UC-NRLF 
 
 ON THE NATURE 
 
 OF LIGHT 
 
 PROF. G. G, STOKES 
 
Irving Stringkiam 
 
BURNETT LECTURES. 
 
 ON LIGHT. 
 
BURNETT LECTURES. 
 
 ON LIGHT. 
 
 Jfhrst 
 ON THE NATURE OF LIGHT, 
 
 DELIVERED AT ABERDEEN IN NOVEMBER, 1883, 
 
 GEORGE GABRIEL STOKES, M.A., F.R.S. &c. 
 
 FELLOW OF PEMBROKE COLLEGE, AND LUCASIAN PROFESSOR OF 
 MATHEMATICS IN THE UNIVERSITY OF CAMBRIDGE. 
 
 Honlron : 
 MACMILLAN AND CO. 
 
 1884 
 
 [ The Right of Translation and Reproduction is reserved.} 
 
9W*W**I 
 
 Cambrttrge: 
 
 PRINTED BY C. J. CLAY, M.A. & SON, 
 AT THE UNIVERSITY PRESS. 
 

 S&2, 
 
 PREFACE. 
 
 THE lectures, of which the first course is con- 
 tained in the present volume, originated in a 
 new direction given to an old endowment. Mr 
 John Burnett, merchant in Aberdeen, who died 
 in 1784, bequeathed the greater part of his 
 property to various charitable and pious objects. 
 Among others, a portion of the property was 
 vested in trustees for establishing prizes for the 
 best and next best essay on the following sub- 
 ject : 
 
 "That there is a Being, all-powerful, wise, and 
 good, by whom everything exists; and particularly 
 to obviate difficulties regarding the wisdom and good- 
 ness of the Deity ; and this, in the first place, from 
 considerations independent of written revelation, 
 
 7 
 
 s. 
 
VI PREFACE. 
 
 and in the second place, from the revelation of the 
 Lord Jesus; and, from the whole, to point out the 
 inferences most necessary for, and useful to man- 
 kind." 
 
 These essays were to be competed for at 
 intervals of 40 years, and awards have been 
 made on two occasions since the original foun- 
 dation. 
 
 But it was thought that the production of 
 essays at such long intervals did not form a 
 satisfactory mode of utilizing the bequest of the 
 founder ; and in 1881 a new direction was given 
 to the foundation by an order of the Secretary 
 of State for the Home Department, in accord- 
 ance with the provisions of the Endowed Insti- 
 tutions (Scotland) Act of 1878. By this order 
 it was provided that a Lecturer should be 
 appointed at intervals of 5 years, to hold office 
 for 3 years, the subject of the lectures being 
 determined by the following regulation : 
 
 " The Trustees and assessors may prescribe as the 
 subject of the course of lectures that specified in the 
 
PREFACE. vii 
 
 codicil to the will of the testator, viz. [as above]. Or 
 otherwise, the trustees may prescribe, as the subject 
 of any course of lectures, recent researches (as at the 
 date of the appointment) into any of the following 
 branches of knowledge, viz : 
 
 1. History, including the illustrations of the forms 
 and effects of theistic doctrines among the older 
 nations of the world. 
 
 2. Archaeology. 
 
 3. Physical science. 
 
 4. Natural science. 
 
 And they shall instruct the lecturer to have regard, 
 in treating of the special subject prescribed, to the 
 illustration afforded by it of the theme proposed by 
 the testator, and that under such conditions or qualifi- 
 cations as they may prescribe." 
 
 The Trustees selected physical science as the 
 subject of the first lectures under the new system, 
 and they did me the honour of appointing me 
 the first Burnett Lecturer. It has been arranged 
 that four lectures are to be given each year of 
 office, and that the subject of the complete course 
 shall be Light, the subject being treated under 
 three divisions, to which the lectures in each 
 year are to be respectively devoted. The first 
 
viii PREFACE. 
 
 division is sufficiently explained by the title of 
 the present course ; the subjects of the second 
 and third divisions will be found at the end of 
 the fourth lecture. 
 
 I am sensible of the difficulty of the task I 
 have attempted in this first year's course, 
 namely, while avoiding all mathematical details, 
 to give the audience some fair idea of the evi- 
 dence on which we accept the views respecting 
 the nature of light which are at present held, I 
 may almost say universally, in the scientific 
 world. I assume on the part of the reader a 
 knowledge of the rectilinear propagation of light 
 in the same medium, of the laws of reflection and 
 refraction, of the compound character and of the 
 decomposition of white light ; but I have not 
 assumed that he is acquainted with the phe- 
 nomena of interference, or diffraction, or double 
 refraction, or polarization, though some acquain- 
 tance with these subjects will make the lectures 
 much more easy to follow. For the sake of 
 those persons to whom these things may be 
 
PREFACE. IX 
 
 nearly or entirely new, I have been obliged to 
 enter into details which I cannot help fearing 
 may be wearisome to those who have already a 
 pretty good acquaintance with the subject ; 
 though I hope that even they may not find the 
 weighing of the evidence wholly uninteresting 
 or unprofitable. 
 
 G. G. STOKES. 
 
 CAMBRIDGE, 
 
 February 5, 1884. 
 
CONTENTS. 
 
 LECTURE I. 
 
 PAGE 
 
 Bearing of the more obvious properties of Light on our view of its 
 nature Theories of emission and of undulations Colours of 
 thin plates Newton's attempt to explain them on the theory 
 of emission Insufficiency of the explanation i 
 
 LECTURE II. 
 
 Interference Explanation of the colours of thin plates afforded by 
 the theory of undulations Diffraction . . . .32 
 
 LECTURE III. 
 
 Closer examination of the fundamental suppositions of the Theory 
 of Undulations Survey of the conclusions arrived at by a 
 study of the phenomena of common light Elementary facts of 
 double refraction and polarization . . . . . 74 
 
 LECTURE IV. 
 
 Phenomena presented on interposing a crystalline block or thin 
 plate in the path of Polarized Light which is subsequently 
 analyzed Laws on Interference of Polarized Light Theory 
 of Transverse Vibrations Conclusion ..... 105 
 
LECTURES ON LIGHT. 
 
 FIRST COURSE. 
 ON THE NATURE OF LIGHT. 
 
 LECTURE I. 
 
 Bearing of the more obvious properties of Light on our view 
 of its nature Theories of emission and of undulations 
 Colours of thin plates Newtoris attempt to explain them 
 on the theory of emission Insufficiency of the explanation. 
 
 AMONG all our senses, there is none more wonder- 
 ful than that of sight. It confers upon us, as Sir 
 John Herschel has remarked, to a considerable extent 
 the character of ubiquity. It is accordingly a matter 
 of extreme interest to find out what we can as to the 
 mode in which this end so important to our well- 
 being is brought about ; whether it be by investigat- 
 ing the properties of any agent external to ourselves 
 which may be concerned in its accomplishment, or 
 by seeking to penetrate some little way into that 
 S. I 
 
2 THE NATURE OF LIGHT. 
 
 mysterious chain of sequence which connects the 
 external agent with the sensation conveyed to our 
 minds. It is true indeed that there is no prospect of 
 our being able to bridge over the gulf which sepa- 
 rates mind from matter; yet there are many things 
 to indicate that that mysterious organ which we pos- 
 sess, the brain, has some intimate connexion with 
 the operations of the mind, and we can do something 
 towards tracing a connexion between the part of our 
 bodies directly affected by the external agent and the 
 brain ; a connexion of such a kind as to leave no 
 doubt that it forms the means whereby the immediate 
 action of the external agent is ultimately perceived 
 by the mind ; though how the final conveyance takes 
 place is a mystery we are not likely to fathom. 
 But this does not prevent us from being able to 
 trace some links in the chain of connexion, nor from 
 recognizing the evidences of design which that portion 
 which we can in a measure follow is calculated to 
 impress upon us. 
 
 I have spoken of an external agent even though 
 it was more especially trie sense of sight that I had 
 in view. We are so accustomed to the contemplation 
 of an objective something, which we call Light, as the 
 external agent by the action of which vision is in 
 some way brought about, that we have a difficulty in 
 conceiving how anyone could think otherwise. We 
 
IDEAS OF THE ANCIENTS. 3 
 
 see the objects in a room, but it is matter of the 
 commonest observation that though the objects may 
 be there and our eyes may be there, we see them not 
 if it be night, or if the room be closely shut up, until 
 a lighted lamp or candle or something of the kind is 
 introduced. We recognize the flame as the seat of 
 some influence, to which we give the name of light, 
 which is essential to vision. Yet obvious as this 
 proposition appears to us, it is remarkable that it was 
 not always so. At least one writer of acute intellect 
 in ancient times held that it was something emanating 
 from the eye, not something from without entering 
 into it, that enabled us to perceive distant objects. 
 This shows by what a slow and gradual progress 
 our knowledge of physical science is built up. We 
 are accustomed to vaunt of our knowledge in this 
 i Qth century; yet it may be that generations hence 
 the scientific men of the day will wonder how we 
 could have failed to perceive things which to them 
 will appear quite obvious. 
 
 A self-luminous body then is, as such, a source of 
 an influence which can be exerted at a distance. In 
 this respect it by no means stands alone ; two bodies 
 at a distance from one another may for example 
 influence each other through the attraction of gravi- 
 tation, and other modes of influence might also be 
 mentioned, but I will confine myself to gravitation. 
 
 i 2 
 
4 THE NATURE OF LIGHT. 
 
 Now between these two modes of influence there are 
 great and striking differences. One of the most 
 salient is this, that in the case of gravitation the 
 influence is exerted independently of the interposition 
 of matter of any kind, whereas in the case of light 
 the influence is capable of being arrested by an 
 extremely thin screen of matter of a suitable kind ; 
 for example, silver foil, or a film of Indian ink spread 
 on glass. 
 
 The consideration of a screen leads us naturally 
 to another fundamental and very obvious property of 
 light. Suppose the screen pierced by one or more 
 rather small apertures ; how will the influence beyond 
 the screen be distributed ? We find that it is per- 
 ceived only within the projections of the aperture or 
 apertures made by straight lines drawn from the 
 luminous body, which for simplicity I here suppose to 
 be a point. 
 
 This indeed is not rigorously true, for about the 
 boundary of the projection of the aperture, that is, 
 near the projection of the edge of the aperture, there 
 is a gradual, not sudden, passage from light within 
 to darkness outside, accompanied by fluctuations of 
 greater and less luminosity which I cannot now enter 
 into particularly ; and when the aperture is extremely 
 small, the spreading out of the light which passes 
 through it is by no means very small compared with 
 
RECTILINEAR PROPAGATION. 5 
 
 the breadth of the projection of the aperture itself. 
 Nevertheless in ordinary cases the spreading out of 
 the light is so small that we may disregard it, and 
 say that light proceeds from a luminous point in all 
 directions in straight lines until it is stopped by some 
 obstacle. It will be understood that I am here speak- 
 ing of light only as it passes in free space, or which 
 comes to nearly the same thing, in air, and not from 
 one medium into another. 
 
 When I speak of light proceeding from a luminous 
 point, all I wish to express is that we recognize the 
 luminous point as the seat or origin of a certain 
 influence which is exerted, though with an intensity 
 which diminishes with increasing distance, at all 
 points from which a straight line can be drawn with- 
 out interruption to the luminous point ; I do not wish 
 to imply the idea of motion, or propagation of any 
 kind. The feature therefore that we are at present 
 considering is common to light and gravitation. 
 
 A very important question now arises, Do these 
 influences take time to travel, or does the influence 
 exerted at any moment of time depend solely on the 
 state and position of the two bodies, the influencing 
 and the influenced, at that moment ? The idea which 
 we may be led to form as to the nature of light must 
 depend most materially on the answer we have to 
 give to this question as applied to light. 
 
6 THE NATURE OF LIGHT. 
 
 That light is propagated in time, cannot be inferred 
 from ordinary observation. Thus when a landscape 
 is illuminated at night by a flash of lightning or an 
 explosion of gunpowder, the flash and the objects 
 illuminated by it are seen, so far as our senses can 
 decide, simultaneously, though in the latter case the 
 light has to travel from the flash to the object 
 illuminated, and from that to the eye, instead of 
 coming straight from the flash. As far as ordinary 
 observation goes, then, the question whether any time 
 is occupied in the transmission is left an open one, 
 and we can only say that if time is required for 
 transmission, the rate of travelling must be enormously 
 great. 
 
 But in the solar system we have distances to deal 
 with compared with which the dimensions of the 
 earth itself on which we dwell, let alone those of a 
 landscape, sink into insignificance. It is conceivable 
 that in travelling over those vast distances, if it does 
 travel at all, light might occupy lengths of time 
 which would not be insensibly small, and which 
 possibly might be put in evidence by some celestial 
 phenomenon. Thus if the light of the sun were 
 emitted by flashes, the sun would take the place of 
 the thunder-cloud in our supposed observation, and 
 the planets that of the objects in the landscape. 
 Though there are changes going on in the sun, as we 
 
VELOCITY OF PROPAGATION. 7 
 
 now know, there are none of such magnitude and 
 suddenness as to be available for such an observation. 
 Nevertheless it was by celestial observations, of a 
 somewhat different kind, that the finite velocity of 
 light was first revealed. 
 
 This was done as long ago as in 1676 by Roemer, 
 who showed that an inequality in the times of 
 occurrence of the eclipses of Jupiter's satellites, which 
 he had observed, was simply explicable on the 
 supposition that light is propagated with a finite 
 velocity. The mean motion of a satellite round the 
 planet being accurately known, from observations 
 extending over a sufficient time, the times of suc- 
 cessive eclipses can be calculated. It was found that 
 the eclipses happened earlier or later than the calcu- 
 lated times, supposing the epoch so chosen as to make 
 the accelerations and retardations balance on an 
 average, according as the earth and Jupiter were on 
 the same side of the sun or on different sides, and 
 the differences in the apparent errors in the times of 
 occurrence of the eclipses at different times of the 
 year were proportional to the differences of the dis- 
 tances of Jupiter from the earth at those times. 
 The greatest difference in that distance is evidently 
 equal to the diameter of the earth's orbit (supposing 
 for simplicity the orbits of the earth and Jupiter cir- 
 cular and in the same plane), and to this corresponds 
 
8 THE NATURE OF LIGHT. 
 
 the greatest difference in the apparent errors of the 
 times of occurrence, which amounts to about 16 
 minutes and a quarter. We learn therefore that if 
 this be the true reason of the observed inequality, 
 light takes 8 minutes and a few seconds to travel 
 over the distance from the earth to the sun. To ex- 
 press the velocity in miles per second, we require to 
 know the dimensions of the earth's orbit, or what 
 comes to the same the solar parallax, which, being 
 the ratio of the radii of the earth and the earth's 
 orbit, serves to express the latter in miles since the 
 former is accurately known. According to the value 
 of the sun's parallax which was accepted till recent 
 years, the velocity of light so determined came out 
 about 192,000 miles per second. More recent de- 
 terminations have reduced this to about 186,000 miles 
 per second. 
 
 For nearly 50 years after Roemer's discovery, no 
 other phenomenon was known which indicated that 
 the propagation of light was other than instan- 
 taneous ; but then Bradley made the very remarkable 
 discovery of the aberration of light. It would 
 occupy too much time to go fully into this, and I 
 must content myself with giving you a general notion 
 of it. 
 
 Suppose a person out on a perfectly calm day 
 when rain was falling, and accordingly, on account of 
 
ABERRATION OF LIGHT. 9 
 
 the perfect calmness supposed, falling vertically. If 
 the person were at rest, he would deem the rain to be 
 falling vertically. But suppose he were carried hori- 
 zontally along with a motion so smooth that he was 
 unconscious of it. The rain though falling vertically 
 would appear to him to fall in a somewhat slanting 
 direction, as if it came from a point not exactly 
 in the zenith, but displaced from it towards the 
 point towards which the observer is befog carried. 
 And if instead of falling vertically the rain be 
 falling in a slanting direction, it will appear to the 
 observer, unconscious of his own motion, to slant 
 differently ; in fact, if we compound the velocity of 
 the falling rain with a velocity equal and opposite 
 to that of the observer, the direction of motion of 
 the rain will appear to be that of the resultant 
 velocity. 
 
 Now Bradley found that just the same thing takes 
 place with regard to light. The earth in revolving 
 round the sun moves at the rate of about 20 miles in 
 a second, towards a point in the heavens lying in the 
 plane of the ecliptic 90 in advance of the heliocentric 
 position of the earth, or rather what would be 90 
 if the earth's orbit were strictly circular. The light 
 which comes from any particular star appears to come 
 from a place deviating from the true place of the star 
 towards the point of the heavens towards which the 
 
10 THE NATURE OF LIGHT. 
 
 earth is moving. And as this point goes round the 
 ecliptic in the course of a year, the apparent place of 
 the star describes annually a closed curve, in fact, a 
 small ellipse, round the mean position of the star. 
 The law of the apparent displacement of the star is 
 found to be what it ought to be on the supposition 
 that the cause of it is what has been above explained, 
 and the coefficient of the displacement gives the ratio 
 of the velocity of light to that of the earth in its 
 orbit. We are thus furnished with a second r^eans of 
 determining the velocity of light, and observation 
 will show whether the two do or do not agree. The 
 result is a remarkably close agreement when we 
 consider on the one hand the difficulty of fixing on 
 the exact moment of disappearance of a satellite 
 which enters the shadow of Jupiter, and on the other 
 the smallness of the displacement which constitutes 
 aberration, amounting at a maximum to only 20 
 seconds and a quarter of angle, about the angle 
 subtended by a six-inch rule at the distance of a 
 mile. 
 
 It is to be noted that the unit of length in terms 
 of which the velocity of light in both of these 
 methods is primarily expressed is the radius of the 
 earth's orbit, and in order to translate it into miles 
 per second we require to know the solar parallax. 
 
 While I am on this point I may mention that in 
 
EXPERIMENTAL DETERMINATION OF VELOCITY. II 
 
 the year 1849 Fizeau, by an extremely ingenious 
 combination of apparatus, succeeded in determining 
 for the first time the velocity of light by direct 
 experiment. The resulting value was confirmatory 
 of the two astronomical determinations, but was not 
 at first considered as capable of being put in com- 
 petition with them for accuracy, and no wonder, since 
 the whole interval of time to be measured in Fizeau's 
 experiment, under the circumstances in which it was 
 performed, amounted to only about the one twenty 
 thousandth part of a second. Subsequent determi- 
 nations, however, first by Foucault, by a different 
 method, and afterwards by Cornu, by Michelson, and 
 by the late Dr James Young and Prof. G. Forbes, 
 by one or other of those methods modified, have 
 rendered the determination so certain and accurate 
 that it is probably quite equal in accuracy to the 
 astronomical determinations. And since the experi- 
 mental determination gives the velocity in terms of a 
 known distance on the earth's surface, and accordingly 
 in miles or kilometres per second, if we assume the 
 experimental and either of the astronomical determi- 
 nations as separately valid and sufficiently accurate, 
 by comparing the two we can determine the radius of 
 the earth's orbit, which fixes the scale of the whole 
 solar system, in miles or kilometres. And as we know 
 accurately the dimensions of the earth, we can thus 
 
12 THE NATURE OF LIGHT. 
 
 determine the solar parallax, by combining accurate 
 measurements of an astronomical phenomenon fre- 
 quently recurring or constantly going on with a 
 laboratory determination made once for all. 
 
 I have been tempted into a digression by the 
 interest of this subject, and I would now resume the 
 consideration of some of the elementary properties of 
 light, with a view of showing how we are gradually 
 led to the formation of a theory, now thoroughly 
 tested, as to the nature of Light itself. 
 
 The observations to which I have last alluded 
 show that light, whatever it may be, takes time to 
 travel, so that in speaking of light as an influence 
 that proceeds from a source of light there is no 
 longer occasion to exclude the idea of motion of some 
 sort. I have compared and contrasted two influences 
 of which I have spoken, light and gravitation, and in 
 this last point again it is a contrast with which we are 
 presented ; or at least if the two are analogous the 
 analogy has never yet been established. After having 
 ascertained that light takes time to travel, and con- 
 templated that exceedingly curious phenomenon re- 
 lating to light, aberration, the question naturally 
 presents itself to the mind, Is there anything analo- 
 gous as regards gravitation ? Does it like light take 
 time to travel, or is it an instantaneous influence ? 
 Now the consequences which would follow as regards 
 
THEORIES OF EMISSION AND OF UNDULATIONS. 13 
 
 the motions of the bodies of the solar system if 
 gravitation like light took time to travel have been 
 calculated, and it has been concluded that if the 
 influence of gravitation takes time to travel, it at any 
 rate travels incomparably more quickly than light, 
 with a velocity accordingly which is incomparably 
 greater than 186,000 miles per second. 
 
 I have reduced to a minimum the mention I have 
 made of the fundamental properties of light, in order 
 not to weary you by repeating what is to be found in 
 every text book, and we may now attack the question, 
 What notion are we to form of the intrinsic nature of 
 this agent, so important to our well-being, so won- 
 derful in the scale of magnitude of the quantities it 
 brings before us, as we have seen already as regards 
 the velocity with which it is propagated, and shall see 
 later on in other respects ? 
 
