two positions 2 midway (or at 45 angle) between these, light is 1 Selenite is the crystalline form of gypsum or sulphate of lime. 2 The two positions might in a sense be termed four, because the analyser, or a crystal in the stage, when rotated 180 is turned upside down. This however brings the polarising planes or axes into the same directions again , when all the phenomena repeat themselves ; hence in polarising experiments positions diametrically opposite, or 180 apart, are considered and spoken of as identical. xn] INTERFERENCE COLOURS 263 restored. With the tourmaline, the restored light would be extinguished by turning the analyser across the position of the tourmaline, the other tourmaline ray being absorbed ; but with the selenite or mica this cannot be done, showing that the original plane-polarised beam has been resolved into two ; either of which can be extinguished by the analyser, but not both together. 149. Interference Colours of Plane - Polarised Light. But if in this experiment the plate of crystal is very thin (such as opticians always supply for experiments) we encounter a fresh and very beautiful phenomenon. The light restored by the thin plate or film is coloured light. This pheno- menon becomes still more beautiful if we use a double-image prism as analyser, and an aperture in the stage along with the film, giving two discs ; then we get two coloured images of the aperture, and if the discs are large enough to overlap, where, they do so the light is white, showing that the two are comple- mentary colours. The most beautiful demonstration of all is with the Huygens apparatus, which was mounted so as to intro- duce a crystal-film between the two prisms ; then each of the two pencils doubly-refracted and polarised by the first prism is resolved by the selenite, and again by the second prism ; and we have therefore four beautifully-coloured images revolving round each other. as the analyser is rotated. With the prisms alone, we could compound one beam when the prisms were crossed ; but with the selenite inserted we can never get less than three, as we readily see on analysis ought to be the case. We can understand this colour. In every bifurcation of the ray, this is doubly-refracted because of the unequal elasticity already referred to ( 132). Hence we not only have the two rays, but one ray is more retarded than the other. We can " see " this in a large piece of Iceland spar, for one of the images of a black spot seen through it appears nearer than the other and it is the same even in the plate of selenite, though the two rays are not in such a thin film visibly separated. The two rays, so 264 LIGHT [CHAP. long as they vibrate in planes at right angles to each other in and after passing through the selenite film, cannot of course inter- fere. But the analyser resolves and doubly refracts each of them a second time, and brings portions from each together again into the same plane. Now in the rigid plane orbit of our original polarised beam, we have that identity of origin which we have already learnt ( ioi)is necessary for two beams to interfere ; and in the identical plane into which portions of the two beams separated by the selenite are again united by the analyser, we have that closeness of path, or nearly so, we also found to be necessary. We bring together again, then, into the same plane (that of the analyser) two rays of originally identical origin, one of which, during separation, has got behind the other in passing through the film, by a given distance depending upon the thick- ness of the film of crystal. But whilst in reflection from a " thin film," one ray is retarded by twice the thickness of the film ; in this case one ray is retarded by the difference in velocity, whilst both traverse the same film. Of course a much thicker film is required to produce the same retardation in this latter case ; and of course also, the greater the difference in the two indices of refraction, the thinner the film must be to produce a given colour. Too great a thickness, of course, gives no colour, for the very same reasons too thick a " thin film " gives none ( io7). We soon find, and it readily appears, that if we turn the analyser round 45 when the film is in the stage, the colour also disappears. Interference no longer takes place, because one of the rays from the film now passes the analyser unchecked and unmodified, while the other is stopped. Similarly, when the polarising planes of the film coincide with and cross those of the polariser and analyser, there is also no colour indeed no effect at all ; the rays from the polariser passing through the parallel one of the two planes in the film without modification. 150. Cause of Complementary Colours. To under stand the " complementary " colours, we must take into ac- xn] COMPLEMENTARY COLOURS 265 count the direction of the motion as well as the plane of vibra- tion of the ether-atoms, at each moment of bifurcation or resolution into two planes, and of re-combination by the analyser. Let us suppose the original ray A, Fig. 171, plane- polarised in a vertical plane, is at the phase when the atoms are moving downwards when it encounters the selenite with its planes at 45. The bifurcated rays must obviously have their motions in the directions B and c. Now B, when again resolved by the analyser, must take the directions D and E, and c of F FIG. 171. Resolution of Vibrations. and G. A double-image prism would transmit both, but by our Nicol analyser, either crossed or parallel, one plane or other is stopped. It will be seen on inspection of Fig. 171 that when the Nicol is in the position which allows the two perpendicular vibrations to get through, these two (D F) are in the same phase of their orbits, and so coincide with or strengthen each other ; but if in the position in which the horizontal vibrations get through, E and G are in contrary phases, or destroy each other. However, therefore, the two sets of waves come together in one position of the analyser, as regards any wave-length, that par- ticular wave-length must meet in exactly opposite phases, in the other position at right angles to it. If the two waves are exactly destroyed in. one position of the analyser, they are fully combined in the other ; if half destroyed in one, they are half reinforced in the other, and so on. 1 Taking therefore the 1 It will be seen in a subsequent chapter that the rectangular vibrations emerging from the film are chiefly compounded into circular and elliptical orbits. These are, however, again resolved by the analyser into rect- 266 LIGHT [CHAP. whole range of wave-lengths throughout the spectrum, and considering the series of interferences, in every one of which the vibrations constituting light are divided into sets differing by half a phase or wave-length, it is evident that whatever is lacking from the spectrum in one position of the analyser, must be present in the opposite position, and that a beam of white light must be divided into two complementary colours. These coloiys may vary indefinitely according to the thickness of the film, but will always be of a composite, and not a pure spectral character. This will be demonstrated presently by spectrum analysis ; but meantime, to put it briefly, half a wave difference in phase reverses all the phenomena in polarised light. A very simple illustration will be found in a plate of crystal " half a wave thick," or so thick that one of the rays is retarded behind the other by half a wave-length. With such a plate in the stage, the crossed analyser gives a bright field, and the parallel analyser a dark field ; and if the plate is used with a coloured film or design, the colours are changed by it to their comple- mentaries. It is further evident, that in addition to any retardation or difference of phase due to the difference of velocity in the two rays while passing through the doubly-refracting film, when the polariser and analyser are crossed there is an additional difference of phase of half a wave length, since E and G (Fig. 171), irre- spective of any thickness of the film, are in opposite phases. We shall see that this fact is of great assistance in accurately measuring the thickness of films. 151. Coloured Designs. A film of selenite, or mica, varying in thickness, will of course give varying colours, so far as the thicknesses lie between the limits of colour. A thin slice split irregularly from selenite soon shows that this is so ; and if we have designs ground away of studied various thick- angular planes ; and the student will easiest grasp the subject at this stage, by confining his attention to the simpler representation of it here given. For the effects of Composition, see 160-164. xn] COLOURED DESIGNS 267 nesses, we may form stars, butterflies, flowers, birds, &c., of their appropriate colours, which they owe to nothing but the interferences of polarised light ! Such designs are prepared in selenite at all prices from 3^. 6d. to ^3 35., and there is a strange fascination about them, changing as they do to complementary colours at every quarter-revolution of the analyser, and giving, as already explained, no colour at all when that is at an angle of 45. A plate ground conclave gives of course " Newton's rings," and a plate ground slightly wedge-shaped, similarly gives straight parallel coloured bands. Such wedges may be ground with water on very fine ground glass, and afterwards mounted in balsam between two glasses. Small reductions of thickness may be ground in selenite with the rounded end of a slate pencil and some putty-powder, and polished with more putty-powder on a piece of wash-leather. 1 The effect just now explained of a half- wave plate, in causing opposite or complementary effects, is often illustrated in selenite work by two designs in which the essential parts are a half-wave in thickness. One is the bust of a lady, which in one position- of the analyser appears white, while in the other she becomes a dark mulatto or negress : the other is a representation of a miller's man with a bag of flour on his shoulder, who by the same revolution of the analyser becomes a sweep with a bag of soot. 152. Mica Designs. But the best crystalline film for students is mica, the same that is used for gas-light covers. Choose for polarising preparations a slab as clear and even as possible, free from minute air-bubbles or opaque deposits. 2 1 The finest selenite preparation I have ever seen was executed entirely with his own hands by Mr. C. J. Fox, F.R.M.S. The subject was one of the grotesque-looking tropical fishes, and it had occupied him at intervals for many weeks. Every detail was worked out with minute care, and by the aid of rotational colours as explained further on, the eye appeared to wink as the analyser was rotated. 2 Mica from different parts of the world differs very greatly in character. Generally it is a bi-axial crystal ; but the angles vary, and one kind known 268 LIGHT [CHAP. This splits easily into thin laminae, and is easily cut through by a penknife to greater or less depth. This rough and simple process will enable any student to prepare illustrations of the elementary phenomena so far described. A piece of mica thin enough to begin to show colour, is readily trimmed round with a strong pair of scissors to a disc the proper size for the wooden frame of a polariscope slide. Then the outline of such a simple design as Fig. 172, or the still simpler outline of a cube, can be cut to a small depth with the penknife, when a needle-point will lift and split off a thin film it will be seen at once that the whole figure is now a different colour from the ground. Cutting further, through the outlines of the points, each is easily made a differ- ent thickness, displaying each point in FIG. 172. Mica Design. a different colour. Laying the prepara- tion on the table polariser shown in Fig. 167, the position in which most colour is shown by a crossed analyser is easily found with sufficient accuracy, and the mica mounted in that position in the frame. Another pattern easily made in this way is one of concentric squares, lifting first a thin film from a large square, then cutting and lifting with the needle another square T V of an inch smaller inside of it, and so on. as Canadian phlogophite, is uni-axial, and shows a strong diffraclivc six- rayed asterism, owing to small particles or crystals. Generally the best for preparations is Indian, and is slightly brown ; but some specimens have a green and others a yellow shade : clearness and minimum colour for a given thickness, are the main points. Occasionally I have found small specimens clear white, but never so large and perfect as to be useful : large pieces of such (heretofore only found in Labrador, I believe) would be very valuable. A great deal of mica has iron deposits between the laminae such is worth- less. The true crystalline form is an elongated hexagon, and I possess a piece showing this perfectly sharp at every angle : iron deposits also some- times show these lines very accurately and curiously in the films. xn] MICA PREPARATIONS 269 Mica can also he scraped away carefully with a penknife to shaded or gradually lessened thicknesses, and fair representa- tions of fruit or large flowers scraped out in this way, working of course on the table polariscope, with the mica in position and viewed through the analyser. The mica will appear clouded or semi-opaque where scraped ; but when mounted in balsam and benzol as presently described, this disappears, and all becomes transparent again. But mica is so easily capable of far more accurate, instruc- tive, and scientific results than these, 1 and practical acquaint- ance with these results is so unequalled for its power of giving an intuitive understanding and realistic conception of the phenomena of polarised light, and their nature, that I would strongly urge every serious student who has leisure, to make for himself a full set of illustrations. 2 The necessary details respecting these will be given as they occur in order ; and in the Appendix to this chapter will be found practical directions as to the general manipulation which I have found most suit- able and easy for producing high-class work of this class. The most valuable of all mica-film preparations is the wedge, designed by Mr. C. J. Fox, F.R.M.S., shown in Plate IV. at A. This consists of twenty-four J wave-films superposed, each one ^ inch shorter than the one beneath it then if the thicknesses are accurate, the whole will give the first three 1 See for the first description of many of these preparations my paper on "Optical Combinations of Crystalline Films," Proc. Physical Soc. of London, 1883, and Phil. Mag., May, 1883. 2 It may encourage him to do so, to state that every slide or preparation described hereafter, into which mica enters, has been executed from first to last by my own hands. It was Mr. C. J. Fox, F.R.M.S., who first allowed me to see what could be done in this way, and told me something of his methods ; and I commenced by merely imitating the beautiful preparations designed and executed by him. As I was soon able to add largely to these, so doubtless some reader may add yet further to such de- monstrations of phenomena not only most instructive, but above all others magnificent in spectacular display. Prof. S. P. Thompson has already added to the repertory his rotation-index shown in Fig. 191. 270 LIGHT [CHAP. orders of Newton's interference colours, each order divided exactly into stages successively increased by | of a wave of retardation. A in Plate IV. shows the effect in the polariscope, with the analyser crossed. Of course the retardation can only be exact for one particular wave-length, which is always chosen for yellow light, as both medium in length and most brilliant. Then with analyser crossed, yellow light is extinguished ; but a little blue (being shorter) and a little red (being longer) is not perfectly destroyed, and these residuals produce a little light of reddish plum-colour, the " tint of passage " as it is called, between the first and second orders. The second and third tints of passage are more positively red. But the precise thick- ness needed depends a little on the light to be chiefly used. For daylight work, very slightly thinner \ wave-films will be needed than for gas-light, which is deficient in blue rays and rich in red. Arc light is a little more blue than daylight ; the lime-light comes between that and gas. Too thick films will make the twenty-fourth band perceptibly bluish, but may be correct for gas-light ; and vice versa. Therefore if such a wedge be ordered of a physical instrument maker, any light to be habitually used should be stated with the order. 153. Demonstrations of Interference. That the colours of crystalline films really are produced by the greater retardation of one ray, and subsequent interference, may be proved by several independent methods. First, we can easily stop one half of the bifurcated ray. Place in the stage any slide say a concave Newton's ring slide. The rings being at their brightest, and with the analyser exactly crossed, introduce, in front of the selenite, the rotating tourmaline at an angle of 45. This stops by absorption one of the two rays into which the original polarised beam is divided; there are no longer two rays to be brought into interference, and accord- ingly, over the area covered by the tourmaline, the colours disappear. Secondly, we may retard the other ray, and thus bring the xn] MICA WEDGES 271 two again into coincidence. If one ray be retarded in the selenite or mica more than that vibrating at right angles to it it is plain that, taking two films of equal thickness, if both are superposed the same way of the crystal, the colour must be that of a plate equal to the sum of both ; but that if one be turned round 90, the retardation of one ray by the first will be neutralised by the second, and no colour at all produced. If we place two similar films in the stage, in the two different separate positions, we find that it is so ; and similarly, if the films be of different thickness, the colour will be in one posi- tion that of their sum, and in the other of their difference. A striking demonstration is furnished by rotating a selenite wedge over a similar one. The colours differ remarkably according to their positions ; black (when the analyser is crossed) being necessarily produced wherever exactly the same thicknesses come into rectangular positions, and so causing in one position a black diagonal line. Therefore if a concave plate be rotated over a convex plate, the phenomena of the rings vary in a beautiful manner, black rings appearing in certain positions; or an even film of the proper thickness, rotated over the concave, will give the same beautiful phe- nomena. Again, if a film of even colour is rotated over a star made of separate points in different positions, the colours of the points are affected very differently, and in what appears (seeing the rotated film is the same thickness all over) a most wonderful manner till we understand the reason. The most instructive and pretty demonstration of these re- versed or counteracted retardations is, however, furnished by two precisely similar " step " wedges built up on Mr. Fox's plan. 1 The glass discs will nicely take a wedge ij inches long 1 The first few g wave thicknesses giving poor colours only pale fawn and blue-greys the broadest or foundation film of the wedge is best about | wave thick, as mentioned for designs. I think about wave thick for the others gives the most pleasing gradations, but it is only matter of preference. 272 LIGHT [CHAP. by i inch wide, and this breadth is conveniently divided into eight steps | inch wide. It is sufficient if each corresponding step in the two wedges is cut from the same film. One wedge being mounted in wood, and the other used in the rotating frame, when one is superposed on the other with the polarising planes in same positions and the thickest part of one over the thinnest in the other, we have an even colour. When the two thickest sides are superposed, if the polarising planes are parallel the tints grade with double the amount of difference in colour ; if the planes are crossed there is no colour at all. When the wedges themselves are crossed, in one position there must be a central diagonal row of black squares, the other squares giving a beautiful chequer pattern of various colours. And when the rotating wedge is diagonal, there will be a pretty pattern of backgammon points. Two wedges built up of similar even films thus offer one of the most fascinating and instructive polariscope combinations. (See C, D, E, Plate IV.) Or, should the student have sufficient skill and patience to build up a wedge of 24 J-wave films, if a single film be super- posed on it with its principal plane crossed, and of a thickness equal to the twelfth stripe, or \\ waves, it is plain that middle stripe must appear black ; and as on each side of it each equi- distant stripe must present an equal difference or essential thick- ness, the coloured stripes will be symmetrically arranged on each side of the black one. (Plate IV. B.) This is easily extended to still more beautiful designs in crossed films. At G on Plate IV. is shown a pair of crossed double-wedges ; that is, each successive narrower film is laid down on the middle of the one underneath it. The pheno- mena of D. are now presented in each corner of the combined pattern, the black stripes crossing in the centre ; or if one wedge is inverted on the other so as to bring the planes into the same direction, we get the same beautiful floor-cloth pattern in the addition colours, instead of the crossed colours. Either a concave selenite showing Newton's rings, or a mica prepara- PI. 4 INTERFERENCES OF POLARIZED LIGHT Wedffe of 24 .Ditto, with /% mica* crossed A. B C. D.E. TwC Wedge* F Two "double" wedges crossed, Spectrum, of tTiucJc, /Urn, of J tz#* wit '& polarizer ami awafyver , xn] SPECTRUM FRINGES 273 tion, built up of concentric circles, as in Fig. 173, may also be crossed upon such a " circular wedge," as is illustrated further on in Fig. 185, using for mica circles the same thickness as for the other slide. The result of either will be most beautiful black radial spirals starting from the centre. Lastly, we can prove the cutting out of certain colours by interference, by our never-failing method of spectrum analysis. Place a slit in the stage with a film which shows colours, and focussing it on the screen, pass the light from the ana- lysing Nicol through the bisulphide prism. There will be crossing the spectrum one or more dark interference bands more with a thicker film : in fact as the film increases, more and more bands appear FIG. 173. in various parts of the spectrum, just as in the light reflected from a film of mica ( 107), and showing, in the same way, how with a certain thickness we fail to get colour. This is well shown by subjecting a wedge to spectrum analysis, a slit being placed in the stage, and the wedge, with its bands parallel to it, gradually advanced over it from the thin edge to the thick one. It will be seen that, as the thick- ness increases, a greater number of the interference bands cross the spectrum, as we should expect, accounting for the paler colours. The spectrum of a plate of selenite too thick to show any colour at all, is shown at Plate IV. H. It is also seen, as we expect, that in contrary positions of the analyser, the bands occur in complementary colours. The two comple- mentary sets of bands are easily shown together by using a double-image prism as analyser, arranging the two images of the slit in one line. The slits will then overlap in the space between the double image, giving there a white slit and com- plete spectrum ; while the two complementary spectra will appear at the top and bottom. If the slit be adjusted so as to cross the centre of a concave film giving Newton's rings, and T 274 LIGHT [CHAI the slice of light be analysed by the prism, we get agai exactly the same interference bands as shown in Plate III. I The best demonstration, however, is with our ever-useful Fo wedge. Turning round the stage so that it stands verticall with the stripes horizontal, we place with it a slit of black car or thin metal long enough to cross all the stripes. Th successive shifting of the interference bands, step by step, i now readily seen, as at F, Plate IV., the bands taking ai obviously parabolic shape. The wedge alone only gives th interferences of Newton's first three orders ; but by superposin with planes the same way, one or more mica or selenite film making up one, two, or more waves in thickness, the mor numerous interferences are readily demonstrated up to an other desired order. 