,,six ,,lectures ,,on ,,light ,,delivered ,,in ,,the ,,united ,,states ,,in #ahgb-ahgc ,,by ,,john ,,tyndall1 ,d4,c4,l41 ,,ll1,d41 ,f4,r4,s4 ,,late ,,professor ,,of ,,natural ,,philosophy ,,in ,,the ,,royal ,,institution ,,of ,,great ,,britain ,illustration3 ,sir ,thomas ,laurence ,,pra ,pinx ,henry ,adlarc4 ,sc4 ,signature3 ,thomas ,young ,london3 ,longmans ,co4 ,,sixth ,,impression ,,longmans1 ,,green1 ,,and ,,co4 #ci ,,paternoster ,,row1 ,,london ,,new ,,york ,,and ,,bombay #aijf ,,preface ,,to ,,the ,,fourth ,,edition4 ,in these ,lectures ,i have sought to render clear a difficult but profoundly interesting subject4 ,my aim has been not only to describe and illustrate in a familiar manner the principal laws and phenomena of light1 but to point out the origin1 and show the application1 of the theoretic conceptions which underlie and unite the whole1 and without which no real interpretation is possible4 ,the ,lectures1 as stated on the title-page1 were delivered in the ,united ,states in #ahgb-c4 ,i still retain a vivid and grateful remembrance of the cordiality with which they were received4 ,my scope and object are briefly indicated in the ',summary and ,conclusion1' which1 as recommended in a former edition1 might be1 not unfitly1 read as an introduction to the volume4 ,j4,t4 ,,alp ,,lusgen3 ,october #ahhe4 ,,contents4 ,,lecture ,i4 ,introductory ,uses of ,experiment ,early ,scientific ,notions ,sciences of ,observation ,knowledge of the ,ancients regarding ,light ,defects of the ,eye ,our ,instruments ,rectilineal ,propagation of ,light ,law of ,incidence and ,reflection ,sterility of the ,middle ,ages ,refraction ,discovery of ,snell ,partial and ,total ,reflection ,velocity of ,light ,roemer1 ,bradley1 ,foucault1 and ,fizeau ,principle of ,least ,action ,descartes and the ,rainbow ,newton's ,experiments on the ,composition of ,solar ,light ,his ,mistake regarding ,achromatism ,synthesis of ,white ,light ,yellow and ,blue ,lights produce ,white by their ,mixture ,colours of ,natural ,bodies ,absorption ,mixture of ,pigments contrasted with ,mixture of ,lights ,,lecture ,,ii4 ,origin of ,physical ,theories ,scope of the ,imagination ,newton and the ,emission ,theory ,verification of ,physical ,theories ,the ,luminiferous ,ether ,wave-theory of ,light ,thomas ,young ,fresnel and ,arago ,conception of ,wave-motion ,interference of ,waves ,constitution of ,sound-waves ,analogies of ,sound and ,light ,illustrations of ,wave-motion ,interference of ,sound ,waves ,optical ,illustrations ,pitch and ,colour ,lengths of the ,waves of ,light and ,rates of ,vibration of the ,ether-particles ,interference of ,light ,phenomena which first suggested the ,undulatory ,theory ,boyle and ,hooke ,the ,colours of thin ,plates ,the ,soap-bubble ,newton's ,rings ,theory of ',fits' ,its ,explanation of the ,rings ,overthrow of the ,theory ,diffraction of ,light ,colours produced by ,diffraction ,colours of ,mother-of-,pearl4 ,,lecture ,,iii4 ,relation of ,theories to ,experience ,origin of the ,notion of the ,attraction of ,gravitation ,notion of ,polarity1 how generated ,atomic ,polarity ,structural ,arrangements due to ,polarity ,architecture of ,crystals considered as an ,introduction to their ,action upon ,light ,notion of ,atomic ,polarity applied to ,crystalline ,structure ,experimental ,illustrations ,crystallization of ,water ,expansion by ,heat and by ,cold ,deportment of ,water considered and explained ,bearings of ,crystallization on ,optical ,phenomena ,refraction ,double ,refraction ,polarization ,action of ,tourmaline ,character of the ,beams emergent from ,iceland ,spar ,polarization by ordinary ,refraction and ,reflection ,depolarization4 ,,lecture ,,iv4 ,chromatic ,phenomena produced by ,crystals in ,polarized ,light ,the ,nicol ,prism ,polarizer and ,analyzer ,action of ,thick and ,thin ,plates of ,selenite ,colours dependent on ,thickness ,resolution of ,polarized ,beam into two others by the ,selenite ,one of them more retarded than the other ,recompounding of the two ,systems of ,waves by the ,analyzer ,interference thus rendered possible ,consequent ,production of ,colours ,action of ,bodies mechanically strained or pressed ,action of ,sonorous ,vibrations ,action of ,glass strained or pressed by ,heat ,circular ,polarization ,chromatic ,phenomena produced by ,quartz ,the ,magnetization of ,light ,rings surrounding the ,axes of ,crystals ,biaxal and ,uniaxal ,crystals ,grasp of the ,undulatory ,theory ,the ,colour and ,polarization of ,sky-light ,generation of ,artificial ,skies4 ,,lecture ,v4 ,range of ,vision not commensurate with ,range of ,radiation ,the ,ultra-violet ,rays ,fluorescence ,the rendering of invisible ,rays visible ,vision not the only ,sense appealed to by the ,solar and ,electric ,beam ,heat of ,beam ,combustion by ,total ,beam at the ,foci of ,mirrors and ,lenses ,combustion through ,ice-lens ,ignition of ,diamond ,search for the ,rays here effective ,sir ,william ,herschel's ,discovery of dark ,solar ,rays ,invisible ,rays the ,basis of the ,visible ,detachment by a ,ray-filter of the ,invisible ,rays from the ,visible ,combustion at ,dark ,foci ,conversion of ,heat-rays into ,light-rays ,calorescence ,part played in ,nature by ,dark ,rays ,identity of ,light and ,radiant ,heat ,invisible ,images ,reflection1 ,refraction1 ,plane ,polarization1 ,depolarization1 ,circular ,polarization1 ,double ,refraction1 and ,magnetization of ,radiant ,heat ,,lecture ,,vi4 ,principles of ,spectrum ,analysis ,prismatic ,analysis of the ,light of ,incandescent ,vapours ,discontinuous ,spectra ,spectrum ,bands proved by ,bunsen and ,kirchhoff to be characteristic of the ,vapour ,discovery of ,rubidium1 ,csium1 and ,thallium ,relation of ,emission to ,absorption ,the ,lines of ,fraunhofer ,their ,explanation by ,kirchhoff ,solar ,chemistry involved in this ,explanation ,foucault's ,experiment ,principles of ,absorption ,analogy of ,sound and ,light ,experimental ,demonstration of this ,analogy ,recent ,applications of the ,spectroscope ,summary and ,conclusion ,,appendix4 ,on the ,spectra of ,polarized ,light ,measurement of the ,waves of ,light ,,index ,,on ,,light ,,lecture ,i4 ,,introductory ,,uses ,,of ,,experiment ,,early ,,scientific ,,notions ,,sciences ,,of ,,observation ,,knowledge ,,of ,,the ,,ancients ,,regarding ,,light ,,defects ,,of ,,the ,,eye ,,our ,,instruments ,,rectilineal ,,propagation ,,of ,,light ,,law ,,of ,,incidence ,,and ,,reflection ,,sterility ,,of ,,the ,,middle ,,ages ,,refraction ,,discovery ,,of ,,snell ,,partial ,,and ,,total ,,reflection ,,velocity ,,of ,,light ,,roemer1 ,,bradley1 ,,foucault1 ,,and ,,fizeau ,,principle ,,of ,,least ,,action ,,descartes ,,and ,,the ,,rainbow ,,newton',s ,,experiments ,,on ,,the ,,composition ,,of ,,solar ,,light ,,his ,,mistake ,,as ,,regards ,,achromatism ,,synthesis ,,of ,,white ,,light ,,yellow ,,and ,,blue ,,lights ,,produce ,,white ,,by ,,their ,,mixture ,,colours ,,of ,,natural ,,bodies ,,absorption ,,mixture ,,of ,,pigments ,,contrasted ,,with ,,mixture ,,of ,,lights4 #a4 ,introduction4 ,some twelve years ago ,i published1 in ,england1 a little book entitled the ',glaciers of the ,alps1' and1 a couple of years subsequently1 a second book1 entitled ',heat a ,mode of ,motion4' ,these volumes were followed by others1 written with equal plainness1 and with a similar aim1 that aim being to develop and deepen sympathy between science and the world outside of science4 ,i agreed with thoughtful men#a who deemed it good for neither world to be isolated from the other1 or unsympathetic towards the other1 and1 to lessen this isolation1 at least in one department of science1 ,i swerved1 for a time1 from those original researches which have been the real pursuit and pleasure of my life4 ,the works here referred to were1 for the most part1 republished by the ,messrs4 ,appleton of ,new ,york1#b under the auspices of a man who is untiring in his efforts to diffuse sound scientific knowledge among the people of the ,united ,states2 whose energy1 ability1 and single-mindedness1 in the prosecution of an arduous task1 have won for him the sympathy and support of many of us in 'the old country4' ,i allude to ,professor ,youmans4 ,quite as rapidly as in ,england1 the aim of these works was understood and appreciated in the ,united ,states1 and they brought me from this side of the ,atlantic innumerable evidences of good-will4 ,year after year invitations reached me#c to visit ,america1 and last year 7#ahga7 ,i was honoured with a request so cordial1 signed by five-and-twenty names1 so distinguished in science1 in literature1 and in administrative position1 that ,i at once resolved to respond to it by braving not only the disquieting oscillations of the ,atlantic1 but the far more disquieting ordeal of appearing in person before the people of the ,united ,states4 ,this invitation1 conveyed to me by my accomplished friend ,professor ,lesley1 of ,philadelphia1 and preceded by a letter of the same purport from your scientific ,nestor1 the celebrated ,joseph ,henry1 of ,washington1 desired that ,i should lecture in some of the principal cities of the ,union4 ,this ,i agreed to do1 though much in the dark as to a suitable subject4 ,in answer to my inquiries1 however1 ,i was given to understand that a course of lectures1 showing the uses of experiment in the cultivation of ,natural ,knowledge1 would materially promote scientific education in this country4 ,and though such lectures involved the selection of weighty and delicate instruments1 and their transfer from place to place1 ,i determined to meet the wishes of my friends1 as far as the time and means at my disposal would allow4 #b4 ,subject of the ,course4 ,source of ,light employed4 ,experiments have two great uses--a use in discovery1 and a use in tuition4 ,they were long ago defined as the investigator's language addressed to ,nature1 to which she sends intelligible replies4 ,these replies1 however1 usually reach the questioner in whispers too feeble for the public ear4 ,but after the investigator comes the teacher1 whose function it is so to exalt and modify the experiments of his predecessor1 as to render them fit for public presentation4 ,this secondary function ,i shall endeavour1 in the present instance1 to fulfil4 ,taking a single department of natural philosophy as my subject1 ,i propose1 by means of it1 to illustrate the growth of scientific knowledge under the guidance of experiment4 ,i wish1 in the first place1 to make you acquainted with certain elementary phenomena2 then to point out to you how the theoretical principles by which phenomena are explained take root in the human mind1 and finally to apply these principles to the whole body of knowledge covered by the lectures4 ,the science of optics lends itself particularly well to this mode of treatment1 and on it1 therefore1 ,i propose to draw for the materials of the present course4 ,it will be best to begin with the few simple facts regarding light which were known to the ancients1 and to pass from them1 in historic gradation1 to the more abstruse discoveries of modern times4 ,all our notions of ,nature1 however exalted or however grotesque1 have their foundation in experience4 ,the notion of personal volition in ,nature had this basis4 ,in the fury and the serenity of natural phenomena the savage saw the transcript of his own varying moods1 and he accordingly ascribed these phenomena to beings of like passions with himself1 but vastly transcending him in power4 ,thus the notion of causality--the assumption that natural things did not come of themselves1 but had unseen antecedents--lay at the root of even the savage's interpretation of ,nature4 ,out of this bias of the human mind to seek for the causes of phenomena all science has sprung4 ,we will not now go back to man's first intellectual gropings2 much less shall we enter upon the thorny discussion as to how the groping man arose4 ,we will take him at that stage of his development1 when he became possessed of the apparatus of thought and the power of using it4 ,for a time--and that historically a long one--he was limited to mere observation1 accepting what ,nature offered1 and confining intellectual action to it alone4 ,the apparent motions of sun and stars first drew towards them the questionings of the intellect1 and accordingly astronomy was the first science developed4 ,slowly1 and with difficulty1 the notion of natural forces took root in the human mind4 ,slowly1 and with difficulty1 the science of mechanics had to grow out of this notion2 and slowly at last came the full application of mechanical principles to the motions of the heavenly bodies4 ,we trace the progress of astronomy through ,hipparchus and ,ptolemy2 and1 after a long halt1 through ,copernicus1 ,galileo1 ,tycho ,brahe1 and ,kepler2 while from the high table-land of thought occupied by these men1 ,newton shoots upwards like a peak1 overlooking all others from his dominant elevation4 ,but other objects than the motions of the stars attracted the attention of the ancient world4 ,light was a familiar phenomenon1 and from the earliest times we find men's minds busy with the attempt to render some account of it4 ,but without experiment1 which belongs to a later stage of scientific development1 little progress could be here made4 ,the ancients1 accordingly1 were far less successful in dealing with light than in dealing with solar and stellar motions4 ,still they did make some progress4 ,they satisfied themselves that light moved in straight lines2 they knew also that light was reflected from polished surfaces1 and that the angle of incidence was equal to the angle of reflection4 ,these two results of ancient scientific curiosity constitute the starting-point of our present course of lectures4 ,but in the first place it will be useful to say a few words regarding the source of light to be employed in our experiments4 ,the rusting of iron is1 to all intents and purposes1 the slow burning of iron4 ,it develops heat1 and1 if the heat be preserved1 a high temperature may be thus attained4 ,the destruction of the first ,atlantic cable was probably due to heat developed in this way4 ,other metals are still more combustible than iron4 ,you may ignite strips of zinc in a candle flame1 and cause them to burn almost like strips of paper4 ,but we must now expand our definition of combustion1 and include under this term1 not only combustion in air1 but also combustion in liquids4 ,water1 for example1 contains a store of oxygen1 which may unite with1 and consume1 a metal immersed in it2 it is from this kind of combustion that we are to derive the heat and light employed in our present course4 ,the generation of this light and of this heat merits a moment's attention4 ,before you is an instrument--a small voltaic battery--in which zinc is immersed in a suitable liquid4 ,an attractive force is at this moment exerted between the metal and the oxygen of the liquid2 actual combination1 however1 being in the first instance avoided4 ,uniting the two ends of the battery by a thick wire1 the attraction is satisfied1 the oxygen unites with the metal1 zinc is consumed1 and heat1 as usual1 is the result of the combustion4 ,a power which1 for want of a better name1 we call an electric current1 passes at the same time through the wire4 ,cutting the thick wire in two1 let the severed ends be united by a thin one4 ,it glows with a white heat4 ,whence comes that heat8 ,the question is well worthy of an answer4 ,suppose in the first instance1 when the thick wire is employed1 that we permit the action to continue until #ajj grains of zinc are consumed1 the amount of heat generated in the battery would be capable of accurate numerical expression4 ,let the action then continue1 with the thin wire glowing1 until #ajj grains of zinc are consumed4 ,will the amount of heat generated in the battery be the same as before8 ,no2 it will be less by the precise amount generated in the thin wire outside the battery4 ,in fact1 by adding the internal heat to the external1 we obtain for the combustion of #ajj grains of zinc a total which never varies4 ,we have here a beautiful example of that law of constancy as regards natural energies1 the establishment of which is the greatest achievement of modern science4 ,by this arrangement1 then1 we are able to burn our zinc at one place1 and to exhibit the effects of its combustion at another4 ,in ,new ,york1 for example1 we may have our grate and fuel2 but the heat and light of our fire may be made to appear at ,san ,francisco4 ,illustration3 ,fig4 #a4 ,removing the thin wire and attaching to the severed ends of the thick one two rods of coke we obtain1 on bringing the rods together 7as in fig4 #a71 a small star of light4 ,now1 the light to be employed in our lectures is a simple exaggeration of this star4 ,instead of being produced by ten cells1 it is produced by fifty4 ,placed in a suitable camera1 provided with a suitable lens1 this powerful source will give us all the light necessary for our experiments4 ,and here1 in passing1 ,i am reminded of the common delusion that the works of ,nature1 the human eye included1 are theoretically perfect4 ,the eye has grown for ages towards perfection2 but ages of perfecting may be still before it4 ,looking