 There appear to be but two modes possible of 
 conceiving of a mechanical influence emanating from 
 an influencing body, travelling with a finite velocity, 
 and ultimately influencing another body at a distance. 
 A mechanical influence implies the action of matter 
 of some kind, and this matter we may suppose to 
 have been either darted forth, in the manner of a 
 projectile, or to have previously existed in the space 
 between the influencing and the influenced body, to 
 have been disturbed by the influencing body, and 
 
14 THE NATURE OF LIGHT. 
 
 then to be successively agitated in successive portions, 
 each portion being agitated by its predecessor, and 
 in its turn yielding to its successor the disturbance 
 so received. We have not far to go to find illustrations 
 of both these kinds of action. Bullets exemplify the 
 first ; the progress of waves at the surface of water 
 illustrates the second. A still better illustration, 
 except that it is not visible, is afforded by the 
 phenomena of sound. 
 
 Such accordingly are the ideas which lie at the 
 base of the two theories as to the nature of light which 
 for a long time divided the scientific world between 
 them, the corpuscular theory, or theory of emission, 
 and the theory of undulations. 
 
 Prima facie there is much to be said in favour of 
 the theory of emission. It lends itself at once to the 
 explanation of the rectilinear propagation of light, 
 and the existence of rays and shadows. It falls in at 
 once with the law of aberration. The laws of reflection 
 and refraction admit of an easy explanation in ac- 
 cordance with it ; at least if we except the existence 
 of both reflection and refraction; for according to this 
 theory we should rather have expected beforehand 
 that light would have been either reflected or refracted, 
 according to circumstances, not that incident light 
 should have divided into a portion reflected and a 
 portion refracted. 
 
THEORIES OF EMISSION AND OF UNDULATIONS. 15 
 
 The theory of undulations on the other hand 
 presents at the outset considerable difficulties. In 
 the first place it requires us to suppose that the 
 interplanetary and interstellar spaces are not, strictly 
 speaking, a vacuum but a plenum ; that though desti- 
 tute of ponderable matter they are filled with a sub- 
 stance of some kind, constituting what we call a 
 medium, or vehicle of transmission of the supposed 
 undulations. When I speak of this medium as a 
 substance, or as material, I mean that it must possess 
 that distinctive property of matter, inertia; that is to 
 say a finite time must be required to generate in a 
 finite portion of it a finite velocity. The necessity of 
 thus filling space with substance seems to have pre- 
 sented a serious difficulty to some minds. In the 
 course of a conversation with Sir David Brewster, 
 who had just returned from France, where he wit- 
 nessed the celebrated experiment by which Foucault 
 had just proved experimentally that light travels 
 faster in air than in water, I asked him what his 
 objection was to the theory of undulations, and I 
 found he was staggered by the idea in limine of 
 filling space with some substance merely in order 
 that "that little twinkling star," as he expressed 
 himself, should be able to send its light to us. 
 
 I cannot say that this particular difficulty is one 
 which ever presented itself as such to my own mind. 
 
1 6 THE NATURE OF LIGHT. 
 
 To me the difficulty is rather that of conceiving such 
 an influence as that of gravitation to extend across 
 an absolute void. Such was the feeling of the great 
 discoverer himself of universal gravitation. In a 
 letter to Bentley, quoted by Faraday as falling in 
 with his own views, Newton thus expressed himself: 
 
 "That gravity should be innate, inherent and 
 essential to matter, so that one body may act on 
 another at a distance through a vacuum, without the 
 mediation of anything else, by and through which their 
 action and force may be conveyed from one to another, 
 is to me so great an absurdity, that I believe no man 
 who has in philosophical matters a competent faculty 
 of thinking, can ever fall into it. Gravity must be 
 caused by an agent acting constantly according to 
 certain laws ; but whether this agent be material or 
 immaterial, I have left to the consideration of my 
 readers." 
 
 If the supposition that light consists in undulations 
 obliges us to suppose that space is filled with some 
 kind of substance, at least as far as the remotest star 
 that our most powerful telescopes reveal to us, may 
 it not be that that same substance forms, in some 
 manner as yet unknown to us, the link of connexion 
 whereby the sun is enabled to attract the earth, and 
 keep it in its orbit ? It is true that notwithstanding 
 the labours of various scientific men we are not in a 
 
LUMINIFEROUS ETHER. I/ 
 
 condition to give an explanation of gravitation, but 
 our inability to explain it by no means proves that it 
 is a primary property of matter, incapable of explana- 
 tion, or forbids us to suppose that it may in some way 
 be brought about through the intervention of that 
 same substance which we find necessary to assume 
 for the explanation of the phenomena of light on the 
 theory of undulations. And it is quite conceivable, 
 and we may now say even probable, that this same 
 substance has yet other offices to fill. Perhaps the 
 most remarkable of all the investigations of the late 
 Professor Clerk Maxwell is that in which he showed 
 that there is a certain velocity, numerically determin- 
 able by purely electrical experiments which can be 
 made and have been made in the laboratory, and 
 expressing the velocity of propagation of an electrical 
 state, which is identical with the velocity of light 
 within the limits of error of the experiments and 
 observations whereby the two have been determined. 
 Assuming for the moment, as a thing at the present 
 day resting on evidence quite overwhelming, that 
 light consists of undulations, we cannot fail to be 
 impressed by the multiplicity of purposes, all bearing 
 so intimately on our well-being, which it seems pro- 
 bable, or not unlikely, are fulfilled by one and the 
 same substance, endowed with properties which we 
 are only gradually learning. 
 
 S. 2 
 
1 8 THE NATURE OF LIGHT. 
 
 I have ventured to allude for a moment to the 
 present state of the theory of light, and I will now 
 go back. The necessity of assuming the existence of 
 some kind of substance in what we commonly speak 
 of as a vacuum, does not appear to have been a serious 
 preliminary difficulty in the way of the reception of 
 the theory of undulations. A far more formidable 
 difficulty appeared at first to be presented by the 
 existence of rays and shadows. It was this that led 
 Newton to adopt the theory of emission, though even 
 he was led in the course of his researches on light to 
 suppose that there was some sort of medium through 
 which the particles of light moved, and in which they 
 were capable in certain cases of exciting a sort of 
 undulation. But the supposition of particles darted 
 forth seemed to him necessary to account for shadows. 
 If light consisted simply of an undulation propagated 
 through a medium of some kind filling the interstellar 
 spaces, as we know sound consists of an undulatory 
 movement propagated in the air, how can we conceive 
 of the existence of shadows, knowing as we do that 
 sound passes freely round corners, and diverges after 
 passing through apertures, though indeed it is true 
 that the freedom is not absolute ? Newton's contem- 
 porary Huygens was more bold, and adopted the 
 theory of undulations pure and simple, rejecting 
 altogether the notion of particles darted forth from 
 
DIFFICULTY OF EXPLANATION OF RAYS. 19 
 
 the luminous body, and travelling with the Velocity 
 of light. Huygens made a grand attempt to explain 
 the existence of rays, the great stumbling-block at the 
 threshold of the theory of undulations. The principle 
 which goes by his name lies at the very foundation of 
 the theory of undulations, and itself rests on a strictly 
 mechanical basis, being in fact merely an application 
 to the particular question under consideration of the 
 general dynamical principle of the superposition of 
 small disturbances. But this principle does not by 
 itself alone suffice for the explanation of rays. It 
 proves, or at least appears to prove, too much. It 
 is as applicable to sound as, on the supposition that 
 light consists in undulations, it is to light ; and if 
 Huygens's explanation of rays were complete there 
 ought equally to be rays of sound, and sound ought 
 to present the same sharp shadows as light. 
 
 Huygens attempted to get over this difficulty by 
 entering on certain speculations as to the ultimate 
 constitution of the ether, as we call the supposed 
 medium which is the vehicle of light, and as to the 
 mode of action, one on another, of the ultimate mole- 
 cules of which he imagined it to consist. In this he 
 abandoned the simplicity of the fundamental concep- 
 tions of the theory of undulations, and adopted a 
 mode of reasoning not strictly allowable. For the 
 transmission of regular undulations, of which the 
 
 2 2 
 
2O - THE NATURE OK LIGHT. 
 
 period is arbitrary, at least within wide limits, requires 
 us to suppose that the transmitting medium is either 
 continuous or may be treated as such ; that if it 
 consist of ultimate molecules, or be otherwise hetero- 
 geneous, the number of intervals from molecule to 
 molecule, or of deviations of one sign or another from 
 an average homogeneity, shall be very great and as 
 good as infinite within the length of a single undula- 
 tion ; and we have no right to extend to the medium 
 treated as a whole, and regarded as continuous, a 
 mode of communication of motion applicable only to 
 the communication from one to another of a set of 
 discrete molecules. 
 
 Accordingly, notwithstanding all that Huygens 
 has done, the existence of rays and shadows, one of 
 the most obvious properties of light, had received no 
 satisfactory explanation on the theory of undulations 
 such as it came from the hands of Huygens ; and in 
 this condition it remained for considerably more than 
 a century. His explanation of the laws of reflection 
 and refraction leaves nothing to be desired, except in 
 so far as these laws involve the conception of rays. I 
 cannot now speak of his discovery of the laws of 
 double refraction in Iceland spar, because it belongs 
 to a different branch altogether of the subject. 
 
 The theory of rays and shadows long remained in 
 this unsatisfactory state ; in fact, till quite the end of 
 
PROGRESS OF THE TWO THEORIES. 21 
 
 the last century. Newton's discovery of the com- 
 pound nature of white light showed that there must 
 be in light an element of some kind susceptible of 
 continuous variation. Each theory, the corpuscular 
 and the undulatory, furnishes elements susceptible of 
 continuous variation. What the element is, on the 
 theory of emission, has not, so far as I know, been 
 specified by the supporters of that theory, and diffi- 
 culties seem to attend whatever supposition in that 
 respect you can make. The theory of undulations 
 presents one, and I may say but one, element which 
 might serve for the purpose, namely, wave length, or 
 what comes to the same thing, periodic time. That 
 in fact periodic time must be the element variations 
 in which correspond to variations in refrangibility, is 
 clearly pointed out by other phenomena which I have 
 not as yet touched upon. But this development of 
 the theory did not take place till the present century, 
 though some of the leading facts on which it is based 
 were known to and studied by Newton. Accordingly 
 from the time of Newton till the end of the last 
 century, and even further, the theory of emission was 
 that chiefly in vogue with scientific men. Various 
 causes probably contributed to this result. The 
 rectilinear propagation of light at first sight looks 
 more like the motion of projectiles than the propa- 
 gation of undulations, which in cases of what are 
 
22 THE NATURE OF LIGHT. 
 
 undoubtedly undulations spread out much after being 
 laterally confined. The impetus given to the study 
 of the motion of particles under the action of known 
 forces by Newton's great discovery of universal gravi- 
 tation, turned the labours of men of science into that 
 channel rather than to a study of the propagation 
 of vibrations. The great weight again of Newton's 
 authority had doubtless its share in leading men to 
 follow the theory as to the nature of light which he 
 had taken up. 
 
 It is probably due to this preponderating influence 
 of the theory of emission that so little notice was 
 taken of the theory of the aberration of light. In the 
 explanation of the phenomenon which is contained in 
 the ordinary text-books of astronomy, which has 
 doubtless descended traditionally from that given in 
 earlier treatises, it is quietly assumed as a matter of 
 course that the rectilinear propagation of the light 
 coming from a heavenly body is not disturbed by the 
 motion of the earth. Did light consist of particles 
 darted forth, there is no reason to suppose that it 
 should ; in fact, to make such a supposition would 
 be to fly in the face of all we know respecting the 
 action of attracting forces, since any motion of the 
 attracting body does not enter into account. But on 
 the theory of undulations it is far otherwise. We 
 should naturally have been disposed to look on the 
 
ABERRATION ON THEORY OF UNDULATIONS. 23 
 
 earth in its motion round the sun as ploughing its 
 way through the ether. Now if light consist of un- 
 dulations propagated through this ether, we might 
 have expected that the ether being pushed by the 
 earth out of its way, the course of the undulations 
 which it carried would be affected, possibly in an 
 irregular way, in case eddies were produced, and at 
 any rate in a manner which there appears no reason 
 a priori should be in conformity with the simple law 
 of aberration. 
 
 Accordingly Dr Young, to whom mainly we owe 
 the revival of the theory of undulations which took 
 place about the beginning of this century, supposed 
 that instead of the earth's pushing the ether out of its 
 way, it allowed it to pass freely through its substance, 
 8000 miles though it be in thickness, far more freely 
 than a grove of trees transmits the wind ; and that in 
 consequence of this perfect freedom of passage, the 
 ether outside the earth's surface was not disturbed by 
 the earth's motion, nor consequently the undulations 
 passing through it. 
 
 Now startling as is this supposition, and contrary 
 to all that we should have anticipated, we cannot say 
 that it must be rejected. For we must remember 
 that we have no direct evidence even of the existence 
 of an ether; it is not directly recognizable by any of 
 our senses ; its properties may be, and doubtless are, 
 
24 THE NATURE OF LIGHT. 
 
 very different from those of ponderable matter, and 
 we must be content to learn them by degrees, as they 
 may be revealed by the study of the phenomena 
 which are referable to actions of the ether. Never- 
 theless we are not absolutely driven to accept Dr 
 Young's hypothesis ; for there is as I have shown 
 another way in which the law of aberration may be 
 obtained; a way which though not free from diffi- 
 culties exempts us from the necessity of supposing 
 that the earth in its motion through the ether allows 
 the ether to 'pass through it with absolute freedom. 
 
 At this point it may be well to pause for a 
 moment and consider the probabilities in favour of 
 the two hypotheses. The existence of rays and 
 shadows seems perfectly simple according to the 
 theory of emissions ; as far as we have gone it pre- 
 sents a serious difficulty on the theory of undulations. 
 The laws of reflection and refraction leave little 
 to choose between the two. In one respect indeed 
 the theory of undulations has the advantage ; for it 
 indicates that there ought to be a partition of the 
 incident light into a portion reflected and a portion 
 refracted, whereas on the other we should rather have 
 expected that the light would have either been re- 
 flected or refracted. This advantage is however of 
 no great weight, for it would not be difficult to frame 
 plausible hypotheses in the theory of emission which 
 
COMPARISON OF THE TWO THEORIES. 25 
 
 would lead to a partition. As regards aberration, the 
 corpuscular theory has a decided advantage, for on 
 it the explanation of the phenomenon is perfectly 
 simple, whereas according to the theory of undula- 
 tions all we can say is that it is not inexplicable. 
 
 The balance on the whole seems to lean towards 
 the side of the corpuscular theory. And yet that 
 theory is now altogether exploded, and the rival 
 theory is established on so firm a basis that no one 
 who has studied the subject can doubt that the second 
 of the two modes of conception with which we started 
 expresses the truth, and that light really consists of a 
 change of state propagated from point to point in a 
 medium existing between the luminous body and that 
 which the light affects. 
 
 It may be said, If the former theory is now r -a-days 
 exploded, why dwell on it at all ? Yet surely the 
 subject is of more than purely historical interest. It 
 teaches lessons for our future guidance in the pursuit 
 of truth. It shows that we are not to expect to 
 evolve the system of nature out of the depths of our 
 inner consciousness, but to follow the painstaking 
 inductive method of studying the phenomena pre- 
 sented to us, and be content gradually to learn new 
 laws and properties of natural objects. It shows that ~ 
 we are not to be disheartened by some preliminary 
 difficulties from giving a patient hearing to a hypo- 
 
26 THE NATURE OF LIGHT. 
 
 thesis of fair promise, assuming of course that those 
 difficulties are not of the nature of contradictions 
 between the results of observation or experiment and 
 conclusions certainly deducible from the hypothesis 
 on trial. It shows that we are not to attach undue 
 importance to great names, but to investigate in an 
 unbiased manner the facts which lie open to our 
 examination. 
 
 I now come to other classes of phenomena with 
 respect to the explanation of which there is the widest 
 possible difference between the two hitherto rival 
 theories respecting the nature of light. We are 
 all familiar with the vivid colours of soap bubbles, 
 colours which are exhibited in the case of transparent 
 solid plates or liquid films which are excessively thin, 
 or of very thin plates of air contained between two 
 surfaces of glass which are in contact, or almost in 
 contact, at one point. It is to Newton that we owe 
 the first investigation of the laws of these " colours of 
 thin plates " as they are called. By placing a convex 
 lens of small curvature in contact with a plane piece 
 of glass, we obtain a separating plate or film of air 
 the thickness of which vanishes at the point of contact, 
 and increases very slowly at first on receding from it. 
 In this case the colours are arranged in circles round 
 the point of contact, the rings forming annuli of 
 increasing diameter but decreasing width as we 
 
COLOURS OF THIN PLATES. 2/ 
 
 recede from the centre outwards. The centre is dark ; 
 and when the incident light is white, on going out- 
 wards about seven alternations can be traced, after 
 which the field is sensibly of uniform illumination 
 and free from colour. The squares of the diameters 
 of the rings are found to increase in arithmetic 
 progression in passing from ring to ring. 
 
 When instead of using white light the system of 
 the rings is illuminated by the colours of a pure 
 spectrum, a vast number of rings is seen ; in fact, they 
 go on till from the increasing narrowness of the annuli 
 they become too fine to be seen. In this case the 
 colour naturally remains the same, being that of the 
 part of the spectrum that is used to illuminate the 
 glasses. The scale of the system changes greatly 
 with the colour, decreasing from the red to the violet. 
 
 The scale of the system depends very greatly 
 upon the curvature of the lens ; and to form the rings 
 on a large scale, which is convenient for examination, 
 it is necessary to use a lens of small curvature. The 
 thickness of the interposed plate of air where any ring 
 is formed can be obtained by an easy calculation 
 from the diameter of the ring and the radius of 
 curvature of the lens, both which can be measured. 
 When this is done it is found that a given ring is 
 always formed where the plate has a given thickness. 
 
 If the interposed medium be water instead of air, 
 
28 THE NATURE OF LIGHT. 
 
 or generally any transparent fluid, the scale of the 
 rings is diminished. It is found that the square of 
 the diameter of a given ring varies inversely as the 
 refractive index of the interposed liquid. 
 
 As my object is not to give a complete account of 
 the phenomena of the rings, much less a complete 
 explanation of the phenomena, I shall dwell no further 
 on the appearances which the rings present under 
 different circumstances, the features I have already de- 
 scribed being sufficient for my purpose, which is to give 
 a fair idea of the evidence on which rests that theory 
 as to the nature of light which we shall be led to adopt. 
 
 Newton endeavoured to account for the various 
 phenomena of thin plates by his celebrated theory of 
 fits of easy reflection and transmission. We have seen 
 that the existence of both reflection and refraction is a 
 difficulty in the theory of emission which has in some 
 way to be accounted for. It will not do to suppose 
 that there are two permanently distinct kinds of light, 
 of which one, when the light falls at a given inclination 
 on a given substance, is always reflected and the other 
 always transmitted, for if either the reflected or the 
 transmitted beam be allowed to fall at the same angle 
 on the same substance, it is divided into a reflected 
 and a transmitted beam. We must therefore suppose, 
 even independently of the phenomena of thin plates, 
 that the same particles of light are sometimes in a 
 
NEWTON'S THEORY OF FITS. 29 
 
 condition to be reflected and sometimes in a condition 
 to be transmitted : and we have only further to postu- 
 late that these changes of state, whatever may be 
 their nature, take place with a regular periodicity in 
 order apparently to account for the phenomena of 
 thin plates, at least if we restrict ourselves to the case 
 of a perpendicular incidence on a plate of given kind, 
 such as a plate of air between two surfaces of glass. 
 For all the light which is transmitted by the first 
 surface must be in a fit of easy transmission which it 
 does not at once lose, so that if it falls immediately on 
 the second surface it is transmitted, and therefore the 
 central spot looks comparatively black. The same 
 must be the case where the distance between the 
 surfaces is equal to the length of a fit, or 2, 3, &c. 
 times the length of a fit; and for intermediate 
 thicknesses of the plate, corresponding to intermediate 
 distances from the point of contact, the effect will be 
 intermediate, and there will be more or less reflection, 
 which will be greatest for thicknesses exactly half 
 way between the critical thicknesses above mentioned. 
 But tempting as this theory at first sight appears, 
 though if it be true it must be left to subsequent 
 research to indicate what that periodic element in 
 relation to the particles of light can possibly be 
 which shows itself by an alternate capacity for 
 reflection and refraction, it fails completely to account 
 
30 THE NATURE OF LIGHT. 
 
 for the other features of the phenomenon, some of 
 which I have mentioned. We should have expected 
 beforehand that the length of a fit would have been 
 independent of the angle of incidence ; and when we 
 learn that to reconcile theory and observation we must 
 suppose it to vary as the secant of the angle of inci- 
 dence, we see no way of accounting for such a law. 
 