154. Crystallisations. Another beautiful series of ol jects showing gorgeous colours in the same way are crystal lisa tions, from films of various solutions poured over glass discs, an< then crystallised by evaporation. The only difficulty is t< obtain the right thickness, as both too thick or too thin giv little or no colour, though light and shade effects can always b had as the analyser is rotated. For this reason, what an called "superposition films " are very useful. These are thii plates of mica or selenite which give uniform colour (such an easily split from mica) mounted between two glasses. On< which gives blue and yellow, and another red and green, shouk be provided ; then a film of crystals, or anything else whicl shows no colour by itself, will give great variety when super posed on the film. There is a sameness about the colour: produced by this plan, however, inferior to a slide which car show its own colours. A good arrangement for making crystallisations by evapora tion is shown in Fig. 174. On a wire tripod is placed one o: the glass candle-chimneys so common, 3 inches diameter, anc on the top of this is laid a square metal plate, not quite cover ing the chimney, having in the centre an aperture nearly at XII] CRYSTALLISATIONS 275 large as the glass disc, with three little projections bent up T ] - inch from the inner edge to keep the glasses in place. A spirit-lamp underneath gives a steady heat, adjustable by raising or lowering it. A saturated solution is not always best ; often one mixed with equal bulk of water does better, and sometimes a little alcohol added helps effect. Great in- terest will be found in preparing slides with weaker or stronger solutions, and less or more heat, which will often entirely alter the character of the crystallisation. Thus, a solution of tartaric acid evaporated in the cold often crystallises in long straight lines, and in the sun in " stars ; " whereas, when evaporated over the lamp, it gives irregular facets, very beautiful on the screen, and larger as the heat is greater. Salts which give a pattern too small in this way, may often be made to give much larger crystals by dis- solving gelatine or gum in the saturated solution, and evaporating in the cold. The following are good polarising salts : -Tartaric acid, and most tartrates ; citric acid, and most citrates ; oxalic acid, and most oxalates ; borax ; chlorates ; many nitrates ; picric acid ; sulphates of copper and magnesia, and the two mixed ; most of the alkaloids and their salts ; sugar but in fact the list is interminable. Cubic crystals, being of equal symmetry and elasticity in all directions, do not polarise, unless in drying the film of crystals becomes subjected to tension, as it sometimes does ( 132, 157). One of the prettiest crystals is salicine, which gives an enormous variety of effect, according to how it is treated. Some salicines I have prepared have been particularly admired T 2 FIG. 174. Apparatus for Crystallisation. 276 LIGHT [CHAP for their gorgeous colours and size of the crystals. Such arc attained by dissolving the substance in one part alcohol to foui parts water, made rather hot, and saturated. Pour a gooc layer of this fluid on the glass, and evaporate quickly wit? rather a strong heat ; the salt then melts in its own watei of crystallisation, and beautiful crystals soon begin to form The heat then needs humouring in a way only experience car give, else crystals already formed may be re-melted and th( slide spoiled ; but when all goes well the result is simpb glorious, the whole slide being covered with circular crystal showing sectors of colour like miniature " Newton's discs," am each, when the analyser is crossed, exhibiting a black cross The same film, cooled and breathed on whilst the crystals form gives quite different phenomena, in the shape of circula ripples, and a thinner film different again. Almost ever] operator has some little secret of his own ; and one of m; correspondents sent me a slide of the small sort of singula beauty, prepared with gelatine. The effects range from disc y 1 ^ of an inch to i inch in diameter, of any colour, or blad and white, according to the thickness. Citrate of magnesi; and other salts may be made to give very similar discs Chlorate of potass crystallises in square tablets ; nitre in Ion: thin prisms which appear as a network of coloured threads To get this latter effect the solution must be rather dilute, an< after the disc is covered, all the solution that will go, jerke< off; then left to evaporate in the cold. Most of the salts ma be mounted in balsam, choosing the best positions befor fixing. Another class of beautiful crystallisations is formed b melting the substance between two glass plates. Make a pai of spring-wire forceps, like Fig. 175 ; then put some of th chemical between two clean plate glass discs, and hold in th forceps over a spirit-lamp : or over the chimney of an Argam gas-burner is not too hot for some. Care, of course, is neede< not to crack the glasses. Most of the substances that crys xn] CRYSTALLISATION ON THE SCREEN 277 tallise well in this way are of the " organic " class, and some require a very thin film, which must be obtained by putting down the two hot glasses on a blotting-pad, and with thick padded gloves working close together till the film is nearly ready to set. The following I have found to make fine slides in this way : Cinnamic acid (gentle heat, very thin) ; suc- cinic acid (rather strong heat, very thin) ; cinchonine (moderate heat and thickness) ; santonine (fair thickness). This last FIG. 175. Spring Wire Forceps. gives very various effects, some slides showing a rough " ferny " pattern, while others are smooth in appearance. The most brilliant of all in colour, however, is benzoic acid, and it is also the easiest. It usually crystallises in long straight crystals ; but with a thinner film and very flat glasses I have obtained exquisite " ferns." l . Benzoic acid is especially convenient for a beautiful experi- ment. It melts at very moderate heat : and by preparing a wooden frame into which the double glass plate can be slipped and secured by a dovetailed slide while still hot, crystallisation may be shown proceeding upon the screen. The effect, as the crystals shoot out in the most gorgeous colours, is exceedingly 1 Micro-crystallisations, as a rule, do not answer for the lantern polar! - scope. The microscopist only requires perfect crystals on a small scale ; whereas, on the screen, these hardly show, except with the greater power of the polarising lantern microscope, which will exhibit them brilliantly. For the low power here considered, we want a much larger "pattern," and brilliant colour, even at the expense of what a microscopist would call coarseness, but which with low power does not appear so. Many beautiful crystals are available for the microscope, such, for instance, as the platino- cyanides, and can be purchased in immense variety for a shilling each. Quinate of quinine and quinate of lime deserve special mention as exquisite micro- crystals. Many of these can be shown by the simpler micro-attach, ment described on page 252. 278 LIGHT [CHAP. beautiful. Cinnamic acid and the others crystallise with the same facility, but it is difficult to get the right thickness to show colour with them, while benzoic acid never fails. Another experiment of this sort is to place between two warm glasses a saturated boiling solution of silver nitrate. As this cools crystals form. The same slide when heated will re-dissolve the crystals, and is then ready to repeat the experiment. Another method is to warm in a test-tube a strong solution of urea in gum-water, pour it over a warmed glass disc which is placed in the stage, and touch the film of fluid with a small crystal held in the end of a tube. If the strength is right (which seems however difficult to arrive at sometimes), this crystallisation is very fine. For the polarising microscope slides are prepared specially for this purpose, of several of the fatty acids. These have simply to be warmed ; when the crystals melt, crystallising out again as the slide cools, the same slide lasting for scores of experiments. One or two of these acids are coarse enough for the large glass discs of the lantern polariscope. 155. Mineral Sections. The majority of these, consist- ing as they do more or less of crystalline constituents, exhibit beautiful chromatic phenomena in the polariscope, which is indeed the most powerful instrument of the petrologist. A petrological microscope is usually fitted, not only with a polariser and analyser as usual, but with a quartz plate which can be introduced at pleasure over the objective (the use of which will be understood from the next chapter) and a system of con- vergent lenses for exhibiting the phenomena described in Chapter XIV. The phenomena can be seen in a portion of the section even the tenth of an inch square. All the varieties can be beautifully shown upon the screen by aid of the polaris- ing projection microscope ; but for the lower power of the ordinary polariscope, only the bolder and coarser sections are on a sufficiently large scale to be distinguished clearly. Such a selection will be found in granites, perthites, agates, zeolites, xii] ORGANIC STRUCTURE 279 labradorite, or any mineral similarly coarse in details. Such a simple microscopic power as described on p. 252 extends the list much. Some minerals should, if possible, be cut different ways to show variation in the consequent phenomena. Thus, what is known as " graphic " granite gives the usual appearance cut in one way ; while cut in another plane it exhibits a sort of marking like an oriental inscription. And labradorite may be cut so as to exhibit mere colour as a film ; or straight coloured stripes, or bands of rotational colours (p. 323). 156. Organic Structure. We have seen that the double refraction in films, and the interference colours we are able to produce from it, are due to a greater and less elasticity in two rectangular planes. Nearly all organic tissues or substances present this structure, or have a decided "grain," as it were. We used a piece of board as an analogy ( 148). Hence all such structures " polarise," and a thin longitudinal section of wood, if transparent enough, behaves as a film of crystal on the polarising microscope. It will be understood without explanation, from what has gone before, that the greatest depolarising or colour effect is obtained when the " grain " of such a section is adjusted at an angle of 45 with the plane of polarisation. This property of organised structure is of the greatest service to the student of histology. Sections of tissue which appear to ordinary methods perfectly transparent and devoid of detailed structure, by these differences in elasticity and conse- quent refractive power in certain directions, make structure conspicuous to him, when he examines them in his microscope by polarised light. He is constantly using this powerful means of analysis, which reveals to him what would otherwise be hidden from his eyes. A vast proportion of these phenomena can also be exhibited on the screen by a good polarising projection-microscope ; but for ordinary lantern demonstration we may make a limited selection of the coarser objects. A quill pen thus placed in 28o LIGHT [CHAP. the stage shows beautiful fringes of colour ; but it is better to cut off the barrels of two pens, slit them both up on one side, and boil for an hour or two. They then become quite soft, and can be rolled out and dried flat between two glass discs, which they nearly cover, and make a fine slide. So does a sheet of horn, such as is used for stable lanterns, and which can be bought for a few pence. So will a piece of bladder, if of the right thickness to come within the colour-limits; or a few large fish-scales or gill plates. The shoulder-blade of a rabbit may be scraped rather thinner and mounted, or the " bone " from a lobster claw. Shrimp or prawn shells, soaked in turpen- tine and then mounted in balsam, polarise well. If the thick- ness is not quite right for colour, this can be brought out by a superposition film. 157. Effects of Strain or Tension. If double refrac- tion and its consequences be really due to unequal elasticities, we can readily demonstrate the fact by subjecting to unequal stress substances which in their natural state are homogeneous, and therefore show no double refraction. Thus, annealed glass, being of equal elasticity in all directions, does not polarise ; but by making the elasticity unequal, it should easily be made to do so. Make a brass frame like Fig. 176, the size of the wooden slides, with a square-headed screw by which, with a "p-handled key, strong pressure can be brought to bear through the centre in one direction, 1 the glass abutting against a convexity, A, opposite the screw, and being protected from the grinding of the screw by a convex padding, c, of brass or copper. At the least touch of the screw double refraction is shown by fringes of colour, and as the strain increases the effect is gorgeous 1 Such pressure-frames are usually made by opticians of wood, with a thumb-screw, and flanges to keep the glass in place. But the chromatic effects heighten with the pressure ; and as the glasses only cost about 2d. each, I prefer the T-key, and "put on " all I can, usually till I break the glass. The effects are far finer with this extra power, and best just before the smash comes, XII] EFFECTS OF STRAIN 281 beyond description. Then let the glass and frame be turned to 45 angle with the planes of polariser and analyser. The effect now is totally different, but equally beautiful. Next put in two bits of copper or brass, B B, in the corners of the frame FIG. 176. Screw Press for Glass. opposite the screw, and abutting against them an oblong piece of glass. The strain now is different, resembling the breaking- load of a bridge. It will be seen how the coloured figures also differ, and how exactly the " lines of strain " are optically represented on the screen. Other transparent substances will give the same effects. A glass trough, made the size of a slide, open at one end and filled with clear cold jelly, will show beautiful phenomena if a rectangular piston is pushed in at the end so as to compress it. So will a glycerine "jujube," if compressed in any manner; but a still better plan, if a slab from which the lozenges are cut can be obtained, is to tie back the studs of the optical- stage, pass the slab of elastic matter through, and extend it with the two hands, of course at an angle of 45 with the polariser and analyser. A strip of thin transparent india-rubber 282 LIGHT [CHAP. will show similar phenomena when stretched. If neither is handy, soak some gelatine in cold water for a few hours, and then melt it with about two-thirds its' weight of glycerine, and pour out upon a smooth stone or iron slab, greased, to cool. The composition will be something like that which printers use for their rollers, but clearer ; and an oblong slab passed through the slide-stage (kept clear by tying back the studs), and stretched, gives beautiful colour phenomena. Not much time must be wasted over such jelly, or it will melt with the heat of the lantern, unless this is absorbed by a water cell. Heat applied to glass produces the same effects, owing to its expansive powers. Even one of the plain glass discs, fixed with a spring wire in one of the frames and held momentarily on alternate sides (so as not to crack it), with its centre over a small spirit-flame, will show a black cross, and transmit light through the rest when the analyser is crossed. But much better effects than this can be obtained. Make a " shell " of sheet-iron, like A B, Fig. 177, with a square hole in each side, i-J inches square, the parallelogram measuring 4 by 2\ inches, so as to go in the slide-stage. A little bit turned over from top and bottom at A A, one end, makes a "stop" for adjustment. Cut a piece of wood, c c, such size and shape that the edge of one of the thick glasses made for the press just described, "jams" into the shallow notch, and when wood and all are pushed in against the end stop, A, the glass stands central with the apertures. Fit a small bar of iron so as to slide in over the top edge of the glass. Having adjusted all except the bar of iron in the stage, and made the iron a dull red heat, slide it in over the glass ; at once fringes of light and darkness, and presently of colour, spread over the screen. 1 1 The private student needs no expensive apparatus for this class of experiments. As a boy, many, many years ago, I first made the above experiment in the following manner. A dinner plate was inverted on a bare polished mahogany table, and on this was laid a rather massive square bar of heated iron. On this was " stood on edge " a 2-inch square of plate glass, XII] EFFECTS OF HEAT 283 In glass made red hot and suddenly cooled, these beautiful effects are permanent. Such are called chilled or unannealed glasses, and cost from 45*. to *js. 6d. each, of various sizes and patterns. In making them, the great thing is to cool rapidly round the edges, and to start with a red heat. A square block made red hot, and stood on one edge on an iron smooth sur- FIG. 177. Apparatus for Heating Glass. face, while any mass of smooth metal is balanced on the top edge, will after cooling show very good phenomena, especially if slid on to fresh cold surfaces till cold. A good chilled glass gives coloured figures particularly vivid, and the figures can always be foretold. The most instructive shapes are a circular its edges ground flat on a stone with sand and water. The table acted as polariser, and a few slips of glass placed in the card case of a medicine- bottle, as analyser. I do not think I have ever experienced such pleasure from any experiment since, 284 LIGHT [CHAP. disc, which naturally gives circular rings, and when the analyser is crossed a black cross ; an oval, which yields very similar effects to a bi-axial crystal with convergent light as described in Chap. XIV., and a square. This latter appears as at I, Plate IV., when polariser and analyser are vertical and hori- zontal; if these are then rotated 45 (but still crossed) the colour and fringes are as shown at J in the same plate ; or if the chilled glass is rotated in an elbow polariscope, the figure is the same in the glass, only this latter stands diagonally. This too is a fact of great practical value, polarised light being a most sensitive test of any lack in perfect annealing. A "Rupert's drop" or "Bologna flask," for instance, shows conspicuous phenomena, as will almost any glass paper-weight, inkstand, or other massive piece. A section of very thick glass tube, ground flat and polished, almost always makes a beautiful slide ; and this prepares us to understand that perfect anneal- ing is by no means easy to get. Hence it is that a great many optical lenses^ especially if of any size, too often exhibit in the polariscope a conspicuous black cross. The lenses of a polariscope need to be tested very carefully indeed; but in other instruments of precision also, the inequality of refrac- tion is sufficient to impair the results, and polarised light thus becomes an analyser absolutely necessary if the instrument is to yield trustworthy results. 158. Stress in Liquids.. By bringing terminals from a powerful Wimshurst machine to within a small distance of each other in a piece of glass, by holes drilled from its surface, Dr. Kerr demonstrated that, as we should expect, a powerful electro- static charge acted very much in the same way as mechanical compression that electric stress had much the same effects as mechanical stress. But he further demonstrated that it was the same with a di- electric fluid ! He placed next the polariser a glass cell containing carbon bisulphide, in which was im- mersed two copper plates facing each other at a small distance say | to \ an inch so that the plane-polarised beam passed xn] STRESS IN LIQUIDS 285 between the plates, and constituted the field shown on the screen. The plates were made the terminals to a powerful machine or Leyden jar, and charged, polariser and analyser being arranged for the dark field, but so that their planes stood at 45 angle with the line from terminal to terminal. At once light, and generally coloured light, flashes upon the screen, as if the fluid in the space between the terminals were a piece of strained glass. This may at first seem a matter of no particular significance, but in reality it is of the deepest. For this one fact alone amounts to absolute demonstration, that the phenomena are not essentially due to any merely mechanical stress in particles of matter, but that the real stress is in the ether. We can cause stress in solids or in jelly by mechanical means; but by no mere mechanical pressure can we produce stress in a fluid, which by its very constitution distributes the pressure equally in every direction. Yet a stress is produced here by the static charge ; and the fact is clear proof that it is the state of the ether which is the essential matter in the phenomena^of light. 