at the dazzling light from our large battery1 ,i see a luminous globe1 but entirely fail to see the shape of the coke-points whence the light issues4 ,the cause may be thus made clear3 ,on the screen before you is projected an image of the carbon points1 the whole of the glass lens in front of the camera being employed to form the image4 ,it is not sharp1 but surrounded by a halo which nearly obliterates the carbons4 ,this arises from an imperfection of the glass lens1 called its spherical aberration1 which is due to the fact that the circumferential and central rays have not the same focus4 ,the human eye labours under a similar defect1 and from this1 and other causes1 it arises that when the naked light from fifty cells is looked at the blur of light upon the retina is sufficient to destroy the definition of the retinal image of the carbons4 ,a long list of indictments might indeed be brought against the eye--its opacity1 its want of symmetry1 its lack of achromatism1 its partial blindness4 ,all these taken together caused ,helmholt to say that1 if any optician sent him an instrument so defective1 he would be justified in sending it back with the severest censure4 ,but the eye is not to be judged from the standpoint of theory4 ,it is not perfect1 but is on its way to perfection4 ,as a practical instrument1 and taking the adjustments by which its defects are neutralized into account1 it must ever remain a marvel to the reflecting mind4 #c4 ,rectilineal ,propagation of ,light4 ,elementary ,experiments4 ,law of ,reflection4 ,the ancients were aware of the rectilineal propagation of light4 ,they knew that an opaque body1 placed between the eye and a point of light1 intercepted the light of the point4 ,possibly the terms 'ray' and 'beam' may have been suggested by those straight spokes of light which1 in certain states of the atmosphere1 dart from the sun at his rising and his setting4 ,the rectilineal propagation of light may be illustrated by permitting the solar light to enter1 through a small aperture in a window-shutter1 a dark room in which a little smoke has been diffused4 ,in pure air you cannot see the beam1 but in smoky air you can1 because the light1 which passes unseen through the air1 is scattered and revealed by the smoke particles1 among which the beam pursues a straight course4 ,the following instructive experiment depends on the rectilineal propagation of light4 ,make a small hole in a closed window-shutter1 before which stands a house or a tree1 and place within the darkened room a white screen at some distance from the orifice4 ,every straight ray proceeding from the house1 or tree1 stamps its colour upon the screen1 and the sum of all the rays will1 therefore1 be an image of the object4 ,but1 as the rays cross each other at the orifice1 the image is inverted4 ,at present we may illustrate and expand the subject thus3 ,in front of our camera is a large opening 7,l1 fig4 #b71 from which the lens has been removed1 and which is closed at present by a sheet of tin-foil4 ,pricking by means of a common sewing-needle a small aperture in the tin-foil1 an inverted image of the carbon-points starts forth upon the screen4 ,a dozen apertures will give a dozen images1 a hundred a hundred1 a thousand a thousand4 ,but1 as the apertures come closer to each other1 that is to say1 as the tin-foil between the apertures vanishes1 the images overlap more and more4 ,removing the tin-foil altogether1 the screen becomes uniformly illuminated4 ,hence the light upon the screen may be regarded as the overlapping of innumerable images of the carbon-points4 ,in like manner the light upon every white wall1 on a cloudless day1 may be regarded as produced by the superposition of innumerable images of the sun4 ,illustration3 ,fig4 #b4 ,the law that the angle of incidence is equal to the angle of reflection has a bearing upon theory1 to be subsequently mentioned1 which renders its simple illustration here desirable4 ,a straight lath 7pointing to the figure #e on the arc in fig4 #c7 is fixed as an index perpendicular to a small looking-glass 7,m71 capable of rotation4 ,we begin by receiving a beam of light upon the glass which is reflected back along the line of its incidence4 ,the index being then turned1 the mirror turns with it1 and at each side of the index the incident and the reflected beams 7,l o1 o ,r7 track themselves through the dust of the room4 ,the mere inspection of the two angles enclosed between the index and the two beams suffices to show their equality2 while if the graduated arc be consulted1 the arc from #e to m is found accurately equal to the arc from #e to n4 ,the complete expression of the law of reflection is1 not only that the angles of incidence and reflection are equal1 but that the incident and reflected rays always lie in a plane perpendicular to the reflecting surface4 ,illustration3 ,fig4 #c4 ,this simple apparatus enables us to illustrate another law of great practical importance1 namely1 that when a mirror rotates1 the angular velocity of a beam reflected from it is twice that of the reflecting mirror4 ,a simple experiment will make this plain4 ,the arc 7m n1 fig4 #c7 before you is divided into ten equal parts1 and when the incident beam and the index cross the zero of the graduation1 both the incident and reflected beams are horizontal4 ,moving the index of the mirror to #a1 the reflected beam cuts the arc at #b2 moving the index to #b1 the arc is cut at #d2 moving the index to #c1 the arc is cut at #f2 moving the index at #d1 the arc is cut at #h2 finally1 moving the index to #e1 the arc is cut at #aj 7as in the figure74 ,in every case the reflected beam moves through twice the angle passed over by the mirror4 ,one of the principal problems of science is to help the senses of man1 by carrying them into regions which could never be attained without that help4 ,thus we arm the eye with the telescope when we want to sound the depths of space1 and with the microscope when we want to explore motion and structure in their infinitesimal dimensions4 ,now1 this law of angular reflection1 coupled with the fact that a beam of light possesses no weight1 gives us the means of magnifying small motions to an extraordinary degree4 ,thus1 by attaching mirrors to his suspended magnets1 and by watching the images of divided scales reflected from the mirrors1 the celebrated ,gauss was able to detect the slightest thrill of variation on the part of the earth's magnetic force4 ,by a similar arrangement the feeble attractions and repulsions of the diamagnetic force have been made manifest4 ,the minute elongation of a bar of metal1 by the mere warmth of the hand1 may be so magnified by this method1 as to cause the index-beam to move through #bj or #cj feet4 ,the lengthening of a bar of iron when it is magnetized may be also thus demonstrated4 ,helmholtz long ago employed this method of rendering evident to his students the classical experiments of ,du ,bois ,raymond on animal electricity2 while in ,sir ,william ,thomson's reflecting galvanometer the principle receives one of its latest and most important applications4 #d4 ,the ,refraction of ,light4 ,total ,reflection4 ,for more than a thousand years no step was taken in optics beyond this law of reflection4 ,the men of the ,middle ,ages1 in fact1 endeavoured1 on the one hand1 to develop the laws of the universe priori out of their own consciousness1 while many of them were so occupied with the concerns of a future world that they looked with a lofty scorn on all things pertaining to this one4 ,speaking of the natural philosophers of his time1 ,eusebius says1 ',it is not through ignorance of the things admired by them1 but through contempt of their useless labour1 that we think little of these matters1 turning our souls to the exercise of better things4' ,so also ,lactantius--',to search for the causes of things2 to inquire whether the sun be as large as he seems2 whether the moon is convex or concave2 whether the stars are fixed in the sky1 or float freely in the air2 of what size and of what material are the heavens2 whether they be at rest or in motion2 what is the magnitude of the earth2 on what foundations is it suspended or balanced2--to dispute and conjecture upon such matters is just as if we chose to discuss what we think of a city in a remote country1 of which we never heard but the name4' ,as regards the refraction of light1 the course of real inquiry was resumed in #aajj by an ,arabian philosopher named ,alhazen4 ,then it was taken up in succession by ,roger ,bacon1 ,vitellio1 and ,kepler4 ,one of the most important occupations of science is the determination1 by precise measurements1 of the quantitative relations of phenomena2 the value of such measurements depending greatly upon the skill and conscientiousness of the man who makes them4 ,vitellio appears to have been both skilful and conscientious1 while ,kepler's habit was to rummage through the observations of his predecessors1 to look at them in all lights1 and thus distil from them the principles which united them4 ,he had done this with the astronomical measurements of ,tycho ,brahe1 and had extracted from them the celebrated 'laws of ,kepler4' ,he did it also with ,vitellio's measurements of refraction4 ,but in this case he was not successful4 ,the principle1 though a simple one1 escaped him1 and it was first discovered by ,willebrord ,snell1 about the year #afba4 ,less with the view of dwelling upon the phenomenon itself than of introducing it in a form which will render subsequently intelligible to you the play of theoretic thought in ,newton's mind1 the fact of refraction may be here demonstrated4 ,i will not do this by drawing the course of the beam with chalk on a black board1 but by causing it to mark its own white track before you4 ,a shallow circular vessel 7,,rig1 fig4 #d71 half filled with water1 rendered slightly turbid by the admixture of a little milk1 or the precipitation of a little mastic1 is placed with its glass front vertical4 ,by means of a small plane reflector 7,m71 and through a slit 7,i7 in the hoop surrounding the vessel1 a beam of light is admitted in any required direction4 ,it impinges upon the water 7at ,o71 enters it1 and tracks itself through the liquid in a sharp bright band 7,o ,g74 ,meanwhile the beam passes unseen through the air above the water1 for the air is not competent to scatter the light4 ,a puff of smoke into this space at once reveals the track of the incident-beam4 ,if the incidence be vertical1 the beam is unrefracted4 ,if oblique1 its refraction at the common surface of air and water 7at ,o7 is rendered clearly visible4 ,it is also seen that reflection 7along ,o ,r7 accompanies refraction1 the beam dividing itself at the point of incidence into a refracted and a reflected portion4#d ,illustration3 ,fig4 #d4 ,the law by which ,snell connected together all the measurements executed up to his time1 is this3 ,let ,a ,b ,c ,d 7fig4 #e7 represent the outline of our circular vessel1 ,a ,c being the water-line4 ,when the beam is incident along ,b ,e1 which is perpendicular to ,a ,c1 there is no refraction4 ,when it is incident along m ,e1 there is refraction3 it is bent at ,e and strikes the circle at n4 ,when it is incident along m' ,e there is also refraction at ,e1 the beam striking the point n'4 ,from the ends of the two incident beams1 let the perpendiculars m o1 m' o' be drawn upon ,b ,d1 and from the ends of the refracted beams let the perpendiculars p n1 p' n' be also drawn4 ,measure the lengths of o m and of p n1 and divide the one by the other4 ,you obtain a certain quotient4 ,in like manner divide m' o' by the corresponding perpendicular p' n'2 you obtain precisely the same quotient4 ,snell1 in fact1 found this quotient to be a constant quantity for each particular substance1 though it varied in amount from one substance to another4 ,he called the quotient the index of refraction4 ,illustration ,fig4 #e ,in all cases where the light is incident from air upon the surface of a solid or a liquid1 or1 to speak more generally1 when the incidence is from a less highly refracting to a more highly refracting medium1 the reflection is partial4 ,in this case the most powerfully reflecting substances either transmit or absorb a portion of the incident light4 ,at a perpendicular incidence water reflects only #ah rays out of every #a1jjj2 glass reflects only #be rays1 while mercury reflects #fff ,when the rays strike the surface obliquely the reflection is augmented4 ,at an incidence of #dj1 for example1 water reflects #bb rays1 at #fj it reflects #fe rays1 at #hj #ccc rays2 while at an incidence of #hi1 where the light almost grazes the surface1 it reflects #gba rays out of every #a1jjj4 ,thus1 as the obliquity increases1 the reflection from water approaches1 and finally quite overtakes1 the perpendicular reflection from mercury2 but at no incidence1 however great1 when the incidence is from air1 is the reflection from water1 mercury1 or any other substance1 total4 ,still1 total reflection may occur1 and with a view to understanding its subsequent application in the ,nicol's prism1 it is necessary to state when it occurs4 ,this leads me to the enunciation of a principle which underlies all optical phenomena--the principle of reversibility4#e ,in the case of refraction1 for instance1 when the ray passes obliquely from air into water1 it is bent towards the perpendicular2 when it passes from water to air1 it is bent from the perpendicular1 and accurately reverses its course4 ,thus in fig4 #e1 if m ,e n be the track of a ray in passing from air into water1 n ,e m will be its track in passing from water into air4 ,let us push this principle to its consequences4 ,supposing the light1 instead of being incident along m ,e or m' ,e1 were incident as close as possible along ,c ,e 7fig4 #f72 suppose1 in other words1 that it just grazes the surface before entering the water4 ,after refraction it will pursue say the course ,e n''4 ,conversely1 if the light start from n''1 and be incident at ,e1 it will1 on escaping into the air1 just graze the surface of the water4 ,the question now arises1 what will occur supposing the ray from the water to follow the course n''' ,e1 which lies beyond n'' ,e8 ,the answer is1 it will not quit the water at all1 but will be totally reflected 7along ,e x74 ,at the under surface of the water1 moreover1 the law is just the same as at its upper surface1 the angle of incidence 7,d ,e n'''7 being equal to the angle of reflection 7,d ,e x74 ,illustration3 ,fig4 #f ,total reflection may be thus simply illustrated3--,place a shilling in a drinking-glass1 and tilt the glass so that the light from the shilling shall fall with the necessary obliquity upon the water surface above it4 ,look upwards through the water towards that surface1 and you see the image of the shilling shining there as brightly as the shilling itself4 ,thrust the closed end of an empty test-tube into water1 and incline the tube4 ,when the inclination is sufficient1 horizontal light falling upon the tube cannot enter the air within it1 but is totally reflected upward3 when looked down upon1 such a tube looks quite as bright as burnished silver4 ,pour a little water into the tube2 as the liquid rises1 total reflection is abolished1 and with it the lustre1 leaving a gradually diminishing shining zone1 which disappears wholly when the level of the water within the tube reaches that without it4 ,any glass tube1 with its end stopped water-tight1 will produce this effect1 which is both beautiful and instructive4 ,total reflection never occurs except in the attempted passage of a ray from a more refracting to a less refracting medium2 but in this case1 when the obliquity is sufficient1 it always occurs4 ,the mirage of the desert1 and other phantasmal appearances in the atmosphere1 are in part due to it4 ,when1 for example1 the sun heats an expanse of sand1 the layer of air in contact with the sand becomes lighter and less refracting than the air above it3 consequently1 the rays from a distant object1 striking very obliquely on the surface of the heated stratum1 are sometimes totally reflected upwards1 thus producing images similar to those produced by water4 ,i have seen the image of a rock called ,mont ,tombeline distinctly reflected from the heated air of the strand of ,normandy near ,avranches2 and by such delusive appearances the thirsty soldiers of the ,french army in ,egypt were greatly tantalised4 ,the angle which marks the limit beyond which total reflection takes place is called the limiting angle 7it is marked in fig4 #f by the strong line ,e n''74 ,it must evidently diminish as the refractive index increases4 ,for water it is #dh1 for flint glass #chda'1 and for diamond #bcdb'4 ,thus all the light incident from two complete quadrants1 or #ahj1 in the case of diamond1 is condensed into an angular space of #dgbb' 7twice #bcdb'7 by refraction4 ,coupled with its great refraction1 are the great dispersive and great reflective powers of diamond2 hence the extraordinary radiance of the gem1 both as regards white light and prismatic light4 #e4 ,velocity of ,light4 ,aberration4 ,principle of least ,action4 ,in #afgf a great impulse was given to optics by astronomy4 ,in that year ,olav ,roemer1 a learned ,dane1 was engaged at the ,observatory of ,paris in observing the eclipses of ,jupiter's moons4 ,the planet1 whose distance from the sun is #dge1fic1jjj miles1 has four satellites4 ,we are now only concerned with the one nearest to the planet4 ,roemer watched this moon1 saw it move round the planet1 plunge into ,jupiter's shadow1 behaving like a lamp suddenly extinguished3 then at the other edge of the shadow he saw it reappear1 like a lamp suddenly lighted4 ,the moon thus acted the part of a signal light to the astronomer1 and enabled him to tell exactly its time of revolution4 ,the period between two successive lightings up of the lunar lamp he found to be #db hours1 #bh minutes1 and #ce seconds4 ,this measurement of time was so accurate1 that having determined the moment when the moon emerged from the shadow1 the moment of its hundredth appearance could also be determined4 ,in fact1 it would be #ajj times #db hours1 #bh minutes1 #ce seconds1 after the first observation4 ,roemer's first observation was made when the earth was in the part of its orbit nearest ,jupiter4 ,about six months afterwards1 the earth being then at the opposite side of its orbit1 when the little moon ought to have made its hundredth appearance1 it was found unpunctual1 being fully #ae minutes behind its calculated time4 ,its appearance1 moreover1 had been growing gradually later1 as the earth retreated towards the part of its orbit most distant from ,jupiter4 ,roemer reasoned thus3 ',had ,i been able to remain at the other side of the earth's orbit1 the moon might have appeared always at the proper instant2 an observer placed there would probably have seen the moon #ae minutes ago1 the retardation in my case being due to the fact that the light requires #ae minutes to travel from the place where my first observation was made to my present position4' ,this flash of genius was immediately succeeded by another4 ',if this surmise be correct1' ,roemer reasoned1 'then as ,i approach ,jupiter along the other side of the earth's orbit1 the retardation ought to become gradually less1 and when ,i reach the place of my first observation1 there ought to be no retardation at all4' ,he found this to be the case1 and thus not only proved that light required time to pass through space1 but also determined its rate of propagation4 ,the velocity of light1 as determined by ,roemer1 is #aib1ejj miles in a second4 ,for a time1 however1 the observations and reasonings of ,roemer failed to produce conviction4 ,they were doubted by ,cassini1 ,fontenelle1 and ,hooke4 ,subsequently came the unexpected corroboration of ,roemer by the ,english astronomer1 ,bradley1 who noticed that the fixed stars did not really appear to be fixed1 but that they describe little orbits in the heavens every year4 ,the result perplexed him1 but ,bradley had a mind open to suggestion1 and capable of seeing1 in the smallest fact1 a picture of the largest4 ,he was one day upon the ,thames in a boat1 and noticed that as long as his course remained unchanged1 the vane upon his masthead showed the wind to be blowing constantly in the same direction1 but that the wind appeared to vary with every change in the direction of his boat4 ',here1' as ,whewell says1 'was the image of his case4 ,the boat was the earth1 moving in its orbit1 and the wind was the light of a star4' ,we may ask1 in passing1 what1 without the faculty which formed the 'image1' would ,bradley's wind and vane have been to him8 ,a wind and vane1 and nothing more4 ,you will immediately understand the meaning of ,bradley's discovery4 ,imagine yourself in a motionless railway-train1 with a shower of rain descending vertically downwards4 ,the moment the train begins to move1 the rain-drops begin to slant1 and the quicker the motion of the train the greater is the obliquity4 ,in a precisely similar manner the rays from a star1 vertically overhead1 are caused to slant by the motion of the earth through space4 ,knowing the speed of the train1 and the obliquity of the falling rain1 the velocity of the drops may be calculated2 and knowing the speed of the earth in her orbit1 and the obliquity of the rays due to this cause1 we can calculate just as easily the velocity of light4 ,bradley did this1 and the 'aberration of light1' as his discovery is called1 enabled him to assign to it a velocity almost identical with that deduced by ,roemer from a totally different method of observation4 ,subsequently ,fizeau1 and quite recently ,cornu1 employing not planetary or stellar distances1 but simply the breadth of the city of ,paris1 determined the velocity of light3 while ,foucault--a man of the rarest mechanical genius--solved the problem without quitting his private room4 ,owing to an error in the determination of the earth's distance from the sun1 the velocity assigned to light by both ,roemer and ,bradley is too great4 ,with a close approximation to accuracy it may be regarded as #ahf1jjj miles a second4 ,by ,roemer's discovery1 the notion entertained by ,descartes1 and espoused by ,hooke1 that light is propagated instantly through space1 was overthrown4 ,but the establishment of its motion through stellar space led to speculations regarding its velocity in transparent terrestrial substances4 ,the 'index of refraction' of a ray passing from air into water is #d_/c4 ,newton assumed these numbers to mean that the velocity of light in water being #d1 its velocity in air is #c2 and he deduced the phenomena of refraction from this assumption4 ,huyghens took the opposite and truer view4 ,according to this great man1 the velocity of light in water being #c1 its velocity in air is #d2 but both in ,newton's time and ours the same great principle determined1 and determines1 the course of light in all cases4 ,in passing from point to point1 whatever be the media in its path1 or however it may be refracted or reflected1 light takes the course which occupies least time4 ,thus in fig4 #d1 taking its velocity in air and in water into account1 the light reaches ,g from ,i more rapidly by travelling first to ,o1 and there changing its course1 than if it proceeded straight from ,i to ,g4 ,this is readily comprehended1 because1 in the latter case1 it would pursue a greater distance through the water1 which is the more retarding medium4 #f4 ,descartes' ,explanation of the ,rainbow4 ,snell's law of refraction is one of the corner-stones of optical science1 and its applications to-day are million-fold4 ,immediately after its discovery ,descartes applied it to the explanation of the rainbow4 ,a beam of solar light falling obliquely upon a rain-drop is refracted on entering the drop4 ,it is in part reflected at the back of the drop1 and on emerging it is again refracted4 ,by these two refractions1 and this single reflection1 the light is sent to the eye of an observer facing the drop1 and with his back to the sun4 ,conceive a line drawn from the sun1 through the back of his head1 to the observer's eye and prolonged beyond it4 ,conceive a second line drawn from the shower to the eye1 and enclosing an angle of #db with the line drawn from the sun4 ,along this second line a rain-drop when struck by a sunbeam will send red light to the eye4 ,every other drop similarly situated1 that is1 every drop at an angular distance of #db from the line through the sun and eye1 will do the same4 ,a circular band of red light is thus formed1 which may be regarded as the boundary of the base of a cone1 with its apex at the observer's eye4 ,because of the magnitude of the sun1 the angular width of this red band will be half a degree4 ,from the eye of the observer conceive another line to be drawn1 enclosing an angle1 not of #db1 but of #dj1 with the prolongation of the line drawn from the sun4 ,along this other line a rain-drop1 at its remote end1 when struck by a solar beam1 will send violet light to the eye4 ,all drops at the same angular distance will do the same1 and we shall therefore obtain a band of violet light of the same width as the red band4 ,these two bands constitute the limiting colours of the rainbow1 and between them the bands corresponding to the other colours lie4 ,thus the line drawn from the eye to the middle of the bow1 and the line drawn through the eye to the sun1 always enclose an angle of about #da4 ,to account for this was the great difficulty1 which remained unsolved up to the time of ,descartes4 ,taking a pen in hand1 and calculating by means of ,snell's law the track of every ray through a raindrop1 ,descartes found that1 at one particular angle1 the rays1 reflected at its back1 emerged from the drop almost parallel to each other4 ,they were thus enabled to preserve their intensity through long atmospheric distances4 ,at all other angles the rays quitted the drop divergent1 and through this divergence became so enfeebled as to be practically lost to the eye4 ,the angle of parallelism here referred to was that of forty-one degrees1 which observation had proved to be invariably associated with the rainbow4 ,from what has been said1 it is clear that two observers standing beside each other1 or one above the other1 nay1 that even the two eyes of the same observer1 do not see exactly the same bow4 ,the position of the base of the cone changes with that of its apex4 ,and here we have no difficulty in answering a question often asked--namely1 whether a rainbow is ever seen reflected in water4 ,seeing two bows1 the one in the heavens1 the other in the water1 you might be disposed to infer that the one bears the same relation to the other that a tree upon the water's edge bears to its reflected image4 ,the rays1 however1 which reach an observer's eye after reflection from the water1 and which form a bow in the water1 would1 were their course from the shower uninterrupted1 converge to a point vertically under the observer1 and as far below the level of the water as his eye is above it4 ,but under no circumstances could an eye above the water-level and one below it see the same bow--in other words1 the self-same drops of rain cannot form the reflected bow and the bow seen directly in the heavens4 ,the reflected bow1 therefore1 is not1 in the usual optical sense of the term1 the image of the bow seen in the sky4 #g4 ,analysis and ,synthesis of ,light4 ,doctrine of ,colours4 ,in the rainbow a new phenomenon was introduced--the phenomenon of colour4 ,and here we arrive at one of those points in the history of science1 when great men's labours so intermingle that it is difficult to assign to each worker his precise meed of honour4 ,descartes was at the threshold of the discovery of the composition of solar light2 but for ,newton was reserved the enunciation of the true law4 ,he went to work in this way3 ,through the closed window-shutter of a room he pierced an orifice1 and allowed a thin sunbeam to pass through it4 ,the beam stamped a round white image of the sun on the opposite wall of the room4 ,in the path of this beam ,newton placed a prism1 expecting to see the beam refracted1 but also expecting to see the image of the sun1 after refraction1 still round4 ,to his astonishment1 it was drawn out to an image with a length five times its breadth4 ,it was1 moreover1 no longer white1 but divided into bands of different colours4 ,newton saw immediately that solar light was composite1 not simple4 ,his elongated image revealed to him the fact that some constituents of the light were more deflected by the prism than others1 and he concluded1 therefore1 that white light was a mixture of lights of different colours1 possessing different degrees of refrangibility4 ,let us reproduce this celebrated experiment4 ,on the screen is now stamped a luminous disk1 which may stand for ,newton's image of the sun4 ,causing the beam 7from the aperture ,l1 fig4 #g7 which produces the disk to pass through a lens 7,e71 we form a sharp image of the aperture4 ,placing in the track of the beam a prism 7,p71 we obtain ,newton's coloured image1 with its red and violet ends1 which he called a spectrum4 ,newton divided the spectrum into seven parts--red1 orange1 yellow1 green1 blue1 indigo1 violet2 which are commonly called the seven primary or prismatic colours4 ,the drawing out of the white light into its constituent colours is called dispersion4 ,illustration3 ,fig4 #g4 ,this was the first analysis of solar light by ,newton2 but the scientific mind is fond of verification1 and never neglects it where it is possible4 ,newton completed his proof by synthesis in this way3 ,the spectrum now before you is produced by a glass prism4 ,causing the decomposed beam to pass through a second similar prism1 but so placed that the colours are refracted back and reblended1 the perfectly white luminous disk is restored4 ,illustration3 ,fig4 #h4 ,in this case1 refraction and dispersion are simultaneously abolished4 ,are they always so8 ,can we have the one without the other8 ,it was ,newton's conclusion that we could not4 ,here he erred1 and his error1 which he maintained to the end of his life1 retarded the progress of optical discovery4 ,dollond subsequently proved that by combining two different kinds of glass1 the colours can be extinguished1 still leaving a residue of refraction1 and he employed this residue in the construction of achromatic lenses--lenses yielding no colour--which ,newton thought an impossibility4 ,by setting a water-prism--water contained in a wedge-shaped vessel with glass sides 7,b1 fig4 #h7--;in opposition to a wedge of glass 7to the right of ,b71 this point can be illustrated before you4 ,we have first of all the position 7dotted7 of the unrefracted beam marked upon the screen2 then we produce the narrow water-spectrum 7,w72 finally1 by introducing a flint-glass prism1 we refract the beam back1 until the colour disappears 7at ,a74 ,the image of the slit is now white2 but though the dispersion is abolished1 there remains a very sensible amount of refraction4 ,this is the place to illustrate another point bearing upon the instrumental means employed in these lectures4 ,bodies differ widely from each other as to their powers of refraction and dispersion4 ,note the position of the water-spectrum upon the screen4 ,altering in no particular the wedge-shaped vessel1 but simply substituting for the water the transparent bisulphide of carbon1 you notice how much higher the beam is thrown1 and how much richer is the display of colour4 ,to augment the size of our spectrum we here employ 7at ,l7 a slit1 instead of a circular aperture4#f ,illustration3 ,fig4 #i4 ,the synthesis of white light may be effected in three ways1 all of which are worthy of attention3 ,here1 in the first instance1 we have a rich spectrum produced by the decomposition of the beam 7from ,l1 fig4 #i74 ,one face of the prism 7,p7 is protected by a diaphragm 7not shown in the figure71 with a longitudinal slit1 through which the beam passes into the prism4 ,it emerges decomposed at the other side4 ,i permit the colours to pass through a cylindrical lens 7,c71 which so squeezes them together as to produce upon the screen a sharply defined rectangular image of the longitudinal slit4 ,in that image the colours are reblended1 and it is perfectly white4 ,between the prism and the cylindrical lens may be seen the colours1 tracking themselves through the dust of the room4 ,cutting off the more refrangible fringe by a card1 the rectangle is seen red3 cutting off the less refrangible fringe1 the rectangle is seen blue4 ,by means of a thin glass prism 7,w71 ,i deflect one portion of the colours1 and leave the residual portion4 ,on the screen are now two coloured rectangles produced in this way4 ,these are complementary colours--colours which1 by their union1 produce white4 ,note1 that by judicious management1 one of these colours is rendered yellow1 and the other blue4 ,i withdraw the thin prism2 yellow and blue immediately commingle1 and we have white as the result of their union4 ,on our way1 then1 we remove the fallacy1 first exposed by ,wnsch1 and afterwards independently by ,helmholtz1 that the mixture of blue and yellow lights produces green4 ,restoring the circular aperture1 we obtain once more a spectrum like that of ,newton4 ,by means of a lens1 we can gather up these colours1 and build them together1 not to an image of the aperture1 but to an image of the carbon-points themselves4 ,finally1 by means of a rotating disk1 on which are spread in sectors the colours of the spectrum1 we blend together the prismatic colours in the eye itself1 and thus produce the impression of whiteness4 ,having unravelled the interwoven constituents of white light1 we have next to inquire1 ,what part the constitution so revealed enables this agent to play in ,nature8 ,to it we owe all the phenomena of colour1 and yet not to it alone2 for there must be a certain relationship between the ultimate particles of natural bodies and white light1 to enable them to extract from it the luxury of colour4 ,but the function of natural bodies is here selective1 not creative4 ,there is no colour generated by any natural body whatever4 ,natural bodies have showered upon them1 in the white light of the sun1 the sum total of all possible colours2 and their action is limited to the sifting of that total--the appropriating or absorbing of some of its constituents1 and the rejecting of others4 ,it will fix this subject in your minds if ,i say1 that it is the portion of light which they reject1 and not that which they appropriate or absorb1 that gives bodies their colours4 ,let us begin our experimental inquiries here by asking1 ,what is the meaning of blackness8 ,pass a black ribbon through the colours of the spectrum2 it quenches all of them4 ,the meaning of blackness is thus revealed--it is the result of the absorption of all the constituents of solar light4 ,pass a red ribbon through the spectrum4 ,in the red light the ribbon is a vivid red4 ,why8 ,because the light that enters the ribbon is not quenched or absorbed1 but in great part sent back to the eye4 ,place the same ribbon in the green of the spectrum2 it is black as jet4 ,it absorbs the green light1 and renders the space on which that light falls a space of intense darkness4 ,place a green ribbon in the green of the spectrum4 ,it shines vividly with its proper colour2 transfer it to the red1 it is black as jet4 ,here it absorbs all the light that falls upon it1 and offers mere darkness to the eye4 ,thus1 when white light is employed1 the red sifts it by quenching the green1 and the green sifts it by quenching the red1 both exhibiting the residual colour4 ,the process through which natural bodies acquire their colours is therefore a negative one4 ,the colours are produced by subtraction1 not by addition4 ,this red glass is red because it destroys all the more refrangible rays of the spectrum4 ,this blue liquid is blue because it destroys all the less refrangible rays4 ,both together are opaque because the light transmitted by the one is quenched by the other4 ,in this way1 by the union of two transparent substances1 we obtain a combination as dark as pitch to solar light4 ,this other liquid1 finally1 is purple because it destroys the green and the yellow1 and allows the terminal colours of the spectrum to pass unimpeded4 ,from the blending of the blue and the red this gorgeous purple is produced4 ,one step further for the sake of exactness4 ,the light which falls upon a body is divided into two portions1 one of which is reflected from the surface of the body2 and this is of the same colour as the incident light4 ,if the incident light be white1 the superficially reflected light will also be white4 ,solar light1 for example1 reflected from the surface of even a black body1 is white4 ,the blackest camphine smoke in a dark room1 through which a sunbeam passes from an aperture in the window-shutter1 renders the track of the beam white1 by the light scattered from the surfaces of the soot particles4 ,the moon appears to us as if ',clothed in white samite1 mystic1 wonderful2' but were it covered with the blackest velvet it would still hang as a white orb in the heavens1 shining upon our world substantially as it does now4 #h4 ,colours of ,pigments as distinguished from ,colours of ,light4 ,the second portion of the incident light enters the body1 and upon its treatment there the colour of the body depends4 ,and here a moment may properly be given to the analysis of the action of pigments upon light4 ,they are composed of fine particles mixed with a vehicle2 but how intimately soever the particles may be blended1 they still remain particles1 separated1 it may be1 by exceedingly minute distances1 but still separated4 ,to use the scientific phrase1 they are not optically continuous4 ,now1 wherever optical continuity is ruptured we have reflection of the incident light4 ,it is the multitude of reflections at the limiting surfaces of the particles that prevents light from passing through snow1 powdered glass1 or common salt4 ,the light here is exhausted in echoes1 not extinguished by true absorption4 ,it is the same kind of reflection that renders the thunder-cloud so impervious to light4 ,such a cloud is composed of particles of water1 mixed with particles of air1 both separately transparent1 but practically opaque when thus mixed together4 ,in the case of pigments1 then1 the light is reflected at the limiting surfaces of the particles1 but it is in part absorbed within the particles4 ,the reflection is necessary to send the light back to the eye2 the absorption is necessary to give the body its colour4 ,the same remarks apply to flowers4 ,the rose is red1 in virtue1 not of the light reflected from its surface1 but of light which has entered its substance1 which has been reflected from surfaces within1 and which1 in returning through the substance1 has had its green extinguished4 ,a similar process in the case of hard green leaves extinguishes the red1 and sends green light from the body of the leaves to the eye4 ,all bodies1 even the most transparent1 are more or less absorbent of light4 ,take the case of water4 ,a glass cell of clear water interposed in the track of our beam does not perceptibly change any one of the colours of the spectrum4 ,still absorption1 though insensible1 has here occurred1 and to render it sensible we have only to increase the depth of the water through which the light passes4 ,instead of a cell an inch thick1 let us take a layer1 ten or fifteen feet thick3 the colour of the water is then very evident4 ,by augmenting the thickness we absorb more of the light1 and by making the thickness very great we absorb the light altogether4 ,lampblack or pitch can do no more1 and the only difference in this respect between them and water is that a very small depth in their case suffices to extinguish all the light4 ,the difference between the highest known transparency and the highest known opacity is one of degree merely4 ,if1 then1 we render water sufficiently deep to quench all the light2 and if from the interior of the water no light reaches the eye1 we have the condition necessary to produce blackness4 ,looked properly down upon1 there are portions of the ,atlantic ,ocean to which one would hardly ascribe a trace of colour3 at the most a tint of dark indigo reaches the eye4 ,the water1 in fact1 is practically black1 and this is an indication both of its depth and purity4 ,but the case is entirely changed when the ocean contains solid particles in a state of mechanical suspension1 capable of sending the light impinging on them back to the eye4 ,throw1 for example1 a white pebble1 or a white dinner plate1 into the blackest ,atlantic water2 as it sinks it becomes greener and greener1 and1 before it disappears1 it reaches a vivid blue green4 ,break such a pebble1 or plate1 into fragments1 these will behave like the unbroken mass3 grind the pebble to powder1 every particle will yield its modicum of green2 and if the particles be so fine as to remain suspended in the water1 the scattered light will be a uniform green4 ,hence the greenness of shoal water4 ,you go to bed with the black water of the ,atlantic around you4 ,you rise in the morning1 find it a vivid green1 and correctly infer that you are crossing the ,bank of ,newfoundland4 ,such water is found charged with fine matter in a state of mechanical suspension4 ,the light from the bottom may sometimes come into play1 but it is not necessary4 ,the subaqueous foam1 generated by the screw or paddle-wheels of a steamer1 also sends forth a vivid green4 ,the foam here furnishes a reflecting surface1 the water between the eye and it the absorbing medium4 ,nothing can be more superb than the green of the ,atlantic waves when the circumstances are favourable to the exhibition of the colour4 ,as long as a wave remains unbroken no colour appears1 but when the foam just doubles over the crest like an ,alpine snow-cornice1 under the cornice we often see a display of the most exquisite green4 ,it is metallic in its brilliancy4 ,the foam is first illuminated1 and it scatters the light in all directions2 the light which passes through the higher portion of the wave alone reaches the eye1 and gives to that portion its matchless colour4 ,the folding of the wave1 producing1 as it does1 a series of longitudinal protuberances and furrows which act like cylindrical lenses1 introduces variations in the intensity of the light1 and materially enhances its beauty4 ,we are now prepared for the further consideration of a point already adverted to1 and regarding which error long found currency4 ,you will find it stated in many books that blue light and yellow light mixed together1 produce green4 ,but blue and yellow have been just proved to be complementary colours1 producing white by their mixture4 ,the mixture of blue and yellow pigments undoubtedly produces green1 but the mixture of pigments is a totally different thing from the mixture of lights4 ,helmholtz has revealed the cause of the green produced by a mixture of blue and yellow pigments4 ,no natural colour is pure4 ,a blue liquid1 or a blue powder1 permits not only the blue to pass through it1 but a portion of the adjacent green4 ,a yellow powder is transparent not only to the yellow light1 but also in part to the adjacent green4 ,now1 when blue and yellow are mixed together1 the blue cuts off the yellow1 the orange1 and the red2 the yellow1 on the other hand1 cuts off the violet1 the indigo1 and the blue4 ,green is the only colour to which both are transparent1 and the consequence is that1 when white light falls upon a mixture of yellow and blue powders1 the green alone is sent back to the eye4 ,you have already seen that the fine blue ammonia-sulphate of copper transmits a large portion of green1 while cutting off all the less refrangible light4 ,a yellow solution of picric acid also allows the green to pass1 but quenches all the more refrangible light4 ,what must occur when we send a beam through both liquids8 ,the experimental answer to this question is now before you3 the green band of the spectrum alone remains upon the screen4 ,the impurity of natural colours is strikingly illustrated by an observation recently communicated to me by ,mr4 ,woodbury4 ,on looking through a blue glass at green leaves in sunshine1 he saw the superficially reflected light blue4 ,the light1 on the contrary1 which came from the body of the leaves was crimson4 ,on examination1 ,i found that the glass employed in this observation transmitted both ends of the spectrum1 the red as well as the blue1 and that it quenched the middle4 ,this furnished an easy explanation of the effect4 ,in the delicate spring foliage the blue of the solar light is for the most part absorbed1 and a light1 mainly yellowish green1 but containing a considerable quantity of red1 escapes from the leaf to the eye4 ,on looking at such foliage through the violet glass1 the green and the yellow are stopped1 and the red alone reaches the eye4 ,thus regarded1 therefore1 the leaves appear like faintly blushing roses1 and present a very beautiful appearance4 ,with the blue ammonia-sulphate of copper1 which transmits no red1 this effect is not obtained4 ,as the year advances the crimson gradually hardens to a coppery red2 and in the dark green leaves of old ivy it is almost absent4 ,permitting a beam of white light to fall upon fresh leaves in a dark room1 the sudden change from green to red1 and from red back to green1 when the violet glass is alternately introduced and withdrawn1 is very surprising4 ,looked at through the same glass1 the meadows in ,may appear of a warm purple4 ,with a solution of permanganate of potash1 which1 while it quenches the centre of the spectrum1 permits its ends to pass more freely than the violet glass1 excellent effects are also obtained4#g ,this question of absorption1 considered with reference to its molecular mechanism1 is one of the most subtle and difficult in physics4 ,we are not yet in a condition to grapple with it1 but we shall be by-and-by4 ,meanwhile we may profitably glance back on the web of relations which these experiments reveal to us4 ,we have1 firstly1 in solar light an agent of exceeding complexity1 composed of innumerable constituents1 refrangible in different degrees4 ,we find1 secondly1 the atoms and molecules of bodies gifted with the power of sifting solar light in the most various ways1 and producing by this sifting the colours observed in nature and art4 ,to do this they must possess a molecular structure commensurate in complexity with that of light itself4 ,thirdly1 we have the human eye and brain1 so organized as to be able to take in and distinguish the multitude of impressions thus generated4 ,the light1 therefore1 at starting is complex2 to sift and select it as they do1 natural bodies must be complex2 while to take in the impressions thus generated1 the human eye and brain1 however we may simplify our conceptions of their action1#h must be highly complex4 ,whence this triple complexity8 ,if what are called material purposes were the only end to be served1 a much simpler mechanism would be sufficient4 ,but1 instead of simplicity1 we have prodigality of relation and adaptation--and this1 apparently1 for the sole purpose of enabling us to see things robed in the splendours of colour4 ,would it not seem that ,nature harboured the intention of educating us for other enjoyments than those derivable from meat and drink8 ,at all events1 whatever ,nature meant--and it would be mere presumption to dogmatize as to what she meant--we find ourselves here1 as the upshot of her operations1 endowed1 not only with capacities to enjoy the materially useful1 but endowed with others of indefinite scope and application1 which deal alone with the beautiful and the true4 ,,lecture ,,ii4 ,,origin ,,of ,,physical ,,theories ,,scope ,,of ,,the ,,imagination ,,newton ,,and ,,the ,,emission ,,theory ,,verification ,,of ,,physical ,,theories ,,the ,,luminiferous ,,ether ,,wave ,,theory ,,of ,,light ,,thomas ,,young ,,fresnel ,,and ,,arago ,,conception ,,of ,,wave-,,motion ,,interference ,,of ,,waves ,,constitution ,,of ,,sound-,,waves ,,analogies ,,of ,,sound ,,and ,,light ,,illustrations ,,of ,,wave-,,motion ,,interference ,,of ,,sound-,,waves ,,optical ,,illustrations ,,pitch ,,and ,,colour ,,lengths ,,of ,,the ,,waves ,,of ,,light ,,and ,,rates ,,of ,,vibration ,,of ,,the ,,ether-,,particles ,,interference ,,of ,,light ,,phenomena ,,which ,,first ,,suggested ,,the ,,undulatory ,,theory ,,boyle ,,and ,,hooke ,,the ,,colours ,,of ,,thin ,,plates ,,the ,,soap-,,bubble ,,newton',s ,,rings ,,theory ,,of ',,fits' ,,its ,,explanation ,,of ,,the ,,rings ,,over-,,throw ,,of ,,the ,,theory ,,diffraction ,,of ,,light ,,colours ,,produced ,,by ,,diffraction ,,colours ,,of ,,mother-,,of-,,pearl4 #a4 ,origin and ,scope of ,physical ,theories4 ,we might vary and extend our experiments on ,light indefinitely1 and they certainly would prove us to possess a wonderful mastery over the phenomena4 ,but the vesture of the agent only would thus be revealed1 not the agent itself4 ,the human mind1 however1 is so constituted that it can never rest satisfied with this outward view of natural things4 ,brightness and freshness take possession of the mind when it is crossed by the light of principles1 showing the facts of ,nature to be organically connected4 ,let us1 then1 inquire what this thing is that we have been generating1 reflecting1 refracting and analyzing4 ,in doing this1 we shall learn that the life of the experimental philosopher is twofold4 ,he lives1 in his vocation1 a life of the senses1 using his hands1 eyes1 and ears in his experiments3 but such a question as that now before us carries him beyond the margin of the senses4 ,he cannot consider1 much less answer1 the question1 ',what is light8' without transporting himself to a world which underlies the sensible one1 and out of which all optical phenomena spring4 ,to realise this subsensible world the mind must possess a certain pictorial power4 ,it must be able to form definite images of the things which that world contains2 and to say that1 if such or such a state of things exist in the subsensible world1 then the phenomena of the sensible one must1 of necessity1 grow out of this state of things4 ,physical theories are thus formed1 the truth of which is inferred from their power to explain the known and to predict the unknown4 ,this conception of physical theory implies1 as you perceive1 the exercise of the imagination--a word which seems to render many respectable people1 both in the ranks of science and out of them1 uncomfortable4 ,that men in the ranks of science should feel thus is1 ,i think1 a proof that they have suffered themselves to be misled by the popular definition of a great faculty1 instead of observing its operation in their own minds4 ,without imagination we cannot take a step beyond the bourne of the mere animal world1 perhaps not even to the edge of this one4 ,but1 in speaking thus of imagination1 ,i do not mean a riotous power which deals capriciously with facts1 but a well-ordered and disciplined power1 whose sole function is to form such conceptions as the intellect imperatively demands4 ,imagination1 thus exercised1 never really severs itself from the world of fact4 ,this is the storehouse from which its materials are derived2 and the magic of its art consists1 not in creating things anew1 but in so changing the magnitude1 position1 grouping1 and other relations of sensible things1 as to render them fit for the requirements of the intellect in the subsensible world4#i ,descartes imagined space to be filled with something that