 Again, as to the effect of a change of medium, the 
 most natural supposition to make would be that the 
 constant element of periodicity which characterises 
 light of any particular refrangibility is a constant 
 periodic time. Now the explanation of the law of 
 refraction according to the theory of emission requires 
 us to suppose that light travels faster in refracting 
 media than in vacuo, in the ratio of the refractive 
 index to unity. We might have expected accordingly 
 that the length of a fit in water would be greater than 
 in air in that ratio. We have seen however that it is 
 less in the inverse ratio. We are unable to frame any 
 plausible hypothesis, on the theory of emission, why 
 it should be so. 
 
 Accordingly the theory, if such it can be called, 
 consists merely of a set of incoherent laws, not 
 indicated beforehand by theory, not even falling 
 in with it after they have been pointed out by obser- 
 vation, and it has accordingly nothing about it which 
 seems to bear the stamp of truth. 
 
INSUFFICIENCY OF THE THEORY. 31 
 
 Nor is this all. Even as regards the formation of 
 the rings at a perpendicular incidence, where at first 
 sight the theory appears to be most successful, it leads 
 to a conclusion which is belied by observation. Accord- 
 ing to this theory, the office of the first surface of the 
 plate is solely one of sifting, by reflecting back those 
 particles of light which are in a fit of reflection, and 
 thereby preparing the way for the alternate transmis- 
 sion and reflection of the particles at the second 
 surface. There should therefore be as much light 
 reflected at the first surface as if the second glass were 
 away altogether, and therefore the dark rings should 
 be only comparatively dark. The experiment may 
 be easily and successfully tried with homogeneous 
 light, such as that of a spirit-lamp with salt on the 
 wick, and it is found that the dark rings are decidedly 
 darker ; in fact as to sense apparently black. 
 
LECTURE II. 
 
 Interference Explanation of the colours of thin plates 
 afforded by the theory of Undulations Diffraction. 
 
 IN my last lecture I pointed out the insufficiency 
 of the theory of emission to account for the various 
 phenomena of the colours of thin plates. Let us now 
 see whether the theory of undulations lends itself to 
 an explanation. In the first place the element of 
 periodicity, instead of being wholly extraneous to 
 the fundamental idea, and hardly if at all to be re- 
 conciled with it even when suggested by phenomena, 
 is one naturally, almost inevitably, involved in the 
 fundamental conception. I say, almost inevitably; 
 for a set'of undulations might consist of a succession 
 of isolated pulses following one another in a wholly 
 irregular manner ; but the analogy of sound would 
 make it far more likely a priori that they should 
 form a series of regularly periodic disturbances; 
 and the supposition that such is their character 
 therefore harmonizes perfectly with what we should 
 have expected beforehand. 
 
INTERFERENCE. 33 
 
 Supposing then that the undulations we have to 
 deal with are regularly periodic, can we on the undu- 
 latory theory give any account of the alternations of 
 light and darkness which we observe in Newton's rings ? 
 
 The explanation which this theory affords is 
 based on a very simple and very general dynamical 
 principle, of very wide application, called the principle 
 of the superposition of small motions. For the sake 
 of those who may not have much attended to dy- 
 namics, I will endeavour to give some idea of what 
 this principle means. 
 
 Suppose a stone thrown into still water. It pro- 
 duces as we know a series of small waves, which 
 spread out in the form of circles from the place of 
 disturbance. What passes outwards is, not the ma- 
 terial particles of the water, but a certain state of 
 things. If we observe a minute floating body, it is 
 seen to retain its average position, and merely to 
 move very slightly backwards and forwards, up and 
 down. So far, we have merely a visible illustration 
 of the progress of an undulation, differing it is true 
 from those belonging to sound or light in the fact 
 that it is only in the neighbourhood of a particular 
 surface that the disturbance is sensible, which does 
 not however prevent it from forming a useful illustra- 
 tion for those to whom the conception may be new. 
 
 But now instead of a single stone, suppose that 
 S. 3 
 
34 THE NATURE OF LIGHT. 
 
 there are two similar stones thrown in simultaneously 
 at a little distance apart. Each will give rise to a 
 series of circular waves which at first will be distinct, 
 each diverging from its own centre, but not yet 
 having reached one another. But presently the waves 
 from the one centre will invade the region occupied 
 by those from the other. What will then take place ? 
 According to theory, each disturbance will find the 
 mass in which it is being propagated under as nearly 
 as possible the same conditions, so far as itself is 
 concerned, as if the other disturbance did not exist. 
 The consequence is that any particle of the mass will 
 be as much displaced from its mean position as if 
 the other disturbance did not exist, and its actual 
 place will therefore be found by compounding, as it 
 is called, the displacements due to the two dis- 
 turbances taken separately. Accordingly where a 
 ridge due to one of the disturbances coincides in 
 position with a ridge due to the other, we have an 
 elevation of double height, supposing we choose a 
 place where the intensities of the disturbances due to 
 the two sources are the same ; but where a ridge due 
 to one falls in with a trough due to the other, we 
 have neither elevation nor depression, but the water 
 is found at its natural level. 
 
 Now if there be any truth in the theory of undula- 
 tions, something of the same kind must take place 
 
INTERFERENCE. 35 
 
 with light. If we have two sets of disturbances 
 always exactly alike, then when the conditions are 
 such that the two disturbances separately considered 
 take place always in opposite directions, being super- 
 posed they simply produce a disturbance nil, whereas 
 when the directions agree they produce a disturbance 
 of greater amount than either separately. And if 
 light consist of such a disturbance in the ether, then 
 in the former case we ought to have no light, whereas 
 in the latter the light ought to be greater than if the 
 one set of disturbances alone existed. And if the 
 two sets of disturbances, while still in other respects 
 alike, differed in amplitude in a constant ratio, the 
 only difference that would make in the result would 
 be that the light would not vanish at the minima. 
 
 But it must be particularly remarked that in order 
 that this neutralization should always take place in 
 the same way at the same place, it is essential that 
 the two sets of disturbances should always agree as 
 to their times of starting, or differ, if they do differ, 
 by a perfectly constant quantity. For if one were 
 half an undulation ahead of the other, that would 
 make all the difference whether the two disturbances 
 strengthened or neutralized each other : and if the 
 relative times of starting varied irregularly a vast 
 number of times in a second, we should have at a 
 given place neutralization and cooperation succeeding 
 
 32 
 
36 THE NATURE OF LIGHT. 
 
 one another so rapidly that nothing but the meari 
 effect would be perceived, and that, as may be shown, 
 would be simply the sum of the mean effects taken 
 separately. Now if the disturbances came from two 
 independent sources, such as two different portions of 
 a flame, the relative starting points of the two would 
 be purely casual, and no fixed and permanent 
 neutralization would be to be expected. And obser- 
 vation shows that none of those alternations of light 
 and shade which on the theory of undulations we 
 refer to interference are manifested unless the two 
 interfering streams of light have come originally from 
 the same source, having subsequently pursued slightly 
 different paths. 
 
 Let us now see how these principles apply to the 
 explanation of Newton's rings. If we consider a 
 small portion of the thin plate of air by reflection 
 from which they are seen, we perceive that there are 
 two reflecting surfaces near one another, and conse- 
 quently two reflected streams, one reflected from the 
 upper surface of the plate of air, that is, internally in 
 the upper glass, and the other reflected from the 
 under surface of the plate of air. that is, from the 
 upper surface of the under glass. These are it is true 
 accompanied by other streams which have been 
 reflected backwards and forwards internally in the 
 plate, so that the total number of reflections in these 
 
EXPLANATION OF NEWTON S RINGS. 37 
 
 streams is 3, 5, 7, 9...; but these streams, being 
 usually comparatively weak, may in a general ex- 
 planation be left out of consideration. Now the 
 second of these streams has had to travel a very 
 little further than the first. In the simplest case, to 
 which we may confine ourselves for the present, that 
 of a perpendicular incidence, the excess of length of 
 path of the second stream is evidently just double 
 the thickness of the plate of air, and varies accordingly 
 from point to point of the field of view, the thickness 
 increasing slowly at first and afterwards rapidly as 
 we recede from the point where the lenses are in 
 contact. Close to the point of contact, the second 
 stream is only imperceptibly behind the first, and the 
 two might be expected to be in accordance, that is, 
 to agitate the ether in the same direction, and there- 
 fore to strengthen one another. As we take a point 
 further outwards from the point of contact, the retar- 
 dation increases, and when it becomes half the length 
 of a wave the two would be in opposition, that is, one 
 would agitate the ether in a way just opposite to 
 the other, and therefore, supposing the intensities of 
 the two the same, as would nearly if not exactly be 
 the case, they would neutralize each other, and dark- 
 ness would be the result. And as the thickness of 
 the plate of air between the two glasses varies as the 
 square of the distance from the point of contact, the 
 
3$ THE NATURE OF LIGHT. 
 
 law of increase of the rings for any one kind of light 
 as the order of the ring increases follows at once, and 
 moreover the law that under different circumstances 
 as to curvature of the glasses the same ring is always 
 formed where the thickness of the plate is the same. 
 
 But there is one marked point of contrast between 
 the results of theory, so far as I have yet explained it, 
 and observation, namely, that we have been led to 
 expect a maximum of brightness where the paths of 
 the two streams are the same, that is close to the 
 point of contact, or where they differ by one, two, or 
 a complete number of undulations, and a maximum 
 of darkness if not absolute blackness where the 
 difference is an odd number of half undulations. 
 This would give the places of light and shade exactly 
 reversed as compared with observation, which would 
 show one of two things, either that the theory must 
 be rejected, or that some circumstance has been over- 
 looked which, had it been taken into account, would 
 have made the theoretical result right in this respect. 
 
 Now the reflections which the two streams re- 
 spectively undergo take place under very different 
 circumstances. The first stream is reflected internally 
 in glass when the light, which had previously been 
 travelling in the glass of the upper lens, arrives at the 
 under surface of the glass, or upper surface of the 
 interposed plate of air, the second is reflected back 
 
EXPLANATION OF NEWTON'S RINGS. 39 
 
 into air at the upper surface of the under lens. As 
 the two reflections take place under different, in some 
 respects opposite, circumstances, there seems nothing 
 unlikely a priori in the supposition that the signs of 
 the reflected vibration should be opposite in the two 
 cases. Dynamical analogies are not far to seek ; for 
 example, we know that when sound travelling along 
 a pipe meets a closed end, it is reflected in such a 
 manner that condensation in the reflected answers to 
 condensation in the incident, and rarefaction to rare- 
 faction ; but when it is reflected, as reflected it is, 
 from the open end of a tube, rarefaction answers to 
 condensation and condensation to rarefaction. And 
 this theoretical conclusion as to the opposition of 
 signs in the two cases, so probable from analogy, is 
 converted into a certainty by the application of a 
 simple dynamical law of great generality, which may 
 be called the law of reversion. Hence then the 
 occurrence and features of the rings at a perpendicu- 
 lar incidence, for any one kind of light, are on the 
 undulatory theory matters of pure prediction. 
 
 Next consider the effect of inclination. It follows 
 from a very easy calculation that the effect of the 
 thickness of the plate of air at any inclination in 
 producing retardation in the stream reflected from 
 the second surface of the plate, relatively to the 
 stream reflected from the first surface, is the same 
 
40 THE NATURE OF LIGHT. 
 
 as it would be at a perpendicular incidence for a 
 thickness smaller in the proportion of the cosine of 
 the inclination of the light while in the plate of air to 
 unity, or, which is the same thing in the case of a 
 lens with nearly parallel surfaces for the upper glass, 
 of the cosine of the angle of incidence on the first 
 surface to unity. Hence follows at once the simple 
 law of dilatation of the rings on increasing the angle 
 of incidence, namely, that the square of the diameter 
 of any ring varies as the secant of the inclination on 
 the first surface. Of this law, as we have seen, the 
 theory of emissions could give no account. 
 
 Again, the effect of the substitution of water for 
 air between the lenses in causing the rings to con- 
 tract, and the law of their contraction already men- 
 tioned, follow immediately on this theory from first 
 principles, since the explanation of refraction on the 
 theory of undulations necessitates the supposition 
 that light travels more slowly in refracting media 
 than in vacuum, in the proportion of the refractive 
 index to unity. 
 
 In short, the theory completely explains the phe- 
 nomena of the rings seen by reflection. And this is 
 true even as regards the more minute features, into 
 which I have refrained from entering. The New- 
 tonian "fit" at a perpendicular incidence expresses 
 half the length of a wave ; and as the scale of the 
 
EXPLANATION OF THE TRANSMITTED RINGS. 4! 
 
 rings decreases from the red to the blue, and accord- 
 ingly as the refrangibility of the light increases, we 
 learn that the variable element in light which corre- 
 sponds to a change of refrangibility and change of 
 colour must be the wave-length in vacuo, or, what 
 comes to nearly the same if not exactly the same 
 thing, the periodic time. The compound tints of the 
 rings are explained here as in all other optical phe- 
 nomena, whatever theory of light we may adopt, by 
 the superposition of the ring-systems corresponding 
 to the different kinds of light of which white light 
 consists, which are on different scales as to size ; 
 and the fact that not more than about seven rings are 
 seen with white light merely depends on the over- 
 lapping of the rings of high orders corresponding to 
 the different colours. 
 
 I have hitherto said nothing about the system of 
 rings in the transmitted light, which are complemen- 
 tary in character to the rings seen by reflection, but 
 far less vivid, resembling in fact a vivid system com- 
 plementary in character to the reflected system, over- 
 laid by a comparatively large quantity of uniform 
 white light. In nearly every respect the theory of 
 these is analogous to that of the reflected system, so 
 that whatever theory explains the one can hardly fail 
 to explain the other. There is just one feature the 
 explanation of which involves considerations into 
 
42 THE NATURE OF LIGHT. 
 
 which I have not entered, and to this I will confine 
 myself. 
 
 The transmitted system, according to the expla- 
 nation afforded by the theory of undulations, depends 
 on the interference of two streams of light, one 
 passing right through the plate of air comprised 
 between the lenses, and the other following it after 
 two reflections in air at the adjacent surfaces of 
 the glasses. These are associated with other por- 
 tions which have been reflected 4, 6 ... or any even 
 number of times ; but these, being usually compara- 
 tively weak, may in a general explanation be disre- 
 garded. 
 
 Now when light is incident perpendicularly, or 
 nearly so, on the surface of crown glass, about 4 per 
 cent, of the incident light is reflected, and the rest 
 enters the glass. The intensity of light once reflected 
 in this manner being thus only the ^th of the in- 
 tensity of the original, the intensity of light twice 
 reflected will be only the -^th of that, or the ^th of 
 the original. Now as the light which passes through 
 one surface loses only 4 per cent, by reflection, the 
 light which passes through the two surfaces of the 
 plate still retains the 0*96 2 or 0*9216 of its original 
 intensity; so that the twice reflected light has an 
 intensity only the -sf^th of the direct, hardly more 
 than one-sixth per cent. How then, it might be said, 
 
EXPLANATION OF THE TRANSMITTED RINGS. 43 
 
 could so small an addition or subtraction of light be 
 perceptible at all, and so produce in homogeneous 
 light differences of intensity, and with white light 
 changes of colour, which though not it is true by any 
 means so striking as in the reflected system of rings 
 are nevertheless very evident, and demand far greater 
 differences of intensity than that ? 
 
 The explanation of this paradox lies in a con- 
 sideration of the relation between intensity and am- 
 plitude of vibration. If light consists in a disturbance 
 of a subtile medium, or ether, then the greater be 
 the disturbance, other circumstances being the same, 
 the stronger must be the light. But supposing the 
 amplitude of excursion of the ether to be doubled, 
 trebled... is the intensity of the light doubled, trebled 
 ... or if not, in what other proportion is it increased ? 
 
 Now a number of different considerations lead 
 decisively and independently to the same conclusion, 
 namely, that the intensity is to be measured by the 
 square of the amplitude of excursion. Hence if the 
 amplitude of excursion to and fro of the ether is 
 increased in the proportion of I to 2, 3..., the inten- 
 sity of the light is increased in the proportion of I to 
 
 49- 
 
 Suppose now that two disturbances from the same 
 source, and following nearly the same path, have a, b 
 for the coefficients of excursion due to them sepa- 
 
44 THE NATURE OF LIGHT. 
 
 rately; when acting together the coefficients of ex- 
 cursion will fluctuate between the limits a + b and 
 a b according as the phases are in agreement or in 
 opposition. Hence whereas the intensities of the two 
 separately will be in the ratio of a* to # 2 , the maximum 
 and minimum intensities due to the compound dis- 
 turbance will be proportional to (a -f frf and (a bf. 
 
 Suppose now the first disturbance to be very 
 much greater than the second, then a will be very 
 much greater than b. Hence whereas the sum or 
 difference of the intensities of the two streams would 
 be got by adding or subtracting tf to or from # 2 , the 
 maximum and minimum intensities of the compound 
 disturbance will be got very nearly by adding or sub- 
 tracting 2ab, a quantity which is greater than the 
 former in the proportion of 2a to b. Thus with the 
 numerical values just mentioned, which are applicable 
 to Newton's rings at a perpendicular incidence, if we 
 take the coefficient of vibration and the intensity of 
 the stronger stream each for the unit of their respec- 
 tive kinds, the coefficient of vibration of the weaker 
 stream will be -^ and the intensity ^ nearly, where- 
 as the maximum and minimum intensities of the 
 compound stream will be I -^ nearly, and the differ- 
 ence between them will be as great as -^. 
 
 In the particular case of Newton's rings, the 
 weaker stream is not readily viewed apart; but in 
 
DIFFRACTION FRINGES. 45 
 
 certain experiments of diffraction, a subject that 
 will be touched on by and by, the two streams lend 
 themselves readily to separate observation, and the 
 occurrence of distinct fringes of interference theo- 
 retically referable to an invisible agent invisible be- 
 cause too faint to be seen is not a little paradoxical 
 in appearance. 
 
 It appears then that the fundamental hypotheses 
 of the undulatory theory suffice to account in the 
 most complete manner for the phenomena of New- 
 ton's rings, and the colours of thin plates in general, 
 without making any fresh assumption whatsoever. 
 It is to Dr Young that we owe the explanation of 
 these colours on the theory of undulations, an expla- 
 nation given at a time when any other theory than 
 the corpuscular could hardly gain a hearing : and to 
 him also we owe the first direct experiment proving 
 that certain fringes which connect themselves by 
 numerical relations with Newton's rings are incon- 
 testably due to interference. 
 
 As introductory to this experiment, it will be 
 convenient to mention another phenomenon which 
 forces itself upo,n the notice of the observer simulta- 
 neously with that with which we are more immedi- 
 ately concerned, and which therefore it is desirable to 
 be able at once to refer to its proper place, besides 
 that at a more advanced stage of our study of the 
 
46 THE NATURE OF LIGHT. 
 
 subject it will be found to be of very great impor- 
 tance. 
 
 Suppose that the sun's light is reflected hori- 
 zontally into a darkened room, passing through a 
 very small hole in the shutter, or what is more con- 
 venient through a lens of short focus. Let the light 
 be allowed to fall on an opaque screen at the distance 
 say of a few feet from the luminous point, the screen 
 being terminated by a straight edge, suppose vertical. 
 Let the light passing the edge of the first screen be 
 received on a white vertical screen which we may 
 suppose a few feet further off from the luminous 
 point. According to geometrical optics, if we project 
 the edge of the opaque screen on to the receiving 
 screen, by straight lines drawn from the luminous 
 point, all to the illuminated, suppose the right-hand, 
 side of the projection we shall have uniform illumina- 
 tion, the same as if the opaque screen were away, 
 while all to the left of it we shall have darkness. 
 According to observation, there is no such abrupt 
 transition on the receiving screen from uniform dark- 
 ness to uniform brightness. The illumination in- 
 creases continuously, though rapidly. The illumi- 
 nation begins to be sensible before we reach the 
 geometrical shadow, or projection of the straight 
 edge, where it is still considerably feebler than the full 
 illumination at a distance on the right. On going in 
 
DIFFRACTION FRINGES. 47 
 
 a right-hand direction from the geometrical shadow 
 the illumination rapidly increases, and actually be- 
 comes considerably greater than the full illumination 
 at a distance. It then decreases to a minimum, 
 increases to a maximum, and so on, the maxima and 
 minima differing less and less, by excess and defect 
 respectively, from the illumination at a distance, and 
 gradually occurring in more rapid succession, till they 
 become insensible. Three such bands can usually 
 be traced before the illumination becomes sensibly 
 uniform. With white light the scale of the bands, 
 and of their distances from the geometrical shadow, 
 changes as usual from colour to colour, decreasing 
 from the red to the blue. The appearance is the 
 same at all distances of the two screens from the 
 luminous point, the scale, merely, of the system vary- 
 ing according to circumstances, and likewise the 
 smallness demanded in the source of light in order 
 that the bands may not be confused. From the 
 constant character of these bands we readily recognise 
 them in experiments in which they appear associated 
 with other phenomena. 
 