159. Effects of Sonorous Vibration. By this time we have a very vivid idea of the subtle power of polarised light as a revealer of the inner structure or molecular condition of bodies, provided they are transparent enough to apply such a test. The slightest difference in elasticity, or density, or, in short, from a homogeneous condition, at once stands revealed before this searching analysis. A singularly beautiful experi- ment, which Daguin describes as first made by Biot, though Dr. Tyndall first exhibited it by the lantern to a public audience, will show this power in a still more striking light. Get a strip of plate glass 5 feet to 6 feet long, 2 inches wide, and about \ inch thick, and smooth the sharp edges with a stone, or with a file and turpentine. Prepare for it a wooden vice, fitting into one of the wooden stands so often used, and thus adjustable for height ; and in this let the exact centre 286 LIGHT [CHAP. of the strip be fixed 1 at an angle of 45 with the plane of polarisation. 2 Draw forward the slide-stage, power, and analyser some little way in front of the polariser, if a direct polariscope ; or if of the elbow form, unscrew the slide-stage and objective from the elbow, leaving only the elbow on the lantern, and support the " front " on a wooden cradle of some sort (easily made by cutting semicircles out of the ends of a cigar-box) in its proper position axially, but leaving a clear space of an inch or so between the parts which ordinarily screw together. Through this interval pass the glass strip, and adjust the height, &c., so that the strip may cross the field as near the middle point held in the vice as possible. Cross the analysing Nicol to give a dark field, and throw a loose cloth on the " front " so as to stop all scattered light as much as possible. (Half the battle in all lantern experiments, especially with an inferior illuminating power, is to avoid such scattered light, and many operators lose much effect by not attending to it.) Now take a \\etflannel cloth (other kinds " bite" the glass too much and drag the vice about), and enveloping the free end of the strip in it, rub it smartly up or down with a long smooth sweep. A shrill but wonderfully clear musical note sounds out, from the longitudinal vibrations into which the glass is thrown, and at each note the dark screen is illuminated ! If now a "chilled" glass be placed in front of the optical slide- stage, and focussed as usual, and the experiment be repeated, at each note a quite different colour appears ; or if a selenite butterfly be inserted, some other colour of that will appear. Or we may vary the experiment by putting in the arrangement for heating glass. Starting with a dark field, on inserting the 1 It is well to glue on the inner side of each jaw of the vice a circular thin slab of cork, so as to give a good pinch without breaking the glass. - If the polariser is a Nicol, or either of the Delezenne forms, it is in some respects more convenient to set the polariser and analyser at 45 with the horizon, when the glass can be horizontal, and pinched at right angles. xn] SONOROUS VIBRATION 287 hot iron bar we get the phenomena varied by the effects of //^/-vibrations ; and when we have got good colour, we vary these again by interposing sound-vibrations. The experiment can be very fairly performed with even an Argand burner, at a screen distance of about 4! feet, giving a disc of 1 5 inches. This beautiful phenomenon is due to the stress caused in the glass near the nodal points, by the vibrations into which its molecules are thrown. Here, however, a difficulty may occur to some solitary student which actually did occur to myself, and which led me for some time to question this explanation. Dr. Tyndall himself states 1 that, upon sounding the glass, the screen effects are rendered "complementary"; and in my own experiments I generally found this to be the case. The change from mere darkness to light only, is easily accounted for on the supposition that the thickness of glass, or the double refraction and consequent retardation, are not enough to produce colour ; but when selenite designs give also " complementary " colours, the supposition naturally arises that the change of phenomena is of some absolute kind, and not one of degree, or comparison, as we should expect from a state of stress. Accordingly, I was for a considerable time inclined to attribute the phenomena to the half-wave retardation ( 150) caused by the mere "resolu- tion " of the plane-polarised ray, by the " absolute " motions of the glass molecules at an angle of 45. But a valued corre- spondent 2 subsequently placed in my hands a translation of the researches of Kundt and Mach into this subject, which clear up the matter by showing that there is degree or variable amount, in the effect produced ; and that therefore the " com- plementary " results must depend upon the strip of glass giving an average retardation of about half a wave length. Kundt having sent the light through the apparatus as described, analysed or spread into it a long band of light by a 1 Six Lectures on Light, second edition, p. 137. 2 The Rev. Philip R. Sleeman. 288 LIGHT [CHAP. revolving mirror. This band was broken like a string of pearls, showing that the doubly refracting effect was periodic, and coincident with the sonorous vibrations. Kundt then further interposed a selenite plate giving bright colour. The light being analysed as before by the revolving mirror, the band was found to vary in colour, the number of tints observ- able in the band increasing with the thickness of the glass or the intensity of the vibrations. Even thus, therefore, was established the degrees in double-refractive effect which the hypothesis of stress required. But Mach carried the investigation still further by means of spectrum analysis. Selecting a selenite which gave at least two or three dark bands ( 153), the light which passed through it and the glass bar was projected through a slit and prism as usual. When the bar was sounded, the dark bands became of course confused, and disappeared. But, assuming the slit and prism to be vertical, and the spectrum there- fore horizontally dispersed, this spectrum was compressed into a narrower and more brilliant one by a cylindrical lens whose axis was horizontal, and then again dispersed vertically by a rotating mirror whose axis was also horizontal. Every colour and dark band was thus drawn out into a vertical string ; and when all this was adjusted, the dark interference spots thus spectrally analysed separately, at successive moments during the sounding of the glass, were found drawn out into zigzag curves, whose amplitude represented the shifting of the bands, by the additional retarding effects of the temporary states of stress. This beautiful experimental analysis places the true nature of the phenomena beyond any doubt. xii] MICA-FILM WORK 289 APPENDIX TO CHAPTER XII Manipulation of Mica-Film Work The necessary implements for mica -work are few. We need first a thin, smooth, and broad paper-knife of ivory or tortoise- shell, carefully thinned down at the end to nearly a knife-edge. One or two very sharp needles will be required, and a few stronger points in handles of some kind for marking-out ; or a steel stiletto such as accompanies sewing-machines answers well for the latter. For cutting, provide a strong pair of scissors with not less than four inches clear cutting edge, and a small pair, of the dissecting type, with pointed blades an inch long. These must be carefully ^///^//r-sharpened on a small stone, as required, which will how r ever not be often : on the other hand two or three good pen-knife blades, or surgeon's lancets, for thin film cutting, will need sharpening constantly. For cutting circles I use pen spring-bows, breaking away one half of the pen and carefully sharpening the other, also tKe steel point on the other leg. The only other necessaries are a pair of forceps (which I prefer to be ivory-tipped), a few of the usual drawing instruments, a graduated rule, and a cutting straight-edge. For the latter a small steel rule will do, or the edge of a microscopic glass slip. I have already mentioned the "doubler" polariscope shown in Fig. 169. Besides a slab or two of mica, which has been sufficiently described, there will be needed some Canada balsam dissolved in benzol, and a little gum Arabic. The latter must be the finest perfectly white gum, kept in a capped bottle with a small sable pencil. The balsam should be the palest procurable, and is prepared by drying in a slow oven till it is as hard as pitch and will chip into flakes ; when it is dissolved in the best benzol. The solution is well known to microscopists, and can be purchased, or the dried balsam can also be procured. It is u 290 LIGHT [CHAP. best to have two capped bottles of the fluid, one as thin as cream, the other like a thick syrup. The first step is to split up a lot of mica, for which a port- folio with leaves, or a large thin book, will be a handy re- ceptacle, as the films should be kept classified. The mica will probably be in slabs from ^ inch to J inch thick, and " even " films cannot usually be split off direct. The first step is to split it into two, and then into four, and so until it is all split into layers as thick as very thick card. This is done by first " starting " the edge with one of the strong steel points, then inserting the paper-knife, and gently coaxing that in further and further, with now and then a little twist to help in starting it apart. The more slowly and gently all this is done, the more chance of getting any of these primary surfaces even and unbroken. In doing it, now and afterwards, the knife will appear to scrape or scratch the smooth surface somewhat, but this is of no consequence whatever, as every such mark totally disappears when in contact with the balsam and benzol. The layers should be thus split down till they just begin to show faint traces of colour when examined with a Nicol, and then laid together again in the position they formerly occupied in the original slab. Each layer, should now be examined carefully with a Nicol, by daylight from a window, over a large polarising surface such as a mahogany table, or plate of glass. The object is to see all inequalities of thickness, where in splitting the surface may have broken through, and a very minute difference of cleavage occurred. With the Nicol at the eye, these will show differ- ences of colour, the boundaries easily identified with fine hair- lines visible on the surface to close scrutiny. Where a surface is much broken up in this way, attempt should be made with great care to split off a thin film from it, to get an even sur- face : some original surfaces will be found good. Absolutely all of a plate is rarely found even, and when the greater part is so, the operator had best be satisfied. There is a great differ- XII] MICA-FILM WORK 291 ence in pieces : a good piece of mica is a prize, while one that persistently refuses to split evenly, may as well be abandoned. Marking the Mica. The next and most important step is to mark the pieces, to show the polarising planes. Choosing one of the thinnest and most even, "thedoubler" is arranged before a window at such a distance as to get the best polar- ising angle, and carefully adjusted so that when the analyser is crossed, the darkest part of the field appears as a dark nebu- lous patch in the exact centre of the mirror at the bottom, which is marked with lines as in Fig. 178. Some care should be expended upon this, and also, by turning the analyser a little each way, to train the " eye " to recognise any slight tendencies of the dark patch to travel either right or left of the centre. Then the sheet of mica, or one end of it probably, is laid on the mirror and carefully orientated by hand, until no colour is seen, and FIG. 179. the nebulous patch occupies its exact central position as before. The positions are now known ; and if a straight-edge be laid over the line ab or cd, and a bold scratch struck, it will give one of the polarising planes of the mica ; or ef Or gh give the lines which, placed parallel with the polariser, give colour effects. Much time and care should be given to this marking of the u 2 292 LIGHT [CHAP. first or " key " plate. It is well to make a number of observa- tions, marking each with a different scratch, and moving the mica between each into a different position then making a final deep scratch as the mean of the results, if there is any difference. Sometimes, instead of using a straight-edge over the lines on the mirror, it is more convenient to strike the axes by laying a broad parallel rule close up to the sides eg or gf of the box, or the other Jines by similarly using an ordinary mathematical 45 square. There is a still more accurate method of. finding not only the axes or planes, but which of them is the principal axis. Laying on the mica-sheet, half of such a convergent lens-system as described in 190, with a suitable focal lens near the analyser, the system of rings shown at D, Plate VI., will appear. The mica should then be so adjusted on the mirror,, that when the analyser is exactly crossed, the long black brush lies exactly straight along the line ab as in Fig. 179. This line ab is then the principal polarising axis or plane of the mica. Splitting Thin Films. The mica-sheets having been preserved in due order, every one can now be marked in succession from this key-sheet. The next sheet is laid over it, so that the edges precisely coincide, and the top one scratched over the scratch lying beneath. The next is laid on that one, and so on, till all the sheets are marked. When that is done, all bad and frayed edges are trimmed off each sheet, down to smooth good mica, with the scissors. And when that is done, the mica is further split down with the greatest care to the various approxi- mate thicknesses desired. This can be done, it will be found, much better from the thinner sheets, with their trimmed and sound edges. The sheets should be laid on several thicknesses of smooth paper, and the paper-knife used with the greatest gentleness, firmly held down to the flat beneath, while it will somewhat bend upwards at the handle end. As the films become very thin, the split will need to be started with one of the finest and sharpest needle-points ; and to insert even that, xn] MICA-FILM WORK 293 it may he necessary to slightly thicken the edge, by rubbing it with the smooth side of the needle. As each film is separated from its fellow, the marking must be repeated on it, making the scratch no deeper than is clearly visible. Every film is also to be carefully examined for even- ness, and any uneven portions plainly scratched at the boundaries with a needle-point ; while the differing part of the surface should be defaced by scratches, unless large enough in area to be used on its own account. The films are finally sorted into the book or portfolio, and marked (if known) as what they are, ready for use. The thinnest film of any real use is what is called an |-wave film that is, in passing through it the ray traversing one plane is retarded behind the other by one-eighth of a wave. Such a film is exceedingly thin, but every endeavour should be made to procure one at least, wherewith to construct the Fox wedge already described, shown in Plate IV. at A. Gauging the Films. This brings us to the very important point of gauging the films. Here especially the Fox wedge is invaluable ; as such a preparation, once made and verified, 'nstantly gauges any other film adjusted to " cross " it. The stripe that is black, (with the dark field) gives the thickness ; or if two stripes are equally dark and not quite black, the thickness lies between them. We easily gauge these all-important |-wave films by the "doubler." It is plain that if we superpose two films the same way, and lay them on the mirror with the principal axis at 45 (i.e. ef or gh in Fig. 178), they will be in the depolarising or colour position, and amount to a quarter wave. The " doubler " itself doubles this, making a half wave (and of course one single quarter wave plate, as mentioned further on, is gauged just the same). And the crossed analyser (see 150) gives another half wave, making a whole-wave difference. But this restores coincidence and means perfect transmission ; while the half wave retarda- tion resulting when the analyser is parallel, means extinction 294 LIGHT [CHAP. (all but the plum-colour caused by the slight residuals already spoken of). Therefore if two films thus laid on the mirror, give this " tint of passage " when the analyser is parallel, and it is known by that " feel " of the film which is speedily recognized that the thickness does not belong to the second or third orders, they are known to be i-wave films, or a single film is known to be a J-wave. Many approximately -J-wavc films may be split before one true one is found ; and it is desirable to test this even more severely by superposing four of them (a very small square is enough for this) with a drop of the balsam between to render them more transparent. The four will give the second tint of passage, and make the matter sure. Cutting the Films. This is done differently, according to their thickness and character. Thin films, from -J to j, which have to be cut exactly, are best handled as follows. Prepare a sheet of cardboard about 16 X 12 inches with the black varnish described on p. 18, lay it on an accurately-squared drawing board the same size, and fix the film to the board through card and all with drawing-pins, at the two top corners, taking care that the scratch marking the axis of the mica which is to stand vertical, lies accurately on the board to a T-square. The pieces are now carefully drawn with steel point. For the 24-film wedge, the simplest plan is to rule the whole film off into horizontal bands \ inch wider than the length of the stripes to be shown, and with a narrow strip or space rather more than \ inch wide between the bands. Then the longest film is measured and scratched on a band, allowing -J inch longer than is to appear. The second film will be one eighth of an inch shorter (because y^ inch at each end of the longest film will be blacked over, while every subsequent film will mark the edge of a stripe at one end). Every film after that will be one-sixteenth of an inch shorter than the preceding. When all are scratched out with the point, one similar corner on each is lightly marked to ensure all being superposed the same way, and the bands are cut apart with the scissors up xn] MICA-FILM WORK 295 the narrow spaces purposely left. But the rest, and all exact cutting, must be done with penknife blade or lancet. Laying the cutting straight-edge exactly to the scratched line, the blade is moved backwards and forwards with a very light pressure indeed, keeping the edge perfectly in line, till the piece separates. The hard black varnish both gives the very best backing to resist the cutting-knife, and enables the scratches and all that is done to be best seen. All precise work is thus drawn with steel point on the mica, and cut with a single blade to a straight-edge, in this manner. Similarly with circles : the spring-bow compass, with half a steel pen as cutter, is revolved repeatedly with a very gentle pressure, till the disc separates. The slight thickening of the edges caused by this method of cutting is of the greatest service in all "fitted" work, by preventing these thin films from sliding underneath the edges of their neighbours. Mere geometrical patterns in thicker films are better handled differently. The patterns desired, such as those shown in Plate V., may be drawn carefully and distinctly in ink on white card, which is further ruled with vertical lines an inch aparTall across it. The mica being fixed to the board through this card as before, with its intended vertical axis parallel to one of these lines, the required pieces are carefully traced over the drawing by means of the steel-point and straight-edge, a key corner being marked on each before the piece is cut loose. In going through a design like any in Plate V., the mica film will be cast loose and shifted along for each successive piece ; hence the convenience of a number of vertical lines, to any one of which its axis may be laid. Then the rough area of each shape is first separated with the large scissors, and finally the shape cut to the scratched lines with the same. Cutting over the blackened card, it will be found that what is done can be readily seen. Shapes which present interior angles, such as those forming the octagon star shown at n, Plate V., are cut round nearly close to the outer points with the large scissors, 296 LIGHT [CHAP- and the interior angles carefully cut out with the small pointed ones. The method of design is a matter of choice and convenience. Mr. Fox, who first executed any work of this kind, put all his patterns together with pieces of different thickness, fitted like a mosaic. I found this process exceedingly difficult, while it did not satisfy me in range of colours ; and therefore devised a method which in my hands proved both easier and superior in effect, viz., designing patterns which allowed of the super- position of geometrical shapes, gradually decreasing in size as a rule, but not necessarily. Plate V. gives sufficient examples, of which details are given further on. The contrasts of colour obtained by thus employing successive orders of colours, is much finer, if the films are judiciously gauged. As the first few bands in the wedge give no colour, it is best to start with a full-sized disc of mica as a foundation, about f thick, where colour practically begins. Then if the succeeding "pattern " films range from a \ thick to about f thick, the harmonies and contrasts are sure to be good : but exact \ waves superposed, naturally give a rather monotonous effect. Cementing and Mounting. For mounting in the usual 4 X z\ inch wooden frames, glass discs slightly over if inch diameter, are most convenient for ordinary preparations : but the 24-film wedge, if the stripes are T ^ inch wide, will need 2-inch discs to lay it down comfortably, and the larger size is better also for some few other preparations. A glass being cleaned, sufficient of the thinner balsam is dropped in the centre from the glass rod, taking care there are no air-bubbles for a large piece more than one drop will be needed ; for a small shape a very tiny one indeed. Then the film to be laid down is taken by one edge in the forceps, cleansed from loose dust between thumb and finger (the greasy marks so caused will all disappear) and gently laid down in position, shifting it a little if required by a couple of steel-points, pushing at oppo- site edges. The axis of any " foundation " film the size of the xii] MICA-FILM WORK 297 entire glass must be plainly scratched, and the first " pattern " film very carefully laid to this and adjusted centrally ; each sub- sequent film of the pattern will be laid as a rule to the points of lie film underneath. This will need care, holding the film below steady with one point, so as not to alter adjustments already made, while the last put down is adjusted to it