transmitted light instantaneously4 ,firstly1 because1 in his experience1 no measurable interval was known to exist between the appearance of a flash of light1 however distant1 and its effect upon consciousness2 and secondly1 because1 as far as his experience went1 no physical power is conveyed from place to place without a vehicle4 ,but his imagination helped itself farther by illustrations drawn from the world of fact4 ',when1' he says1' one walks in darkness with staff in hand1 the moment the distant end of the staff strikes an obstacle the hand feels it4 ,this explains what might otherwise be thought strange1 that the light reaches us instantaneously from the sun4 ,i wish thee to believe that light in the bodies that we call luminous is nothing more than a very brisk and violent motion1 which1 by means of the air and other transparent media1 is conveyed to the eye1 exactly as the shock through the walking-stick reaches the hand of a blind man4 ,this is instantaneous1 and would be so even if the intervening distance were greater than that between earth and heaven4 ,it is therefore no more necessary that anything material should reach the eye from the luminous object1 than that something should be sent from the ground to the hand of the blind man when he is conscious of the shock of his staff4' ,the celebrated ,robert ,hooke at first threw doubt upon this notion of ,descartes1 but he afterwards substantially espoused it4 ,the belief in instantaneous transmission was destroyed by the discovery of ,roemer referred to in our last lecture4 #b4 ,the ,emission ,theory of ,light4 ,the case of ,newton still more forcibly illustrates the position1 that in forming physical theories we draw for our materials upon the world of fact4 ,before he began to deal with light1 he was intimately acquainted with the laws of elastic collision1 which all of you have seen more or less perfectly illustrated on a billiard-table4 ,as regards the collision of sensible elastic masses1 ,newton knew the angle of incidence to be equal to the angle of reflection1 and he also knew that experiment1 as shown in our last lecture 7fig4 #c71 had established the same law with regard to light4 ,he thus found in his previous knowledge the material for theoretic images4 ,he had only to change the magnitude of conceptions already in his mind to arrive at the ,emission ,theory of ,light4 ,newton supposed light to consist of elastic particles of inconceivable minuteness1 shot out with inconceivable rapidity by luminous bodies4 ,optical reflection certainly occurred as if light consisted of such particles1 and this was ,newton's justification for introducing them4 ,but this is not all4 ,in another important particular1 also1 ,newton's conceptions regarding the nature of light were influenced by his previous knowledge4 ,he had been pondering over the phenomena of gravitation1 and had made himself at home amid the operations of this universal power4 ,perhaps his mind at this time was too freshly and too deeply imbued with these notions to permit of his forming an unfettered judgment regarding the nature of light4 ,be that as it may1 ,newton saw in ,refraction the result of an attractive force exerted on the light-particles4 ,he carried his conception out with the most severe consistency4 ,dropping vertically downwards towards the earth's surface1 the motion of a body is accelerated as it approaches the earth4 ,dropping downwards towards a horizontal surface--say from air on to glass or water--the velocity of the light-particles1 when they came close to the surface1 is1 according to ,newton1 also accelerated4 ,approaching such a surface obliquely1 he supposed the particles1 when close to it1 to be drawn down upon it1 as a projectile is deflected by gravity to the surface of the earth4 ,this deflection was1 according to ,newton1 the refraction seen in our last lecture 7fig4 #d74 ,finally1 it was supposed that differences of colour might be due to differences in the 'bigness' of the particles4 ,this was the physical theory of light enunciated and defended by ,newton2 and you will observe that it simply consists in the transference of conceptions1 born in the world of the senses1 to a subsensible world4 ,but1 though the region of physical theory lies thus behind the world of senses1 the verifications of theory occur in that world4 ,laying the theoretic conception at the root of matters1 we determine by deduction what are the phenomena which must of necessity grow out of this root4 ,if the phenomena thus deduced agree with those of the actual world1 it is a presumption in favour of the theory4 ,if1 as new classes of phenomena arise1 they also are found to harmonise with theoretic deduction1 the presumption becomes still stronger4 ,if1 finally1 the theory confers prophetic vision upon the investigator1 enabling him to predict the occurrence of phenomena which have never yet been seen1 and if those predictions be found on trial to be rigidly correct1 the persuasion of the truth of the theory becomes overpowering4 ,thus working backwards from a limited number of phenomena1 the human mind1 by its own expansive force1 reaches a conception which covers them all4 ,there is no more wonderful performance of the intellect than this2 but we can render no account of it4 ,like the scriptural gift of the ,spirit1 no man can tell whence it cometh4 ,the passage from fact to principle is sometimes slow1 sometimes rapid1 and at all times a source of intellectual joy4 ,when rapid1 the pleasure is concentrated1 and becomes a kind of ecstasy or intoxication4 ,to any one who has experienced this pleasure1 even in a moderate degree1 the action of ,archimedes when he quitted the bath1 and ran naked1 crying ',eureka6' through the streets of ,syracuse1 becomes intelligible4 ,how1 then1 did it fare with the ,emission ,theory when the deductions from it were brought face to face with natural phenomena8 ,tested by experiment1 it was found competent to explain many facts1 and with transcendent ingenuity its author sought to make it account for all4 ,he so far succeeded1 that men so celebrated as ,laplace and ,malus1 who lived till #ahab1 and ,biot and ,brewster1 who lived till our own time1 were found among his disciples4 #c4 ,the ,undulatory ,theory of ,light4 ,still1 even at an early period of the existence of the ,emission ,theory1 one or two great men were found espousing a different one4 ,they furnish another illustration of the law that1 in forming theories1 the scientific imagination must draw its materials from the world of fact and experience4 ,it was known long ago that sound is conveyed in waves or pulses through the air2 and no sooner was this truth well housed in the mind than it became the basis of a theoretic conception4 ,it was supposed that light1 like sound1 might also be the product of wave-motion4 ,but what1 in this case1 could be the material forming the waves8 ,for the waves of sound we have the air of our atmosphere2 but the stretch of imagination which filled all space with a luminiferous ether trembling with the waves of light was so bold as to shock cautious minds4 ,in one of my latest conversations with ,sir ,david ,brewster1 he said to me that his chief objection to the undulatory theory of light was1 that he could not think the ,creator capable of so clumsy a contrivance as the filling of space with ether to produce light4 ,this1 ,i may say1 is very dangerous ground1 and the quarrel of science with ,sir ,david1 on this point as with many estimable persons on other points1 is1 that they profess to know too much about the mind of the ,creator4 ,this conception of an ether was advocated1 and successfully applied to various phenomena of optics1 by the illustrious astronomer1 ,huyghens4 ,he deduced from it the laws of reflection and refraction1 and applied it to explain the double refraction of ,iceland spar4 ,the theory was espoused and defended by the celebrated mathematician1 ,euler4 ,they were1 however1 opposed by ,newton1 whose authority at the time bore them down4 ,or shall we say it was authority merely8 ,not quite so4 ,newton's preponderance was in some degree due to the fact that1 though ,huyghens and ,euler were right in the main1 they did not possess sufficient data to prove themselves right4 ,no human authority1 however high1 can maintain itself against the voice of ,nature speaking through experiment4 ,but the voice of ,nature may be an uncertain voice1 through the scantiness of data4 ,this was the case at the period now referred to1 and at such a period1 by the authority of ,newton1 all antagonists were naturally overborne4 ,the march of mind is rhythmic1 not uniform1 and this great ,emission ,theory1 which held its ground so long1 resembled one of those circles which1 according to your countryman ,emerson1 the intermittent force of genius periodically draws round the operations of the intellect1 but which are eventually broken through by pressure from behind4 ,in the year #aggc was born1 at ,milverton1 in ,somersetshire1 a circle-breaker of this kind4 ,he was educated for the profession of a physician1 but was too strong to be tied down to professional routine4 ,he devoted himself to the study of natural philosophy1 and became in all its departments a master4 ,he was also a master of letters4 ,languages1 ancient and modern1 were housed within his brain1 and1 to use the words of his epitaph1 'he first penetrated the obscurity which had veiled for ages the hieroglyphics of ,egypt4' ,it fell to the lot of this man to discover facts in optics which ,newton's theory was incompetent to explain1 and his mind roamed in search of a sufficient theory4 ,he had made himself acquainted with all the phenomena of wave-motion2 with all the phenomena of sound2 working successfully in this domain as an original discoverer4 ,thus informed and disciplined1 he was prepared to detect any resemblance which might reveal itself between the phenomena of light and those of wave-motion4 ,such resemblances he did detect2 and1 spurred on by the discovery1 he pursued his speculations and experiments1 until he finally succeeded in placing on an immovable basis the ,undulatory ,theory of ,light4 ,the founder of this great theory was ,thomas ,young1 a name1 perhaps1 unfamiliar to many of you1 but which ought to be familiar to you all4 ,permit me1 therefore1 by a kind of geometrical construction which ,i once ventured to employ in ,london1 to give you a notion of the magnitude of this man4 ,let ,newton stand erect in his age1 and ,young in his4 ,draw a straight line from ,newton to ,young1 tangent to the heads of both4 ,this line would slope downwards from ,newton to ,young1 because ,newton was certainly the taller man of the two4 ,but the slope would not be steep1 for the difference of stature was not excessive4 ,the line would form what engineers call a gentle gradient from ,newton to ,young4 ,place underneath this line the biggest man born in the interval between both4 ,it may be doubted whether he would reach the line2 for if he did he would be taller intellectually than ,young1 and there was probably none taller4 ,but ,i do not want you to rest on ,english estimates of ,young2 the ,german1 ,helmholtz1 a kindred genius1 thus speaks of him3 ,his was one of the most profound minds that the world has ever seen2 but he had the misfortune to be too much in advance of his age4 ,he excited the wonder of his contemporaries1 who1 however1 were unable to follow him to the heights at which his daring intellect was accustomed to soar4 ,his most important ideas lay1 therefore1 buried and forgotten in the folios of the ,royal ,society1 until a new generation gradually and painfully made the same discoveries1 and proved the exactness of his assertions and the truth of his demonstrations4 ,it is quite true1 as ,helmholtz says1 that ,young was in advance of his age2 but something is to be added which illustrates the responsibility of our public writers4 ,for twenty years this man of genius was quenched--hidden from the appreciative intellect of his country-men--deemed in fact a dreamer1 through the vigorous sarcasm of a writer who had then possession of the public ear1 and who in the ,edinburgh ,review poured ridicule upon ,young and his speculations4 ,to the celebrated ,frenchmen ,fresnel and ,arago he was first indebted for the restitution of his rights2 for they1 especially ,fresnel1 independently remade and vastly extended his discoveries4 ,to the students of his works ,young has long since appeared in his true light1 but these twenty blank years pushed him from the public mind1 which became in time filled with the fame of ,young's colleague at the ,royal ,institution1 ,davy1 and afterwards with the fame of ,faraday4 ,carlyle refers to a remark of ,novalis1 that a man's self-trust is enormously increased the moment he finds that others believe in him4 ,if the opposite remark be true--if it be a fact that public disbelief weakens a man's force--there is no calculating the amount of damage these twenty years of neglect may have done to ,young's productiveness as an investigator4 ,it remains to be stated that his assailant was ,mr4 ,henry ,brougham1 afterwards ,lord ,chancellor of ,england4 #d4 ,wave-,motion1 ,interference of ,waves1 ',whirlpool ,rapids' of ,niagara4 ,our hardest work is now before us4 ,but the capacity for hard work depends in a great measure on the antecedent winding up of the will2 ,i would call upon you1 therefore1 to gird up your loins for coming labours4 ,in the earliest writings of the ancients we find the notion that sound is conveyed by the air4 ,aristotle gives expression to this notion1 and the great architect ,vitruvius compares the waves of sound to waves of water4 ,but the real mechanism of wave-motion was hidden from the ancients1 and indeed was not made clear until the time of ,newton4 ,the central difficulty of the subject was1 to distinguish between the motion of the wave itself1 and the motion of the particles which at any moment constitute the wave4 ,stand upon the seashore and observe the advancing rollers before they are distorted by the friction of the bottom4 ,every wave has a back and a front1 and1 if you clearly seize the image of the moving wave1 you will see that every particle of water along the front of the wave is in the act of rising1 while every particle along its back is in the act of sinking4 ,the particles in front reach in succession the crest of the wave1 and as soon as the crest is past they begin to fall4 ,they then reach the furrow or sinus of the wave1 and can sink no farther4 ,immediately afterwards they become the front of the succeeding wave1 rise again until they reach the crest1 and then sink as before4 ,thus1 while the waves pass onwards horizontally1 the individual particles are simply lifted up and down vertically4 ,observe a sea-fowl1 or1 if you are a swimmer1 abandon yourself to the action of the waves2 you are not carried forward1 but simply rocked up and down4 ,the propagation of a wave is the propagation of a form1 and not the transference of the substance which constitutes the wave4 ,the length of the wave is the distance from crest to crest1 while the distance through which the individual particles oscillate is called the amplitude of the oscillation4 ,you will notice that in this description the particles of water are made to vibrate across the line of propagation4#aj ,and now we have to take a step forwards1 and it is the most important step of all4 ,you can picture two series of waves proceeding from different origins through the same water4 ,when1 for example1 you throw two stones into still water1 the ring-waves proceeding from the two centres of disturbance intersect each other4 ,now1 no matter how numerous these waves may be1 the law holds good that the motion of every particle of the water is the algebraic sum of all the motions imparted to it4 ,if crest coincide with crest and furrow with furrow1 the wave is lifted to a double height above its sinus2 if furrow coincide with crest1 the motions are in opposition and their sum is zero4 ,we have then still water4 ,this action of wave upon wave is technically called interference1 a term1 to be remembered4 ,to the eye of a person conversant with these principles1 nothing can be more interesting than the crossing of water ripples4 ,through their interference the water-surface is sometimes shivered into the most beautiful mosaic1 trembling rhythmically as if with a kind of visible music4 ,when waves are skilfully generated in a dish of mercury1 a strong light thrown upon the shining surface1 and reflected on to a screen1 reveals the motions of the liquid metal4 ,the shape of the vessel determines the forms of the figures produced4 ,in a circular dish1 for example1 a disturbance at the centre propagates itself as a series of circular waves1 which1 after reflection1 again meet at the centre4 ,if the point of disturbance be a little way removed from the centre1 the interference of the direct and reflected waves produces the magnificent chasing shown in the annexed figure4#aa ,the light reflected from such a surface yields a pattern of extraordinary beauty4 ,when the mercury is slightly struck by a needle-point in a direction concentric with the surface of the vessel1 the lines of light run round in mazy