 Suppose now that instead of the opaque screen 
 extending indefinitely on one side, the light is inter- 
 cepted by a narrow slip, a knitting-needle, or any- 
 thing of the kind. The shadow is bounded on both 
 sides externally by fringes of the character of those 
 
48 THE NATURE OF LIGHT, 
 
 just described, and which accordingly we must attrir 
 bute to the same cause, referring the right-hand set 
 to the light which passed to the right of the obstacle, 
 acting independently of that which passed to the left, 
 and similarly as regards the external fringes of the 
 left. But besides these the shadow itself is occupied 
 by another set of coloured fringes, finer usually than 
 the former, and unlike them of equal width through- 
 out. They may be viewed through an eye-lens ; and 
 thereby magnified. If the screen be semi-transparent, 
 we may view them with the lens from behind, and 
 now if we take away the screen altogether, using 
 nothing but the lens, and receiving the light directly 
 into the eye, we see them as before. But now they 
 are much brighter, since the light is no longer scat- 
 tered in all directions by a screen, so that we can 
 afford to use a narrower source of light, suppose a 
 lens of shorter focus in the window ; and having the 
 narrower source we may use a wider opaque slip 
 without the fringes getting confused. Under these 
 circumstances the system of internal fringes occupies 
 only the middle portion of the shadow, being well 
 separated from the external fringes on both sides. 
 The very centre of the shadow is bright for all the 
 colours of the spectrum, and the middle bright band 
 is accordingly white, except just at the edges, where 
 it is slightly reddish, but after that the bands right 
 
DIFFRACTION FRINGES. 49 
 
 and left soon become coloured, on account of the 
 difference of scale for the different colours. 
 
 Now what account can we give of the formation 
 of these internal fringes on the theory of undulations? 
 We have seen that when light passes by an opaque 
 screen, it does not at once become insensible within 
 the limits of the geometrical shadow ; a little light 
 bends round the edge into the darkness, enough to 
 produce a feeble and rapidly decreasing illumination 
 on a screen placed to receive it. This " inflexion " of 
 light is a fact, account for it as we will : and if light 
 consists of undulations, the analogy of those undu- 
 lations which we can directly examine would lead us 
 to infer that light must be inflected into a shadow. 
 Indeed the grand original difficulty which for so long 
 a time prevented the reception of the theory of 
 undulations was that of accounting for the com- 
 parative absence of inflexion ; in other words, for the 
 existence of rays and the sharpness of shadows. 
 Admitting this small inflexion as a fact, we see that 
 at any rate we can not be far wrong in supposing the 
 bending to take place close to the edge of the 
 obstacle. On this supposition, the length of path of 
 the inflected stream in travelling from the luminous 
 point to the point of the field, or focal plane of the 
 eye-lens, where we seek the illumination, will equal 
 the path from the luminous point to the edge of the 
 S. 4 
 
5O THE NATURE OF LIGHT. 
 
 obstacle,///^ the distance from thence to the point in 
 the field. The difference of paths for the two in- 
 flected streams which reach the same point of the 
 field is accordingly easily found, especially as we are 
 only concerned with points lying but a very small 
 distance from the plane passing through the luminous 
 pojnt and the middle of the obstacle, or say the 
 central plane. The difference of path vanishes at the 
 central plane, where accordingly we have a maximum 
 of brightness, and on receding in a lateral direction 
 from the central plane the difference of path changes 
 in proportion to the lateral distance, and accordingly 
 it is equal to I, 2, 3... wave-lengths for a series of 
 equidistant straight lines parallel to that in which the 
 central plane cuts the field. These lines are what 
 ought according to theory to be the middle lines of 
 bright fringes, and lines midway between them ought 
 to be the middle lines of dark bands separating the 
 fringes. The theoretical breadth of a fringe, being 
 sensibly independent of the distance of the luminous 
 point, is connected with the wave-length by a very 
 simple formula, involving only the distance from the 
 opaque slip to the screen on which the light is received 
 and the breadth of the slip, both of which can easily be 
 measured. On the other hand, the fringes are actually 
 seen, and their breadths can be measured. Com- 
 paring the theoretical and observed breadth of a 
 
DIFFRACTION FRINGES. 51 
 
 fringe, we obtain the value of the quantity which if 
 the theory be true expresses the length of a wave. 
 On comparing this with the measure obtained from 
 Newton's rings, we obtain identically the same value 
 within the limits of errors of observation. 
 
 This numerical relation indicates that the alter- 
 nation of light and dark in these two different pheno- 
 mena is referable to a common cause, whatever that 
 may be. Newton endeavoured to explain the rings 
 which go by his name by the theory of fits of easy 
 reflection and transmission. We have seen that this 
 theory failed to account for the dilatation of the rings 
 produced by increasing the angle of incidence, and 
 for their contraction produced by the substitution of 
 water for air as the interposed medium. Still, it gives 
 correctly the law of increase of the radii of the rings 
 at a perpendicular incidence as the order increases, 
 and the law connecting the scale with the curvatures 
 of the lenses. Now confining ourselves to the case of 
 a perpendicular incidence, where the theory of fits is 
 most successful, we may notice one radical difference 
 between the explanations offered by the theory of fits 
 and the theory of undulations. According to the 
 former, the office of the first surface of the thin plate 
 is simply one of sifting, and it is by reflection or non- 
 reflection from the second surface that the rings are 
 formed. According to the theory of undulations on 
 
 42 
 
52 THE NATURE OF LIGHT. 
 
 the other hand, there is no sifting at all : the light 
 reflected from and the light transmitted by the first 
 surface have both one and the other just the same 
 properties as the incident light, and it is by the 
 simultaneous working of the light reflected from the 
 upper and that reflected from the under surface that 
 the alternations of illumination are produced. Now 
 in the experiment of the internal fringes, there is 
 absolutely nothing to sift the light, and yet we get 
 alternations of light and darkness as in Newton's 
 rings, and what is more are conducted to the very 
 same measurable length, clearly representing some- 
 thing inherent in the nature of light, which according 
 to the theory of undulations is simply the length of a 
 wave, the conception of which is radically involved 
 in the fundamental points of the theory. We can 
 hardly refuse to admit that the alternations of light 
 and dark witnessed in these two phenomena are 
 really due to interference; to the simultaneous 
 working of two portions of light. 
 
 This conclusion was converted we may say into a 
 certainty by a celebrated experiment of Dr Young's 
 on the internal fringes. He showed that if a small 
 opaque screen were placed so as to intercept the light 
 going to fall on one side of the narrow slip, or else 
 which had already passed it, in either case the central 
 fringes disappeared as well as the external fringes on 
 
YOUNG'S EXPERIMENT OF INTERFERENCE. 53 
 
 the same side of the slip. And if a plate of glass 
 were substituted for the opaque screen the internal 
 fringes disappeared as before, but now the external 
 fringes were seen on both sides. It is clear therefore 
 that the internal fringes are really due to the joint 
 working of the two portions of light inflected in 
 passing the two edges, while as regards the external, 
 those which appear on the right and left are inde- 
 pendently produced by the light which passes on the 
 right and left respectively of the opaque slip. The 
 disappearance of the internal fringes occasioned by 
 the interposition of a piece of glass on one side only 
 of the opaque slip is explained in the same way as 
 the non-exhibition of Newton's rings, when white 
 light is used, outside a very moderate number sur- 
 rounding the point of contact of the glasses. 
 
 After what precedes, the reality of the interference 
 of light might well be taken as established. It is to 
 be noted however that in the theory of the last 
 experiment we have had to take for granted the in- 
 flexion of light. It is true that the fundamental con- 
 ceptions of the theory of undulations lead us to expect 
 inflexion, the difficulty being rather to explain how there 
 is so little. We have not however as yet seen how 
 the determination of the inflexion is to be brought 
 within the domain of theory, and to that extent we 
 have been working in a field not yet fully explored. 
 
54 THE NATURE OF LIGHT. 
 
 It is to Fresnel that we owe the first experiment of 
 interference in which there is neither a thin plate, the 
 first surface of which might according to Newton's 
 views have exercised a sifting action on the light, nor 
 anything unusual, such for example as inflexion, 
 occurring in the progress of the light, but in which 
 the two portions of light that interfere are simply 
 regularly reflected or refracted as the case may be. 
 
 This object was accomplished by Fresnel in two 
 ways, by reflection and by refraction : by a pair of 
 interference mirrors, and by an interference prism, 
 which is a prism with a very obtuse angle, such as 179. 
 It will be sufficient to mention the former method. 
 
 Let two plane mirrors be procured, such as two 
 pieces of plate glass, blackened on the back, each 
 mirror being bounded by a straight edge. Let them 
 be mounted so that the straight edges are close 
 together, and the planes of the mirrors are nearly but 
 not quite continuations of each other ; the planes of 
 the faces making with each other a very obtuse 
 angle, suppose only a fraction of a degree less than 
 1 80, the concavity being on the side of the reflecting 
 faces. Great care must be taken that neither mirror 
 juts out above the other where they meet along the 
 straight edges, which may be ascertained by passing 
 the finger lightly across the junction. Let the sun's 
 rays be reflected into a darkened room, and brought 
 
INTERFERENCE SHOWN BY TWO MIRRORS. 55 
 
 to a point, or what may be regarded as such, by a lens 
 of short focus. Let the light proceeding from the 
 luminous point be received, say at the distance of a 
 few feet, on the pair of mirrors. According to geo- 
 metrical optics, the light reflected from each mirror 
 will proceed after reflection as if it came from the 
 virtual image of the point in the mirror. If each 
 mirror be projected into space by lines drawn from 
 the virtual image belonging to it, we see that there is 
 a narrow wedge of space within which both reflected 
 streams mix. If the light be received on a screen 
 there will be two illuminated areas corresponding to 
 these two projections respectively, and a narrow more 
 highly illuminated band where the two overlap, cor- 
 responding in fact to a section, by the plane of the 
 screen, of the wedge above spoken of. If this doubly 
 bright portion of the field be more carefully scru- 
 tinized, by removing the screen and receiving the 
 light directly into the eye through an eye-lens, we 
 see the field marked on both sides by the usual 
 external fringes at the boundary of an illuminated 
 field. But besides these we see, running parallel to 
 these along the middle of the field, a set of sharply 
 defined, and commonly much narrower fringes, which 
 as usual are on a different scale for the different 
 colours, coarser for the red, finer for the blue. These 
 are quite different in appearance from the compara- 
 
56 THE NATURE OF LIGHT. 
 
 tively vague external fringes which are seen at both 
 sides of the field. And if any suspicion were enter- 
 tained that after all these sharply defined fringes, said 
 to be due to the interference of two regularly reflected 
 streams, were really connected with the external 
 fringes, their complete independence would be shown 
 by a very simple modification of the experiment. 
 Adjust the mirrors so that one shall jut out a very 
 little above the other towards one end of the line of 
 junction, and the other towards the other, this will be 
 sufficient to make the line of intersection of the planes 
 of the mirrors altogether oblique to the line of junc- 
 tion. The region of space within which the two 
 streams mix remains as before, and the external 
 fringes which bound it on the two sides, but the 
 sharply defined fringes which before ran along the 
 middle of the doubly bright region, being parallel to 
 the line of intersection of the planes of the mirrors, 
 are now altogether oblique to the line of junction, and 
 accordingly inclined at a considerable angle to the 
 external fringes. When the sharply defined fringes 
 begin to run out of the doubly bright portion of the 
 field, they and the external fringes begin to modify 
 one another, but under the conditions which usually 
 prevail, and at any rate are easily obtained, the 
 former pursue for a long way their oblique course 
 quite undisturbed. 
 
INTERFERENCE BELONGS TO LIGHT. 57 
 
 It is proved therefore to absolute demonstration 
 that the property of interference is one essentially 
 belonging to light from its very nature. Two lights 
 of the same kind, that is, of the same refrangibility, 
 from the same source do really strengthen or oppose 
 each other, in the latter case producing darkness if the 
 intensities are equal, according as their lengths of 
 path from the source to where they mix are the same 
 or differ by a multiple of a certain length depending 
 on the nature of the light, or as they differ by an odd 
 multiple of half that constant. And if part of the 
 path lies in some refracting medium, as water, instead 
 of air, it is equivalent, so far as interference is con- 
 cerned, to a path in air greater in the proportion of 
 the refractive index to unity, and which accordingly 
 would take exactly the same time to be travelled over 
 according to the theory of undulations, since according 
 to that theory the velocity of propagation in media is 
 less than in vacuo in the proportion of unity to the 
 refractive index. 
 
 This fundamental constant, which according to 
 the undulatory theory expresses the length of a wave, 
 may be determined more or less accurately by any of 
 the instances of interference above mentioned ; though 
 the progress of our knowledge has furnished us with 
 methods of determining it of still greater exactness. 
 It increases as we have seen, and that considerably, 
 
58 THE NATURE OF LIGHT. 
 
 something like in the proportion of 2 to 3, in 
 passing from the blue to the red. As to its absolute 
 value, it will be sufficient to say that for rays of mean 
 refrangibility we may take it in round numbers at the 
 ^^th part of an inch. 
 
 We have seen with what admirable simplicity the 
 theory of undulations explains the various phenomena, 
 in all their details, which have been mentioned as 
 referable to interference. And yet the grand original 
 difficulty, that of explaining the existence of rays and 
 shadows, has been left untouched, or received at most 
 only a lame explanation. Yet if the theory be true it 
 ought to be capable of accounting for these phenomena 
 as well as for those, in some respects simpler in 
 character, which have been so successfully referred to 
 interference. 
 
 It is remarkable that it was not till the study 
 of the theory of light had made great progress, 
 subsequently to the revival of the undulatory theory 
 about the beginning of the present century, that 
 the elementary phenomena of rays and shadows 
 received their full explanation ; and yet, once that 
 explanation is propounded, it is seen to involve 
 nothing more than the very elements of the theory of 
 undulations ; to be in fact nothing more than might 
 have been foreseen from the beginning had the human 
 race been sufficiently acute. The history of the 
 
RAYS ARE A PHENOMENON OF DIFFRACTION. 59 
 
 explanation compared with our present knowledge 
 affords a remarkable example of the manner in which 
 we start on our course of investigation by mounting 
 on the shoulders of our predecessors ; and so it may 
 very likely be in the future that things that appear to 
 us mysterious, and which we labour hard to explain, 
 will to our successors seem so simple that they will 
 wonder why we did not find them out. 
 
 I have mentioned the external fringes seen on the 
 illuminated side of the geometrical projection of a 
 straight edge bounding an opaque body exposed to 
 light coming from a luminous point, which is taken as 
 the point of projection. This phenomenon is modified 
 in a great variety of ways according to the outline of 
 the opaque body. It may for instance be a screen 
 containing 1 one or more apertures. Suppose the 
 aperture circular. If the circle be moderately large, 
 and the light be received on a screen beyond, we have 
 a circular illuminated patch corresponding nearly with 
 the projection of the hole, which is seen to be fringed 
 within its boundary by fringes resembling the external 
 fringes spoken of just now. If the size of the hole be 
 diminished, or the distance of the receiving screen 
 increased, which produces a similar effect, the fringes 
 invade what had previously been the uniformly 
 illuminated area corresponding to the projection of 
 those portions of the hole which are at a little distance 
 
60 THE NATURE OF LIGHT. 
 
 from its edge ; and after a very curious and complicated 
 set of changes we are ultimately, when the hole is 
 made very small, left with a circular patch of rather 
 weak light on the screen, surrounded by a dark ring, 
 followed by other rings alternately bright and dark, 
 but of rapidly decreasing intensity, till they are lost 
 in the dark shadow of the screen in which the hole is 
 pierced. The central bright patch is much larger 
 than the geometrical projection of the hole. 
 
 The continuity of the phenomenon connects the 
 diffusion of the light which passes through the hole in 
 the last case, and the comparative absence of diffusion 
 in the first case, with the formation of coloured fringes 
 and alternations of intensity about the boundary of 
 shadows in general, and with the external fringes 
 belonging to a straight edge in particular, and makes 
 it probable that if we could explain these last the 
 principles of the explanation would enable us also to 
 explain the existence of rays, at least in so far as rays 
 have a real existence at all. 
 
 Can we then explain the external fringes in the 
 simple case of a straight edge ? Newton made careful 
 observations of the phenomenon ; but guided as he 
 was by ideas belonging to the corpuscular theory of 
 light, he advanced no further towards an explanation 
 than a few vague conjectures. Dr. Young, guided by 
 the theory of undulations, was more successful. He 
 
EXPLANATION OF EXTERNAL FRINGES. 6l 
 
 attributed these fringes to the interference of two 
 portions of light, one coming direct from the luminous 
 point, and one reflected at a grazing incidence at the 
 edge of the opaque screen, losing 'half an undulation 
 at the reflection. This theory explained very well 
 the leading features of the fringes, showing them to 
 be hyperbolic in form, that is to say that a section of 
 the fringes, conceived as existing in space, made by a 
 plane passing through the luminous point and perpen- 
 dicular to the edge, is a system of hyperbolas having 
 for their common transverse axis the line joining the 
 luminous point with the edge, and having small con- 
 jugate axes, differing from one fringe to another of 
 the system. It explained also the decreasing width 
 of the fringes as we recede from the shadow, and their 
 dilatation when the luminous point approaches nearer 
 to the opaque screen from the edge of which they 
 start. It even gives very nearly the breadths of the 
 fringes and their distances from the geometrical 
 shadow. 
 
 Accordingly when Fresnel, many years later, 
 commenced his celebrated researches on diffraction, he 
 in the first instance adopted Young's theory as to the 
 cause of the formation of the external fringes. In the 
 course however of his study he met with phenomena 
 of diffraction which did not fall in with Young's view, 
 and which at last opened his eyes to perceive the 
 
62 THE NATURE OF LIGHT. 
 
 grand principle which underlies the whole. We have 
 seen that Huygens successfully explained the laws of 
 reflection and refraction on the undulatory theory by 
 introducing the principle that each element of the 
 front of a wave may be regarded as the source of an 
 elementary disturbance, and these disturbances must 
 then be joined together. Now we have only to com- 
 bine that principle with this other principle, that in 
 so compounding them we must take due account 
 of their respective phases, in order to account 
 for the whole of the phenomena of diffraction, 
 curious and complicated as they are. In other words, 
 we have only to combine Huygens's principle with the 
 principle of interference. These two principles again 
 are nothing more than special applications of the 
 general dynamical principle of the superposition of 
 small motions ; a principle which lies at the very 
 basis of the theory of undulations, and of which the 
 special applications just mentioned might have been 
 foreseen. 
 
 The application of this principle to special cases, 
 among others to the case of the external fringes, 
 involves calculations of considerable complexity. 
 Fresnel executed these calculations for the external 
 fringes, and also made a series of most careful and 
 accurate measurements of the positions of the fringes 
 referred to the geometrical shadow under a variety of 
 
EXPLANATION OF EXTERNAL FRINGES. 63 
 
 circumstances. The theoretical distances of the 
 several fringes from the geometrical shadow were a 
 matter of pure prediction ; for the only unknown 
 quantity involved in the theoretical expression, the 
 length of a wave, had been determined by Fresnel by 
 independent methods, some of them, as for example 
 that depending on the measurement of the fringes 
 produced by interference mirrors, not involving 
 diffraction at all, so that not a single arbitrary 
 constant was left, to be determined by some one 
 measurement of a fringe in some one particular case, 
 whereby an at least partial accordance between theory 
 and observation might have been brought about. 
 On the other hand the distances of the fringes from 
 the geometrical shadow in a variety of cases were 
 most carefully measured micrometrically, and the 
 comparison of the calculated and observed places 
 manifested a truly wonderful accordance, the average 
 error being only about the -gwo tn P art f an inch. 
 
 The distances calculated from the imperfect theory 
 of Dr. Young agreed nearly, but not exactly, with 
 those deduced from the complete theory of Fresnel : in 
 spite of the smallness of the difference, the measure- 
 ments were sufficient to discriminate between the two, 
 and the result was decisively in favour of the complete 
 theory as given by Fresnel. 
 
 As the geometrical shadow is not, like the fringes, 
 
64 THE NATURE OF LIGHT. 
 
 a visible object, it may not be superfluous to mention 
 briefly the mode of referring the places of the fringes 
 to the geometrical shadow. The fringes were formed 
 by the cheeks of an aperture with parallel edges, one 
 of which was moveable by a micrometer screw, by 
 which means the breadth of the aperture could be 
 very accurately measured. The cheeks were set a 
 sufficient distance apart to prevent the fringes formed 
 by the one affecting in any sensible way those formed 
 by the other. We thence get from similar triangles, 
 by the rule of three, the distance apart of the geo- 
 metrical shadows at the focal plane of the eye-lens. 
 Now the distance of any particular fringe, say the 
 first dark fringe, on the right from the same fringe on 
 the left can be measured by a micrometer moveable in 
 the focal plane of the eye-lens. Half the excess of 
 distance between the geometrical shadows in the 
 focal plane over this gives the distance of the first 
 minimum from the geometrical shadow. 
 