in turn by another point. The balsam should run nearly, if not quite, to the points or edges. When all are laid down, before the top glass, or a quarter-wave film, or anything covering the whole, is cemented down upon the preparation, the latter should be put aside for at least a week, protected from the dust by an inverted tumbler, for the balsam round the edges 'of each layer to become dry. This is essential, to prevent the films from slipping out of adjustment when the cover glass is pressed down. The Fox wedge will need special handling. For very thin films, like -J-wave, the balsam also must be very thin. The largest film has only to be laid down on the centre of the glass disc, and whilst the films are long enough to be distinctly oblong, it is best to lay rather a streak of balsam, as it will thus spread out better. The second film is then merely laid even with what is to be the thick end of the wedge, the other end of it marking the first stripe. It is well next to fix the glass in a frame by a couple of morsels of putty, so that this stripe is parallel to a small T-square laid across the frame. And the successive films are laid down so that their ends coincide with the divisions on a rule laid along over the wooden frame from time to time, not in contact w r ith the mica. The films are easily adjusted by steel points so long as the balsam is thin and moist ; but it must be done then, as it soon begins to set round the edges. The most delicate adjustment of all is required when the small parts of a preparation in thin mica, such as the quarter- waves shown in Fig. 188, have to fit accurately edge to edge. At first they will slip under each other ; but the thicker edges 298 LIGHT [CHAP. caused by the knife help much, and after a few trials it will be accomplished. It is in these very precise preparations that^v/w is useful. Colourless gum is practically invisible, and when these delicate preparations, or any parts of them, are success- fully laid down, a very tiny drop of thin gum may be taken on the point of the sable pencil and introduced under two points of the piece. When " run in " the gum should not occupy more than -Jg- of an inch square. For a moment or two the film may still be moved if necessary ; but the gum rapidly dries, and that piece is then fixed, as the gum is not at all affected by the thin balsam afterwards added, as dried balsam is. With wedges, the balsam will rarely spread at first to the outer corners of the successive films, and the best plan is, when all are laid down, to draw a narrow streak of the thin gum all along the top and bottom of the wedge, which will run a little under each corner. All is then left to dry as before. After some days the cover-glass may be put on. The disc should be laid on something rather smaller a pill-box or short piece of brass tube will answer well and sufficient balsam be dropped on to the centre as speedily as possible. Then the cover is laid down very gently and accurately, so that it may not have to be dragged about. The balsam will "run in " to any points not quite filled, as it reaches them in extending outwards, and should nearly reach the edge of the glass. Any bubbles should be pricked before laying the glass on. Some small bubbles may occur from little dry spaces left between the films ; but if the balsam is thin, all but large ones will gradually disappear of themselves. Finally, a weight of about half an ounce, with a flat bottom, is laid on the centre of the top glass. This will probably squeeze some balsam out at the edges hence the need of a smaller support underneath. If any considerable space is left, a little balsam applied at the edge will readily '' run in," in most cases. With all possible care there will be a good percentage of failures, which is disheartening if much trouble and labour XII] MICA-FILM WORK 299 lias resulted in a specimen apparently very successful up to that point. Obstinate large bubbles will occur, and it is almost impossible to get them out. They are easily enough moved outwards and excluded, by squeezing the glasses to- gether ; but the thin balsam rapidly re-dissolves the dried balsam on which fixity depended, and the films slip about also and spoil the slide, in nearly every such case. Practically, very little if anything can be done to mend a preparation when the cover-glass is once laid down. It is to avoid such mischances that a little gum is so useful in many cases ; but it is rather difficult to use it much without being visible on the screen. The preparation is left undisturbed under the small weight for a week or so, after which it should be gently baked in heat of about 100 or ITO. If access can be had to a place where there is a steam-engine, a small box containing the objects is well placed somewhere in the boiler-house ; or the egg-drawer of an incubator does well. A domestic oven is far too hot, but the plate-rack over a kitchen range is a good place, provided the operator be a persona grata to the -pre- siding genius. The baking should occupy some days, looking at the preparations now and then in case any air-space may open at the edge which may especially happen if too much weight has been used in which case a little fresh balsam can generally be run in. When sufficiently hard and dry, any loose balsam is scraped off with a knife, and the glasses finally cleaned with a few drops of sulphuric ether on a bit of soft rag. The thicker balsam is used to fill large vacant spaces. There will be, for instance, vacancies at the top and bottom of the 24-film wedge ; and it is better to lay down some thick balsam there, before putting the thin balsam on the mica and applying the cover-glass. The thick solution gives more sup- port, and air-spaces are less likely to run into it. Such a slide as this wedge will have rough or irregular edges to the 300 LIGHT [cir. xii mica, by the way : and after it is finished and cleaned, the superfluous area, to the circumference of the disc, is blacked out on one of the glasses with photographer's black varnish. These are the methods I have found best in constructing preparations of this class. Failure at first is almost inevitable more or less is likely to occur always ; but the beauty of the phenomena, and their clear instructiveness, amply repay the student when success has finally been achieved. Such pre- parations cannot be hurried, and a month is required to carry one through : but most of this is occupied in waiting. The manipulation itself does not take very long, and the similar stages of several preparations can be conducted at the same time. CHAPTER XIII CIRCULAR, ELLIPTIC, AND ROTARY POLARISATION Composition of Vibrations into Circular Orbits --Quarter- wave Plates Other Methods Fresnel's Rhomb Plane and Elliptical Composition Rota- tional Colours Circularly Polarised Designs Waves of Colour Contrary Rotations Effect of Polarising and Analysing Circularly Spectrum of Rotational Colours Phenomena of Quartz Right- and Left-handed Quartz Quartz in circularly-polarised Light Use of a Mi-quartz Rotation in Liquids The Saccharometer Other Rotatory Crystals - Electro-magnetic Rotation Optical Torque Rotation or Torque of Common Light Reusch's Artificial Quartz Rotation and Molecular Constitution Effects of a Revolving Analyser. 1 60. Composition of Vibrations. We have hitherto chiefly considered the resolution of plane-polarised vibrations, and its chromatic effects. We have now to consider the results of compounding them. We have seen that two plane-polarised rays vibrating in the planes and | , even though both originally from the same polarised ray, cannot possibly inter- fere with or quench each other. In that way, they can have no relations. But they may act on each other in another way. Let a pendulum be mounted as in Fig. 180, so that it swings on gymbals, G, from two axes at right angles to each other ; l if swung on one axis the bob will vibrate in the path A B ; if 1 The illustration in this form is, I believe, first due to Professor Baden- Powell. 302 LIGHT [CHAP. on the other, in the path c D at right angles with it. Let these represent two rectangular planes of plane polarisation, and the bob a molecule of ether, and let it have arrived at B in the plane orbit A B. It has therefore reached the limit of its swing, and the next moment will begin to swing back, but at this FIG. 180. Composition of a Circular Vibration. moment has no motion. Just at that moment, then, imagine the bob of a duplicate pendulum, moving in an orbit at right angles to A B, and in the full power or exact middle of its swing, to strike against it as represented by the arrow c 1 D 1 . This second bob will yield up its motion and come to rest, and may be withdrawn ; but its transferred motion thus applied xin] QUARTER-WAVE PLATES 303 tangentially, will be compounded with the other, and drive the bob, B, into a new circular orbit, B o D A, in the direction of the arrow. We can see at a glance that the second vibration, to have this effect, must be exactly a quarter of a ivhole (i.e. double) vibration or wave before or behind the other, or must be at its middle point when the other is at the moment of rest. It follows, therefore, that supposing us to be dealing with actual physical realities real atoms of ether vibrating in real paths a circularly-polarised ray ought to result, if we caused one plane-" polarised beam to be retarded exactly a quarter of a wave, or any odd number of quarter-waves, behind the other. 1 161. Quarter-Wave Plates. Such being the theoretical view of the matter, we have already learnt that in several ways we can accomplish such a quarter-wave retardation. The simplest is the use of a thin film of selenite or mica, called a quarter-wave or quarter-undulation plate. It is exceedingly difficult to get a large even film sufficiently thin in selenite ; 2 and therefore mica is usually employed, with which it is very easy to procure one, splitting and gauging the film in "the manner described in the last chapter. A film of the proper thickness, when placed in the stage in the position that w r ould give colour were it thicker (the film is generally used in the rotating frame), gives the same illumination as the analyser is rotated, with only a little variation in colour, from a rather bluish grey to a rather yellow or fawn-coloured grey. The reason of 1 The student is strongly recommended to work all these cases out by diagram. With a small bat of flat wood as a striker, the effect of two rectangular impulses is readily shown upon a rather heavy ball hung by a string. And the result of the actual compounded motions is readily projected on the screen by a fork or reed apparatus in the manner of Lissajous ; or by a little pendulum apparatus scratching the figures on a slide of smoked glass. 2 I am not aware of any full-sized quarter-wave plate in selenite being in existence, except one in my own possession, which formerly belonged to the late Mr. J. Darker, and was obtained by a rare accident. 304 LIGHT [CHAP. this is, that all the colours cannot be exactly a quarter-wave different, simply because the wave-lengths vary. The test of an equal light will be sufficient for most experiments, if the student cannot undertake the more sensitive and exact test with the Norrenberg " doubler." This then is our " quarter-wave " plate, which should be at once mounted between two glasses in balsam, and its working planes marked on the edges by scratching with a diamond or quartz crystal. It can now be observed that all the phenomena correspond with theory ; for, placing the plate in the optical stage in the rotating frame, in the proper position it will be seen that a double-image prism gives equal images in all posi- tions ; while yet we shall find, by beautiful phenomena of colour when colour-films are introduced subsequently, that the light is still " polarised/' though in a different way. A second smaller quarter-wave film should also be mounted between glass discs, and set in a short bit of brass tube, or a narrow edging of cork, by which it can be fitted at pleasure into the end, B, of the crystal stage shown in Fig. 198. Thus equipped we are ready for a further most interesting set of experiments. Before commencing them, however, we must clearly understand the positions of the apparatus. Repre- senting a quarter-wave plate by Fig. 181, A B and c D are its planes or axes of polarisation, here shown at angles of 45 with the supposed planes of polariser and analyser. This is the position of the plate for producing circular polarisa- IMG. ioi. Ouarter Wave , i i i 111 11 .1 plate. tion, in which it should be marked on the edges at E F, G H ; it is also the usual position of a coloured film. But in many experiments the plate is used at an angle of 45 with this position, bringing the axes A B, c D vertical and horizontal ; the plate should therefore be so marked that either position can be adopted with accuracy. XIN] FRESNEL'S RHOMB 305 For my own use, however, I prefer to permanently mount a large film in each of the positions, making the wooden frame as thin as possible. It will readily be seen, and must be thoroughly understood by the student, that the whole effect of a quarter-wave film, or any other " compounding " film, depends upon its axes, or planes of vibration, being placed at an angle of 45 with the last preceding plane or planes of polarisation. The "compo- sition " which takes place as soon as the rays emerge from the film, is preceded by the " resolution " into two plane rays within the film, which we studied in the last chapter. 162. Other Methods. Light can also be circularly polar- ised by placing the glass press in the stage, with the screw pressure at an angle of 45 with the polariser, and adjusting the pressure so as to give the necessary amount of retardation. ]}y this method, however, only about one-fourth of the area of the glass, in the centre, gives at all uniform effects, the edges being too strongly doubly-refracting, owing to the greater stress in those regions. Light is also circularly or clliptically polarised by reflection from metals almost circularly by silver. 1 163. Fresnel's Rhomb. Fresnel calculated from mathe- matical conceptions, that if he constructed a rhomb of glass with parallel opposite faces, so disposed that a ray (A B, Fig. 182) was "totally reflected" twice within it at an angle of 54 37' as shown ; if that ray was plane-polarised in a plane inclined at 45 to the reflecting surfaces, it would be (as it were) so divided and spun round by the relation of the reflecting surfaces to its vibrations, as to emerge circularly polarised ; as at c. 2 This 1 Light is not plane-polarised by silver at any angle, and circularly only at a certain angle. Hence we see why the silvered surface of the "thin film" in 105 did not quench the light. 2 I give this as conveying a rough, realistic idea ; in reality, the original ray is divided at the first reflection into two, of which one is retarded \ of a wave-length ; and still more differentiated to a quarter- vibration by the second reflection. The rest follows as in mica-films. X 306 LIGHT [CHAP. was entirely worked out first in theory ; but experiment verified it. The ray did emerge circularly polarised ; for rotation of the analyser showed no difference in brilliancy, and yet it differed /\ FIG. 182. Fresnel's Rhomb. from common light in causing colour, when passed before analysation through doubly-refracting films. 164. Plane and Elliptical Composition. Both pendu- lums and diagrams will readily demonstrate, that if the com- pounded rectangular vibrations differ by half a phase, the resultant must be another plane vibration, at an angle of 45 with them both, but at an angle of 90 with the original plane of polarisation. This is easily demonstrated in fact by a large mica-film equal to the fourth band in Fox's wedge, or half a wave thick. The "dark field " with analyser crossed becomes bright when this film is inserted, and is dark with the analyser parallel. This is another way of analysing the " complementary " effects of a half-w r ave plate referred to in 150. Intermediate differences in phase must result in elliptical orbits. It follows further that with almost any colour-film, much of the light transmitted must, upon emergence, become either circularly or elliptically polarised. With any regularly graded film, such as a wedge or a Newton's-ring slide, regularly recurring bands must be circularly polarised, and intermediate bands elliptically and plane polarised. The usual tests show that this is the case. It likewise follows that any thickness equal to an odd number of quarter-waves must give substantially the same phenomena as a single quarter, and an xni] ROTATIONAL COLOURS 307 odd number of half-waves, of a single half-wave. With any homogeneous light to which the film is adjusted, it is so ; but with white light the amount of the residual colours which have before encountered us in all interference phenomena, from waves not exactly of the same length, gradually increases with the thickness of the film. This is well shown in the colour modifications of similarly numbered bands in the successive orders of a Fox wedge. 165. Rotational Colours. But we must now study the beautiful optical phenomena which result when a quarter-wave plate is placed in the stage after some other preparation which exhibits interference colours. Let us suppose the vibrations transmitted through the polariser are vertical. Then w r e place in the stage a selenite or mica preparation, in the usual position; for simplicity, let it be a simple "even " film. Its axes are in rectangular azimuths at 45 angle with the polariser, and by it the plane-polarised ray is resolved into two whose vibrations are in those azimuths. Next to this comes our quarter-wave plate. For the latter to exert its resolving power in turn, its axes must lie at angles of 45 with the preceding planes or axes hence those of the quarter-wave film stand vertical and horizontal. They have now to deal, however, with both of two rectangular sets of vibrations. What must happen ? By diagram analysis we see at once, that each of the first plate's two sets of vibra- tions is now, separately, resolved into two by the quarter-wave film ; that each pair on leaving that film must be " com- pounded " into a circular orbit ; but that these two circular orbits will be in opposite directions, and that one of them will have been retarded behind the other, so that the circular motions no longer meet and pass at the exact top or bottom point of the circular orbit, but more or less to one side of it. Let its see how this will work out when all is resolved and compounded again into plane motions by the analyser. The original plane-polarised ray A B (Fig. 183) is shown here divided into two contrary circular orbits, w r hose directions are x 2 3o8 LIGHT [CHAP, FIG. 183. Rotation of the Ray. denoted by the contrary arrow-heads at R. Had not one (that resulting from the slowest ray in the first film) been retarded, their meeting-point would always be at either A or B, since from one of these was the starting-point : as it is, the meeting must take place at some other point R, de- pending upon the thickness of the first film ; on which side of the point A depends upon which is the most retarded ray, that de- pending upon the relations of the planes in the two films. But each circular orbit is compounded of two motions, one being tangential, and the other an equal radial motion at right angles to it (vide pendulum experi- ment, Fig. 1 80). The two tangential components, shown by s R and T R, meet however in direct conflict, and so destroy each other ; and there are now only left the two radial motions, both in accordance, and which therefore unite in the plane vibration R p, which represents a final new plane of vibration, or, in other words, a more or less rotated plane-polarised ray. Thus it would seem to follow, that if we employ a sodium- flame or any other homogeneous light to which the quarter- wave film is adjusted, the analyser, which apart from these films must have been turned to a position at right angles to A E to extinguish the light, must now be rotated to a position at right angles to some new plane R P (depending on the thickness of the first film), but will then again extinguish the light : so that the plane of vibration * has been rotated through the angle A c R. Experiment justifies all this to the very letter. It is exactly 1 I purposely here use the expression "plane of vibration" instead of "plane of polarisation," because it is the direction of actual motion which must be clearly in the mind of the reader. xin] CIRCULARLY POLARISED DESIGNS 309 so : the analyser has to be rotated more or less, and then again cuts off the sodium-light. That is all, so long as we employ homogeneous light. But if we employ white light, it manifestly cannot be all. Here we have all manner of wave- lengths to deal with ; and by our whole course of experiments, we have learnt that all these are differently retarded, and accord- ingly their contrary circular orbits cannot all have the same meeting-point R, but these points must follow one another in succession. The analyser must therefore cut off (as it is rotated) one colour at a time in orderly succession of the wave-lengths ; and the residuals, as usual, will exhibit gradually changing u composite " complementary colours, passing approximately in turn through all the colours of the spectrum. This also is justified to the letter ; and very beautiful it is. From one to two waves thickness for the first film gives the most apparently complete spectral series of colours ; but ' using any colour-film, either simple, or a geometrical or other design in selenite or mica, on rotating the analyser we get, instead of two complementary colours, and two positions with no colour at all as heretofore, all the colours passing into each otherjn beautiful succession. 