coils1 interlacing and unravelling themselves in a wonderful manner4 ,when the vessel is square1 a splendid chequer-work is produced by the crossing of the direct and reflected waves4 ,thus1 in the case of wave-motion1 the most ordinary causes give rise to most exquisite effects4 ,the words of ,emerson are perfectly applicable here3-- ,illustration3 ,fig4 #aj4 ',thou can'st not wave thy staff in the air1 ,or dip thy paddle in the lake1 ,but it carves the brow of beauty there4 ,and the ripples in rhymes the oars forsake4' ,the most impressive illustration of the action of waves on waves that ,i have ever seen occurs near ,niagara4 ,for a distance of two miles1 or thereabouts1 below the ,falls1 the river ,niagara flows unruffled through its excavated gorge4 ,the bed subsequently narrows1 and the water quickens its motion4 ,at the place called the ',whirlpool ,rapids1' ,i estimated the width of the river at #cjj feet1 an estimate confirmed by the dwellers on the spot4 ,when it is remembered that the drainage of nearly half a continent is compressed into this space1 the impetuosity of the river's escape through this gorge may be imagined4 ,two kinds of motion are here obviously active1 a motion of translation and a motion of undulation--the race of the river through its gorge1 and the great waves generated by its collision with the obstacles in its way4 ,in the middle of the stream1 the rush and tossing are most violent2 at all events1 the impetuous force of the individual waves is here most strikingly displayed4 ,vast pyramidal heaps leap incessantly from the river1 some of them with such energy as to jerk their summits into the air1 where they hang suspended as bundles of liquid pearls1 which1 when shone upon by the sun1 are of indescribable beauty4 ,the first impression1 and1 indeed1 the current explanation of these ,rapids is1 that the central bed of the river is cumbered with large boulders1 and that the jostling1 tossing1 and wild leaping of the waters there are due to its impact against these obstacles4 ,a very different explanation occurred to me upon the spot4 ,boulders derived from the adjacent cliffs visibly cumber the sides of the river4 ,against these the water rises and sinks rhythmically but violently1 large waves being thus produced4 ,on the generation of each wave there is an immediate compounding of the wave-motion with the river-motion4 ,the ridges1 which in still water would proceed in circular curves round the centre of disturbance1 cross the river obliquely1 and the result is1 that at the centre waves commingle which have really been generated at the sides4 ,this crossing of waves may be seen on a small scale in any gutter after rain2 it may also be seen on simply pouring water from a wide-lipped jug4 ,where crest and furrow cross each other1 the wave is annulled2 where furrow and furrow cross1 the river is ploughed to a greater depth2 and where crest and crest aid each other1 we have that astonishing leap of the water which breaks the cohesion of the crests1 and tosses them shattered into the air4 ,the phenomena observed at the ,whirlpool ,rapids constitute1 in fact1 one of the grandest illustrations of the principle of interference4 #e4 ,analogies of ,sound and ,light4 ,thomas ,young's fundamental discovery in optics was that the principle of ,interference was applicable to light4 ,long prior to his time an ,italian philosopher1 ,grimaldi1 had stated that under certain circumstances two thin beams of light1 each of which1 acting singly1 produced a luminous spot upon a white wall1 when caused to act together1 partially quenched each other and darkened the spot4 ,this was a statement of fundamental significance1 but it required the discoveries and the genius of ,young to give it meaning4 ,how he did so will gradually become clear to you4 ,you know that air is compressible3 that by pressure it can be rendered more dense1 and that by dilatation it can be rendered more rare4 ,properly agitated1 a tuning-fork now sounds in a manner audible to you all1 and most of you know that the air through which the sound is passing is parcelled out into spaces in which the air is condensed1 followed by other spaces in which the air is rarefied4 ,these condensations and rarefactions constitute what we call waves of sound4 ,you can imagine the air of a room traversed by a series of such waves1 and you can imagine a second series sent through the same air1 and so related to the first that condensation coincides with condensation and rarefaction with rarefaction4 ,the consequence of this coincidence would be a louder sound than that produced by either system of waves taken singly4 ,but you can also imagine a state of things where the condensations of the one system fall upon the rarefactions of the other system4 ,in this case 7other things being equal7 the two systems would completely neutralize each other4 ,each of them taken singly produces sound2 both of them taken together produce no sound4 ,thus by adding sound to sound we produce silence1 as ,grimaldi1 in his experiment1 produced darkness by adding light to light4 ,through his investigations on sound1 which were fruitful and profound1 ,young approached the study of light4 ,he put meaning into the observation of ,grimaldi1 and immensely extended it4 ,with splendid success he applied the undulatory theory to the explanation of the colours of thin plates1 and to those of striated surfaces4 ,he discovered and explained classes of colour which had been previously unnoticed or unknown4 ,on the assumption that light was wave-motion1 all his experiments on interference were accounted for2 on the assumption that light was flying particles1 nothing was explained4 ,in the time of ,huyghens and ,euler a medium had been assumed for the transmission of the waves of light2 but ,newton raised the objection that1 if light consisted of the waves of such a medium1 shadows could not exist4 ,the waves1 he contended1 would bend round opaque bodies and produce the motion of light behind them1 as sound turns a corner1 or as waves of water wash round a rock4 ,it was proved that the bending round referred to by ,newton actually occurs1 but that the inflected waves abolish each other by their mutual interference4 ,young also discerned a fundamental difference between the waves of light and those of sound4 ,could you see the air through which sound-waves are passing1 you would observe every individual particle of air oscillating to and fro1 in the direction of propagation4 ,could you see the luminiferous ether1 you would also find every individual particle making a small excursion to and fro2 but here the motion1 like that assigned to the water-particles above referred to1 would be across the line of propagation4 ,the vibrations of the air are longitudinal1 those of the ether transversal4 ,the most familiar illustration of the interference of sound-waves is furnished by the beats produced by two musical sounds slightly out of unison4 ,when two tuning-forks in perfect unison are agitated together the two sounds flow without roughness1 as if they were but one4 ,but1 by attaching with wax to one of the forks a little weight1 we cause it to vibrate more slowly than its neighbour4 ,suppose that one of them performs #aja vibrations in the time required by the other to perform #ajj1 and suppose that at starting the condensations and rarefactions of both forks coincide4 ,at the #ajast vibration of the quicker fork they will again coincide1 that fork at this point having gained one whole vibration1 or one whole wavelength1 upon the other4 ,but a little reflection will make it clear that1 at the #ejth vibration1 the two forks condensation where the other tends to produce a rarefaction2 by the united action of the two forks1 therefore1 the sound is quenched1 and we have a pause of silence4 ,this occurs where one fork has gained half a wavelength upon the other4 ,at the #ajast vibration1 as already stated1 we have coincidence1 and1 therefore1 augmented sound2 at the #aejth vibration we have again a quenching of the sound4 ,here the one fork is three half-waves in advance of the other4 ,in general terms1 the waves conspire when the one series is an even number of half-wave lengths1 and they destroy each other when the one series is an odd number of half-wave lengths in advance of the other4 ,with two forks so circumstanced1 we obtain those intermittent shocks of sound separated by pauses of silence1 to which we give the name of beats4 ,by a suitable arrangement1 moreover1 it is possible to make one sound wholly extinguish another4 ,along four distinct lines1 for example1 the vibrations of the two prongs of a tuning-fork completely blot each other out4#ab ,the pitch of sound is wholly determined by the rapidity of the vibration1 as the intensity is by the amplitude4 ,what pitch is to the ear in acoustics1 colour is to the eye in the undulatory theory of light4 ,though never seen1 the lengths of the waves of light have been determined4 ,their existence is proved by their effects1 and from their effects also their lengths may be accurately deduced4 ,this may1 moreover1 be done in many ways1 and1 when the different determinations are compared1 the strictest harmony is found to exist between them4 ,this consensus of evidence is one of the strongest points of the undulatory theory4 ,the shortest waves of the visible spectrum are those of the extreme violet2 the longest1 those of the extreme red2 while the other colours are of intermediate pitch or wavelength4 ,the length of a wave of the extreme red is such1 that it would require #ci1jjj such waves1 placed end to end1 to cover one inch1 while #fd1fca of the extreme violet waves would be required to span the same distance4 ,now1 the velocity of light1 in round numbers1 is #ahf1jjj miles per second4 ,reducing this to inches1 and multiplying the number thus found by #ci1jjj1 we find the number of waves of the extreme red1 in #ahf1jjj miles1 to be four hundred and sixty millions of millions4 ,all these waves enter the eye1 and strike the retina at the back of the eye in one second4 ,in a similar manner1 it may be found that the number of shocks corresponding to the impression of violet is six hundred and seventy-eight millions of millions4 ,all space is filled with matter oscillating at such rates4 ,from every star waves of these dimensions move1 with the velocity of light1 like spherical shells in all directions4 ,and in ether1 just as in water1 the motion of every particle is the algebraic sum of all the separate motions imparted to it4 ,one motion does not blot out the other2 or1 if extinction occur at one point1 it is strictly atoned for1 by augmented motion1 at some other point4 ,every star declares by its light its undamaged individuality1 as if it alone had sent its thrills through space4 #f4 ,interference of ,light4 ,illustration3 ,fig4 #aa4 ,the principle of interference1 as just stated1 applies to the waves of light as it does to the waves of water and the waves of sound4 ,and the conditions of interference are the same in all three4 ,if two series of light-waves of the same length start at the same moment from a common origin 7say ,a1 fig4 #aa71 crest coincides with crest1 sinus with sinus1 and the two systems blend together to a single system 7,a m n7 of double amplitude4 ,if both series start at the same moment1 one of them being1 at starting1 a whole wavelength in advance of the other1 they also add themselves together1 and we have an augmented luminous effect4 ,the same occurs when the one system of waves is any even number of semi-undulations in advance of the other4 ,but if the one system be half a wave-length 7as at ,a' a'1 fig4 #ab71 or any odd number of half wavelengths1 in advance1 then the crests of the one fall upon the sinuses of the other2 the one system1 in fact1 tends to lift the particles of ether at the precise places where the other tends to depress them2 hence1 through the joint action of these opposing forces 7indicated by the arrows7 the light-ether remains perfectly still4 ,this stillness of the ether is what we call darkness1 which corresponds with a dead level in the case of water4 ,illustration3 ,fig4 #ab4 ,it was said in our first lecture1 with reference to the colours produced by absorption1 that the function of natural bodies is selective1 not creative2 that they extinguish certain constituents of the white solar light1 and appear in the colours of the unextinguished light4 ,it must at once occur to you that1 inasmuch as we have in interference an agency by which light may be self-extinguished1 we may have in it the conditions for the production of colour4 ,but this would imply that certain constituents are quenched by interference1 while others are permitted to remain4 ,this is the fact2 and it is entirely due to the difference in the lengths of the waves of light4 #g4 ,colours of thin ,films4 ,observations of ,boyle and ,hooke4 ,this subject may be illustrated by the phenomena which first suggested the undulatory theory to the mind of ,hooke4 ,these are the colours of thin transparent films of all kinds1 known as the colours of thin plates4 ,in this relation no object in the world possesses a deeper scientific interest than a common soap-bubble4 ,and here let me say emerges one of the difficulties which the student of pure science encounters in the presence of 'practical' communities like those of ,america and ,england2 it is not to be expected that such communities can entertain any profound sympathy with labours which seem so far removed from the domain of practice as are many of the labours of the man of science4 ,imagine ,dr4 ,draper spending his days in blowing soap-bubbles and in studying their colours6 ,would you show him the necessary patience1 or grant him the necessary support8 ,and yet be it remembered it was thus that minds like those of ,boyle1 ,newton and ,hooke were occupied2 and that on such experiments has been founded a theory1 the issues of which are incalculable4 ,i see no other way for you1 laymen1 than to trust the scientific man with the choice of his inquiries2 he stands before the tribunal of his peers1 and by their verdict on his labours you ought to abide4 ,whence1 then1 are derived the colours of the soap-bubble8 ,imagine a beam of white light impinging on the bubble4 ,when it reaches the first surface of the film1 a known fraction of the light is reflected back4 ,but a large portion of the beam enters the film1 reaches its second surface1 and is again in part reflected4 ,the waves from the second surface thus turn back and hotly pursue the waves from the first surface4 ,and1 if the thickness of the film be such as to cause the necessary retardation1 the two systems of waves interfere with each other1 producing augmented or diminished light1 as the case may be4 ,but1 inasmuch as the waves of light are of different lengths1 it is plain that1 to produce extinction in the case of the longer waves1 a greater thickness of film is necessary than in the case of the shorter ones4 ,different colours1 therefore1 must appear at different thicknesses of the film4 ,take with you a little bottle of spirit of turpentine1 and pour it into one of your country ponds4 ,you will then see the glowing of those colours over the surface of the water4 ,on a small scale we produce them thus3 ,a common tea-tray is filled with water1 beneath the surface of which dips the end of a pipette4 ,a beam of light falls upon the water1 and is reflected by it to the screen4 ,spirit of turpentine is poured into the pipette2 it descends1 issues from the end in minute drops1 which rise in succession to the surface4 ,on reaching it1 each drop spreads suddenly out as a film1 and glowing colours immediately flash forth upon the screen4 ,the colours change as the thickness of the film changes by evaporation4 ,they are also arranged in zones1 in consequence of the gradual diminution of thickness from the centre outwards4 ,any film whatever will produce these colours4 ,the film of air between two plates of glass squeezed together1 exhibits1 as shown by ,hooke1 rich fringes of colour4 ,a particularly fine example of these fringes is now before you4 ,nor is even air necessary2 the rupture of optical continuity suffices4 ,smite with an axe the black1 transparent ice--black1 because it is pure and of great depth--under the moraine of a glacier2 you readily produce in the interior flaws which no air can reach1 and from these flaws the colours of thin plates sometimes break like fire4 ,but the source of most historic interest is1 as already stated1 the soap-bubble4 ,with one of the mixtures employed by the eminent blind philosopher1 ,plateau1 in his researches on the cohesion figures of thin films1 we obtain in still air a bubble ten or twelve inches in diameter4 ,you may look at the bubble itself1 or you may look at its projection upon the screen2 rich colours arranged in zones are1 in both cases1 exhibited4 ,rendering the beam parallel1 and permitting it to impinge upon the sides1 bottom1 and top of the bubble1 gorgeous fans of colour1 reflected from the bubble1 overspread the screen1 rotating as the beam is carried round4 ,by this experiment the internal motions of the film are also strikingly displayed4 ,not in a moment are great theories elaborated3 the