 The phenomena of diffraction may be varied in- 
 definitely by varying the outline of the opaque body, 
 or aperture or apertures pierced in an opaque screen, 
 as well as the two distances concerned ; and there is a 
 large class of interesting appearances which may be 
 seen by using a telescope with which a luminous point 
 is viewed in focus, and covering the object-glass with 
 a screen containing one or more apertures of any form 
 
EXPLANATION OF RAYS. 6$ 
 
 that may be chosen. In this case especially most 
 curious and beautiful coloured patterns are produced, 
 so strange and complicated that a person looking at 
 them for the first time could never guess from the 
 pattern what was the form of the aperture which 
 produced it. 
 
 Besides the case of the internal fringes which was 
 so carefully examined by Fresnel, a number of other 
 instances in both classes, that is, without and with a 
 lens or object-glass combined with the diffracting 
 body, have been investigated theoretically, and the 
 results compared with observation. The accordance 
 is found to be absolutely complete even in the most 
 minute particulars. 
 
 And now at last, as part and parcel of the com- 
 plete theory of diffraction, we are able to explain the 
 existence of rays; to show why it is that it is so 
 nearly true that light proceeds in a straight course 
 past bodies and through apertures. 
 
 The explanation may be given without entering 
 into mathematical details. Suppose light coming 
 from a luminous point which for simplicity's sake we 
 may suppose to be at a practically infinite distance, an 
 element of the sun's disk for example. Let it fall on 
 a screen in which is a moderately small aperture, and 
 consider the disturbance produced beyond the screen 
 at a point, P, well outside the projection of the 
 S. 5 
 
66 THE NATURE OF LIGHT. 
 
 aperture. Make P the centre of a set of concentric 
 spheres with radii increasing by half the length of a 
 wave. These will cut the plane of the aperture in a 
 series of circular arcs, very close to one another in 
 consequence of the extreme smallness of the wave 
 length, and comprising between any two consecutive 
 circles narrow slips of the aperture, such that two 
 adjacent slips are very nearly equal in area. Now we 
 have a right to regard each element of each slip as 
 the source of an elementary disturbance, which reaches 
 P after the lapse of a time proportional to its distance 
 from P. Since corresponding points in consecutive 
 slips differ by half a wave's length in their dist^hce 
 from P, and the elementary disturbances from them 
 accordingly always reach P in opposite phases, so as 
 to neutralize each other, we easily see that the total 
 effect of one slip is very nearly indeed neutralized by 
 that of its neighbour. This is still more nearly true 
 if we take the disturbance produced by one slip and 
 the mean of those produced by its two neighbours ; 
 and in this way, by taking each alternate slip and the 
 mean of its two neighbours, each slip gets counted 
 once, and once only, except at the two ends, where, 
 however, the length of the slips dwindles away to 
 nothing. Hence there is no sensible disturbance, and 
 therefore no sensible light, for a point P situated as 
 we have supposed. 
 
EXPLANATION OF RAYS. 67 
 
 If now we take a point P situated well inside the 
 projection of the boundary of the aperture, it may be 
 shown by similar reasoning that the disturbance, and 
 therefore the illumination, is sensibly the same as if 
 the screen in which the aperture is pierced were away. 
 
 This conclusion rests, it will be seen, on the ex- 
 treme smallness of the length of a wave, in con- 
 sequence of which an aperture, unless extremely 
 small, is cut a great number of times by a series of 
 concentric spheres with radii increasing by half a 
 wave's length. There is no difference of explanation 
 as regards light and as regards sound, save what de- 
 pends on the difference of scale entailed by the 
 difference of wave length. Take as regards light the 
 case of a small circular hole say the tenth of an inch 
 in diameter, and of distances from the luminous point 
 to the screen in which the hole is pierced, and from 
 that again to the screen on which the light is re- 
 ceived, of say 8 feet 4 inches, or 100 inches, each. In 
 this case, regarding the luminous patch on the screen 
 as a whole, there would be no great diffusion of 
 light, but the phenomena of diffraction would never- 
 theless be fairly pronounced. There ought to be a 
 corresponding case of diffraction for sound ; but on 
 what scale ? Take 50 inches as the length of a wave 
 of sound, which would correspond to a musical note 
 of moderate pitch. Taking as before the 
 
 52 
 
68 THE NATURE OF LIGHT. 
 
 part of an inch as the wave length for light, the 
 length of the wave of sound will be two and a half 
 million times as great as the wave length of light. 
 Consequently to obtain the corresponding case of 
 diffraction for sound, our " small " circular hole would 
 be obliged to have a diameter of rather more than 
 4 miles, say 4 miles, and the distances from the source 
 of sound to the hole through which it passes, and 
 from that again to the place where the sound is 
 listened to, would have to be 4000 miles each. 
 
 It is remarkable that the existence of rays, which 
 formed the great stumbling-block in the way of the 
 early reception of the theory of undulations, is now 
 shown to belong to a class of phenomena, those of 
 diffraction, the complete and marvellously simple 
 explanation of which afforded by the theory of undu- 
 lations now forms one of the great strongholds of that 
 theory. 
 
 Before leaving this subject I will briefly mention 
 two or three instances of diffraction which from their 
 paradoxical character or their importance are de- 
 serving of notice. 
 
 Reverting to the case in which light from a 
 luminous point passes through a circular aperture, and 
 is received on a screen beyond, consider the brightness 
 at a point just in the axis on the receiving screen. 
 If the relation between the two distances already so 
 
SPECIAL INSTANCES OF DIFFRACTION. 69 
 
 often mentioned and the diameter of the hole be such 
 that the sum of the distances from the luminous point 
 to the edge of the hole and from thence to the central 
 point on the receiving screen exceeds the direct 
 distance from the luminous point to the latter by just 
 half a wave's length, theory shows that the illumina- 
 tion is actually four times as great as if the screen in 
 which the hole is pierced were taken away altogether. 
 Suppose now the hole be enlarged. We might have 
 said at first sight, supposing we were ignorant of the 
 theory, " Of course that must increase the illumination 
 at the central point, or at any rate cannot diminish 
 it." On the contrary it does diminish it ; and if the 
 hole be enlarged till its area is just double what it 
 was in the first instance, the centre of the illuminated 
 space on the screen is a black spot. This theoretical 
 result is easily realized in experiment ; only as the 
 wave length varies from colour to colour, and the 
 proper distance of the receiving screen varies with 
 the wave length, when the screen is in adjustment for 
 the brightest part of the spectrum it is not quite in 
 adjustment for the fainter ends, so that the spot 
 instead of being perfectly black is faintly purple. 
 
 Again, suppose a circular disk is exposed to 
 radiation from a luminous point, and the shadow is 
 received on a screen at some distance, or rather 
 viewed directly through an eye-lens. According to 
 
70 THE NATURE OF LIGHT. 
 
 theory, the very centre of the shadow will be a bright 
 point, as bright as if the disk were away. This 
 strange result, again, can easily be verified experi- 
 mentally, easily at least if we are not too ambitious 
 as to the size of the disk ; for the delicacy of the 
 experiment increases with the size of the disk, and at 
 the same time the total quantity of light that we 
 have to work with decreases. In repeating the ex- 
 periment I have seen without difficulty the central 
 spot, with the system of rings round it well formed, 
 in the centre of the shadow of a disk of about the 
 size of a sovereign. 
 
 Among the class of diffraction phenomena in 
 which a luminous point or line is viewed in focus 
 through a telescope, and a screen with one or more 
 apertures is placed in front of the object-glass, there 
 is one case of very special interest. It is that in 
 which a line of light is used, suppose an extremely 
 narrow slit through which the sun's light is reflected 
 horizontally, and a fine carefully ruled grating is 
 placed opposite to the object-glass, the lines of the 
 grating being parallel to the slit. The best results 
 are obtained with gratings consisting of glass, or 
 sometimes metal, on which fine parallel lines are 
 ruled with a diamond point. It is requisite that the 
 lines should be very accurately equidistant, and in 
 fine gratings they are so close that several thousand 
 
SPECTRA WITH A GRATING. 71 
 
 go to an inch. If the grating thus constructed be 
 of metal, it can only of course be used for reflec- 
 tion. 
 
 Now on viewing through the telescope the light 
 transmitted through or reflected from such a grating, 
 a most remarkable appearance is presented. The 
 luminous line is seen through or by reflection from 
 the grating as if the ruled lines were away, and right 
 and left of it for some way the field is dark. But 
 then on both sides we get pure spectra, the blue ends 
 being nearest to the axis. These are followed by a 
 second set of spectra, the blue ends of which overlap 
 the red ends of the former, and so on, the spectra as 
 we proceed overlapping one another more and more. 
 So pure are these spectra if the grating be a good one, 
 that they show the fixed lines of Fraunhofer to per- 
 fection. 
 
 The formation of these pure spectra can easily be 
 explained, and the formula expressing the deviation 
 for light of any one kind in the spectrum of any 
 order in terms of the interval of the grating, the 
 angle of incidence, and the wave length for that kind 
 of light obtained, from the general principles of the 
 theory of undulations. But by mounting the grating 
 in the axis of a horizontal graduated circle which 
 carries the telescope, the deviations can be measured 
 with extreme precision. The interval of the grating 
 
72 THE NATURE OF LIGHT. 
 
 is got by measuring the breadth of the ruled space, 
 and dividing by the number of ruled lines less one. 
 We thus have the means of determining the wave 
 lengths, if the theory be true, for as many definite 
 kinds of light marked by definite lines as we please; 
 and by comparing the wave lengths measured by 
 means of spectra of different orders, at different 
 inclinations of the incident light to the grating, and 
 by different gratings, we have a very sharp test of the 
 truth of the formula deduced from theory. The 
 accordance is complete ; and that being so we are 
 justified in the interpretation assigned to that measur- 
 able quantity which we call a wave's length, and 
 obtain its value with great precision. 
 
 I may here perhaps mention that it has even been 
 proposed to take the length of a wave of light of some 
 particular kind, such for example as that belonging to 
 one component of the double yellow line of a soda 
 flame, as a natural standard to which a national 
 standard of length might be referred in case of loss. 
 The French refer their metre to the dimensions of 
 the earth. The English refer their yard to the 
 length of the seconds' pendulum. But supposing 
 the earth to be slowly contracting by cooling, both 
 these natural standards would be liable to be affected 
 in the course of ages ; and if such a catastrophe were 
 to occur as the impact on the earth of some great 
 
ACCURATE MEASUREMENT OF WAVE LENGTH. 73 
 
 globe visiting our solar system, the dimensions of the 
 earth and the value of gravity, and accordingly the 
 length of the seconds' pendulum, would at once be 
 affected to an unknown degree. But the wave length 
 of light of a given kind would remain unchanged, 
 and the survivors of such a catastrophe might have 
 recourse to it to recover the ancient standard of 
 length. 
 
LECTURE III. 
 
 Closer examination of the fundamental suppositions of the 
 Theory of Undulations Survey of the conclusions ar- 
 rived at by a study of the phenomena of common light 
 Elementary facts of double refraction and polarization. 
 
 IT has been my aim in these lectures to endeavour 
 to give you some definite idea of the evidence on the 
 strength of which we assert that light consists in un- 
 dulations propagated in a medium filling the inter- 
 stellar spaces. To enable you to judge more fairly of 
 the evidence, I have attempted to present the subject 
 in an inductive rather than in a deductive form. Instead 
 of starting with a number of hypotheses, originating 
 you would not know how, and then showing how the 
 conclusions following from them are in accordance with 
 observed results, I have commenced with only the 
 most fundamental conceptions of undulations, and of 
 the conditions which we must suppose to obtain in 
 order that they may exist, and have afterwards supple- 
 mented our original rather crude conceptions in the 
 manner which a study of the phenomena showed to 
 
CLOSER EXAMINATION OF HYPOTHESES. 75 
 
 be necessary. We have seen that not merely are the 
 laws of reflection and refraction in agreement with 
 the theory, but the curious and complicated phe- 
 nomena of interference and diffraction are explained 
 by it to the minutest particular. What strikes one 
 most about the theory is what has been truly de- 
 scribed as its astounding simplicity. This so carries 
 on the face of it the stamp of truth, that to one who 
 is familiar with the phenomena as well as the theory, 
 an overwhelming conviction is produced that it is 
 indeed true to nature. That being the case, it may 
 be well now to examine the various hypotheses 
 which must be made in some greater detail than 
 has hitherto been done. 
 
 The fundamental hypothesis of the existence of a 
 medium to which we give the name of ether, I have 
 already mentioned. To account for undulations in this 
 medium, we must attach to it the two radical con- 
 ceptions of inertia and elasticity. First, a finite time 
 must be required in order to generate in a finite 
 portion of it a finite velocity by the action of a finite 
 force. Secondly, a change of condition of some kind 
 in the ether consequent on a relative displacement of 
 its parts must call into play a force of restitution 
 tending to restore it to its primitive condition. Thus 
 in air condensations and rarefactions produce re- 
 spectively an increase and a diminution of pressure, 
 
76 THE NATURE OF LIGHT. 
 
 so that any small portion of the air which has been 
 contracted or expanded tends to push out the sur- 
 rounding parts, or to be compressed by them, and so 
 to return to its primitive state ; and it is to the forces 
 of restitution thus called into play that the propaga- 
 tion of sound is due. Naturally therefore those who 
 adopted the undulatory theory of light were led to 
 imagine the ether as possessing a similar kind of 
 elasticity. There is however a whole class of phe- 
 nomena which I have not yet so much as named, and 
 which have no counterpart in sound, the study of 
 which has led us to conclude that the elasticity of 
 the ether is of an altogether different nature from 
 that of air. The question of the relation between the 
 direction of vibration of the particles of ether and the 
 direction of propagation of the light is bound up 
 with that of the character of the elasticity by virtue 
 of which the undulations are propagated. In the 
 explanation, however, of the ordinary phenomena of 
 interference and diffraction, we are not concerned 
 with the direction of vibration ; in interference for 
 instance, where we always have two streams of light 
 from the same source pursuing nearly the same paths, 
 and coming together either in the same direction, or 
 in directions very slightly inclined to each other, 
 whatever be the direction of vibration in one of the 
 interfering streams, the same, or very nearly indeed 
 
CLOSER EXAMINATION OF HYPOTHESES. 77 
 
 the same, will be the direction in the other, and that 
 is all that we are concerned with in the explanation. 
 And the explanation of the ordinary phenomena of 
 diffraction has, as we have seen, been resolved into 
 the interference, not of two, but of an infinite number 
 of infinitely small disturbances all coming originally 
 from the same source, and following very nearly the 
 same paths. 
 
 The mode of excitement of the undulations in the 
 first instance is in some respects analogous to the 
 mode of excitement of sound by a vibrating body, 
 such as a bell, but in some respects distinctly different. 
 A bell in exciting vibrations in the surrounding air 
 acts as a continuous elastic body ; in explaining the 
 mechanical action, we have nothing to do with 
 speculations as to the molecular constitution of 
 ponderable matter. But the fact that the spectra of 
 flames show bright lines depending on the nature of 
 the chemical substances in the flame, shows that in 
 the excitement of the ethereal vibrations we have in 
 many cases, if not in all, to do with the vibrations of 
 the constituent parts of the chemical molecules of 
 which we have reason to believe that ponderable 
 matter consists. 
 
 The explanation of refraction on the theory of 
 undulations requires us to suppose that in refracting 
 media, such as glass or water, the vibrations are 
 
78 THE NATURE OF LIGHT. 
 
 propagated more slowly than in what we call vacuum. 
 In fact, theory shows that the sine of the angle of 
 incidence must be to the sine of the angle of refrac- 
 tion in the ratio of the velocity of propagation in 
 vacuo to the velocity of propagation in the medium. 
 The question then arises, When light passes through 
 water or air, what is the vibrating medium ? 
 
 At first sight we might say, of course the water or 
 the glass itself. But this supposition will not bear 
 examination. We know too much of the elasticity of 
 water and glass to allow us to explain the result in 
 that way. Water is sometimes spoken of as incom- 
 pressible, but we know that it yields slightly to a 
 compressive force. The amount of compressibility 
 can be measured by hydrostatic means, and from 
 thence the velocity of propagation of sound in water 
 can be determined by calculation. It comes out 
 about four times as great as that of sound in air, 
 which agrees very well with the experimental measure- 
 ment of the velocity which has been made in the Lake 
 of Geneva. 
 
 Glass, and isotropic elastic solids in general, 
 possess two distinct kinds of elasticity, one, by which 
 they resist compression of volume, the other, by 
 which they resist a distortion not involving alteration 
 of volume, but opposed by the force by which the 
 substance resists the gliding of one part over another, 
 
CLOSER EXAMINATION OF HYPOTHESES. 79 
 
 a gliding which takes place freely in liquids. The 
 two elastic constants of glass have been carefully 
 determined, and from them can be calculated the two 
 velocities of propagation of two kinds of disturbance 
 which a large mass of glass would be capable of 
 transmitting. These come out greater no doubt than, 
 but still comparable with, the velocity of propagation 
 of sound in air, and are therefore almost immeasurably 
 smaller than the velocity required to account for the 
 refraction of light on the supposition that it is the 
 glass itself that vibrates. In fact, the velocity of 
 light in vacuum is nearly 1,000,000 times as great as 
 that of sound in air, and the velocity of light in 
 glass would be equal to its velocity in air divided by 
 the index of refraction of glass, or say about 600,000 
 times that of sound in air, so that it is altogether of a 
 different order of magnitude. 
 
 Again, consider a gas or mixture of gases, such as 
 air, in its relation to Light. Air can be rarefied till 
 we have a near approach to an interstellar vacuum, or 
 again can be condensed till its density becomes 
 comparable with that of a liquid. Yet all through 
 these changes there is a perfectly continuous change 
 in its relations to light. It will not do therefore to 
 say that light is propagated through air in one way, 
 by one sort of mechanism, when the air is very rare, 
 and by another when the air is very dense. But 
 
80 THE NATURE OF LIGHT. 
 
 when air is rare, and makes a near approach to what 
 we call vacuum, but which we must now conceive as 
 space filled with the luminiferous ether, it is clear that 
 it must be by the vibration of the ether that light is 
 propagated in it. We are led therefore to conclude, 
 from these considerations again, that when light is 
 propagated in a gas condensed till its density becomes 
 comparable with that of a liquid, and accordingly 
 in liquids also, and in solids like glass, which 
 behave with respect to light just as liquids, it is 
 ether existing in the interstices between the molecules 
 of the bodies, of which the vibrations constitute the 
 light that passes through them. 
 
 We might not perhaps have been disposed in the 
 first instance to suppose that such a solid material 
 as glass really had ether pervading it. But we must 
 beware of applying to the. mysterious ether the gross 
 notions which we get from the study of ppnderable 
 matter. The ether is a substance, if substance it may 
 be called, respecting the very existence of which our 
 senses give us no direct information : it is only 
 through the intellect, by studying the phenomena 
 which nature presents to us, and finding with what 
 admirable simplicity those of light are explained by 
 the supposition of the existence of an ether, that we 
 become convinced that there is such a thing. We 
 know that a magnet attracts iron through a piece of 
 
CLOSER EXAMINATION OF HYPOTHESES. 8 1 
 
 glass ; and yet the magnetic influence is one which we 
 can neither see nor feel : why then should not ether 
 exist within glass, and be capable of vibrating within it? 
 
 It may readily be imagined, as more probable 
 than the contrary, that the presence of the ponderable 
 molecules interspersed through the ether, within the 
 region of space which is enclosed by the surface of 
 the glass, may have the effect of altering the velocity 
 of propagation of the ethereal vibrations within it, and 
 very probably diminish it. But what may be the 
 precise mechanism by which this result is brought about 
 we do not know. It is easy to frame plausible hypothe- 
 ses which would account for the result, but it is quite 
 another matter to establish a theory which will admit 
 of, and which will sustain, cross-questioning in such a 
 variety of ways that we become convinced of its truth. 
 