166. Circularly Polarised Designs. Any ordinary selenite design, such as a star or a chameleon, will exhibit these phenomena when followed by a quarter- wave plate properly arranged. But in selenite it is difficult to get films thin enough to exhibit the lower orders of colours, which are most vivid ; and hence the most brilliant phenomena are obtained from mica designs, prepared as already described. Mosaics such as Mr. Fox executed are practically the same in effect as a selenite star, prepared of separate fitted pieces in the same way ; but by starting from the lowest good colour, and adding thin films, we secure all the most vivid tints and a pleasing gradation. Such single designs are easily prepared after any such patterns as are shown in Plate V. ; and after the successive pattern - films are cemented and the balsam is tolerably dry, a 3 io LIGHT [CHAP. quarter- wave film in its proper position is superposed with fresh balsam, at the same time as the cover-glass is applied. The magnificence of some of these low-order thin-film colours, whilst in transition by the rotation of the analyser, can hardly be imagined until it is seen. If such a circularly-polarised design be placed in the stage with the quarter-wave film first, it behaves precisely like an ordinary selenite or mica, because the polarised vibrations pass through this film quite unaffected. If however, while the analyser is crossed or parallel, the polariser be rotated, the rotational colours appear precisely as if the film came last and the analyser were rotated. In seeking beautiful screen demonstrations of these pheno- mena, I found the most magnificent effects of all no other adjective adequately describes them from superposing in the stage two geometrical mica designs, each circularly polarised. The two may either be identical, or different from each other though designed in relation. In this case the rotational colours produced by the first design are again resolved, re-compounded, and circularly polarised by the second design ; and the result is a magical " play " of colour in beautiful kaleidoscopic patterns, which I have never seen equalled, and which is apparently inscrutable until the mechanism is analysed. Even this does not exhaust the variation ; for if when the analyser has been completely rotated (which should be done very slowly, in order that each change in tint may be appreciated) the original polarising plane be rotated a few degrees, the relations of all the film-axes are so altered, that the series of colour variations becomes different ; and so on yet again, until when the polariser stands in an azimuth of 45 the first of the two designs (one of its axes being in the same plane) becomes altogether obliterated, and only the second single design stands in colours upon the screen. These compound mica preparations have given so much delight wherever seen, that I add some details, and in Plate V. xin] COMPOUNDED DESIGNS 311 some patterns which I have used, to show the principle and method of combination. The designs lettered A, B, c, are all planned in combination. Both A and B are effective when two similar ones are superposed (of course with their hexagonal points in intermediate positions), in that case making rosettes of twelve points. Any two of the series may also be used in combination ; and when either A or c is thus used superposed upon , each has two positions, yielding totally different patterns. The construction is easy and simple. The basis of each design is a film about f wave thick, covering the entire circle. Then for A (Plate V.), a triangular film ABC about wave thick is laid down, and upon this a similar inverted triangle D E F, the other smaller triangles superposing in the same way ; all the films being of course so cut that the axis of the mica has the same direction when they are superposed. Finally the quarter-wave film and the top glass covers all. Fig. B is constructed by laying down two circles edge to edge vertically ; then two others FIG. 184. edge to edge at an angle of 60 ; then the third pair at the other angle of 60, and finally one in the centre. Design C looks complicated, but is easy when analysed. On the base-film is first laid down a film cut as Fig. 184, then a similar shape inverted ; then a couple of triangles like the largest in design A ; and finally the central six-pointed star. At D E F are shown a similar set of octagonal designs. Of this set only D is suitable for duplicating ; this makes the most beautiful "rosette" of all. In that figure each successive smaller shape for superposition is readily traced ; and E also needs no remark. The design at F can be built up either by superposing four films like A B C D, or four like A B C E j the effect will be precisely the same, if the mica axes are properly kept, but A B C D is easiest, since the 312 LIGHT [CHAP. points of two films coincide at A c. The design F superposed upon D has two positions, giving totally different patterns. Care should be taken to lay down all "combination" pre- parations truly centred on the glass. When finished, their combination should be studied, holding a pair in hand. The first or bottom one should be in the usual colour-film position, or most effective position used singly. The other will first be tried in the same position over it, when it may be satisfactory, or not. If not, it should be turned round, one-twelfth or one- sixteenth of a revolution at a time according to the number of " points " in the design, and the effect observed, till this has been seen in every azimuth possible to the combination. Sometimes a pair whose effect is only moderate when one is used as the bottom design, becomes far finer when upper and lower ex- change places. When the best result is ascertained, the bottom preparation may be fixed with red putty in a rather thick wooden frame, while the other is dropped loosely into the frame over it so as to be movable, and kept there by a spring wire ring ; a little cross or other mark being scratched at the two points (for the two pattern positions usually possible) which, when brought to the top of the vertical diameter, give the finest effects. Both designs will of course be so super- posed and placed that their covering quarter-wave films stand next the analyser. 167. Waves of Colour. But we have not nearly ex- hausted the beautiful phenomena of rotary polarisation. If the film which we are circularly polarising is regularly graded in thickness, it is obvious that as the colour at any one par- ticular thickness (a) passes into the next tint, a slightly greater or less thickness (b} next to it (depending on the direction of the rotation) will pass into the former colour of (a). And the whole effect will be as if a " wave of colour " had passed across the whole gradation of the thicknesses. We place in the stage the Fox 24-film wedge, and superpose our quarter- wave : on rotating the analyser, a beautiful wave of colour MICA DESIGNS D. B, E. C. A. B. C. D. E.F. JhterchangeaMe; #ctagonn which they are, as it were, built up. This line of inquiry takes us into a new and magnificent range of optical phenomena, to enter which we have simply to abandon the nearly parallel beam of light we have hitherto employed, bringing to bear upon our crystals pencils of polarised rays distinctly con- vergent. Provide a plate of Iceland spar, cut across the axis, and about \ inch thick. It need not be large ; and for the lantern polariscope it may be conveniently mounted between two thin glass circles, in the centre of a wooden slider four inches long by 1 1 inches wide (Fig. 196). Placed in the centre of the FIG. 196. Calcite Plate in Slider. optical stage, so as to get the parallel beam of polarised light we have already discovered ( 132) that it acts as a mejre plate of glass, producing no effect ; its image is dark or light, according as the analyser is crossed or parallel. But now imagine converging or diverging rays, or a conical pencil of plane-polarised rays, such as are produced by a converging lens, passing through the plate. It is evident that only the central rays can pass exactly along the optic axis ; and that all inclined rays must be more or less doubly-refracted. At equal distances all round the axis of the pencil, therefore, the plate must act as a thin film, and give colour arranged in symmetrical circles. But this is not all. We have already learnt the two directions into which the original polarised plane of vibration must be resolved in the crystal, and that one of the two planes must pass through the axis. The other of course is at z 333 LIGHT [CHAP right angles to it ( 133). Taking therefore Fig. 197 as a diagram of our plate, and supposing A B to be the original plane of vibration from the polariser, the plate of calcite resolves that, everywhere, into vibrations passing through the axis, represented by the radii ; and others at right angles to them, represented by tangents. Further still, it is evident that in the B FIG. 197. Vibration Planes in the Calcite. planes of the two radii, A B and C D, there will be no double refraction at all, since there the planes of vibration in the crystal coincide with that of the polariser, and that perpendicular to it. Along those lines, therefore, the plate can have no influence, and must appear black when the analyser is crossed, and white when it is parallel with the polariser ( 149). All this is so in experiment ; but to exhibit it on the screen, we must add to the polariscope what is called a " crystal stage," which will hold the plate in a converging cone 5] B of rays from the objective. Fig. 198 shows the construction of it. A tube, A B, fits on the nozzle of the objec- FIG. 198. Crystal Stage. tive, and has transversely cut through it a slit, S, through which the crystal sliders are passed, kept in place by a spiral spring as usual, XIV] APPARATUS FOR CRYSTALS 339 The end, B, of the tube is of exactly the same size as the nozzle, so that the Nicol or other analyser fits and rotates in it, as on the nozzle. We place this addition on the nozzle, add the analyser, and insert our plate of calcite in the slit, s. We at once get on the screen the beautiful figures represented at A and B, Plate VI. according as the analyser is crossed, or parallel with the polariser. In the former position the beautiful coloured rings are traversed by the black cross we were led to expect ; in the other position, we get the complementary rings traversed by a white cross. The centre, of course, shows no phenomena at all beyond white or black, as the rays there pass along the optic axis. 184. Apparatus for Observing the Rings. The objective described in Fig. i gives, in practical work, about the best convergence for average effect with " crystal rings," unless an addition to be presently described is made to the ap- paratus. Much more convergence, unless the extra lenses are added, causes a great deal of light not to get through the analyser ; and much less gives fewer rings, unless a very thick plate be employed. For a moment's consideration will show that the amount of retardation in a plate of crystal thus cut, depends on both the thickness of the plate, and the amount of convergence ; and that the rings must become closer and more numerous as the plate increases in thickness, or the light is more converged. The private student will often find a simple tourmaline pincette (Fig. 199) the most convenient apparatus. A slice of tourmaline is mounted so as to be capable of rotation at each end of the spring tongs, and the crystal plate to be examined is held z 2 FlG. 199. Tourmaline Pincette. 340 LIGHT [CHAP. between them : the rays passing through this simple polariscope into the small pupil of the eye, are sufficiently convergent to exhibit the phenomena. Or a single loose tourmaline, such as the one used in the rotating frame, held close to the eye, with the crystal close up to it, will show the rings well, if the whole, and the eye, are turned towards the plane-polarised light from a glass plate or any other polarising surface, or even towards certain portions of a bright sky (see Chapter XV.). 185. Preparation of Crystals. Many crystals can only be prepared, as a rule, by skilled workmen ; and an immense variety of uni-axials and the bi-axials to be next considered, may be obtained from Messrs. Steeg and Reuter, Homburg vor der Hohe, who prepare this class of objects for almost the whole world. The rarer crystals can hardly, in fact, be obtained elsewhere ; but Messrs. Darker, Hofmann of Paris, and one or two other opticians, prepare calcite, quartz, borax, sugar, and some dozen others of those most usually inquired for. Several crystals, however, are within the reach of the amateur. Nitrate of soda, if a good clear crystal can be found, is a fine uni-axial. A plate may be ground on ground glass, polished partially with a little water, and mounted in Canada balsam between two glass circles. Or, in winter a piece of clear ice^ f inch thick, held (for it can hardly be placed in the stage) in front of the bare nozzle, with the Nicol held in front and rotated, will give beautiful rings. Ferro-cyanide of potassium (prussiate of potash) is a cheap crystal, found in prisms or tablets, and easily split across the optic axis in slices, which have natural polished faces, and therefore need no other preparation than to be protected in balsam between two glasses. It is normally a uni-axial showing circular rings ; its other frequent phenomena will be treated of presently. Hyposulphate of potash is another crystal which gives fair rings, as do phosphates of ammonia or potash. Many of the soft crystals, uni-axial or bi- axial, after grinding on ground glass or stone, only need rubbing once or twice with the wet finger, the balsam in which xiv] APOPHYLLITE RINGS 341 they are mounted perfecting the polish, as it is nearly the same index of refraction as most of them. Others can generally be polished with a little putty powder or colcothar on a piece of fine silk. Sugar must be done dry or with a little oil. 1 86. Artificial Crystals. Dr. Brewster made artificial crystals by melting together equal parts of white wax and rosin, thoroughly mixed, and with a pointed rod dropping two or three drops on a small circle of glass, on which was laid a similar circle, forced down on the composition with a strong pressure. The molecules are thus subjected to strong com- pression in a direction perpendicular to the plates ; and the result is not only double refraction, but the slide shows rings like a crystal in convergent light. 1 Mr. H. G. Madan tells me that about a dozen layers of sheet gelatine cemented together with balsam give very fair results, the films shrinking so much in drying as to acquire doubly refractive effects. 187. Anomalous Dispersion. Apophyllite Rings. From the phenomena of anomalous dispersion ( 60, 72) we should expect that some crystals would show exceptional phenomena, similarly due to exceptional retardation of various colours. The fact is so. Apophyllite, for instance, is remarkable for the fact that it is " positive " ( 135) for one end of the spectrum, " negative " for the other, and non-doubly- refracting for some intermediate colour, generally yellow. Hence we have, instead of rainbow circles as in most cases, rings nearly white and black : the usual effect being black rings lined, as it were, with green only. We have here, therefore, a phenomenon of another kind due to "anomalous dispersion." By combining slices of certain positive and negative crystals cut of suitable thicknesses, it would be supposed that this curious phenomenon should be produced artificially. Such is the fact : but each pair of crystals has to be mutually selected, 1 It is very easy to get colour in this way, but in the few trials I have made I have never got perfect rings to please me ; probably for want of pressure, as I only used that of my hand. 342 LIGHT [CHAP. one with reference to the other, else the counter-action is not sufficiently accurate. 1 Apophyllite also shows in some specimens a most beautiful tesselated or " mosaic " construction. This, however, is more analogous to the compound crystals mentioned further on. Such crystals have to be specially sought for and selected. 188. Quartz in Convergent Light. The phenomena of quartz are what we should expect from those already observed in parallel light. Where the light is distinctly con- vergent, the ordinary doubly-refracting forces come into play ; showing circular rings and a cross. Towards the centre, how- ever, the rotatory power of the nearly parallel axial rays comes more into play ; and hence there is never a black centre as in most other crystals, but a coloured area, of a size according to the convergence of the rays, the colours changing with rotation of the analyser. The quartz system is represented in A, B, Plate VIII. As a plate of quartz cut parallel to the axis only produces plane vibrations like those of selenite, Sir George Airy suggested that the normal vibrations in such crystals were elliptical, of which the circular and plane waves were extreme limits. This theory, when applied mathematically, is found perfectly to account for all the phenomena, including those of superposed plates presently described ( 200). 189. Bi-axial Crystals. It has been stated already ( 136) that there are many crystals in which neither of the two doubly- refracted rays follows the ordinary law, but both are extraordinary; the index of retraction varying with the direction of the ray, and the refracted ray not being always in the plane of incidence. Such crystals, upon careful experi- ment, are found to contain two directions in which a ray is not doubly-refracted, inclined to each other at some angle ; and 1 Calcite is generally used for one of the pair ; but the reader should be specially warned against lead hyposulphate for the other, as often supplied by crystal cutters. The lead salt invariably becomes perfectly opaque in a short time, xiv] BI-AXIAL CRYSTALS 343 each of these optic axes is surrounded by a system of rings. Such are accordingly termed " bi-axial " crystals. The only bi-axial crystals suitable for the ordinary lantern polariscope are those whose axes are not much inclined to each other, so that both systems of rings can be seen at once. The four best are nitre, native crystals of lead carbonate (cerussite), glauberite, and some varieties of the felspar called adularia. The last must as a rule be purchased ; but the only difficulty about nitre is procuring a good crystal to work on. They all look beautiful as they come out of the crystallizing vats ; but as they dry, nearly all spoil by decrepitation and striae, and very few remain clear. A far from perfectly clear one, however, will show very fairly. We want a six-sided prism about J inch diameter. Split a slice about a 5 inch or more thick, as truly across as possible, with a knife ; and then care- fully grind it down on a dry stone till about J inch thick, transversely to the axis of the prism. Finish it with a little water, on first a roughish and lastly a smooth ground glass, finally wiping off the moisture with the finger. If necessary give it a lick on each side, and again rub with the finger, which will nearly polish it as already described ; then mount it with balsam, or balsam and benzol, between two circles of glass, and finally mount in a wooden slide with some soft cement, that will allow of adjustment rectangularly to the axis of the polari- scope. When adjusted with the line joining the optic axes parallel to or across the plane of polarisation, and the analyser crossed, the appearance is as in D, Plate VI. ; with the analyser parallel, of course the cross is white and colours complemen- tary. But if with analyser crossed the crystal be rotated, the phenomena change beautifully, the cross opening out into hyperbolic curves (E, Plate VI.), which, when the axes of the nitre stand at 45 across the plane of polarisation, assume the shape of F. The shape of these rings (lemniscates) and black brushes can all be mathematically calculated on the principle of interference, 344 LIGHT [CHAP. The following is a list of a few good crystals most easily procured, the angles being quoted from various authorities. These are the real angles of the axes in the crystal itself, but the apparent angle is much increased by the refraction into air of the oblique rays. The angles vary somewhat, ( 199), and scarcely two authorities quote the same. Glauberite . . 2 tO 10 Lead Carbonate, or Cerussite 8 7 ' Nitre. 7 12' Arragonite , i8i8' Titanite . 30 Borax .... 38 32' Mica i .... 45 Sulphate of Zinc 44 4' Topaz - 50 Sugar 50 Selenite . .. . 57 3' Nitrate of Silver 62 16' 190. Apparatus for Exhibiting or Projecting Wide- angled Bi-axials. With the usual moderate convergence of the lantern polariscope, we cannot thus see both systems of rings in bi-axials whose axes include great angles ; and it is usual to cut such crystals at right angles to one of the axes, when of course we get approximate circles round that axis alone, traversed by one arm of the nitre cross, i.e. by a straight black brush through the centre. Topaz (C, Plate VI.) is a fine crystal cut in this way ; so are borax and sugar. By some addition to our apparatus, however, it is possible to see at once, or to project, both systems of rings in wide-angled bi-axials. Norrenberg first invented a system of lenses to accomplish this object, the arrangement mainly consisting of 1 Mica differs exceedingly, from a uni-axial up to as much as 75 (see 199). xiv] APPARATUS FOR BI-AXIALS 345 two nearly hemispherical lenses about J inch diameter, be- tween which the crystal is placed, backed by other lenses still further to converge the light ; and with an additional focusing or projecting " power " on the side next the eye or screen. Fig. 200 is a section of such an arrange- ment made by Hofmann of Paris, the plate of crystal being shown between the two hemispheres. Such a combination converges the pencil of rays to a point within ^ inch or less of the plane surface of the first hemisphere, from which point they as widely diverge, but are re-collected by the second similar set, and finally pro- jected through the analyser by another focusing lens or pair of lenses. 1 If the utmost possible angle be desired, a plan must be adopted which we owe to the ingenuity of Professor W. G. Adams. It consists essentially in forming the two hemispheres 1 The precise arrangement of the lenses has been varied by Continental opticians and physicists. Laurent, following Descloiseaux, adopts four plano-convex lenses of increasing diameter, nearly in contact, for each series, with a separate single focal power. My own first system was composed of two pairs of plano-convex lenses nearly hemispheres, which I picked up ready mounted, and adapted for the purpose. This was much improved just after the publication of the former edition of this work, by placing a somewhat larger convex "field lens" i| inches behind the second series, according to an arrangement of Von Lang's described in Miiller-Pouillet's Lehrbuch der Physik. I still think a field lens thus placed the best for projection, but for the systems themselves prefer three lenses of shallower curves : the whole arrangement being shown in Fig. 161, page 249. By moving the position of the lens H to some extent, some variation may be made in the focal power, but for extensive range of distances two powers for use at K should be provided. The size of the image can also be enlarged, if necessary, by using a concave lens as " amplifier" beyond the analyser. The proper adjustment of the lenses is the chief point. The fringes are of the nature of shadows, and are so projected when the ordinary crystal FIG. 200. Convergent Lenses. 