facts which demand them become first prominent2 then1 to the period of observation succeeds a period of pondering and of tentative explanation4 ,by such efforts the human mind is gradually prepared for the final theoretic illumination4 ,the colours of thin plates1 for example1 occupied the attention of ,robert ,boyle4 ,in his ',experimental ,history of ,colours' he contends against the schools which affirmed that colour was 'a penetrative quality that reaches to the innermost parts of the object1' adducing opposing facts4 ',to give you a first instance1' he says1 ',i shall need but to remind you of what ,i told you a little after the beginning of this essay1 touching the blue and red and yellow that may be produced upon a piece of tempered steel2 for these colours1 though they be very vivid1 yet if you break the steel they adorn1 they will appear to be but superficial4' ,he then describes1 in phraseology which shows the delight he took in his work1 the following beautiful experiment3-- ',we took a quantity of clean lead1 and melted it with a strong fire1 and then immediately pouring it out into a clean vessel of convenient shape and matter 7we used one of iron1 that the great and sudden heat might not injure it71 and then carefully and nimbly taking off the scum that floated on the top1 we perceived1 as we expected1 the smooth and glossy surface of the melted matter to be adorned with a very glorious colour1 which1 being as transitory as delightful1 did almost immediately give place to another vivid colour1 and that was as quickly succeeded by a third1 and this1 as it were1 chased away by a fourth2 and so these wonderfully vivid colours successively appeared and vanished till the metal ceasing to be hot enough to hold any longer this pleasing spectacle1 the colours that chanced to adorn the surface when the lead thus began to cool remained upon it1 but were so superficial that how little soever we scraped off the surface of the lead1 we did1 in such places1 scrape off all the colour4' ',these things1' he adds1 'suggested to me some thoughts or ravings which ,i have not now time to acquaint you with4'#ac ,he extends his observations to essential oils and spirits of wine1 'which being shaken till they have good store of bubbles1 those bubbles will 7if attentively considered7 appear adorned with various and lovely colours1 which all immediately vanish upon the retrogressing of the liquid which affords these bubbles their skins into the rest of the oil4' ,he also refers to the colour of glass films4 ',i have seen one that was skilled in fashioning glasses by the help of a lamp blowing some of them so strongly as to burst them2 whereupon it was found that the tenacity of the metal was such that before it broke it suffered itself to be reduced into films so extremely thin that they constantly showed upon their surface the varying colours of the rainbow4'#ad ,subsequent to ,boyle the colours of thin plates occupied the attention of ,robert ,hooke1 in whose writings we find a dawning of the undulatory theory of light4 ,he describes with great distinctness the colours obtained with thin flakes of ',muscovy glass' 7talc71 also those surrounding flaws in crystals where optical continuity is destroyed4 ,he shows very clearly the dependence of the colour upon the thickness of the film1 and proves by microscopic observation that plates of a uniform thickness yield uniform colours4 ',if1' he says1 'you take any small piece of the ,muscovy glass1 and with a needle1 or some other convenient instrument1 cleave it oftentimes into thinner and thinner lamin1 you shall find that until you come to a determinate thinness of them they shall appear transparent and colourless2 but if you continue to split and divide them further1 you shall find at last that each plate shall appear most lovely tinged or imbued with a determinate colour4 ,if1 further1 by any means you so flaw a pretty thick piece that one part begins to cleave a little from the other1 and between these two there be gotten some pellucid medium1 those laminated or pellucid bodies that fill that space shall exhibit several rainbows or coloured lines1 the colours of which will be disposed and ranged according to the various thicknesses of the several parts of the plate4' ,he then describes fully and clearly the experiment with pressed glasses already referred to3-- ',take two small pieces of ground and polished looking-glass plate1 each about the bigness of a shilling3 take these two dry1 and with your forefingers and thumbs press them very hard and close together1 and you shall find that when they approach each other very near there will appear several irises or coloured lines1 in the same manner almost as in the ,muscovy glass2 and you may very easily change any of the colours of any part of the interposed body by pressing the plates closer and harder together1 or leaving them more lax--that is1 a part which appeared coloured with a red1 may presently be tinged with a yellow1 blue1 green1 purple1 or the like4 ',any substance1' he says1 'provided it be thin and transparent1 will show these colours4' ,like ,boyle1 he obtained them with glass films2 he also procured them with bubbles of pitch1 rosin1 colophony1 turpentine1 solutions of several gums1 as gum arabic in water1 any glutinous liquor1 as wort1 wine1 spirit of wine1 oyl of turpentine1 glare of snails1 c4 ,hooke's writings show that even in his day the idea that both light and heat are modes of motion had taken possession of many minds4 ',first1' he says1 'that all kind of fiery burning bodies have their parts in motion ,i think will be easily granted me4 ,that the spark struck from a flint and steel is in rapid agitation ,i have elsewhere made probable2444 that heat argues a motion of the internal parts is 7as ,i said before7 generally granted2444 and that in all extremely hot shining bodies there is a very quick motion that causes light1 as well as a more robust that causes heat1 may be argued from the celerity wherewith the bodies are dissolved4 ,next1 it must be a vibrative motion4' ,his reference to the quick motion of light and the more robust motion of heat is a remarkable stroke of sagacity2 but ,hooke's direct insight is better than his reasoning2 for the proofs he adduces that light is 'a vibrating motion' have no particular bearing upon the question4 ,still the ,undulatory ,theory had undoubtedly dawned upon the mind of this remarkable man4 ,in endeavouring to account for the colours of thin plates1 he again refers to the relation of colour to thickness3 he dwells upon the fact that the film which shows these colours must be transparent1 proving this by showing that however thin an opaque body was rendered no colours were produced4 ',this1' he says1 ',i have often tried by pressing a small globule of mercury between two smooth plates of glass1 whereby ,i have reduced that body to a much greater thinness than was requisite to exhibit the colours with a transparent body4' ,then follows the sagacious remark that to produce the colours 'there must be a considerable reflecting body adjacent to the under or further side of the lamina or plate3 for this ,i always found1 that the greater that reflection was the more vivid were the appearing colours4 ,from which observation1' he continues1 'it is most evident1 that the reflection from the further or under side of the body is the principal cause of the production of these colours4' ,he draws a diagram1 correctly representing the reflection at the two surfaces of the film2 but here his clearness ends4 ,he ascribes the colours to a coalescence or confusion of the two reflecting pulses2 the principal of interference being unknown to him1 he could not go further in the way of explanation4 #h4 ,newton's ,rings4 ,relation of ,colour to ,thickness of ,film4 ,illustration3 ,fig4 #ac ,in this way1 then1 by the active operation of different minds1 facts are observed1 examined1 and the precise conditions of their appearance determined4 ,all such work in science is the prelude to other work2 and the efforts of ,boyle and ,hooke cleared the way for the optical career of ,newton4 ,he conquered the difficulty which ,hooke had found insuperable1 and determined by accurate measurements the relation of the thickness of the film to the colour it displays4 ,in doing this his first care was to obtain a film of variable and calculable depth4 ,on a plano-convex glass lens 7,d ,b ,e1 fig4 #ac7 of very feeble curvature he laid a plate of glass 7,a ,c7 with a plane surface1 thus obtaining a film of air of gradually increasing depth from the point of contact 7,b7 outwards4 ,on looking at the film in monochromatic light he saw1 with the delight attendant on fulfilled prevision1 surrounding the place of contact1 a series of bright rings separated from each other by dark ones1 and becoming more closely packed together as the distance from the point of contact augmented 7as in fig4 #ad74 ,when he employed red light1 his rings had certain diameters2 when he employed blue light1 the diameters were less4 ,in general terms1 the more refrangible the light the smaller were the rings4 ,causing his glasses to pass through the spectrum from red to blue1 the rings gradually contracted2 when the passage was from blue to red1 the rings expanded4 ,this is a beautiful experiment1 and appears to have given ,newton the most lively satisfaction4 ,when white light fell upon1 the glasses1 inasmuch as the colours were not superposed1 a series of iris-coloured circles was obtained4 ,a magnified image of ,newton's rings is now before you1 and1 by employing in succession red1 blue1 and white light1 we obtain all the effects observed by ,newton4 ,you notice that in monochromatic light the rings run closer and closer together as they recede from the centre4 ,this is due to the fact that at a distance the film of air thickens more rapidly than near the centre4 ,when white light is employed1 this closing up of the rings causes the various colours to be superposed1 so that after a certain thickness they are blended together to white light1 the rings then ceasing altogether4 ,it needs but a moment's reflection to understand that the colours of thin plates1 produced by white light1 are never unmixed or monochromatic4 ,illustration3 ,fig4 #ad ,newton compared the tints obtained in this way with the tints of his soap-bubble1 and he calculated the corresponding thickness4 ,how he did this may be thus made plain to you3 ,suppose the water of the ocean to be absolutely smooth2 it would then accurately represent the earth's curved surface4 ,let a perfectly horizontal plane touch the surface at any point4 ,knowing the earth's diameter1 any engineer or mathematician in this room could tell you how far the sea's surface will lie below this plane1 at the distance of a yard1 ten yards1 a hundred yards1 or a thousand yards from the point of contact of the plane and the sea4 ,it is common1 indeed1 in levelling operations1 to allow for the curvature of the earth4 ,newton's calculation was precisely similar4 ,his plane glass was a tangent to his curved one4 ,from its refractive index and focal distance he determined the diameter of the sphere of which his curved glass formed a segment1 he measured the distances of his rings from the place of contact1 and he calculated the depth between the tangent plane and the curved surface1 exactly as the engineer would calculate the distance between his tangent plane and the surface of the sea4 ,the wonder is1 that1 where such infinitesimal distances are involved1 ,newton1 with the means at his disposal1 could have worked with such marvellous exactitude4 ,to account for these rings was the greatest optical difficulty that ,newton1 ever encountered4 ,he quite appreciated the difficulty4 ,over his eagle eye there was no film--no vagueness in his conceptions4 ,at the very outset his theory was confronted by the question1 ,why1 when a beam of light is incident on a transparent body1 are some of the light-particles reflected and some transmitted8 ,is it that there are two kinds of particles1 the one specially fitted for transmission and the other for reflection8 ,this cannot be the reason2 for1 if we allow a beam of light which has been reflected from one piece of glass to fall upon another1 it1 as a general rule1 is also divided into a reflected and a transmitted portion4 ,the particles once reflected are not always reflected1 nor are the particles once transmitted always transmitted4 ,newton saw all this2 he knew he had to explain why it is that the self-same particle is at one moment reflected and at the next moment transmitted4 ,it could only he through some change in the condition of the particle itself4 ,the self-same particle1 he affirmed1 was affected by 'fits' of easy transmission and reflection4 #i4 ,theory of ',fits' applied to ,newton's ,rings4 ,if you are willing to follow me in an attempt to reveal the speculative groundwork of this theory of fits1 the intellectual discipline will1 ,i think1 repay you for the necessary effort of attention4 ,newton was chary of stating what he considered to be the cause of the fits1 but there can hardly be a doubt that his mind rested on a physical cause4 ,nor can there be a doubt that here1 as in all attempts at theorising1 he was compelled to fall back upon experience for the materials of his theory4 ,let us attempt to restore his course of thought and observation4 ,a magnet would furnish him with the notion of attracted and repelled poles2 and he who habitually saw in the visible an image of the invisible would naturally endow his light-particles with such poles4 ,turning their attracted poles towards a transparent substance1 the particles would be sucked in and transmitted2 turning their repelled poles1 they would be driven away or reflected4 ,thus1 by the ascription of poles1 the transmission and reflection of the self-same particle at different times might be accounted for4 ,consider these rings of ,newton as seen in pure red light3 they are alternately bright and dark4 ,the film of air corresponding to the outermost of them is not thicker than an ordinary soap-bubble1 and it becomes thinner on approaching the centre2 still ,newton1 as ,i have said1 measured the thickness corresponding to every ring1 and showed the difference of thickness between ring and ring4 ,now1 mark the result4 ,for the sake of convenience1 let us call the thickness of the film of air corresponding to the first dark ring d2 then ,newton found the distance corresponding to the second dark ring #b d2 the thickness corresponding to the third dark ring #c d2 the thickness corresponding to the tenth dark ring #aj d1 and so on4 ,surely there must be some hidden meaning in this little distance1 d1 which turns up so constantly8 ,one can imagine the intense interest with which ,newton pondered its meaning4 ,observe the probable outcome of his thought4 ,he had endowed his light-particles with poles1 but now he is forced to introduce the notion of periodic recurrence4 ,here his power of transfer from the sensible to the subsensible would render it easy for him to suppose the light-particles animated1 not only with a motion of translation1 but also with a motion of rotation4 ,newton's astronomical knowledge rendered all such conceptions familiar to him4 ,the earth has such a double motion4 ,in the time occupied in passing over a million and a half of miles of its orbit--that is1 in twenty-four hours--our planet performs a complete rotation2 and in the time required to pass over the distance d1 ,newton's light-particle might be supposed to perform a complete rotation4 ,true1 the light-particle is smaller than the planet1 and the distance d1 instead of being a million and a half of miles1 is a little over the ninety thousandth of an inch4 ,but the two conceptions are1 in point of intellectual quality1 identical4 ,imagine1 then1 a particle entering the film of air where it possesses this precise thickness4 ,to enter the film1 its attracted end must be presented4 ,within the film it is able to turn once completely round2 at the other side of the film its attracted pole will be again presented2 it will1 therefore1 enter the glass at the opposite side of the film and be lost to the eye4 ,all round the place of contact1 wherever the film possesses this precise thickness1 the light will equally disappear--we shall therefore have a ring of darkness4 ,and now observe how well this conception falls in with the law of proportionality discovered by ,newton4 ,when the thickness of the film is #b d1 the particle has time to perform1 two complete rotations within the film2 when the thickness is #c d1 three complete rotations2 when #aj d1 ten complete rotations are performed4 ,it is manifest that in each of these cases1 on arriving at the second surface of the film1 the attracted pole of the particle will be presented4 ,it will1 therefore1 be transmitted2 and1 because no light is sent to the eye1 we shall have a ring of darkness at each of these places4 ,the bright rings follow immediately from the same conception4 ,they occur between the dark rings1 the thicknesses to which they correspond being also intermediate between those of the dark ones4 ,take the case of the first bright ring4 ,the thickness of the film is d2 in this interval