 It follows from Huygens's explanation of the law of 
 refraction, which assumes nothing but what lies at the 
 very foundation of the theory of undulations, that the 
 ratio of the velocity of propagation of light in vacuo 
 to its velocity in a medium, such as glass or water, 
 must be equal to the index of refraction, and must 
 therefore vary from one colour to another, increasing 
 from the red to the violet, sometimes, as in the case of 
 oil of cassia, as much as 6 per cent, and upwards 
 within the limits of the visible spectrum. Now we 
 know that in sound notes of different pitch are propa- 
 S. 6 
 
82 THE NATURE OF LIGHT. 
 
 gated with the same velocity, as also follows from 
 theory, and it has been suggested that it is a difficulty 
 in the way of the theory of undulations that the case 
 must be so different with light. I cannot say that it 
 appears as such to my own mind ; for the case of the 
 vibration of one of two mutually penetrating media, as 
 for example glass and the ether, is so different from 
 any that we have to deal with in the case of sound 
 that we cannot argue from the one phenomenon to the 
 other. If indeed it were established that the velocity 
 of light in a vacuum differs from one colour to another, 
 we should then have to allow that an analogy which 
 might have been expected to hold good between the 
 two phenomena does not really do so. But till very 
 lately the observed phenomena which reveal a finite 
 velocity of light, and the experiments which had been 
 made to determine the velocity directly, all yielded a 
 negative result as to any difference of velocity between 
 one colour and another, so that the difference in the 
 ratio above-mentioned was attributable to a difference 
 of velocity in the refracting medium. I have said 
 " till lately," because in a paper by the late Dr James 
 Young and Professor George Forbes, presented to the 
 Royal Society between two and three years ago, and 
 printed in the Philosophical Transactions, in which 
 the authors have determined experimentally the ve- 
 locity of light by a method founded on that of Fizeau, 
 
CLOSER EXAMINATION OF HYPOTHESES. 83 
 
 but presenting certain new features, it is mentioned as 
 a result of the observations that blue light seemed to 
 travel faster in air than red light. The method 
 employed is founded on the judgment of the observer 
 as to the equality of intensity of two points of light, or 
 artificial stars, seen simultaneously in the field of view. 
 It is difficult to see any possible source of instrumental 
 error which could have led to the above conclusion as 
 to a variation of velocity depending on the colour : on 
 the other hand, the conclusion rests on the judgment 
 of the eye of a single observer ; and till the question 
 has been further tested it would seem to be premature 
 to regard the difference as established. Should it be 
 confirmed by further observation, it will then be 
 necessary to consider whether the circumstance that 
 the light was propagated in a field of magnetic force, 
 namely the earth's magnetic force, may have had some- 
 thing to do with it. However even if the result of 
 further enquiry should be to show that the different 
 colours are propagated at different rates in a simple 
 vacuum free from disturbing influences, all we should 
 be entitled to say is that the expectation which we were 
 led to form beforehand from the analogy of sound, 
 and from the supposition that the forces whereby one 
 portion of ether acts directly on another are insensible 
 at finite distances, at distances even comparable with 
 tne sooooth part of an inch, has not been verified. 
 
 62 
 
84 THE NATURE OF LIGHT. 
 
 As regards the mode of perception, while there 
 are analogies between sound and light there are at 
 the same time notable differences. In sound, the tym- 
 panum of the ear is thrown mechanically into vibration, 
 and the nerves of hearing are mechanically affected, as 
 a mechanical disturbance of a point on the surface of 
 the body is made known by the sense of touch. But 
 in light, just as we have seen reason to believe that it 
 is the disturbance of the ultimate molecules, or of their 
 constituent parts, by which the vibratory motion which 
 constitutes light is in the first instance communicated 
 from ponderable matter to the ether, so we have reason 
 to think that when light is absorbed what takes place is 
 that the disturbance of the ether is communicated, not 
 to portions of matter regarded as forming portions of a 
 continuous elastic body, but to the ultimate molecules 
 of which matter consists, or to their constituent parts. 
 It may be that temporary chemical changes are 
 thereby produced in the ultimate filaments of the 
 nerves of the retina, in which case the sense of sight 
 would be more analogous to the sense of taste than to 
 that of touch. 
 
 Corresponding theoretically to this difference is 
 the fact that in light we have absolutely nothing 
 answering to the sensation of harmony in sound. 
 When two musical notes have their times of vibration 
 in some simple ratio, we have concord when they are 
 
STRIKING CHARACTER OF CONCLUSIONS. 85 
 
 sounded together; thus the ratio of 2 to 3 gives 
 a fifth, that of 4 to 5 a major third &c., whereas 
 when two notes sounded together have their times of 
 vibration in no simple ratio, we have discord. But 
 when two kinds of light, each of definite refrangibility, 
 and accordingly of definite periodic time, are mixed 
 together, there is no pleasing or disagreeable sensation 
 depending on whether the periodic times are in some 
 simple proportion or not. 
 
 And now before passing on to a totally different 
 branch of the subject, the study of which leads us to 
 believe that the properties of this mysterious ether 
 must be very different from what we should have 
 imagined beforehand, it may be well to pause and 
 contemplate for a little the wonders with which our 
 study of the phenomena up to the present point has 
 shown that we are surrounded. 
 
 First, we learn to regard the interplanetary and 
 interstellar spaces as no mere void, or empty space 
 passed through by swift messengers in the shape of 
 particles of light conveying information from distant 
 worlds, but as filled with an ever present, all pervading 
 substance, in which the ultimate particles of ponderable 
 matter, including those of our own bodies, are con- 
 tinually as it were bathed, and yet of which our senses 
 give us no direct cognizance. 
 
 Secondly, that whatever other important offices 
 
86 THE NATURE OF LIGHT. 
 
 this ether may fulfil, this one at any rate belongs to it, 
 that it forms the medium of visual communication 
 between ourselves and our fellow creatures, between 
 ourselves and the various objects around us, between 
 ourselves and distant worlds. 
 
 Thirdly, that this communication is carried on by 
 tremors of some kind propagated through the ether 
 with a velocity so enormous that for all practical 
 purposes of communication oil earth it maybe deemed 
 instantaneous. In fact, light would travel about 
 seven and a half times round the whole earth in one 
 second. But so rapid are these tremors that many 
 hundredsof millionsof millionstake place in one second. 
 Notwithstanding therefore the enormous rate of pro- 
 pagation, the lengths of the waves are excessively 
 small, ranging about the 50 ^ OQ th part of an inch. 
 
 It has been shown that it is this excessive small- 
 ness of wave lerigf h which enables light to be propa- 
 gated so nearly in' a straight course, in independent 
 rays. Were it not for this, the formation of sharp 
 images would be impossible. Were the lengths of 
 the waves of light comparable with the lengths of the 
 waves of sound, we should as regards the use of our 
 eyes be nearly in the condition of a man who was all 
 but blind ; who could just distinguish light from 
 darkness, or a gleam of red from a gleam of green, 
 and no more. We should be in this condition if the 
 
STRIKING CHARACTER OF CONCLUSIONS. 8/ 
 
 time of a vibration were anything like so great as the 
 one hundred millionth part of a second, in which case 
 the length of a wave of light would be comparable 
 with that of a wave of sound. 
 
 Fourthly, we learn that notwithstanding the 
 almost inconceivable shortness of the time of vibra- 
 tion, a variation in this periodic time is nevertheless 
 recognisable by our senses, and that it is to this cause 
 it is due that the face of nature does not present 
 to us simply light and shade, like a photograph, but 
 that we have that endless variety of colour which we 
 enjoy. 
 
 Fifthly, in the plan of an elastic medium con- 
 veying small vibrations, we have a mechanism of the 
 simplest possible kind having for result that rays of 
 light from objects all around cross each other's paths 
 in all sorts of ways without any mutual disturbance. 
 
 When we survey a varied landscape, each visible 
 point in it,however minute, may be regarded as an inde- . 
 pendent source of light, from which the light proceeds 
 in all directions. True, the objects are not in general 
 self-luminous ; they are seen by the light of the sun or 
 of the clouds which they irregularly reflect, but as 
 regards the behaviour of the pencils which proceed 
 from them they are as good as self-luminous. Well 
 then ; from each visible point, however minute, there 
 enters the eye every second a. length of light of 
 
88 THE NATURE OF LIGHT. 
 
 about 186,000 miles, that is, light which would have 
 travelled that distance had not the eye been there to 
 catch it, this immense length being filled with undu- 
 lations of lengths ranging about 50,000 to the inch. 
 And if the landscape be contemplated by a multitude 
 of persons, from each visible point in it that vast 
 length of light, consisting of undulations of such 
 excessive minuteness, enters the eye of each spec- 
 tator every second of time ; and all these various 
 streams of light, proceeding in all sorts of directions, 
 cross each other's paths in all sorts of ways without 
 the slightest mutual disturbance. 
 
 To one previously unacquainted with the subject, 
 these statements seem like the dreams of an enthu- 
 siast, or at best the speculations of some wild theorist, 
 and yet there is nothing in what I have stated 
 beyond the sober conclusions of scientific investiga- 
 tion, conclusions supported by an amount of evidence 
 altogether overwhelming. In saying this it is to be 
 remembered that the precise mode of disturbance of 
 the ether has been left an open question. 
 
 In studying this subject, one can hardly fail to be 
 struck with the combination of these two things : 
 the importance of the ends, the simplicity of the 
 means. When I say the importance of the ends, I 
 use a form of expression which is commonly employed 
 as expressing design. And yet on that very account 
 
EVIDENCE OF DESIGN. 89 
 
 we must be on our guard against too narrow a view. 
 When we consider the subject of vision in its entirety, 
 the construction of the recipient organ as well as the 
 properties of the external agent which affects it, the 
 evidence of design is such, it seems to me, as must 
 to most minds be irresistible. Yet if I may judge of 
 other men's minds by my own, it is rather in the 
 construction of the recipient organ than in the pro- 
 perties of the agent that affects it, that the evidence 
 of design is so strongly perceived. And the reason 
 of this may be that we are here dealing with what 
 more nearly resembles design as we know it in our- 
 selves. Man takes the laws of matter as he finds 
 them ; the laws of cohesion, of the conversion of 
 liquid into vapour, of the elasticity of gases and 
 vapours, and so forth ; and in subserviency to those 
 laws he constructs a machine, a steam-engine for 
 instance, or whatever it may be ; but over the laws 
 themselves he has absolutely no control. Now when 
 we contemplate the structure of the eye, we think of 
 it as an organ performing its functions in subserviency 
 to laws definitely laid down, relating to the agent 
 that acts upon it, laws which are not to be interfered 
 with. We can it is true go but a little way towards 
 explaining how it is that through the intervention of 
 the eye the external agent acts upon the mind. Still, 
 there are some steps of the process which we are able 
 
90 THE NATURE OF LIGHT. 
 
 to follow, and these are sufficient to impress us 
 strongly with the idea of design. The eye is a highly 
 specialized organ, admirably adapted for the important 
 function which it fulfils, but, so far as we can see, of no 
 other use ; and this very specialization tends to make 
 the evidence of design simpler and more apparent. 
 But when we come to the properties of the external 
 agent which affects the eye, we begin to get out of 
 our depth. These more nearly resemble those ulti- 
 mate laws of matter over which man has no control ; 
 and to say that they were designed for certain 
 important objects which we perceive to be accom- 
 plished in subserviency to them, seems to savour of 
 presumption. It is but a limited insight that we can 
 get into the system of nature ; and to take the very 
 case of the luminiferous ether, while as its name 
 implies it is all important as regards vision, the present 
 state of science enables us to say that it serves for 
 one object of still more vital importance ; we seem to 
 touch upon another ; and there maybe others again 
 of which we have no idea. 
 
 In the study of those phenomena of light which I 
 have hitherto brought before you, we derived .con- 
 stant assistance from our knowledge of the theory of 
 sound. . I now come to a branch of the subject where 
 the theory of sound fails us altogether, to a class of 
 
DOUBLE REFRACTION. 91 
 
 optical phenomena which have nothing answering to 
 them in sound. I refer to double refraction and po- 
 larization. 
 
 Of these phenomena, the former of which is so 
 closely related to the latter, double refraction was the 
 first to be discovered. It was in 1669 that Bartho- 
 linus published his account of the discovery of a 
 strange and unusual refraction in Iceland spar. The 
 subject was taken up and investigated with the keen- 
 est interest by Huygens, whom we must regard as the 
 founder of the theory of undulations. It would not 
 be in accordance with the object which I have had in 
 view in these lectures to enter into details respecting 
 the phenomenon, and I must content myself with 
 mentioning a few of the more salient features. 
 
 Iceland spar stands we may say alone among 
 minerals in at the same time possessing powerful 
 double refraction and occurring in large clear crys- 
 talline masses. It was this circumstance which led 
 to the discovery. The mineral cleaves very readily 
 in three definite directions, so that a block obtained 
 by cleavage is of the form of a parallelepiped. The 
 three obtuse dihedral angles of this parallelepiped are 
 all exactly equal, and are so turned that two opposite 
 solid angles are contained by three equal obtuse 
 plane angles, while each of the remaining six is 
 contained by one obtuse and two acute. A direction 
 
Q2 THE NATURE OF LIGHT. 
 
 not, observe, any special line equally inclined to 
 the three edges which meet in one of the obtuse solid 
 angles is called the axis of the crystal. The crystal- 
 line structure, so far at least as it is revealed by the 
 cleavage planes, or I may add by the natural faces, is 
 symmetrical with respect to three planes and no 
 more, each of these being parallel to one of the edges 
 which meet in an obtuse solid angle, and perpendicu- 
 lar to the plane of the other two, and accordingly 
 being parallel to the axis of the crystal. Any one 
 of these planes is what Huygens called a principal 
 plane. 
 
 If an object near at hand be viewed through such 
 a block, as for example if the block be laid on a 
 printed page, two images of the object are seen, of 
 which one appears more elevated than the other when 
 both eyes are used, indicating a stronger refraction. 
 This image is called the ordinary, because it obeys 
 the ordinary law of refraction. That such is the 
 case was found by Bartholinus, and confirmed by 
 Huygens ; and the accuracy of the ordinary law as 
 applicable to this pencil had stood the test of the 
 most refined measurements carried out by the most 
 improved modern methods, among which I may 
 specially mention the measurements made by Pro- 
 fessor Swan and Mr Glazebrook. But the rays 
 belonging to the other or extraordinary, as it is called, 
 
DOUBLE REFRACTION. 93 
 
 image must obey some totally different law. If the 
 eye and object be in the principal plane of the block, 
 the extraordinary ray obeys the laws of ordinary 
 refraction so far as this, that the refracted ray lies 
 in the plane of incidence ; but whereas in ordinary 
 media there is no refraction at a perpendicular inci- 
 dence, and at oblique incidences there is refraction, 
 which goes on increasing as the angle of incidence 
 increases, in the case we are now considering there 
 is refraction at a perpendicular incidence, and at one 
 particular oblique incidence a ray passes through 
 without refraction. And if the block be turned round 
 in the plane of its surface, so that the plane through 
 the eye and the object, which I suppose perpendicu- 
 lar to the plane of the surface, is no longer a principal 
 plane of the crystal, the refracted extraordinary ray 
 does not so much as lie in the plane of incidence. 
 
 If a distant object be viewed through the block, 
 there is no duplication, so that whether a ray passes 
 through the block as ordinary or as extraordinary, 
 the emergent ray to which it gives rise is parallel to 
 the incident, just as in the case of ordinary refraction. 
 This is true whatever be the inclination of the inci- 
 dent ray to the surface, and whatever be the plane of 
 incidence. It depends however on the parallelism of 
 the surfaces of incidence and emergence ; and if these 
 surfaces be inclined to each other, forming a prism, 
 
94 THE NATURE OF LIGHT. 
 
 then the duplication of a distant object is at once 
 perceived. If a slit of light be viewed through such 
 a prism, two spectra are seen, which are unequally 
 deviated, and show in general unequal dispersion. 
 
 Now what notion are we to form of the cause of 
 double refraction if we adopt the theory of undula- 
 tions ? According to the fundamental explanation 
 of refraction given by Huygens, as there are two 
 refracted rays, there must be two disturbances pro- 
 pagated within the crystal as the result of an elemen- 
 tary disturbance excited at a point of its surface, and 
 these two must travel with different velocities. They 
 will spread out from the centre of disturbance in two 
 closed surfaces respectively, or it may be a surface 
 with two sheets. For one of these, the velocity of 
 propagation will be the same in all directions, and the 
 surface will therefore be a sphere. This follows from 
 the fact that the ordinary ray obeys the ordinary law 
 of refraction. But as the other obeys some more 
 complicated law, the surface for it must be other than 
 a sphere, and the velocity of propagation must be 
 different in different directions. 
 
 It has been already remarked that there are three 
 planes of crystalline symmetry, and these, as might 
 have been expected from the intimate relation of the 
 optical properties to the crystalline structure, are 
 also planes of optical symmetry ; that is to say, all the 
 
DOUBLE REFRACTION. 95 
 
 optical properties are symmetrical with respect to 
 each of them. But there are other planes which are 
 planes of optical, though not of crystalline, symmetry. 
 Thus if a plate be cut perpendicular to the axis, the 
 optical properties in it are symmetrical with respect 
 to any plane through the axis ; and if a plate be cut 
 parallel to the axis, the plane perpendicular to the 
 axis is a plane of optical symmetry as well as the 
 plane passing through the axis, though the former 
 cannot be, and the second is not in general, a plane 
 of crystalline symmetry. In short, all the optical 
 properties are symmetrical about the axis, the two 
 poles of which are alike, so that the optical properties 
 present the same degree of symmetry as an ellipsoid 
 of revolution*. Accordingly the wave surface re- 
 lating to the extraordinary ray must have thus much 
 symmetry ; and Huygens assumed for trial that it 
 was a spheroid of revolution. As far as he could 
 make out, the refraction in the direction of the axis 
 appeared to be the same for the two rays, and he 
 accordingly supposed that the sphere belonging to 
 the ordinary ray, and the spheroid which he assumed 
 
 * According to Sir David Brewster, this is not altogether the case 
 so far as relates to the properties of the light reflected from an artificial 
 surface of the crystal. His observations appear never to have been 
 published in detail, nor has anyone else, so far as I know, taken up the 
 subject. 
 
96 THE NATURE OF LIGHT. 
 
 as the form for the extraordinary, touched one 
 another in the axis. This equality of refraction 
 along the axis we now know to be rigorously exact. 
 The form of the wave surface being assumed, the 
 refraction of the extraordinary ray followed at once 
 from Huygens's construction ; and the mode and 
 amount of refraction were found to agree with the 
 construction as near as the most accurate measure- 
 ments made by Huygens could decide. Mr Glaze- 
 brook has recently executed a series of measurements 
 of the refraction of the extraordinary ray in Iceland 
 spar with all the exactitude of modern methods, 
 guided by our increased knowledge of the subject; 
 and the result is that no certain error of Huygens's 
 construction can be detected. 
 
 So far however the laws of the extraordinary 
 refraction in Iceland spar are merely empirical, based 
 upon a happy guess as to the form of the extra- 
 ordinary wave surface ; it remains to be explained, 
 if explain it we can, why there should be these two 
 kinds of disturbance at all within the crystal, and why 
 the form of the wave surface should be what we find 
 it must be if the most fundamental principles of the 
 wave theory are true, by which the form of the 
 surface is connected with the observed refraction. 
 
 Huygens imagined that the ordinary ray was pro- 
 pagated by the vibration of the ether within the 
 
POLARIZATION. 97 
 
 crystal, while in the extraordinary the molecules of 
 the crystal took part as well as the ether. I have 
 already mentioned some of the strong objections 
 which exist to the supposition that the propagation 
 of light in media such as water or glass takes place 
 by vibrations of the ponderable matter ; and similar 
 objections in good measure apply to the supposition 
 that both the molecules and the ether take part in it. 
 But be that as it may, Huygens himself, when he had 
 nearly concluded his researches, discovered a remark- 
 able phenomenon which ill accords with the supposi- 
 tion of his which I have just mentioned. 
 
 Suppose a second block of Iceland spar to be 
 placed on top of the first, so that the two are in the 
 same relative position which they would occupy if 
 they formed one larger block. Then neither of the 
 images, ordinary or extraordinary, seen through the 
 first block is split into two in passing through the 
 second block, but the ordinary of the first furnishes an 
 ordinary in the second, and nothing more, and simi- 
 larly the extraordinary an extraordinary. The same 
 is still the case if the second block be separated from 
 the first, or even inclined by turning in the principal 
 plane. But reverting for simplicity's sake to the first 
 relative position of the blocks, suppose that the second 
 is turned round the common normal to the two 
 adjacent surfaces. The moment the second block is 
 S. 7 
 
98 THE 'NATURE OF LIGHT. 
 
 turned from the primitive position, each of the images 
 which the first block furnishes is split into two by 
 the second block. The relative positions of the two 
 images forming the pair into which either of the 
 original images is split is just the same as if that 
 original image had been formed by common light, 
 but the intensities are different. When the second 
 block has been turned through only a small angle, 
 the ordinary of the first furnishes mainly an ordinary 
 in the second, but also a faint extraordinary, and 
 similarly the extraordinary of the first furnishes main- 
 ly an extraordinary in the second, but also a faint 
 ordinary. As the turning goes on, the faint images 
 get brighter, and the bright images get weaker, till 
 after turning through 45 the four are alike. As the 
 rotation continues, the pair of images that had been 
 the weaker get the brighter, and the pair that had 
 been the brighter get the fainter, till after turning 
 through 90 the pair of images that had at first 
 appropriated the whole of the light disappear alto- 
 gether, and the pair that began to spring into exis- 
 tence on first turning now alone are seen. In this 
 position, that is to say when the principal planes of 
 the two blocks are perpendicular to each other, the 
 image formed by light which suffered ordinary refrac- 
 tion in the first block furnishes nothing but an extra- 
 ordinary in the second, and the image formed by 
 
POLARIZATION. 99 
 
 light which suffered extraordinary refraction in the 
 first furnishes nothing but an ordinary in the second. 
 As the rotation goes on, the same series of changes 
 are repeated, so that in a complete revolution the two 
 pairs of images vanish alternately at every quarter of 
 a revolution. 
 