346 LIGHT [CHAP. into the front and back sides of a cell, which is filled with oil in which the crystal is immersed. This prevents the much greater divergence of the oblique rays caused by refraction from or into air, the direction in the oil being little altered. In this way the extreme angle of 90 can be collected ; without the oil, extreme angles are kept within the crystal by total reflection (35). The rings and brushes can be finely shown in any micro- scope which possesses a draw-tube and the customary wide collar under the stage, or a sub-stage. The usual "sub-stage condenser" of N.A. 1*0. (i.e. angle in air of 180) mounted over the usual polarising Nicol, answers perfectly for the first set of lenses, racked up level with the stage ; or such a con- denser, or Abbe condenser, may be pushed up in the usual under-stage fitting, and a glass pile used for polarising, if the Nicol is too small. For moderate angles many objectives will suffice for the second set ; but a combination much like an erector must be fitted into the lower end of the draw-tube, ad- justed to focus the back lens of the objective in the field of the eye-piece, over which an analyser is fitted as usual. I found a Reichert No. 6 (i) give beautiful images up to the usual angle of mica, and many immersion lenses give excellent results (used dry). For higher angles, a system should be made up instead of an ordinary objective ; but as the lenses need not be achromatic, the cost of this should be small. A quarter- wave stage alone is used ; with the convergent system, they are focused as they appear at the back of the second system. If the rays from the very edge of the back lens of this do not converge so as to pass through the focusing power, the edge of the disc projected on the screen will be dark. This convergence can hardly be obtained by lenses in actual contact ; but a very slight distance between the second and third convergent lenses of the second system increases trje convergence materially ; and the large field lens increases it still more. When properly arranged the image is equally bright to the edge ; and it is by slight adjustments of distance, proper proportions, and a suitable field lens, that this is to be accomplished. The analyser also must be capable of adjustment at the crossing-point of the focusing rays, Xiv] ANOMALOUS CRYSTAL DISPERSION 347 is easily inserted if required. All the range of phenomena in this chapter are therefore brought within reach of the micro- scopist at very little extra cost. For a convergent apparatus very small crystals suffice, the light being converged to a mere point. Some of the best crystals can only be obtained large enough to give sections about | inch across ; but such are perfectly exhibited if blacked round. With an immersion lens on the microscope the figures can be seen in a small bit of a mineral section i mm. in diameter, which is very convenient in examining many petro- logical slides. 191. Anomalous Dispersion in Bi-axials. The phenomena analogous to anomalous dispersion are still more remarkable and interesting in bi-axial crystals than in uni-axials. Not only are the axes, as a rule, somewhat differently inclined for different colours, but in some bi-axial crystals they do not even lie in the same plane. Borax is a good case of this kind. If a plate cut across both axes be placed in the polariscope, with the line joining its axes parallel with or across the polariser, when the analyser is crossed it will be found impos- sible to produce a perfectly straight black brush in the line of the axes ; both arms are perceptibly curved, and when the long arm is vertical there is a perceptible tint on the left of the top arm, corresponding to one on the right-hand of the bottom arm. In adularia, the centres of the " eyes " for red and blue are dispersed on lines parallel to each other, perpendicular to the long arm of the cross. In other crystals, whose axes lie in the same plane for all colours, the inclination varies very greatly, and progresses in reverse order for some crystals com- pared with others. Thus, when the plate is turned round so that its axial rings are at 45 angle with the polarising plane (Fig. F, Plate VI.), the parabolic " brushes " are in nitre margined with red inside and blue outside, while in lead carbon- ate the reverse is the case. In lead carbonate and many other crystals, the dispersion of the axes is so strong, that the hyper- 348 LIGHT [CHAP. bolic brushes appear only as red and blue, there being no black brush whatever ; while the rings in white light assume very peculiar and beautiful forms. In monochromatic light, however, true lemniscates will be observed. The most remarkable example of anomalous dispersion in the axes is in a few crystals such as brookite, in which the axes for red light lie in one arm of the cross, while those for violet lie in the other arm ; or, in other words, the axes for the two ends of the spectrum lie in rectangular planes ! Hence the figure presented even in white light somewhat resembles that of a "crossed" crystal ( 198). Brookite is rather difficult to project clearly, owing to its red colour ; but similar pheno- mena may be seen in the sel de seignette, or triple tartrate of soda, potass, and ammonia, which is colourless and transparent. Viewing or projecting this crystal, with a red and blue glass alternately in the large slide-stage of the polariscope, the rect- angular planes of axial dispersion will be readily seen ; and if a coloured glass can be procured of such a shade and density as cuts out the middle of the spectrum and leaves the blue and red only, the two systems of fringes can be seen superposed. In Plate I. (Frontispiece) the figure of brookite or sel de sei- gnette in white light is shown at A, while at B is shown the extraordinary modification produced when the crystal is pro- jected or examined by light containing blue and red only. 1 In green light the crystal is nearly uni-axial, the rings, however, being more square than circular. 192. Theory of Bi-axials. The theory of bi-axial crystals was gradually elucidated by the labours of Brewster, until Fresnel framed the one simple general conception of three axes of elasticity in three rectangular directions. If all these were equal, rays proceeding from a point in the crystal in 1 It is rather difficult to get sufficient light for projection. I have succeeded best by using two or more gelatines selected with a prism, and cemented between glasses with balsam and benzol. They are much more transparent thus mounted. xiv] HEATING A CRYSTAL 349 all directions would at the same moment reach the surface of a sphere, and the crystal could have no double refraction. If two were equal, both being perpendicular to the third, all perpendicular to that third must also be equal, and the crystal must be uni-axial. If all three were unequal, it was shown by a beautiful mathematical analysis that the crystal must be bi-axial ; the axes of no double refraction being simply resultants of the three different elasticities, both lying in the plane of the greatest and least elasticities, at an angle dependent on the relative magnitude of the third or mean elasticity. This beauti- ful theory was shown- to be exactly what ought to follow from the simple assumptions of the undulatory theory, and to ac- count for every detail of the known phenomena ; but several necessary deductions followed, which did not become apparent till after Fresnel's death. It is interesting to see how these purely theoretical deductions were justified. 193. Mitscherlich's Experiment. It followed, first of all, that any alteration of the respective elasticities must necessarily alter the inclination of the axes ; and should the change go so far that the mean elasticity became first equal to either of the others, and then reversed in relative magnitude compared with it, the crystal must first become uni-axial, and afterwards bi-axial with axes in a plane at right angles to the first. Now we have already seen ( 132) that heat will effect such changes ; selenite especially being considerably altered in relative dimensions and relative elasticities, by a very moderate rise of temperature. Professor Mitscherlich therefore took a plate of this crystal cut so as to show both the axes ; and ex- posing it gradually to a heat not exceeding that of boiling water, he had the satisfaction of seeing the two systems of rings gradually approach each other. A point was soon reached at which they coincided, and the crystal became uni- axial ; and the moment after the axes began to open out in a direction at right angles to the former. This fine experiment is projected with the greatest ease, the 350 LIGHT [CHAP. only difficulty being in cutting the crystal. Unlike mica, whose natural laminae are at right angles to the median line between two axes, the laminae of selenite include it, and the crystal has therefore to be cut across its cleavages. A plate of copper or brass, A (Fig. 201), has a hollow turned in its centre so as to leave only a very thin plate of metal to support the crystal, an aperture sufficiently large for the rays being bored in the thin plate. The crystal, rather larger than the aperture, should be set in a disc of cork (shaded black in the figure) and shaped to fit the hollow : the whole being covered by another thin metal plate, c. The arrangement is then placed on the stage FIG. 201. Slide for Mitscherlich's Experiment. of the projecting apparatus, so that the ends of the metal project w r ell, and these ends are heated by spirit-lamps, or by one lamp alternately. 1 Suppose the crystal is so arranged on the stage that the two systems of rings appear at first to stand vertically upon the screen. As the slide warms, there will probably be a mist for a minute or two, owing partly to moisture on the lenses, and partly to heating of the air between the laminae of the crystal ; and the heat should be applied gently till this clears away, as it will soon do. Then the axes will gradually be seen to approach, till the rings exactly re- semble those of a plate of calcite ; 2 and after this they open 1 Another good way is to cut a hole, large enough to hold the crystal loosely, quite through the middle of a slip of brass the same thickness, retaining the crystal by doubling over both sides a piece of card in which are cut holes too small for'the crystal to fall through. The ends of the brass are better bent away from the stage. A special slide with projecting ears for heating is made for the purpose. Crystals cost 3^. to $s. each. - At this stage the lamps had better be removed till it is seen how things go. The metal slide will probably have taken up sufficient heat to go on further without more ; and a very moderate excess of heat will calcine the clear crystal into mere plaster of Paris. CONICAL REFRACTION 351 FIG. 202. Bi-axial Wave-Shells out again in a horizontal direction. On the lamp being removed the whole process is reversed. 194. Conical Refraction. A more striking proof of the truth of Fresnel's hypothesis was discovered by Sir W. Hamil- ton. On projecting the wave- shells geometrically according to this theory, they were found to resem- ble those partially shown in Fig. 202 (from Muller-Pouillef). Now if a single ray traverses the crystal in the line P P, or p' P', on reach- ing the surface it is refracted into air, as usual, from the perpen- dicular. That perpendicular has reference to the tangents of two different curves, and so produces two different refractions. If the shells are completed, however, as in a solid model, it is found that the four points p are cusps, or hollows resembling that surrounding the stem of an apple ; 1 and it therefore follows that on emergence from the poiut_p the ray must be spread out into a diverging conual shell of rays. Here, therefore, was a mathematical prediction of a phenome- non never foreseen by Fresnel, who had confined himself to the single plane through the points P shown in the diagram ; and such a kind of refraction was not only opposed to all past experience, but to all apparent probability. At Sir William Hamilton's request the matter was tested by Dr. Humphrey Lloyd in a crystal of arragonite. The lines p P and P' P' are lines of single velocity, and coincide nearly with the optic axes, but not exactly, their angle being nearly 1 Tt is very difficult to give a clear idea of the complicated wave-surfaces of bi-axials to ordinary readers. Some may derive assistance from another and differently shaded figure, which will be found under the article " Un' dulatory Theory," in Chambers' Cyclopedia. 352 LIGHT [CHAP. FIG. 203. Conical Refraction. 20. A plate is needed J inch or a little more in thickness for this experiment, cut across both axes. Then a thin metal plate with a very small aperture was fixed on one side of the crystal plate, and a movable one placed on the other, while the crystal was fixed in a frame movable by a screw so as to present the crystal at various angles. A beam of light was then condensed on the aperture o (Fig. 203) at an angle of 15 or 1 6, so as to be refracted in the direction of o M, or o N, which is nearly an optic axis. 1 When the ad- justment was complete, on looking through the second aperture, instead of two apertures a brilliant ring of light appeared to the observer; Sir William Hamilton's prediction being thus justified to the letter ! In a similar way it was shown that if a very small pencil of parallel rays (sensibly apparent as a single ray) were incident at o, so as to be refracted exactly into the optic axis, it should be divided into an internal cone within the crystal, which on emergence would resume parallelism and appear as a hollow cylinder of rays, since the cone would reach the wave-shells at the points where the common tangent-plane touched them in a small circle surrounding the cusp. The cone in this case was so small that the phenomena were much more difficult to observe : but by adjusting the crystal with extreme care, this prediction also was verified in actual fact. The easiest way of observing conical refraction is to sub- stitute for the aperture o, a fine slit, in the plane of the optic axes. Then if the aperture M be fixed on the other face 1 The convergence of the rays, to produce a single ray within the crystal, must of course correspond with the calculated divergence on leaving the crystal. The optic axis is the normal to the common tangent -plane touching both wave-surfaces. XIV] HEMITROPE CRYSTALS 353 tolerably near the correct position, on gradually tilting the crystal in the plane of the axes, when the right point is reached the slit will be seen to split in the middle into two oval curves. The experiment is only one for the student, the small pencil of light not permitting of projection. 195. Relation of the Axes in Uni-axial and Bi- axial Crystals. It further follows that, according to this theory, the optic axis of a uni-axial crystal by no means coin- cides in character with one of the axes of a bi-axial ; but is simply a limiting case in which both these axes coincide. Professor Mitscherlich's experiment is one beautiful proof that this is the case : and further optical proof of it will be found in 206, where it will be seen that important optical pheno- mena of both axes in a bi-axial, are preserved distinctly in uni-axial crystals. 196. Composite, Irregular, and Hemitrope Crystals. Twin or macled crystals are found very often : a slice of nitre, for instance, can be found without difficulty that will ex- hibit four systems of rings. Calcite is often found in which thin layers crystallised in the opposite direction are frequent. A large crystal of such calcite, if a ray is sent through it to the screen, gives a greater or less number of coloured images : the in- terrupting film answering to the films of mica or selenite in our earlier experiments, and the thicker masses to analyser and polariser the whole being a sort of natural Huygens's appara- tus fixed in one position, with a film between the two prisms. But far more beautiful effects are obtained if a plate be cut across the axis, including one of these films or planes, and it be examined in the convergent light. The system of rings is then modified by glorious brushes of coloured light, which radiate somewhat like the spokes of a wheel ; and the pattern of the rings themselves may be varied in a beautiful manner. If such a plate is cut thin enough to exhibit in the very con- vergent system, on moving it about so that the conical pencil may traverse different points in succession, the phenomena will A A 354 LIGHT [CHAP. sometimes vary in an extraordinary degree. Composite quartz crystals have already been referred to ( 172). These effects may be partially imitated by placing a film or mica or selenite between two thin plates of calcite cut across the axis ; and are perfectly imitated if the calcites are ground into a pair of wedges making together a parallel plate. Pieces of calcite subjected to strong pressure and then cut, also give fine irregular phenomena; or a plate may be projected while squeezed in a small vice. Other irregularities are often found. Ferro-cyanide of potas- sium (prussiate of potash) for instance, is properly a uni-axial crystal. But crystals can be found, out of any sample, of which slices gives bi-axial effects : and yet others, which give symmetrical coloured patterns, which are very beautiful, though crystallographically irregular. 197. Mica and Selenite Combinations. Norrenberg to some extent demonstrated the cause of these beautiful phenomena, or at least closely imitated them, by combining films of selenite with films of mica, a selenite being placed between two micas to form one " element," as he called it. The micas were parallel : and in some combinations the principal axis in the selenite was parallel to the mica axis, and in some across it. In one case he called the triple film a positive element, in the other a negative element ; and these may be superposed, either parallel or crossed, in any way, though Norrenberg confined himself to symmetrical com" binations. It will be manifest that the effect of these combinations is very complicated ; but the results are so beautiful, and so instructive when studied with care, that I attempt some elementary explanation, and give two pairs of examples ; each example of a pair, as in the case of the brookite crystal, containing precisely the same material, but differently arranged (C D, E F, Plate I. Frontispiece}. If we call the three rectangular axes of elasticity in any crystal x y z in order of xiv] NORRENBERG'S MICA-SELENITES 355 their magnitudes, then a selenite film contains x and z, while the intermediate one y is normal to the film. In mica, on the other hand, y and z are in the plane of the film, and x is normal to it. Thus if we conceive a cube built up of films, in mica the rings are seen in the face of the films ; in selenite on two opposite sides of the cube represented by their edges. It is evident that such relations of the retardations, must in convergent light produce very beautiful chromatic phenomena. The simplest of these are with parallel micas only. If we take one Norrenberg element alone, i.e. a single selenite between two micas, the ordinary figure is not very greatly altered, beyond a great widening and enrichment of the colour- fringes ; and there is not very conspicuous difference between them, whether the principal axis of the selenite is parallel to that of the mica or crosses it. 1 But let us give the selenite functions of elasticity more effect. In C D, Plate I. (Frontispiece), are shown preparations, each of which is built of five parallel half-wave micas (half-wave is thin for this class of work) with four parallel selenites interleaved ; but in C the selenites cross the micas, and in D are parallel with them. It will be seen that in both cases we have peculiar curves having their origin approximately in the mica axes, but reversed in character ; and that the tendency in C is to bring the centres of the two systems closer together, and in D to draw them farther apart. This is what we should expect. If however we employ red instead of white light, we get approximate lemniscates only, but with the rings closer in the case of C. All through, in these prepa- rations, a most extraordinary difference will be seen in the phenomena when either red or blue light alone is employed. I give two more examples. In E F of the same plate are shown preparations each built up of four of Norrenberg's "negative" triple elements; i.e., the selenite crosses the micas in each. I owe to Mr. Fox the practical hint which I J The films are considered "crossed" when the two, if of same tint of same order, counteract each other in parallel light. A A 2 356 LIGHT [CHAP. gladly give in turn to others, that one of the best thicknesses of selenite for quadrilateral preparations is if waves, which gives the rich orange inclining to red in the second j^rder of the mica wedge. The figures shown are built of these, with | wave micas. The preparation^ is made by superposing two of the elements parallel, and crossing upon them two others parallel ; while E is constructed of the very same four elements, but crossed one-and-one alternately. Positive elements give utterly different figures. Positive may also be crossed on negative ; and the films may be varied and crossed in all sorts of ways. Very fine figures not quadri- lateral are produced by crossing two parallel elements between single elements ; and a very simple effective preparation is made by crossing a negative element, made of if selenite and two i -wave micas, between two i-wave micas alone. These preparations are perhaps the most difficult of all to construct ; selenite not being easy to split nicely, to begin with, and the difficulty of getting the axes of micas and selenites exactly parallel or rectangular, being very great. If they are not exact, the black brushes are not straight and sharp. Any fault in this is a great eyesore, though the beauty of the figure otherwise remains ; and a good proportion are spoilt from this cause. The manipulation varies. Mr. Fox built square cells with strips of glass on square glass plates, in which his films were inserted. Messrs. Steeg and Reuter prepare theirs between small square glasses, which when cemented and dry are mounted in square plates of cork like their crystals. The method I prefer is to cut the films in | inch squares ; superpose them, with a small drop of benzol-balsam on each, in the centre of a microscopic glass slip, and cover with a micro cover-glass. If truly cut they are easily got pretty true after all are laid down, by using a steel point in each hand ; and may be left to dry with a very small weight, such as a printer's type, standing on each. Such slides can be kept in ordinary micro slide-boxes, which is convenient. The mica sheets should be scratched JPt. 7. CROSSED AND SUPERPOSED CRYSTALS. A . Jivo MicfLS crossed.- D. lZig/t JMicfis crossed B. Ditto, aacej rotated 43 E. sSawart's Bands C. Jbur Mic&s crossed* F. .Jltrys SprraZs N.Ji. A.C.D. are. B.C.D. ofJforrernAerg'f series showing proyress towards the I7ni< xiv] CROSSED CRYSTALS 357 into true squares all over, any portions not the exact thickness of the main part of the sheet being defaced for rejection ; the sheet can then be cut up with the large scissors. Selenites can only be cut with the single blade, used gently. Negative elements may however be imitated to some extent by mica films alone ; and there is no difficulty with these about accuracy, because so long as the axes are marked alike on two sheets, squares will cross truly, even if the marks themselves are not quite true to the axes. Ternary elements may be made by crossing |-wave mica-films between two thicker ones. Using 4 wave or f wave for the thicker micas, the student may construct very beautiful preparations in this way with no difficulty, crossing either doubles like F in Plate I., or single elements alternately like E in same plate, or two crossed between a pair of single elements. 198. Crossed Crystals. These give beautiful effects, but also require the convergent system. Two plates of mica are easiest put together, and give four systems of rings (A, Plate VII.), or when the preparation is rotated 45 degrees show beautiful hyperbolic curves in the centre (B). Crossed arrago- nite or topaz gives similar effects. Crossed titanite is very effective, owing to its peculiar dispersion. Two ordinary films of selenite i mm. or more thick, too thick to show any colours alone, when crossed give hyperbolic curves in convergent light ; as do two quartz-plates cut parallel to the axis. 199. Nbrrenberg's Uni-axial Mica Combinations. The most interesting, however, of this kind of combinations are also due to Professor Norrenberg. Mica is found occa- sionally uni-accial ; and bi-axial specimens are found of all angles from o up to 75, in this respect resembling the ferro- cyanide of potassium. Senarmont had proved by experiment the results of combining salts crystallising in identical forms geometrically opposite. Thus, the double tartrate of soda and potash (Rochelle salt) crystallises in prisms ; and 'if we replace 358 LIGHT [CHAP. the potash by ammonia, we get similar prisms. Both are bi- axial crystals with an angle of 76, and a peculiar dispersion of the axes pointed out by Sir John Herschel is the same in each. The one optical difference is, that the plane of the optic axes passes through the smaller diagonal of the rhomb which forms the base of the prism in one case, and of the longer diagonal in the other. Senarmont showed that by crystallising mixtures of the two double salts, the angle of the axes could be dimi- nished ; and that with a certain proportion the crystal became uni-axial like calcite ; though, owing to the great dispersion of the axes, it can only be strictly uni-axial for one colour in any given combination, whence the peculiar dispersion noticed in 191- Hence Norrenberg supposed there might be two kinds of micas ; isomorphous, but geometrically opposite : and that the variable angles, and uni-axial micas, might be produced by superpositions of infinitely thin films of each, in different proportions and positions. Experiment seemed to justify this. A number of thin films of mica crossed alternately at an angle of 60, reduced the angle of a bi-axial mica from about 70 to about 46. But far more interesting was the gradual passage to the uni-axial form when the films were crossed at 90. Denoting a thickness of one wave by w, Norrenberg constructed the following series, where the figure under the alphabetical letter denotes the number of films, and the bottom fractions the thickness, the total of all being three wave-lengths of retardation. A B C D E F i 2 4 8 12 24 $w \\w \w \w \w \w In this series of preparations, A of course gives the ordinary bi-axial phenomena. B gives four systems of rings with hyper- bolic curves (A, B, Plate VII.). In c we get the first approach xiv] MICA COMBINATIONS 359 to the uni-axial character, which becomes more and more perfect as we proceed, until at last there is absolutely no difference between the phenomena and those of a plate of calcite. There is no magic in three exact wave-lengths as the total thickness, but approximately it seems the best total. All that is necessary in making these instructive preparations is that, as before described, all the films of any one preparation be of the same thickness, and the two polarising axes, in each alternate film, accurately crossed. The method of obtaining both con- ditions has been already given. I prefer to add an interme- diate preparation of six films between c and D, which gives a more complete black square ring. Then eight films give two such rings, the inside one more circular and the outer one square ; while twelve films give three rings, sixteen four rings, and so on. Very beautiful and instructive preparations can be made by varying the thicknesses of these crossed films. Eight crossed of Norrenberg's thickness we have seen to give us two rings, the outer one rather square (D, Plate VII). But if we cross eight thin films say \ wave we get circular rings even with this number, and twelve give us really fine rings, only broader and bolder than the 24 films. On the other hand, let us now cross both 4 and 8 of thick films say i wave thick. The rings now entirely disappear, and the coloured fringes are all turned the other way, their convex sides towards the centre. A really splendid figure is produced by 12 crossed films f wave in thickness. Squares of mica may also be cut of the same size as the others, but with the axes at angles of 45, and combined with the foregoing. The following will be found instructive, the lines showing the successive positions of the mica axis in films successively superposed. 1 The first four are \ wave films : the 1 I take them from my paper " On Optical Combinations of Crystalline Films," in Proc. London Physical Societv> 1883. 360 LIGHT [CHAP. other four |- wave and whole-wave films : a cross denotes a pair crossed. 2- |~ -/ - 3. ||_||-| = | = 4. I " I " I - - I - I - I 5. | - | x | - | 6. + + x + + 7. + x + x 8. | / \ | / \ (**, successively rotated 45). 200. Airy's Spirals. Owing to the peculiar character of the doubly-refracted rays in quartz, if a plate of " right " and another of " left," of equal thickness, be placed together in the crystal stage and analysed by convergent light, the colour is not exactly neutralised, as it is in parallel light, but we get a most beautiful quadruple spiral (shown in F, Plate VII.). These spirals were discovered by Mr. Airy, and are called by his name. They form a most beautiful screen projection, when the thickness is adapted for the convergence employed. About T Vth of an inch to J inch each is a good thickness for each plate, for the objective alone. A single quartz plate will show the spirals in Norrenberg's "doubler." If truly cut across the axis, it may be laid on the bottom mirror, holding a lens about i^ inches diameter, and 2 inches focus above it, so as to converge and re-collect the rays which have twice passed through the plate ; but should the quartz not be quite true, the lens must be laid on it, and both together adjusted by hand till accurate spirals appear. This experiment is particularly interesting as showing the reversal of the rotation described in 177. ft 8 CIRCULAR POLARIZATION IN CRYSTALS. A. Qiuirtg, -trie/is anafy-ser crossed. D. Colette polarigcel' ; efractive properties of the quartz ; and the two ought to give us double spirals ; in fact an adequate column of liquid ought successfully to replace the quartz in all the foregoing experiments. 1 The rotatory effect of liquids is so inferior to that of quartz, that it is not easy to transmit sufficient light to give good pro- jections through a column of liquid of adequate length. Ly employing a tube eight inches long and two inches in diameter with plane glass ends, filled with oil of lemons (i Ib. of which costs about IDS. 6d., and is just sufficient to fill such a tube) the object can however be effected. We introduce this next the polariser in lieu of the quartz. In the crystal stage we place the calcite or any other uni-axial crystal ; and now introducing the quarter- wave plate between crystal and analyser, we obtain at once the double spirals. The liquid will also give the same phenomena as the quartz with other crystals, its slightly yellow colour only slightly interfering with the effect, for the same reason that the figures fail to appear in homogeneous light. Spirit of turpentine is free from this defect, but requires a column of almost unmanageable length. Finally, it may be mentioned that Reusch's artificial quartz made of mica-films ( 180), and Norrenberg's artificial uni- axial crystals made of crossed micas ( 199), give in each case similar results to the natural crystals. So also does a circular disc of unannealed glass in parallel light. 207. All the Phenomena due to Interferences of Waves. The student who has followed any considerable part of the experiments in this chapter, cannot fail to form a vivid idea of the reality of those invisible waves in the ether, whose interferences produce such complicated phenomena. 1 It is probable that a bar of heavy glass in the electro-magnetic field would give similar effects ; but I have not been able to test the matter experimentally, and there is the very interesting difference between the behaviour of such a bar and other rotatory substances described in 177. It seems scarcely probable that this difference would affect the above phenomena ; but the settlement of that point would be interesting* xiv] ALL DUE TO ETHER-WAVES 371 He will .ave grasped the fact, that in no case is anything visible or- materially tangible in the crystal itself, imaged on. the screen. The beautiful patterns have indeed a centre ; but the centre of the crystal plates has absolutely nothing to do with that let the pencil of light pass anywhere through his plate, and the effect is the same all over its area, so long as a given direction is preserved. In his combinations, beautiful designs have 'been produced, more resembling the richest Turkey carpets or Persian rugs than anything else ; yet beyond the simple crossing of films in various ways, there is in the pattern nothing from the hand of man. And in his single crystal sections, by merely varying the polarised character of the light employed, he has produced at will either the simple rings with brushes, dislocated rings, unbroken rings with no brushes at all, or beautiful spirals. All the modifications are produced by transformations which simple mechanical analysis enables him to produce at will, in invisible and intangible ether-waves. B B 2 C PI AFTER XV POLARISATION AND COLOUR OF THE SKY. POLARISATION BY SMALL PARTICLES Polarisation of the Sky Light Polarised by all Small Particles Blue Colour similarly Caused Polarisation by Black Surfaces Experi- mental Demonstration of the Phenomena Multi-coloured Quartz Images Identity of all Radiant Energy. 208. Polarisation of the Sky. On a clear day, in morning or afternoon, almost any of the colour phenomena we have now reviewed may be tolerably seen, by using the tourmaline close to the eye as analyser, and looking through the selenite or other object to the sky as polariser, in any direction at a tolerably wide angle with the direction of the sun, the maximum effect being at 90. For instance, if the sun were due east, the greatest polarisation will be found any- where in an arc extending due north and south. In the most favourable positions the quantity of polarised light is about one-fourth of the whole, and the rings in crystals can be seen very plainly with the sky as polariser. The direction of greatest polarisation of course depends upon the place of the sun ; and upon this fact Sir Charles Wheatstone based the construction of a " polar clock," which gives the astronomical time by the effects of light from the sky upon slips of selenite in certain positions. CH. xv] SMALL PARTICLES 373 209. Cause of the Phenomenon. Briieke and Pro- fessor Tyndall have beautifully explained not only this phenomenon, but also the blue colour of the sky, by proving experimentally that the light reflected laterally, or at right angles with the incident rays, from any particles whatever suffi- ciently small, is both polarised and of a blue colour. The blue colour is easily understood, if we remember what we have always found, that the blue waves are the shortest or smallest. Hence, from particles so small as to be in commensurable relations with them, the smaller waves may be wholly reflected, while larger ones are broken up or shivered into fragments, as it were, and so destroyed ; just as to quote Dr. TyndalPs own image pebbles on a shore reflect small ripples entire, while they scatter and break larger ones. A secondary proof of this is ready to hand in the colour of the transmitted light. If it is partially robbed of its blue by these transverse re- flections, the light transmitted ought to be more short of blue, or perceptibly yellowish, or in extreme cases reddish. That this is so, we see at every sunset, and also by the colour transmitted through any of the media presently men- tioned. 210. Polarisation by Small Particles. The polarisa- tion at an angle of 90 with the incident ray, or at an angle of 45 with the surface of each minute spherical particle, has been considered a difficulty. Sir John Herschel remarked, that it supposes an index of refraction of unity ; or that in the case of the sky, we have to suppose reflection in air upon air. There will be no difficulty in supposing this, if we conceive the molecules of air reflecting light at all ; and the angle of 45 is exactly what we shall expect, if we receive the reasoning advanced in 129. We have only to suppose that in any case of this scattered reflection, the reflecting molecules are too small to exert any refractive influence, and the whole difficulty is solved. While some, therefore, have considered polarisation by small particles to be a fourth method of polarising light, it 374 LIGHT [CHAP. is not so considered here, but simply regarded as another case of polarisation by reflection. 211. Black Surfaces. This seems also proved by, and is in fact the only method of explaining, the curious phenome- non of polarisation on analysation by a black surface, which was brought to my notice some time ago by Sir Thomas S. Bazley. It is stated in many works upon physical optics, that a black ribbon absorbs all the colours of the spectrum ; but this is by no means practically the case in most instances, with the bright colours of the solar spectrum, which have a peculiar and attractive effect of course owing to scattered reflection on a black ground. Further, however : if we pass the light from the lantern through a polarising Nicol and a plate of selenite, and without any apparatus usually known as an analyser, receive the light at right angles on a dead-black card, the colour due to the selenite will appear, though it will not if the card be white. 1 Hence the black card itself acts as an analyser ; and we can only explain this on the supposition that the black colouring matter, by absorbing or quenching the reflections from the flat surface as such, allows us to perceive the com- paratively feeble results of the light reflected laterally from the small particles of carbon or other colouring matter. These particles are however so large, that it will be found the polaris- ing angle considerably exceeds 45. And the colour is ot course comparatively feeble. 212. Experimental Demonstration. Professor Tyn- dall precipates fine vapours 2 in an exhausted glass tube with glass ends ; but simpler apparatus will amply suffice for us. Small particles in water show the same phenomena, and either (i) a very little soap, or (2) a few drops of milk, or (3) about 1 That is, with the card in a normal position. An inclined white card analyses as a reflecting surface. - Professor Tyndall has employed vapour from nitrite of butyl and hydrochloric acid, nitrite of amyl, bisulphide of carbon, and many other compounds. A friend of mine has obtained beautiful results from a whilT of tobacco smoke. xv] LUMINOUS TUBE 375 six Bruins of resin in an ounce of alcohol, or (4) about five grainfl of pure mastic in the same, will answer very well. On the whole I have myself found the best, results, however, from a i.f;r;pooMful per Dillon of the solution of coal-tar in alcohol known as Wright's Liquor Carbonis, stirred into filtered hot water. We may take [a common glass lamp-chimney, 12 melies by 2 inches, grind one end flat and cement on it a flat glass plate, and fit a vulcanised stopper into the other. Fill carefully with the prepared water, filtered into the tube to remove dust, whieh mars the effect by re-fleeting common light. Mount the tube T in two semicircular notches of a cradle-stand, I 1 n.. -,',. lv..|,.-iiiii'-nf;il 'I 11!,.:. ai in c, Fig. 206, and adjust the tube horizontally in front of the plain optical objective i.e. taking away the polariser so as to throw the beam of light from the lantern along its axis. If a dead-black board or sheet of card is held behind the tube, it is soon seen that it appears blue. The black back-ground is not even necessary, for the tube shines with a sky-blue light, unless the quantity of solid matter is much too large. It will also be readily seen, on looking as nearly as possible at right angles towards the tube through a Nicol, that most of the scattered light is " polarised " ; for rotating the Nicol in the hand alternately quenches and restores it, and a selenite held 376 LIGHT [CHAP- between the tube and the Nicol at the eye, shows its usual colours. We have already learnt, however ( 125), that any apparatus which will act as a polariser, may also be employed as an analyser ; and by polarising the light first, and using the tube as analyser, we can make the phenomena visible to a number of people at once. Add the Nicol, N (Fig 206), to the nozzle ; the light from the lantern is now polarised, so that all who sit nearly at right angles with the tube can see the phenomena. As the Nicol is rotated, the light proceeding laterally from the tube is quenched or restored ; and when quenched from a spectator on the same level, it is of course brightest to an eye looking down upon the tube from the top. Finally, if we hold a large quartz plate at Q, as the Nicol is rotated we get beautiful successions of colours in the tube. 213. Multi-coloured Images. This is the simplest adaptation of the usual mode of performing this beautiful experi- ment ; but there is a far better method one not only easier, but which produces effects of surpassing brilliance and beauty, and which, as a truly magnificent lecture demonstration, may fitly conclude this work. 1 Procure a plain cylindrical glass jar on a foot, j (Fig, 207), 12 inches to T6 inches high, and 2 inches to 2\ inches diameter. Having cleaned it bright, filter the solution into that, and over it adjust the plane reflector, R, at an angle of 45. The reflector throws the light from the Nicol, N, down through the fluid, which needs no glass plate, while the quartz can be laid on the top of the jar at Q. The first great advantage of this method is, that the audience all over the room see the effects perfectly, if about the same height as the jar ; whereas with the other more usual plan, only 1 I was originally indebted for this beautiful modification of the experi- ment to Mr. John Thomson, of Dundee, a very able demonstrator. The beauty of the effect is a great tribute to his ingenuity, but the method has been so little known as to have been re-discovered, even since my publica- tion of it, by Mr. G. J. Burch, B.A. (see Nature, Jan. 22, 1885). xv] MULTI-COLOURED EFFECTS 377 those who can look nearly at right angles towards the tube perceive much of the phenomena, which depend upon an angle of nearly 90. Still further, however : if two additional silvered mirrors, M M, about the height of the jar, by 6 inches or 7 inches wide, are arranged vertically behind the tube, inclosing it as it were within a right angle, though not touching, they give by reflection two additional images of the illumi- nated tube. Each of these, since the light leaves the tube FIG. 207. Multi-coloured Images. from a different side, exhibits when the quartz is used a dif- ferent colour^ all three changing to successive colours with the rotation of the Nicol. With a large Nicol polariser embracing the full parallel beam from the lantern, the effect is finer still, and may be varied by employing a jar of greater diameter, and throwing the polarised light down through two apertures covered with quartzes of opposite rotations. In this case, in all but two positions of the analyser, there will be two beams 378 LIGHT [CH. xv of light in each image of the jar, glowing with different colours. 