 On account of the fundamental importance of this 
 phenomenon, I must crave your indulgence for dwelling 
 on it at some length, even though from its elementary 
 character it must be familiar to those of you who have 
 paid any attention to this branch of the subject. 
 
 Suppose that light coming directly from a lumi- 
 nous source, such as the flame of a lamp, is received 
 on a screen with a circular hole. The screen will 
 isolate a beam of light which, as I shall have 
 occasion to deal with it only at short distances 
 from the hole, I will call cylindrical. Let this beam 
 be received, suppose perpendicularly, upon a block 
 of Iceland spar bounded as usual by cleavage planes. 
 In passing through the spar, it will be divided into 
 two, an ordinary beam, which will pass straight on, 
 and an extraordinary which will be deviated in a 
 lateral direction in passing through the block, and 
 will give rise to an emergent beam parallel to the 
 incident, and accordingly parallel to the first emergent 
 beam. If the hole in the screen be not too large to 
 suit the thickness of the block, the two beams will 
 
 72 
 
IOO THE NATURE OF LIGHT. 
 
 come out without overlapping, and may be examined 
 apart. They are found to be of sensibly equal in- 
 tensity whatever be the azimuth of the block around 
 its normal. Making abstraction of the small quantity 
 of light which goes elsewhere by reflection, we may 
 say that the whole of the incident light is divided 
 equally between the two beams. 
 
 Suppose now that we fix the block in any position, 
 say with its principal plane vertical, and place a second 
 screen with a circular hole to let pass the beam which 
 went straight through the first block, while it stops the 
 other. On examining this beam by a second block, 
 which is turned round, we find that it is divided into 
 two of unequal intensity, which vanish alternately at 
 every quarter of a revolution, the whole of the light 
 passing into an ordinary beam in the second rhomb 
 when its principal plane is vertical, and into an 
 extraordinary when it is horizontal. Hence whereas 
 a beam of common light is propagated in some 
 definite direction, but possesses no relation to space 
 in any other direction, so that there is no plane 
 passing through it which we can distinguish, merely 
 by the properties of the beam itself, from any other, 
 the beam we are now considering, namely that which 
 passed through the second screen, possesses properties 
 with respect to directions in space transverse to its 
 direction of propagation ; and if we knew nothing of 
 
POLARIZATION. % t , / /, ; 1C I 
 
 its history, but it were merely presented to us for 
 examination, that would not hinder us from recog- 
 nising, by means suppose of a rhomb of Iceland spar, 
 the peculiar properties which it possesses, nor from 
 fixing by observation alone the direction of those two 
 rectangular planes, vertical and horizontal in the case 
 supposed, with respect to which its properties are 
 symmetrical, and in either of which if the principal 
 plane of the examining rhomb be placed, an ordinary 
 or an extraordinary beam, as the case may be, is 
 alone produced in it Light possessing this property, 
 however it may have acquired it, is said to be polarized, 
 and the plane with respect to which its properties are 
 the same as are those of the ordinary ray in Iceland 
 spar with respect to the principal plane, is called the 
 plane of polarization. Its azimuth may be determined 
 experimentally as being that of the principal plane of 
 an examining rhomb when so turned as to transmit 
 only an ordinary beam. 
 
 To go back now to the first arrangement, namely, 
 that of a beam isolated by a first screen falling on a 
 rhomb of Iceland spar, and then on a second screen 
 provided like the first with a suitable hole, let this 
 second screen be so placed as to transmit the beam 
 which passed through the rhomb by extraordinary re- 
 fraction, and stop the other, and then let the beam be 
 presented for observation. On examining it with a 
 
102 THE NATURE OF LIGHT. 
 
 second rhomb we should find that it possessed iden- 
 tically the same properties as the beam obtained by 
 ordinary refraction in the first rhomb, save that the pro- 
 perties of this beam are related to the horizontal plane 
 precisely as were those of the former beam to the verti- 
 cal plane ; and it is into the horizontal plane that the 
 principal plane of the examining rhomb must be turned 
 in order that nothing but an ordinary beam may be 
 transmitted through it. Hence, according to our 
 former definition, we must say that the extraordinary 
 beam passing through Iceland spar is polarized in a 
 plane perpendicular to the plane of incidence. 
 
 More than a century elapsed after Huygens's 
 discovery of what we now call polarization before 
 it was known that polarized Light could be obtained 
 otherwise than by or as an accompaniment of double 
 refraction. But in 1808 Malus made the very impor- 
 tant discovery that when Light is reflected from glass 
 at a certain angle, the reflected ray is wholly polarized ; 
 and since the properties of the reflected ray are the 
 same with reference to the plane of incidence as are 
 those of the ordinary ray in Iceland spar with reference 
 to the principal plane of the crystal, we must in 
 accordance with our definition say that the reflected 
 light is polarized in the plane of incidence. The 
 light reflected at other inclinations possesses all the 
 properties of a mixture of. common light with light 
 
POLARIZING ANGLE. 1 03 
 
 polarized in the plane of incidence, and may accord- 
 ingly be said to be partially polarized in the plane of 
 incidence. The transmitted light, whether the light 
 be incident at the polarizing angle or the angle of 
 incidence be arbitrary, is found to be partially po- 
 larized in a plane perpendicular to the plane of 
 incidence. 
 
 Malus found that Light is thus polarized by 
 reflection from transparent substances in general, 
 from varnishes &c., but not from metals, the light 
 reflected from which is found to be only partially 
 polarized in the plane of incidence. The angle of 
 incidence on transparent substances required for com- 
 plete polarization Malus found to vary from one to 
 another, though he did not discover according to 
 what law, a law afterwards made out by Brewster, 
 namely, that the polarizing angle is that for which 
 the reflected and refracted rays are perpendicular to 
 each other ; or, as it may be otherwise expressed, the 
 tangent of the polarizing angle is equal to the index 
 of refraction. 
 
 Malus's important discovery of the polarization of 
 Light by reflection proves that polarization, whatever 
 it may be, is something that may exist altogether 
 independently of double refraction, and must therefore 
 be something intimately bound up with the nature of 
 Light in itself. The intimate connexion of double 
 
104 THE NATURE OF LIGHT. 
 
 refraction with polarization shows that we cannot 
 hope to explain the former of these phenomena 
 unless we can obtain some insight into the nature of 
 what constitutes polarization. 
 
LECTURE IV. 
 
 Phenomena presented on interposing a crystalline block or thin 
 plate in the path of Polarized Light which is subsequently 
 analyzed Laws of Interference of Polarized Light 
 Theory of Transverse Vibrations- Conclusion. 
 
 WE have seen that when a beam of polarized light 
 is examined by a rhomb of Iceland spar, it is divided 
 into two of in general unequal intensity passing 
 through the spar. As before, make abstraction of the 
 small quantity of light which goes elsewhere by 
 reflection, and call the intensity of the incident beam 
 unity, and let us consider in the first instance the 
 intensity of the beam which passes through the 
 examining spar as ordinary. Let A be the azimuth 
 of the principal plane of the examining rhomb referred 
 to the plane of primitive polarization. Then the in- 
 tensity, the relation of which to the angle A is the 
 object of our search, must be such that it is equal to 
 unity when A is nothing, decreases to nothing as A 
 increases to 90, increases to unity again as A increases 
 to 1 80, decreases again to nothing as A increases to 
 
IO6 THE NATURE OF LIGHT. 
 
 270, and finally increases to unity as at first as A 
 increases to 360, having furthermore the same value 
 for A negative as for A positive, and for 90 A 
 negative as for 90 A positive. A very simple 
 function possessing this property is cos* A. If this 
 be the intensity of the ordinary, since the rest of the 
 light passes into the extraordinary, the intensity of 
 the latter must be I cos 2 A, or sin 2 A, or the squared 
 cosine of the angle between its plane of polarization 
 and the plane of primitive polarization. Such was 
 the law assumed by Malus, and called after his name. 
 It has been verified by photometric measurements, 
 and is of great importance with reference to the 
 theory of what it is which constitutes polarization. 
 
 Suppose that light polarized in any way is subse- 
 quently analyzed, as it is called, whether by a thick 
 block of Iceland spar furnished with screens so as to 
 stop out one of the transmitted pencils, or by any of the 
 more convenient methods more commonly employed. 
 Let the analyzer be turned till the field of view is 
 dark, the light falling upon the analyzer in that posi- 
 tion being stifled, as in the case of a good tourmaline, 
 or else sent elsewhere. If a block of Iceland spar 
 be interposed between the polarizer and the analyzer, 
 and turned round in its own plane, in general there is 
 more or less restoration of light, there being only 
 four azimuths of the block, separated by 90, in a 
 
RESTORATION OF LIGHT BY CRYSTAL. IO/ 
 
 complete turn in which the field remains dark as 
 before the interposition of the block. 
 
 This restoration of light is very easily explained 
 as a consequence of what has already been mentioned. 
 The polarized light falling on the block is divided 
 into two beams polarized respectively in and perpen- 
 dicularly to its principal plane, which traverse the 
 crystal independently though overlapping, and which 
 emerge blended together. Each of these on entering 
 the analyzer is again divided into two, polarized in 
 rectangular planes, which are those of the plane of 
 primitive polarization and the perpendicular plane, 
 of which the latter alone is retained, and the two 
 retained portions of each of the streams enter the eye 
 together, and their illuminations are added together. 
 A very simple application of Malus's law shows that 
 if we take the intensity of the primitively polarized 
 light for unity, and disregard the small loss by 
 reflection, the intensity of the light entering the eye 
 will be half the square of the sine of double the 
 azimuth of the block, measured from one of the 
 vanishing positions. This restoration of light in 
 the dark field forms a very sensitive and easily 
 applied test of the possession of double refraction by 
 the substance interposed. 
 
 But an observation made by Arago about 1811 
 opened out quite a new field of research, remarkable 
 
108 THE NATURE OF LIGHT. 
 
 alike for the beauty of the phenomena, for the light 
 they throw upon the nature of polarization, and for 
 the information they afford us respecting the inmost 
 structure of bodies. Arago found that when the in- 
 terposed crystalline plate was very thin, as may easily 
 be obtained with mica or sulphate of lime, the re- 
 stored light was not as before white, but showed the 
 most gorgeous colours, varying with the thickness of 
 the plate, its nature, and the direction in which and 
 amount by which it is inclined, if inclined it be. 
 
 The more powerfully doubly refracting be the 
 substance interposed, the thinner as a rule is the 
 interposed plate required to be in order to show 
 these colours. But with a given substance, such for 
 example as Iceland spar, the amount of double 
 refraction varies immensely with the direction. Thus 
 in Iceland spar, one of the most powerfully doubly 
 refracting substances known, we have seen that 
 in the direction of the axis the two rays are 
 refracted alike. Accordingly if a plate of Iceland 
 spar, even a thick plate, be cut perpendicular to the 
 axis, and be interposed perpendicularly to the inci- 
 dent light in the dark field, a splendid system of 
 coloured rings is seen, which are interrupted by a 
 dark cross. The arrangement of coloured curves is 
 still more remarkable in the case of biaxal crystals, 
 but the simpler case of a thin crystalline plate is 
 
COLOURS OF CRYSTALLINE PLATES. 1 09 
 
 better adapted to our present purpose, since in the 
 other case there are too many things crowded at 
 once upon the attention. 
 
 Let us revert then to the case of a thin crystalline 
 .plate interposed in the dark field, being held, as 
 I will suppose, perpendicularly to the incident light. 
 Even with this restriction, it would take too long to 
 mention all the phenomena exhibited, and would be 
 wearisome; nor is it advisable to treat the subject 
 in this way, for in fact they have all been brought 
 under the dominion of theory, and are best studied 
 in connexion with it, except in so far as may be 
 necessary to establish the theory in the first instance. 
 
 I shall restrict myself therefore to mentioning a 
 few leading features of the phenomenon, premising 
 that in the case of a doubly refracting plate in 
 general, as in that of a block of Iceland spar, there 
 are two rectangular directions in which the beams 
 independently transmitted are respectively polarized, 
 and that if the incident light is polarized, and the 
 plane of polarization coincides with either of those 
 directions, the whole of the light entering the crystal 
 passes into the beam which is polarized in the plane 
 of primitive polarization. The two rectangular direc- 
 tions above mentioned have been named the neutral 
 axes of the plate. 
 
 If the thin crystalline plate interposed be of uni- 
 
IIO THE NATURE OF LIGHT. 
 
 form thickness, it is seen of a uniform colour ; if the 
 thickness vary irregularly, as in the case of a plate 
 of selenite obtained by casual cleavage, the colours 
 are arranged in patches, corresponding to the varying 
 thickness. If the plate be turned in its own plane, 
 there are four rectangular positions in which the 
 field is left dark as at first, which are those in which 
 one or other of the neutral axes lies in the plane 
 of primitive polarization, and in which accordingly 
 there is no bifurcation of the incident light on passing 
 into the crystal. 
 
 If the analyzer be turned through 90, so that the 
 planes of polarization of the polarizer and analyzer 
 are now coincident instead of perpendicular, and the 
 field before the introduction of the crystal is at its 
 maximum of brightness, on interposing the crystal- 
 line plate the colours now seen are complementary 
 in character to the former. They vanish altogether 
 when either neutral axis comes into the plane of 
 primitive polarization, and are less vivid than in the 
 dark field except when the neutral axes are at an 
 azimuth of 45 from the vanishing positions. 
 
 If the planes of polarization and analyzation be 
 set at an arbitrary angle, and the crystal be turned in 
 its own plane, there are eight positions in a com- 
 plete revolution in which the colours disappear, giving 
 place to white light of the same intensity as when the 
 
COLOURS OF CRYSTALLINE PLATES. Ill 
 
 plate is away. Between these critical positions, the 
 colours have the character of those of the dark and 
 of the bright field alternately. The critical positions 
 are those in which one of the neutral axes lies in 
 the plane of polarization or analyzation. Hence 
 and this is to be specially noticed for the production 
 of the colours it is essential that the polarized light 
 we start with should be divided into two pencils 
 in passing through the crystal, and that each of these 
 again should be divided into two by the analyzer, of 
 which one portion is retained. 
 
 If the crystalline plate be ground into the form of 
 a slender wedge, the colours are arranged in bands 
 parallel to the edge of the wedge, the bands for any 
 colour being equidistant, and the scale larger for the 
 red than for the blue. If the analyzer be set to give 
 the dark and the bright field in succession, the tints 
 of the wedge agree with those of the reflected system 
 of Newton's rings in the former case, and the trans- 
 mitted system in the latter. 
 
 The equidistance of the bands for any particular 
 colour shows that the law of the order of the tints, 
 as depending on the thickness of the plate, is the 
 very same as in the case of Newton's rings, the 
 magnitude of the thickness merely being very much 
 greater than in that case. Nor is this all. If we 
 know the doubly refracting energy of any particular 
 
112 THE NATURE OF LIGHT. 
 
 substance, suppose sulphate of lime, we. can calculate 
 the retardation of phase of one relatively to the other 
 of the two rectangularly polarized pencils which a 
 thin plate of the substance can independently trans- 
 mit, in terms of the thickness of the plate, to which 
 that retardation is proportional. Now Dr Young 
 showed that when this is done the thickness of plate 
 by which any particular tint is produced is just what 
 it ought to be on the supposition that the colour is 
 due to the interference of the two rectangularly 
 polarized pencils which traversed the crystal inde- 
 pendently. After all this we can hardly help sup- 
 posing that the colours must in some way be due 
 to interference. But if so, why are they not seen 
 with common light, just as Newton's rings ; why 
 should it be necessary that the light should in some 
 way be polarized, and the polarized light should in 
 some way be analyzed, and that the crystalline plate 
 should be interposed between the polarizer and the 
 analyzer in order that any colours at all should be 
 seen ? 
 
 If we assume that the colours of crystalline plates 
 in polarized light are due to interference, the laws 
 of the interference of polarized light may be deduced 
 from the observation of those colours without any 
 experimental difficulty. But if it still be regarded as 
 in any way an open question whether those colours 
 
INTERFERENCE OF POLARIZED LIGHT. IIJ 
 
 are due to interference, it becomes important to in- 
 vestigate those laws by means of experiments free 
 from any such doubt. 
 
 Accordingly the series of researches by which 
 Arago and Fresnel determined in a direct manner 
 the laws of interference of polarized light must be 
 regarded as making an epoch in the progress of the 
 study of this branch of the subject. These experi- 
 ments were made on the fringes of interference with 
 which we had already become familiar as exhibited 
 by common light ; such fringes as those produced 
 by the interference of two streams of light from the 
 same source, such as two virtual images of a lumin- 
 ous point, or of two streams from the same luminous 
 point, which after passing through two parallel ex- 
 tremely narrow apertures near one another diverged 
 and mixed together. We have seen what a trium- 
 phant explanation the theory of undulations affords 
 of the phenomena of interference and diffraction in 
 the case of common light ; and if we obtain the same 
 fringes, with the appearance of which we are so 
 familiar, in working with polarized instead of com- 
 mon light, we cannot refuse to admit that they too 
 are due to interference. 
 
 The study of the interference of two streams of 
 light polarized in the same way presents no experi- 
 mental difficulty whatsoever. It is merely necessary 
 s. 8 
 
114 THE NATURE OF LIGHT. 
 
 to use polarized light instead of common light in 
 any of the ordinary experiments of interference. On 
 doing this the phenomena of interference are found 
 to be absolutely the same with polarized as with 
 common light. But to polarize two portions of light 
 from the same source, and proceeding nearly along 
 the same course, in two rectangular directions, and 
 yet ensure a very near equality in the lengths of their 
 paths, or rather equivalent paths in air, is a matter 
 of very great nicety, so small is the difference of 
 path that would suffice to prevent any exhibition 
 of interference of the usual kind. Nevertheless by 
 a series of ingeniously devised and carefully executed 
 experiments Arago and Fresnel succeeded in estab- 
 lishing conclusively under what circumstances polar- 
 ized light is, and under what it is not, capable of 
 manifesting the usual phenomena of interference. 
 
 The result of this enquiry was summed up in five 
 laws relating to the interference of polarized light, 
 which were derived directly from observation. One 
 of these has already been mentioned. Another is 
 that when two streams of light from the same source 
 are polarized in rectangular planes, they show no 
 phenomena of interference, notwithstanding a near 
 equality of paths. Another, that the mixed stream 
 as in the last case may be analyzed without any 
 phenomena of interference being thereby revealed. 
 
INTERFERENCE OF POLARIZED LIGHT. 115 
 
 Another that when two streams of light from the 
 same source are polarized in rectangular planes, and 
 afterwards analyzed, they do manifest the phenomena 
 of interference provided the original source were one 
 of polarized instead of common light. Lastly, in the 
 phenomena of interference produced by rays which 
 have experienced double refraction, the place of the 
 fringes is not in all cases determined solely by the 
 difference of equivalent paths ; in certain cases it is 
 necessary to alter the difference of paths by half 
 an undulation. And the rule they gave for deter- 
 mining under what circumstances the half undulation 
 should be added and under what circumstances not 
 amounted to this : when the planes of polarization 
 and analyzation lie in the same quadrant made by 
 the neutral axes of the crystalline plane, the cha- 
 racter of the interference is determined simply by 
 the difference of paths ; but when they lie in adjacent 
 quadrants, we must alter the difference of paths by 
 half an undulation. 
 
 These five empirical laws embrace the necessity 
 for a polarizer and for an analyzer in order that colours 
 should be seen in a crystalline plate; and taken in 
 conjunction with Malus's law, regarded at present 
 merely as an empirical law, they enable us to cal- 
 culate completely the colours of crystalline plates 
 under all the varied conditions which may exist as 
 
 82 
 
Il6 THE NATURE OF LIGHT. 
 
 to thickness of the plate, doubly refracting energy 
 of the substance of which it is formed, azimuth of 
 the neutral axes relatively to the plane of primitive 
 polarization, azimuth of the plane of analyzation ; 
 and for that we have no occasion to enter into any 
 speculation at all as to what it is that constitutes 
 polarization. Nay more ; if we take the laws of 
 double refraction as known empirically as the result 
 of direct observation, we may even calculate com- 
 pletely the coloured rings and curves about the optic 
 axis or axes of uniaxal or biaxal crystals, without 
 entering into any speculation as to what the theo- 
 retical interpretation of polarization may be. . 
 
 The question now arises, can we embrace the five 
 laws of interference of polarized light, and Malus's 
 law, in a theory which shall comprehend them all, 
 and which shall be at least hopeful for the explanation 
 of double refraction and of the polarization of light by 
 reflection ; though as these may depend on a know- 
 ledge of what is the actual state of things which we 
 do not possess, we cannot demand of necessity that 
 it shall lead to their explanation. 
 
 In applying Malus's law to the calculation of the 
 colours of crystalline plates, we are led to contem- 
 plate an intensity which we may take as unity in the 
 incident original polarized light as giving rise to 
 intensities cosM and sinM belonging to light 
 
TRANSVERSE VIBRATIONS. 1 1/ 
 
 polarized in a plane making an angle A with the 
 plane of primitive polarization and in the perpen- 
 dicular plane respectively, and these again as giving 
 rise to polarized beams the intensities of which are 
 obtained by a re-application of the very same law. 
 Now in studying the interference of common light, 
 we saw reason to conclude that for light of a given 
 kind, that is, of a given refrangibility, the intensity is 
 measured by the square of the coefficient of vibra- 
 tion, and consequently the coefficient of vibration 
 by the square root of the intensity. It is true that 
 I have not been able to lay before you the full 
 evidence on which this conclusion is based, as it 
 would have involved some considerations of too 
 mathematical a nature to be suitable to the present 
 lectures, so that I have been obliged to leave the 
 result to be accepted in some measure on the strength 
 of authority. Consequently we are led by pure 
 observation, combined with so much of theory as 
 belongs to the study of common light, to contem- 
 plate a beam of polarized light in which the co- 
 efficient of vibration may be taken as unity as being 
 divided (as for example in passing through a crystal- 
 line lamina) into two polarized in rectangular planes, 
 at azimuths of A and 90 A to the plane of primitive 
 polarization, the coefficients of vibration belonging to 
 which are expressed by cos A and sin A. But this is 
 
Il8 THE NATURE OF LIGHT. 
 
 identically the law according to which forces, or dis- 
 placements, or velocities in directions perpendicular to 
 that of propagation, and in or equally inclined to the 
 planes of polarization, would be resolved. We are 
 inevitably driven to the contemplation of a something 
 about polarized light which admits of composition 
 and resolution according to the above simple law. 
 This "something" can hardly be other than the 
 vibrations themselves, and we are thus led to conclude 
 that in polarized light the vibrations are rectilinear, 
 but instead of being in the direction of propagation, 
 as from the analogy of sound the vibrations of Light 
 might naturally have been expected to be, are trans- 
 verse to the direction of propagation. 
 
 When polarized light is obtained by ordinary 
 refraction through Iceland spar, or by reflection from 
 glass at the proper angle or incidence, everything is 
 symmetrical with respect to the plane of polarization. 
 We must suppose therefore that in polarized light 
 the vibrations are symmetrical with respect to the plane 
 of polarization. This leaves two alternatives open : 
 they may either be in the plane of polarization or 
 perpendicular to the plane of polarization. So far as 
 the explanation of the laws of interference of polarized 
 light is concerned, it is a matter of absolute in- 
 difference which alternative we adopt, and some 
 undulationists have adopted the one and some the 
 
TRANSVERSE VIBRATIONS. 1 19 
 
 other. The question can only be decided, if it can be 
 decided at all, by introducing more or less of dy- 
 namical considerations, and that introduces more or 
 less of speculation, since the dynamical nature of the 
 mutual action of ponderable matter and ether is in 
 great measure unknown to us. Perhaps the argument 
 which introduces least speculation as to the dy- 
 namical nature of such actions is that derived from 
 diffraction at a considerable angle ; though it is true 
 that even here we cannot produce that diffraction 
 without the intervention of ponderable matter. The 
 result in this case, as I have elsewhere shown, is 
 decidedly in favour of the supposition that the vibra- 
 tions are perpendicular to the plane of polarization, 
 which is the alternative that was adopted by Fresnel, 
 and ultimately by Cauchy, though at first he adopted 
 the other ; and it is the one for which, independently 
 of diffraction, there is I think the most to be said. 
 But as I have remarked the theory of transverse 
 vibrations taken by itself does not involve the decision 
 of this question. 
 
 If such be the nature of polarized light, what 
 notion are we to form as to the nature of common 
 light ? Suppose light coming in some definite direc- 
 tion to fall on a screen with a hole, and to be 
 received at the other side on a block of Iceland spar. 
 Then if the hole be not too large, the two beams 
 
I2O THE NATURE OF LIGHT. 
 
 which are produced within the spar will come out 
 separated from one another, and will show their 
 polarization in rectangular planes. This will still be 
 true however the screen may be moved about, so that 
 the light falls- on different parts of the face of the 
 block. Now let the screen be removed altogether. 
 The light will still be decomposed into two beams 
 within the spar, giving rise on emergence to two 
 beams polarized in rectangular planes, but the beams 
 will be broad, and will mix on emergence. But the 
 mixture is identical with, or at any rate is undis- 
 tinguishable from, common light* Now the two 
 disturbances in rectangular planes give rise by their 
 composition to a disturbance which is in the fronts of 
 the waves, but is in general elliptical, including the 
 extreme cases of circular and rectilinear vibrations, 
 but with the elements of the ellipse changing, as we 
 have every reason to expect, irregularly in all sorts of 
 ways a great number of times in a second. For 
 though the vibrations may be sensibly regular for 
 thousands or it may be myriads together (and the 
 phenomena of interference show that they must have 
 
 * Abstraction is here made of the loss by reflection, which is not 
 quite the same for the ordinary and extraordinary, the higher refraction 
 of the former being accompanied by a slightly more copious reflection, 
 so that in the transmitted light there is a slight theoretical preponder- 
 ance of intensity in favour of the extraordinary. This is however so 
 small as to be barely sensible in refined experiments, and for our present 
 purpose it is best neglected. 
 
TRANSVERSE VIBRATIONS. 121 
 
 a high degree or regularity) yet we should have no 
 reason a priori to expect that they would remain 
 regular for the fifty millions of millions or so of vibra- 
 tions which must take place in the tenth of a second, 
 the time for which an impression made on the retina 
 is estimated to last. 
 
 Such being our notion of common light, the division 
 of common light into two rectangularly polarized beams 
 which follow different paths must be taken to imply 
 that for some cause yet to be investigated the vibra- 
 tions, which at first were in the fronts of the waves, 
 but in other respects of any kind, are decomposed 
 into two rectilinear vibrations in rectangular directions, 
 which are propagated along different paths. 
 
 This fundamental conception as to the nature of 
 polarized light, and its relation to common light, ex- 
 plains in the simplest manner the six laws relating to 
 the interference of polarized light, and to the intensity 
 of the polarized streams into which polarized light may 
 be divided, to which I have just referred. The inter- 
 ference of light merely demands, so far as direction 
 of vibration is concerned, that it should be as nearly 
 as possible the same for the two interfering streams, 
 a condition satisfied by two streams polarized in the 
 same way. Again, the kinetic energy of a set of 
 vibrations, to which for light of a given kind the 
 intensity is theoretically proportional, is the sum of 
 
122 THE NATURE OF LIGHT. 
 
 the kinetic energies of the components in any two 
 rectangular directions, irrespective of their difference 
 of phase, and therefore no phenomena of interference 
 ought to be visible in the mixture of two rectangularly 
 polarized portions of light, even though they came 
 originally from the same polarized source. Again, if 
 common light be divided into two rectangularly 
 polarized portions, which are afterwards subdivided 
 in a similar manner, and a pair of these latter com- 
 ponents which are polarized alike mix, having had 
 but a small difference of path from the original source, 
 they ought not to show any signs of interference. 
 For as there is no fixed and permanent relation 
 between the relative magnitudes or the relative 
 starting-times of the first components, they are as 
 good as if they came from two independent sources, 
 in which case no phenomena of interference are 
 either theoretically observable or experimentally ob- 
 served, do what we will with the streams of light 
 afterwards. But if the original source of light be one 
 of polarized instead of common light, the case is 
 altogether different. Then, whatever changes take 
 place during the tenth of a second in the amplitude 
 or starting-time of one of the first components, exactly 
 the same take place in the other, and are carried on 
 into the second components, of which therefore those 
 which are polarized in the same way are in a condition 
 
ELLIPTICALLY POLARIZED LIGHT. 123 
 
 to interfere. And as to the circumstances under 
 which in this kind of interference the difference of 
 path must sometimes be imagined altered by half an 
 undulation, the matter is simple to the last degree on 
 the theory of transverse vibrations ; it merely involves 
 attention to the sign of a geometrical projection ; and 
 if we express the intensity of the mixed light, for the 
 case in which the planes of polarization and analyza- 
 tion lie in the same quadrant formed by the neutral 
 axes of a crystalline plate, by a formula in which the 
 symbols denote displacements or velocities or of an 
 ethereal particle instead of intensities, the formula 
 takes care of itself, and applies equally to the case in 
 which the planes of polarization and analyzation lie 
 in adjacent quadrants. 
 
 If polarized light be incident on a crystalline plate 
 of uniform thickness, and the emergent light be 
 viewed through an analyzer which is turned round, 
 then except in certain special cases which I need not 
 particularize, the light is not extinguished by the 
 analyzer however it be turned, but merely be- 
 comes, in general, alternately a maximum and a 
 minimum alternately at every quarter of a turn. So 
 far it agrees exactly with partially polarized light. 
 And yet the two are altogether different, and the 
 difference may be seen at a glance by viewing them 
 through a Nicol's prism capped by a plate of Iceland 
 
124 THE NATURE OF LIGHT. 
 
 spar cut perpendicular to the axis. The light we are 
 now considering is called elliptically polarized light, 
 and in contradistinction to it the light which I have 
 hitherto called polarized has been denominated plane- 
 polarized. 
 
 Elliptically polarized light may be obtained inde- 
 pendently altogether of double refraction. The theory 
 of transverse vibrations presents to the mind a very 
 clear picture of what constitutes it. But as this 
 is a matter of detail not involving any fresh principle, 
 I forbear to enter further into it. 
 
 Being now armed with a definite theory as to the 
 nature of polarized light, we are prepared to consider 
 whether any explanation can be given of double 
 refraction, as an accompaniment of which polarization 
 was first discovered. Whether we are able or not to 
 give a complete explanation of it, we might expect 
 that the theory would at least so far fall in with it as 
 to point hopefully towards an explanation. 
 
 The most salient feature of double refraction, 
 interpreted by the aid of the theory which makes 
 light to consist in undulations, and of that which 
 specifies the nature of polarized light, is that when 
 light falls on a crystalline plate or prism it gives rise 
 to two kinds of disturbance within the crystal, which 
 are propagated with different velocities, and in which 
 the vibrations are rectilinear, and take place in planes 
 
EXPLANATION OF DOUBLE REFRACTION. 125 
 
 which are perpendicular to each other, or at least 
 very approximately so, and of which the directions 
 are determined by lines fixed in the crystal. 
 
 Now we have not far to go to find a mechanical 
 illustration of such a mode of action. Imagine an 
 elastic rod terminated at one end, and extending 
 indefinitely in the other direction. Let the rod be 
 rectangular in section, the sides of the rectangle 
 being unequal, so that the rod is stiffer to resist 
 flexure in one of its principal planes than the other. 
 Let this rod be joined on to a cylindrical rod forming 
 a continuation of it which extends indefinitely. Con- 
 ceive the compound rod as capable of propagating 
 small transverse disturbances in which the axis of the 
 rod suffers flexure. Imagine a small disturbance, 
 suppose periodic, to be travelling in the cylindrical 
 rod towards the junction. It will travel on without 
 change of type even though the flexure of the axis be 
 not in one plane. But to find what disturbance it 
 excites in the rectangular rod, we must resolve the 
 disturbance in the cylindrical rod into its components 
 in the principal planes of the rectangular rod, and con- 
 sider them separately. Each will give rise in the rec- 
 tangular rod to a disturbance in its own plane, but the 
 two will travel along the rod with different velocities. 
 This illustrates the subdivision of a beam of common 
 light falling on a block of Iceland spar into two beams 
 
120 THE NATURE OF LIGHT. 
 
 polarized in rectangular planes, which are propagated 
 in the spar with different velocities. Again, suppose 
 the original disturbance in the cylindrical rod confined 
 to one plane. If this be either of the principal planes 
 of the rectangular rod, the more slowly or the more 
 quickly travelling kind of disturbance, as the case 
 may be, will alone be excited in the latter ; and if the 
 plane of the original disturbance be any other, the 
 components into which we must resolve it in order to 
 find the disturbance excited in the rectangular rod 
 will in general be of unequal intensity, their squares 
 varying with the azimuth of the plane of the original 
 disturbance in accordance with Malus's law. This 
 illustrates the subdivision of a beam of polarized light 
 incident on Iceland spar into two of unequal intensity 
 polarized in rectangular planes, and their alternate 
 disappearance at every quarter of a turn. We see 
 with what perfect simplicity the theory of transverse 
 vibrations falls in with the elementary facts of polari- 
 zation discovered by Huygens, standing in marked 
 contrast in this respect with the conjecture by which 
 Huygens himself attempted to account for double 
 refraction. 
 
 But can we go further, and account for, or 
 discover, from theory the laws of double refraction 
 and the accompanying polarization in different direc- 
 tions in doubly refracting crystals ? 
 
FRESNEL'S LAW OF DOUBLE REFRACTION. 127 
 
 It is to Fresnel we owe the first theoretical deduc- 
 tion of the laws of double refraction in Iceland spar, 
 and the discovery of the beautiful laws of double refrac- 
 tion in biaxal crystals ; laws some of which had been 
 previously known from observation, while in other 
 respects theory served to correct what had been 
 supposed to be the result of observation, but which 
 more careful observation carried out in directions indi- 
 cated by theory proved to have been incorrect. The 
 generalization by which Fresnel passed from the laws 
 of double refraction in uniaxal to those in biaxal 
 crystals is one of the most splendid things which has 
 been done in science. And yet the theory which 
 guided him to the discovery of these laws is not one 
 which is rigorous throughout, nor did Fresnel himself 
 profess that it was, though in some reproductions of 
 his theory contained in text-books it is presented as 
 if it were, to the detriment of the student. Fresnel 
 was a man of singular sagacity, endowed apparently 
 with a mind of the inductive class, leading him often 
 to the discovery of truth from conflicting or imperfect 
 evidence. We may even say it is fortunate that 
 Fresnel did not rigorously follow out to their con- 
 clusions the premises with which he started, for had he 
 done so he would have missed the discovery of the 
 elegant laws of double refraction. In fact, Cauchy 
 and Neumann independently worked out the con- 
 
128 THE NATURE OF LIGHT. 
 
 elusions which rigorously follow from the state of 
 things assumed by Fresnel ; but with all the squeezing 
 which the arbitrary constants furnished by theory 
 admit of, they were not able to obtain Fresnel's laws 
 except as an approximation. Had this been all, it is 
 possible that the more complicated laws expressed by 
 their formulae might have fitted observation as well as 
 the simpler and more elegant laws of Fresnel. But 
 the theory is hampered by a third ray which cannot 
 be got rid of, and which leads to conclusions at 
 variance with observation. While admiring therefore 
 the geometrical part of Fresnel's theory, we must 
 reject the mechanical conditions which he supposed to 
 exist in crystals, as not being in conformity with 
 nature. 
 
 Fresnel's laws have been obtained in an extremely 
 elegant manner, as the result of a rigorous theory, by 
 Green, who starting with an assumed mechanical state 
 inclusive of but more general than that assumed by 
 Fresnel, and subsequently limiting the generality by 
 a single condition which the phenomena of light 
 would naturally lead us to introduce, arrived directly 
 at Fresnel's laws. It was necessary however to sup- 
 pose the vibrations of polarized light to be in the 
 plane of polarization. In the same paper he showed 
 however that by starting with a mechanical state still 
 more general, limiting it as before, and introducing 
 
THEORIES OF DOUBLE REFRACTION. 1 29 
 
 two simple linear relations between the arbitrary 
 constants remaining, Fresnel's laws were again ob- 
 tained, but this time by supposing that in polarized 
 light the vibrations are perpendicular to the plane of 
 polarization. Almost simultaneously with Green 
 MacCullagh obtained equations of motion of the 
 ether in a crystal identical with those of Green in his 
 first theory, though by a method which does not seem 
 quite so satisfactory as that of Green. They led of 
 course to the same laws, and required the same 
 supposition as to the direction of the vibrations in 
 polarized light. Lame has given a theory sub- 
 stantially agreeing with Green's first theory ; and last 
 but not least we have the electro-magnetic theory of 
 Maxwell, which without any straining or assumption 
 of relations between constants leads directly to 
 Fresnel's laws. 
 
 It may seem strange that we should arrive at the 
 very same laws by such different theories ; first by 
 one which is not a rigorous theory at all, and then by 
 others which are rigorous, but which differ among 
 themselves, even to such an extent that in one the 
 vibrations in polarized light must be assumed to be 
 in, in another perpendicular to the plane of polariza- 
 tion. In explanation of this it is to be observed, first, 
 that all these theories alike involve the idea of 
 transverse vibrations, and secondly that Fresnel's laws 
 S. 9 
 
130 THE NATURE OF LIGHT. 
 
 are really the simplest which can in any way suit the 
 phenomena. Fresnel's laws are embraced in an 
 elegant construction applied to an ellipsoid ; and just 
 as an ellipsoid is the simplest generalization of a 
 sphere when we pass from what is alike in all directions 
 to what varies from one direction to another, so 
 Fresnel's laws are really the simplest that the nature 
 of the phenomenon, viewed in the light of the 
 theory of transverse vibrations, admits of. It is not 
 therefore so wonderful as at first sight might appear 
 that the same laws should be arrived at from theories 
 so different ; and while the deduction of these laws is 
 a strong confirmation of the truth of the theory of 
 transverse vibrations which is common to all the 
 methods, it is not itself alone to be taken as establish- 
 ing the truth of the supposition as to the mechanical 
 state of things in crystals which has been made in the 
 deduction of the laws. 
 
 I have mentioned Malus's discovery of the polari- 
 zation of light by reflection, and the question may 
 naturally arise, is this reconcileable with the theory of 
 transverse vibrations ? To show that it is, I need 
 only refer to Fresnel's deduction of the intensity of 
 the light reflected from an isotropic transparent 
 medium, according as the vibrations are in or per- 
 pendicular to the plane of incidence. These formulae 
 were obtained by Fresnel with his wonted sagacity 
 
THEORIES OF OTHER PHENOMENA. 131 
 
 from a process only partially complete, since we must 
 either allow that a part only of the necessary equations 
 of condition at the common boundary of the media 
 are satisfied, or else that the mechanical state for 
 which the conditions employed give the complete 
 solution remains to be defined. 
 
 Fresnel's deduction of his laws for the intensity of 
 reflected light was made on the supposition that in 
 polarized light the vibrations are perpendicular to the 
 plane of polarization. A slight difference of hypo- 
 thesis as to the state of things would lead, by reason- 
 ing very similar to that of Fresnel, to the very same 
 two formulae only with the directions of vibration to 
 which they respectively apply interchanged. On the 
 present supposition therefore the vibrations in polarized 
 light must be supposed to be in the plane of polari- 
 zation. 
 
 The polarization of light through the unequal 
 absorption belonging to the two rectangularly polarized 
 pencils within certain coloured doubly refracting 
 crystals, such as tourmaline, readily falls in with the 
 theory of transverse vibrations. For there can be no 
 doubt that absorption in general consists in the ex- 
 penditure of the incident ethereal vibrations in pro- 
 ducing molecular agitation; and it is easily under- 
 stood that the molecules may be more easily agitated 
 by an ethereal vibration in one direction than in 
 another. 
 
132 THE NATURE OF LIGHT. 
 
 The aim which I have proposed to myself in this 
 first course of the Burnett lectures has been to lay 
 before you, as impartially as I could, a summary of 
 the evidence on which we accept the answer to the 
 question, What is Light ? given when we say, Light 
 consists of undulations in a medium, called ether, per- 
 vading the interplanetary and interstellar spaces, and 
 existing also within bodies formed of ponderable 
 matter. Difference of refrangibility, with the ac- 
 companying difference of colour, depends upon a 
 difference in the frequency of these undulations. The 
 direction of vibration of the particles of the ether is 
 transverse to the direction of propagation of the 
 light, and accordingly (at any rate in the case of 
 vacuum or an isotropic medium) the vibrations take 
 place in the fronts of the waves, but in common light 
 are not otherwise restricted, while in polarized light 
 they are rectilinear, taking place in a direction which 
 is symmetrical with respect to the plane of polari- 
 zation. 
 
 Naturally the full force of the evidence can be felt 
 only by those who have well studied the subject. I 
 hope however that I may have succeeded in showing, 
 even to those who previously may have paid little 
 attention to the matter, that at least there are powerful 
 arguments in favour of the accepted answer. The 
 inductive arrangement, which seemed best fitted for 
 
CONCLUSION OF FIRST COURSE. 133 
 
 the object I had in view, naturally led to a treatment 
 in good measure historical, but I have not, I hope, 
 neglected recent researches. I have endeavoured to 
 discriminate, and to lead you to discriminate, between 
 what is well established and what is still speculative, 
 and have confined myself almost entirely to the 
 former. 
 
 Should i be permitted to deliver courses of 
 lectures again in the two following years, it is my 
 intention, in accordance with a scheme communicated 
 in outline to and approved by the Burnett Trustees, to 
 devote next year's course to researches in which 
 light has been used as a means of investigation, 
 while the third year's course would be assigned to 
 light considered in relation to its beneficial effects. 
 While the different objects to be held in view in 
 these lectures are more or less blended together, the 
 second course would more especially relate to recent 
 researches, while the third would naturally harmonize 
 with the original intentions of the Founder of the 
 Trust. 
 
 END OF FIRST COURSE. 
 
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