214. Identity of all Radiant Energy. That heat rays and " chemical " rays are subject to the same laws as luminous rays, as regards reflection, refraction, and dispersion, has been already stated ( 93), and is a familiar truth proved in every camera every day. It only remains to state that they obey also the laws of polarisation and double refraction. If the two beams which have passed through a double-image prism are tested with a thermopile, this is readily demonstrated, as is the fact that the ray is quenched whenever polariser and analyser are crossed. The actinic rays may be similarly tested with a sensitive plate, thus making the demonstration complete as regards all the rays of the visible and invisible spectrum, and proving that the sole difference between any of them is in period of vibration ; some periods being more adapted to produce physical effects of certain kinds, and some of others. Captain Abney has shown that it is possible to obtain in a dark room a photographic image of a kettle heated far short of the lumin- ous degree ; or on the other hand, to impress a sensitive plate .with a photographic image of large portions of the spectrum through an apparently opaque plate of the di-electric ebonite. And Professor Tyndall has proved experimentally that a plane- polarised beam of dark heat, filtered of all visible rays by a solution of iodine in carbon bisulphide, is rotated, like the luminous rays ( 177), by a powerful electric current, or when the glass or other diathermous material is placed in a mag- netic field. The far longer and slower waves of electric radia- tion obey the same laws, and when examined experimentally by proper appliances, exhibit essentially the same phenomena. From the quickest vibrations to the slowest, the series and the unity are unbroken ; invisible waves of disturbance in the invisible Ether are alike at work, and constitute the physical basis of the whole of the phenomena. CHAPTER XVI LIGHT AS A SYMBOL THROUGH all the experiments now described, we have dis- covered that the phenomena and sensations we know as Light and Colour, when traced back and examined, found their ultimate explanation in forms of Motion. We were shut up very early to that conclusion : we were absolutely compelled to travel in our thoughts from what we " saw " to something we could not see at all, and to form mental images of invisible waves, whose undulations were propagated with incredible swiftness all around us. Later on we found phenomena which appeared to reveal to us the actual directions, or orbits, of the vibrations in those waves ; and applying to that hypothesis delicate and beautiful experimental tests, such as can be readily understood by any educated mechanic or other intelligent reader, we found our supposed orbits respond to those tests in every particular. The motions were, so far as we could judge from any possible mode of examination, modified, varied, re- solved, or compounded, in all respects as our hypothesis led us to expect. This is the nature of the evidence, and we have thus reviewed in actual experiment the principal facts, on which is built up the Undulatory or Wave Theory of Light. The pro- foundest mathematical researches, applied to the most refined experiments varied in every possible way, have so far only confirmed that theory in every particular. Let us fully grasp the grand conception ; for there is no 3 8o LIGHT [CHAP. grander throughout the entire material Universe ! All around us everywhere space is traversed in all directions by myriads of waves. Not more surely does a nail take up from a ham- mer the force of a blow, than does each particle of a mysterious and invisible Something, take up and pass on the motion of the preceding particle. Heat, Light, Colour, Electricity, Chemical Actinism, all alike are simply disturbances in, or propagations of disturbance through, that Something which we call Ether. Invisible themselves, these wonderful motions make all Things visible to us, and reveal to us such things as are. Take away from the diapason of these invisible waves those of any given period ; and if we lose the dazzling whiteness which results from them all in due proportion, we but increase the soft splendour of the phenomena, as the hues of the rainbow appear before our eyes. Let them clash against, oppose, and so destroy one another ; and even their very interferences, though dark shadows may cross our vision, produce amidst these, forms and colours of almost unearthly beauty. Motion in the Ether accounts for all. Here we have taken another step from the seen to the un- seen ; for we have conceived and named this Ether. The name is of course nothing ; but we cannot do without the thing itself : we must conceive it. No eye has seen it ; no instruments can weigh it ; no vessel can contain it ; nothing we have can measure it ; yet it must be there. " There ? " yea, here also, and everywhere. Absolutely invisible, it yet is the sole key to all physical phenomena ; and the most recent, most widely received, and altogether most probable theory about Matter itself, is that atoms are but Vortices in its infinite bosom. Ask for " absolute proof " of its verity, in the sense some attach to the word proof, and there is absolutely none ; and there are even about the conception itself some stupendous difficulties. The physicist has to endow his Ether with the most contradic- tory properties. He conceives it as rarer and more subtle than the most exhausted atmosphere, with the principal pro- XVI] THE PHYSICAL TRINITY 381 perti^s of a perfectly elastic fluid ; and yet, withal, the chief distinguishing property of a solid ! All these paradoxes do not deter him ; and he believes implicitly in this Ether he has never seen and never will see, simply because without it he can ex- plain no solitary phenomenon around him, while with it and its motions he can explain everything. Light is thus, to him, a Revealer of all Nature, both visible and invisible. The inquiry seems irresistibly suggested, whether the com- parison and the analogy may not go further, and afford hint or revelation which goes deeper still. That inquiry is indeed strictly legitimate. If our Universe be in truth an objective and conditioned manifestation of any Absolute Foundation of all Being, it should be thus ; the Actual ought, in its limited measure, however limited that measure may be, to reveal to us truly the Essential and Eternal. The student of Nature, at all events, does hold expressly that if she has any Author she must speak truly of Him, if she speak at all ; and as for the so-called religious man, though any book can only take a secondary place in such an inquiry as this, he also admits that it ought to be thus, since his book actually says so. It is therefore a point of surpassing interest, whether as regards this question there is any definite agreement between these two, as to which physical Science can really have anything to say. What then do we find? We are bound to ask the ex- pounders of physical science first, for every reason. We in- quire, therefore, what purely physical science, and experiment, and speculation what they at present profess to teach us ? 1. They tell us of an intangible, invisible Ether, which can- not be touched, or tasted, or contained, or measured, or weighed, but yet is everywhere ; which contains within itself the potentiality of all the essential properties of Matter, fluid and solid ; and yet which is not Matter, though it can communicate its own motions to Matter, and receive motions from it. 2. They speak to us next, according to the very widely 382 LIGHT [CHAP. received Vortex Theory of Sir William Thomson, 1 something vaguely about this Ether taking Form. They suggest to us how Vortices in it may appear to us as those atoms of Matter which we do see, and feel, and handle ; and which in this finite and conditioned Form can be limited, and contained, ;~nd measured, and weighed; in which the Ether may becomes it were, incarnate and embodied. 3. They tell us in the third place, of a mysterious Energy, which also takes protean forms. But in one form or other this Energy is doing all the physical work of the Kosmos ; and by it even Matter itself is manifested to us, and becomes a part of our own consciousness. And this is all ; and Light embodies them all and reveals them all. It is Motion, a form of Energy ; it is Motion in the Ether ; and it is invisible, inconceivable, unknown to us, unless Matter, to make it visible, be in its path. There are these Three and these only ; each distinct and separate ; and yet the three making up One, a mysterious unity which cannot be dissolved. So far the purely physical philosopher. Pondering atten- tively this wonderful triune conception which he has put before us, it will appear impossible that he at least should sneer at any other Trinity in Unity, seeing the kindred mystery in which he himself acknowledges that he dwells. Ether : Matter : Energy : no one of them can be conceived of apart from the others ; yet each is separate and distinct. Take away either, and what becomes of the Universe, as we know it or can conceive it ? And yet we say and think that this Universe is monistic is one harmonious whole. The mystery of Nature is not only as great, but actually appears to be of the very same kind, as that which theologians have taught concerning the mystery of its Author. 1 It is almost unnecessary to 'say that this is only a hypothesis. And equally so to remark that in spite of difficulties, it makes more progress and receives further adherents every day. xvi] A STRIKING PARALLEL 383 For now we are at liberty to turn to the other, and ask him. He knew nothing of all this ; never even dreamt of it, since it is the last growth of the nineteenth century. But, purely from an -old Book he possesses, he too had, somehow or other, and lor,g before the other, also gathered a conception, and even /Earned it into a theological formula. It will be at least ii ..esting to see now what his conception is. iv^ He tells us first, that he believes in an eternal, immortal, invisible, inconceivable, infinite Essence or Absolute, the one Source and Father of all. 2. He believes that this essential Being has in some mysterious way become embodied in a Second, in some inconceivable manner co- existent with, and yet derived from Him ; who is the brightness of His glory and the visible Image of His substance ; 1 and in whom and by whom all Things were made. 3. He affirms that these two work or act by and through an equally mysterious Energy ; whose operations assume many forms ; who does all things, alike in matter and in spirit ; and who finally brings all conscious agencies that yield to Him, into harmonious relation and equilibrium with all that surrounds them. That is the creed of the Christian, so much derided during the last twenty years. He also says and believes, like the other, that although he cannot explain it any more than the physical philosopher, these Three are One. Still more strange to say, he goes so far as to affirm that the Motions of the third originally produced that Light which we have found such a fascinating study ; that to him, also, this Light is an express symbol and revelation of the Three ; that it is even " as a garment " in which the Eternal and Invisible One clothes Himself, to be manifest to men ! This is but a suggestion. But // there should be reality and fact behind the belief of both parties as we have listened to 1 " The very Image [or impress] of His substance." R. V. 384 LIGHT [CHAP. them, is there not indeed here an obvious, deep, fundamental, marvellous agreement ? More than this : if there should be true wisdom in what has been taught us by one of the most popular teachers of modern philosophy ; * if it be true that " Religion and Science are therefore necessary correlatives ; " if it be true that " Force, as we know it, can be regarded only as a certain conditioned effect of the Unconditioned Cause- as the relative reality indicating to us an Absolute Reality by which it is immediately produced ;" if it be further true that " objective Science can give no account of the world which we know as external, without regarding its changes of form as manifestations of something that continues constant under all forms ; " and if it be finally true as regards Spirit and Matter, that " the one is, no less than the other, to be regarded as but a sign of the Unknown Reality which underlies both ; " if these conceptions of one whom all regard as at least a great thinker, embody anything more than a foolish dream, is not this correspondence which we have found, precisely of the sort we ought to have expected to find ? The comparison and the inquiry appear in any case to be singularly interesting. The student of Nature, at least, should not object to it. And as for the other, he also may perhaps learn to hear of Matter possessing " the promise and potency of every form of life " without resentment, and to attach to the phrase a new meaning that might perchance be the basis of a great reconciliation, which has been long and sorely needed. He may perhaps learn to trust more fully what Nature and Science really have to say to him ; and will at least have learnt in another way, that "the invisible things of Hun since the creation of the world are clearly seen, even His eternal power and Godhead being understood by the things which are made.' 1 '' 1 Mr. Herbert Spencer. All the sentences quoted are from First Principles, 3rd edition ; and the last one cited is the final sentence of all in that remarkable volume, INDEX A ABBE THEORY, 203 Aberration, chromatic, 67 spherical, 41, 59 Absorption of Colour, 104, 122 reciprocal with radiation, 130, 140 Achromatic lenses, 79 Adams' arrangement for Bi-axials, 345 Ahrens' prism, 244 Air, films of, 158 Airy's spirals, 360 Analyser, 213, 256 Delezenne's, 170 revolving, 333 Analysis of waves, 97 of polarisation, 219 Angles of reflection, 28, 29, 5 1 of pd^risation, 222 of bi-axial crystals, 343 Anomalous dispersion, 80, 101, 341 Apophyllite rings, 341 Apparatus, . r -22 polarising, 241 for bi-axial crystals, 251 Arragonite, conical refraction in, 351 Artificial crystals, 341 quartz, 327 Axes, optic, 227 relations of, 353 Balmain's paint, 137, 145 Balsam for mounting, 269 Bands in spectrum of Newton's spectrum, 162 of mica, 165 of selenite, 273 Barton's buttons, 184 Beams, parallel, 35 Becquerel on phosphorescence, 145 Bi-axial crystals, 231-342 apparatus for exhibiting, 344 axes of, 353 dispersion in, 347 theory of, 348 Biot's experiment on sonorous vibra- tions, 285 Bi-quartz, use of, 321 Bi-sulphide prisms, 17, 82 Black surfaces, polarisation by, 374 Blue and yellow, variety of effects, 116 Brewster, on artificial crystals, 341 common light, 234 polarising angle, 223 Brookite, 348 Briicke on polarisation, 373 Bunsen's holder, 18 Calcite, 210 Calorescence, 144 Camera obscura, 24 Cascade, luminous, 52 Cauchy on dispersion, 101 Change in wave-lengths, 135 Chemistry, solar, 133 stellar, 133 c c 3 86 INDEX Chlorophyll, 107, 143 Chromatic aberration, 67 Circular polarisation, 301, 317 crystals in, 361 quartz in, 365 Clock, polar, 372 Collimating lens, use of, 80 Colour, absorption of, 105 analysis of, 66 as a sensation, 115 suppression of, 68 Colourblindness, 119, 120 Colours, complementary, 109, 264 compounding of, 69 reflection of, 108 refraction of, 63 of thick plates, 1 70 transmission of, 108 waves of, 312 Combinations, mica and selenite, 354, 357 Common light, theories of, 235 vibrations of, 233 Complementary colours, 109 cause of, 264 Composite crystals, 353 Composition of Colours, 69 of vibrations, 311 Conical refraction, 351 Conservation of energy, 146 Continuous spectra, 122 Convergent lenses, 345 Convergent light, quartz in, 342 Cord, displacement of, analogous to light, 238 Cornu's saccharometer, 322 Crossed crystals, 357 Crossed films, 271 Crova's disc, 93 Crystals, artificial, 341 bi-axial, 231, 342 composite, 353 crossed, 357 heating of, 349 hemitrope, 353 irregular, 353 negative, 231 optic axis of, 227 positive, 231 preparation of, 340 rotatory, 324 uni-axial, 230, 336, 353 Crystallizations, 274 on screen, 277 Cylindrical lens, 69 1) De Dominis' rainbow experiment, 75 Deflection of rays, 54 Delezenne's analyser, 170 Descartes on rainbow, 76 Deviation in prism, 57 Diagrams for lantern, 19 Diffraction, 176 in the microscope, 198 spectrum, 184 Direct vision prisms, 79 Disc, Crova's, 93 Newton's colour, 71 Dispersion, 64, 77 anomalous, 80, 101, 341, 347 Dolbear's opheidoscope, 38 Doppler's principle, 121 Double image prisms, 209 Double refraction, 209, 227 "Doubler," Norrenberg's, 258 Dove on common light, 237 on fluids, 331 Eidotrope slides, 70 Elasticity of ether, 103 in crystals, 225, 348 Electric light, 10 Electro-magnetic rotation, 324 Elliptic polarisation, 265, 301 Emission theory, 88, 160 Energy, conservation of, 146 Energy, identity of radiant, 378 Ether, the, 98 Eye, deception of, in mechanism of, 96 Films, mica, manipulation of, 289- 300 soap, 153 thicker films, 164 thin, colours of, 151 INDEX 387 Fizeau's experiment on velocity of light, 86 Fluids, see Liquids Fluorescence, 138 and phosphorescence, 145 Forbes on velocity of light, 87 Forces, result of two, 147 Foucault on velocity of light, 87 Foucault's prism, 242 Fox on diffracted patterns, 179 on mica films, 269 Fraunhofer's lines, 130 Fresnel on common light, 234 on rotary polarisation in fluids, 331 FresnePs mirrors, 172 prism, 173, 319 rhomb, 305 Fuchsine, anomalous dispersion of, 83 Gas regulator, 6 Gases, spectra of, 124 Geological sections. See Minerals Glass in sonorous vibrations, 285 Glass piles, polarising, 252 Gold-leaf, colours of, 108 Gratings, 178 Green not a compound, 1 1 1 Grey, nature of, 71 Gypsum, effect of heating, 348 Iceland spar, 210 Identity of radiant energy, 378 Images, 23. See also Mirrors in lenses, 58 inversion of, 26, 40 multiple, 30 multi-coloured, 326 virtual, 29, 42 Indices of refraction, 49 Intensity, law of, 28 Interference, 147 bands in spectrum, 162, 273, 320 demonstrations of, 190, 270 Inverse squares, law of, 28 Inversion of images, 26, 40 Invisible spectrum, 135 Invisibility of light, 44 of polished surfaces, 43 Iodide prisms, 78 Irregular refraction, 175 crystals, 353 Isolating phenomena, 25 Ivory balls as illustrating waves, 90 K Kaleidophone, 36 Kaleidoscope, 32 Kundt on sonorous vibrations, 287 II Halos, 1 80 Hamilton on conical refraction, 351 Heat, effects of, 283 vibrations of, made visible, 34 Hemitrope crystals, 353 Herschel on quartz, 320 reversal of phase, 189 sky polarisation, 373 water-colours, 114 Hertz's Experiments, 191 Hofmann's apparatus for bi-axials, 345 Huygen s experiments, 21 1 on double refraction, 217 Hyperbolic curves, 162, 357 Lantern, the, 1-22 accessory apparatus, 14-19 diagrams, 19 lamps for, 5, 6, IO, 12 mounting, 12 screws, 18 vertical attachment, 20 Lantern polariscope, 247 Lenses, 57 achromatic, 79 concave, 61 convergent, 345 images formed by, 58, 60 Light for lanterns, 5, 10, 12 invisible, 44 3 88 INDEX Light for Lanterns, continued theories of, 85, 96 velocity of, 85 Lime-light for lantern, 6 Line spectra, 126 Lines, Fraunhofer's, 130 reversed, 128 thickened, 131 Lippich on common light, 237 Lippmann's Experiment, 190 Liquid waves, interference of, 148 Liquids, rotation in, 321 stress in, 280 Lissajous' experiment, 35, 36, 236 Lloyd on conical refraction, 35 1 Lockyer on transmission of states, 89 Lommel on fluorescence, 139 Luminous cascade, 52 Lycopodium, diffraction by, 180 M Mach on sonorous vibration, 287 Magnesium light, 139 Magnetic rotation, 324 Matter, possibly vortices in ether, 38i Measurement of molecules, 194 of wave lengths, 185 Metals, reflection from, 305 Mica designs, 267 double, 314 film work, 289 quartz, 329 selenite combinations, 354, 357 wedges, 271 Microscope, diffraction in, 198 Micro slides, 252, 277 Minerals, polarised sections of, 278 Mirror, concave, 38, 40 convex, 42 Fresnel's, 172 reflecting, 33 Mitscherlich's experiment, 349 Mixed plates, 175 Mixtures of light and pigments, ill Molecular constitution and rotation, 330 Molecules, size of, 194 Mother of pearl, 182 Motion, light must be, 87 Motions, result of two, 147 Mounts for lenses, 13 Multiple images, 30 N Narrow slit for spectrum, 74 Nature and her Author, 379 384 Newton's colour disc, 71 rings, 159, 162 spectrum experiments, 65 Nicol prism, 241 Nobert's gratings, 178 Norrenberg's " Doubler, 258 mica selenites, 355, 357 artificial crystals, 357 O Objective, optical, 2 Oil-lamps, 5 Opheidoscope, 38 Opposite rotations, 313 Optic axes, 227, 351 Optical objective, 2 torque, 325 Organic substances, 279 Oxide films, 153 Oxygen. See Lime-light Particles, polarisation by, 373 Pencil attachment, 4 Pencils of light, 26 Pendulum experiments, 301 parallel, 33 Perforated cards, experiments, 181 Phase, reversal of, 189, 265 Phoneidoscope, 166 Phosphorescence, 137 and fluorescence, 145 Photographs of Interference, 190 Pigments, mixtures of, 1 1 1 Pincette, tourmaline, 339 Plane polarised light, 263 chromatic dispersion of, 260, 263 INDEX Plateau's soap solution, 153 Pleurosigma angulatum, 201 Polar clock, 372 Polarisation, 209, 212, 217 arfgle of, 222 apparatus for, 241, 266 by black surfaces, 374 by double refraction, 225 by reflection and refraction, 216, 219 circular, 301, 317 elliptic, 301 nature of, 217 plane of, 228 rotary, 301 vibrations, direction, 224, 228 Polariscopes, 247, 249 direct reflecting, 254 Polarised light, coloured designs for, 309, 266 mica designs for, 266 Polarising apparatus, 241, 266 Polished surfaces, 43 Prazmowski's prism, 243 Primary colours, 115 Prismatic colours, experiments, 68 Prisms, Ahrens', 244 bi-sulphide, 7? 82 care of, 247 deviation, 57 direct vision, 79 Foucault's, 242 Fresnel's, 173, 319 improved, 243 Nicol's, 241 position, effect of, 66 Prazmowski's, 243 Propagation of waves, 96 Pulse, made visible, 33 Quarter-wave plates, 303 Quartz, artificial, 327 in circularly polarised light, 365 in convergent light, 342 left-handed, 320 mica, 329 phenomena of, 318 plates, 225 prism, 319 right-handed, 320 K Radiant energy, identity of, 378 Radiants for lanterns, 5 Rainbow, the, 74 Rayleigh's (Lord) experiments, Il6 Rays of light, 23, 26 deflected, 54 Red ink experiments, 108 Reflection, 28. See also Images curved surfaces, 38 doubled angle of, 32 equal angles of, 28 of colours, 64 repeated, 31 scattered, 42 total, 50, 100 from rarer medium, 188 at unpolished surfaces, 44 Refraction, 47, 77 conical, 351 double, 209, 227 explanation of, 98 index of, 49 irregular, 175 law of, 48 of colours, 63 Religion and Science, 383 Resolution of vibrations, 260 Retardation, 101 Reusch's artificial quartz, 327 Reversal of phase, 189, 265 Reversed lines, 128, 130 Reversibility of rays, 29 Rhomb, Fresnel's, 305 Rings, Newton's, 159 analysis of, 162 in crystals, 336 Rocking spectrum, 73 Rotation, contrary, 313 electro-magnetic, 324 and molecular constitution, 330 register, 326 Rotational colours, 307 spectrum, 317 Rotary polarisation, 301 Saccharometer, 321 Salicine crystals, 275 Santonine, effects of on eyesight, 120 390 INDEX Savart's bands, 361 Scattered reflection, 42, 46 Screens, 18 Sections of minerals, 278 Set de Seignette, 348 Selenite combinations, 354 Senarmont on quartz plates, 226 Sensation of colour, 115 Shadows, 27 Sines, law of, 49 Sky, polarisation of, 372 Slide, to show wave-motion, 94 Slits, experiments with, 177 Smoke in jar, 45 Snell's law of sines, 49, 75 Soap films, 153 sound vibrations in, 165 Sodium lines, 126, 128 Solar chemistry, 133 Solar spectrum, 125 Soleil's saccharometer, 322 Sonorous vibrations, 285 Sound vibrations in soap films, 165 Sound waves, 96 Spectra, absorption of, 123 continuous, 122 line, 126 non-existent, 136 Spectrum, the, 62 diffraction, 184 fringes, 273 invisible parts, 135 Newton's experiments, 65 pure, 74 solar, 125 Sphinx illusion, 43 Spiral figures, 365 Spirals, Airy's, 360 Squares inverse, law of, 27, 28 Stellar chemistry, 133 Stokes on fluorescence, 139 Strain, effects of, 280 Striated surfaces, 189 Subjective colours, 118 Substances, structure of, 279 Suppression as cause of colour, 68 T Table-stands, 17 Tank for refraction, 47 Taylor (Mr. Sedley), on sound vibrations, 165 Telescopes, reflecting, 41 refracting, 61 Tension, effects of, 280 Theories of light, 85, 96, 102, 160 Thick plates, colours of, 170 Thickened lines, 131 Thicker films, 164 Thin films, 151 sound vibrations in, 165 Thompson's rotation register, 326 Tidal waves, 149 Tisley's phoneidoscope, 116 Torque, optical, 325 Tourmalines, phenomena of, 214, 232 pincette, 339 Transmission of states, 89 of waves, 90 Transparency, 54 Trevelyan rocker, 34 Tripod stand for lantern, 12 Tuning-fork experiments, 35 Turpentine films, 152 Tyndall on calorescence, 144 fluorescence, 145 Newton's rings, 161 polarisation, 373 sonorous vibration, 287 subjective spectrum, 119 U Unannealed glass, 283 Undulatory theory. See Wave Uni-axial crystals, 230, 336, 353 V Velocity of light, 85 Vibrations, absorption of, 134 common light, 233 composition of, 311 resolution of, 260 Virtual images, 29, 42 Vision, mechanism of, 96 INDEX W Water-colours, effects of, 114 Wave-lengths, change in, measurement of, 87, 185 Wave -motion, 90 Wave-slide, 94 Wave-shells in crystals, 230, 35 1 Waves, light, 96 sound, 96 Wedges, mica, 271 Wernicke's prism, 81 Wheatstone's kaleidophone, 36 polar clock, 372 1 3S '> White light, composition of, 68 Wild's saccharometer, 322 Young on diffraction, 175, 177 on velocity of light, 78 THE END RICHARD CLAY AND SONS, LIMITED, LONDON AND BUNGAY. 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. 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