the rotating particle can perform only half a rotation4 ,when1 therefore1 it reaches the second surface of the film1 its repelled pole is presented2 it is1 therefore1 driven back and reaches the eye4 ,at all distances round the centre corresponding to this thickness the same effect is produced1 and the consequence is a ring of brightness4 ,the other bright rings are similarly accounted for4 ,at the second one1 where the thickness is #a;d1 a rotation and a half is performed2 at the third1 two rotations and a half2 and at each of these places the particles present their repelled poles to the lower surface of the film4 ,they are therefore sent back to the eye1 and produce there the impression of brightness4 ,this analysis1 though involving difficulties when closely scrutinised1 enables us to see how the theory of fits may have grown into consistency in the mind of ,newton4 ,it has been already stated that the ,emission ,theory assigned a greater velocity to light in glass and water than in air or stellar space2 and that on this point it was at direct issue with the theory of undulation1 which makes the velocity in air or stellar space greater than in glass or water4 ,by an experiment proposed by ,arago1 and executed with consummate skill by ,foucault and ,fizeau1 this question was brought to a crucial test1 and decided in favour of the theory of undulation4 ,in the present instance also the two theories are at variance4 ,newton assumed that the action which produces the alternate bright and dark rings took place at a single surface2 that is1 the second surface of the film4 ,the undulatory theory affirms that the rings are caused by the interference of waves reflected from both surfaces4 ,this also has been demonstrated by experiment4 ,by a proper arrangement1 as we shall afterwards learn1 we may abolish reflection from one of the surfaces of the film1 and when this is done the rings vanish altogether4 ,rings of feeble intensity are also formed by transmitted light4 ,these are referred by the undulatory theory to the interference of waves which have passed directly through the film1 with others which have suffered two reflections within the film1 and are thus completely accounted for4 #aj4 ,the ,diffraction of ,light4 ,newton's espousal of the ,emission ,theory is said to have retarded scientific discovery4 ,it might1 however1 be questioned whether1 in the long run1 the errors of great men have not really their effect in rendering intellectual progress rhythmical1 instead of permitting it to remain uniform1 the 'retardation' in each case being the prelude to a more impetuous advance4 ,it is confusion and stagnation1 rather than error1 that we ought to avoid4 ,thus1 though the undulatory theory was held back for a time1 it gathered strength in the interval1 and its development within the last half century has been so rapid and triumphant as to leave no rival in the field4 ,we have now to turn to the investigation of new classes of phenomena1 of which it alone can render a satisfactory account4 ,newton1 who was familiar with the idea of an ether1 and who introduced it in some of his speculations1 objected1 as already stated1 that if light consisted of waves shadows could not exist2 for that the waves would bend round the edges of opaque bodies and agitate the ether behind them4 ,he was right in affirming that this bending ought to occur1 but wrong in supposing that it does not occur4 ,the bending is real1 though in all ordinary cases it is masked by the action of interference4 ,this inflection of the light receives the name of ,diffraction4 ,to study the phenomena of diffraction it is necessary that our source of light should be a physical point1 or a fine line2 for when a luminous surface is employed1 the waves issuing from different points of the surface obscure and neutralize each other4 ,a point of light of high intensity is obtained by admitting the parallel rays of the sun through an aperture in a window-shutter1 and concentrating the beam by a lens of short focus4 ,the small solar image at the focus constitutes a suitable point of light4 ,the image of the sun formed on the convex surface of a glass bead1 or of a watch-glass blackened within1 though less intense1 will also answer4 ,an intense line of light is obtained by admitting the sunlight through a slit and sending it through a strong cylindrical lens4 ,the slice of light is contracted to a physical line at the focus of the lens4 ,a glass tube blackened within and placed in the light1 reflects from its surface a luminous line which1 though less intense1 also answers the purpose4 ,in the experiment now to be described a vertical slit of variable width is placed in front of the electric lamp1 and this slit is looked at from a distance through another vertical slit1 also of variable aperture1 and held in the hand4 ,the light of the lamp being1 in the first place1 rendered monochromatic by placing a pure red glass in front of the slit1 when the eye is placed in the straight line drawn through both slits an extraordinary appearance 7shown in fig4 #ae7 is observed4 ,firstly1 the slit in front of the lamp is seen as a vivid rectangle of light2 but right and left of it is a long series of rectangles1 decreasing in vividness1 and separated from each other by intervals of absolute darkness4 ,the breadth of these bands is seen to vary with the width of the slit held before the eye4 ,when the slit is widened the bands become narrower1 and crowd more losely together2 when the slit is narrowed1 the individual bands widen and also retreat from each other1 leaving between them wider spaces of darkness than before4 ,illustration3 ,fig4 #ae4 ,leaving everything else unchanged1 let a blue glass or a solution of ammonia-sulphate of copper1 which gives a very pure blue1 be placed in the path of the light4 ,a series of blue bands is thus obtained1 exactly like the former in all respects save one2 the blue rectangles are narrower1 and they are closer together than the red ones4 ,if we employ colours of intermediate refrangibilities1 which we may do by causing the different colours of a spectrum to shine through the slit1 we obtain bands of colour intermediate in width1 and occupying intermediate positions1 between those of the red and blue4 ,the aspect of the bands in red1 green1 and violet light is represented in fig4 #af4 ,when white light1 therefore1 passes through the slit the various colours are not superposed1 and instead of a series of monochromatic bands1 separated from each other by intervals of darkness1 we have a series of coloured spectra placed side by side4 ,when the distant slit is illuminated by a candle flame1 instead of the more intense electric light1 or when a distant platinum wire raised to a white heat by an electric current is employed1 substantially the same effects are observed4 ,illustration3 ,fig4 #af4 #aa4 ,application of the ,wave-theory to the ,phenomena of ,diffraction4 ,of these and of a multitude of similar effects the ,emission ,theory is incompetent to offer any satisfactory explanation4 ,let us see how they are accounted for by the ,theory of ,undulation4 ,and here1 with the view of reaching absolute clearness1 ,i must make an appeal to that faculty the importance of which ,i have dwelt upon so earnestly here and elsewhere--the faculty of imagination4 ,figure yourself upon the sea-shore1 with a well-formed wave advancing4 ,take a line of particles along the front of the wave1 all at the same distance below the crest2 they are all rising in the same manner and at the same rate4 ,take a similar line of particles on the back of the wave1 they are all falling in the same manner and at the same rate4 ,take a line of particles along the crest1 they are all in the same condition as regards the motion of the wave4 ,the same is true for a line of particles along the furrow of the wave4 ,the particles referred to in each of these cases respectively1 being in the same condition as regards the motion of the wave1 are said to be in the same phase of vibration4 ,but if you compare a particle on the front of the wave with one at the back2 or1 more generally1 if you compare together any two particles not occupying the same position in the wave1 their conditions of motion not being the same1 they are said to be in different phases of vibration4 ,if one of the particles lie upon the crest1 and the other on the furrow of the wave1 then1 as one is about to rise and the other about to fall1 they are said to be in opposite phases of vibration4 ,there is still another point to be cleared up--and it is one of the utmost importance as regards our present subject4 ,let ,o 7fig4 #ag7 be a spot in still water which1 when disturbed1 produces a series of circular waves3 the disturbance necessary to produce these waves is simply an oscillation up and down of the water at ,o4 ,let m n be the position of the ridge of one of the waves at any moment1 and m' n' its position a second or two afterwards4 ,now every particle of water1 as the wave passes it1 oscillates1 as we have learned1 up and down4 ,if1 then1 this oscillation be a sufficient origin of wave-motion1 each distinct particle of the wave m n ought to give birth1 to a series of circular waves4 ,this is the important point up to which ,i wish to lead you4 ,every particle of the wave m n does act in this way4 ,taking each particle as a centre1 and surrounding it by a circular wave with a radius equal to the distance between m n and m' n'1 the coalescence of all these little waves would build up the large ridge m' n' exactly as we find it built up in nature4 ,here1 in fact1 we resolve the wave-motion into its elements1 and having succeeded in doing this we shall have no great difficulty in applying our knowledge to optical phenomena4 ,illustration3 ,fig4 #ag4 ,now let us return to our slit1 and1 for the sake of simplicity1 we will first consider the case of monochromatic light4 ,conceive a series of waves of ether advancing from the first slit towards the second1 and finally filling the second slit4 ,when each wave passes through the latter it not only pursues its direct course to the retina1 but diverges right and left1 tending to throw into motion the entire mass of the ether behind the slit4 ,in fact1 as already explained1 every point of the wave which fills the slit is itself a centre of a new wave system which is transmitted in all directions through the ether behind the slit4 ,this is the celebrated principle of ,huyghens3 we have now to examine how these secondary waves act upon each other4 ,illustration3 ,fig4 #ah4 ,let us first regard the central band of the series4 ,let ,,ap 7fig4 #ah7 be the width of the aperture held before the eye1 grossly exaggerated of course1 and let the dots across the aperture represent ether particles1 all in the same phase of vibration4 ,let ,e ,t represent a portion of the retina4 ,from ,o1 in the centre of the slit1 let a perpendicular ,o ,r be imagined drawn upon the retina4 ,the motion communicated to the point ,r will then be the sum of all the motions emanating in this direction from the ether particles in the slit4 ,considering the extreme narrowness of the aperture1 we may1 without sensible error1 regard all points of the wave ,a ,p as equally distant from ,r4 ,no one of the partial waves lags sensibly behind the others3 hence1 at ,r1 and in its immediate neighbourhood1 we have no sensible reduction of the light by interference4 ,this undiminished light produces the brilliant central band of the series4 ,let us now consider those waves which diverge laterally behind the second slit4 ,in this case the waves from the two sides of the slit have1 in order to converge upon the retina1 to pass over unequal distances4 ,let ,a ,p 7fig4 #ai7 represent1 as before1 the width of the second slit4 ,we have now to consider the action of the various parts of the wave ,a ,p upon a point ,r' of the retina1 not situated in the line joining the two slits4 ,illustration3 ,fig4 #ai4 ,let us take the particular case in which the difference of path from the two marginal points ,a1 ,p1 to the retina is a whole wave-length of the red light2 how must this difference affect the final illumination of the retina8 ,let us fix our attention upon the particular oblique line that passes through the centre ,o of the slit to the retina at ,r'4 ,the difference of path between the waves which pass along this line and those from the two margins is1 in the case here supposed1 half a wavelength4 ,make e ,r' equal to ,p ,r'1 join ,p and e1 and draw ,o d parallel to ,p e4 ,a e is then the length of a wave of light1 while ,a d is half a wave-length4 ,now the least reflection will make it clear that not only is there discordance between the central and marginal waves1 but that every line of waves such as x ,r'1 on the one side of ,o ,r'1 finds a line x' ,r' upon the other side of ,o ,r'1 from which its path differs by half an undulation--with which1 therefore1 it is in complete discordance4 ,the consequence is1 that the light on the one side of the central line will completely abolish the light on the other side of that line1 absolute darkness being the result of their coalescence4 ,the first dark interval of our series of bands is thus accounted for4 ,it is produced by an obliquity of direction which causes the paths of the marginal waves to be a whole wave-length different from each other4 ,when the difference between the paths of the marginal waves is half a wave-length1 a partial destruction of the light is effected4 ,the luminous intensity corresponding to this obliquity is a little less than one-half--accurately #j4d--that of the undiffracted light4 ,if the paths of the marginal waves be three semi-undulations different from each other1 and if the whole beam be divided into three equal parts1 two of these parts will1 for the reasons just given1 completely neutralize each other1 the third only being effective4 ,corresponding1 therefore1 to an obliquity which produces a difference of three semi-undulations in the marginal waves1 we have a luminous band1 but one of considerably less intensity than the undiffracted central band4 ,with a marginal difference of path of four semi-undulations we have a second extinction of the entire beam1 because here the beam can be divided into four equal parts1 every two of which quench each other4 ,a second space of absolute darkness will therefore correspond to the obliquity producing this difference4 ,in this way we might proceed further1 the general result being that1 whenever the direction of wave-motion is such as to produce a marginal difference of path of an even number of semi-undulations1 we have complete extinction2 while1 when the marginal difference is an odd number of semi-undulations1 we have only partial extinction1 a portion of the beam remaining as a luminous band4 ,a moment's reflection will make it plain that the wider the slit the less will be the obliquity of direction needed to produce the necessary difference of path4 ,with a wide slit1 therefore1 the bands1 as observed1 will be closer together than with a narrow one4 ,it is also plain that the shorter the wave1 the less will be the obliquity required to produce the necessary retardation4 ,the maxima and minima of violet light must therefore fall nearer to the centre than the maxima and minima of red light4 ,the maxima and minima of the other colours fall between these extremes4 ,in this simple way the undulatory theory completely accounts for the extraordinary appearance above referred to4 ,when a slit and telescope are used1 instead of the slit and naked eye1 the effects are magnified and rendered more brilliant4 ,looking1 moreover1 through a properly adjusted telescope with a small circular aperture in front of it1 at a distant point of light1 the point is seen encircled by a series of coloured bands4 ,if monochromatic light be used1 these bands are simply bright and dark1 but with white light the circles display iris-colours4 ,if a slit be shortened so as to form a square aperture1 we have two series of spectra at right angles to each other4 ,the effects1 indeed1 are capable of endless variation by varying the size1 shape1 and number of the apertures through which the point of light is observed4 ,through two square apertures1 with their corners touching each other as at ,a1 ,schwerd observed the appearance shown in fig4 #bj4 ,adding two others to them1 as at ,b1 he observed the appearance represented in fig4 #ba4 ,the position of every band of light and shade in such figures has been calculated from theory by ,fresnel1 ,fraunhofer1 ,herschel1 ,schwerd1 and others1 and completely verified by experiment4 ,your eyes could not tell you with greater certainty of the existence of these bands than the theoretic calculation4 ,illustration3 ,fig4 #bj4 ,the street-lamps at night1 looked at through the meshes of a handkerchief1 show diffraction phenomena4 ,the diffraction effects obtained in looking through a bird's feathers are1 as shown by ,schwerd1 very brilliant4 ,the iridescence of certain ,alpine clouds is also an effect of diffraction which may be imitated by the spores of ,lycopodium4 ,when shaken over a glass plate these spores cause a point of light1 looked at through the dusted plate1 to be surrounded by coloured circles1 which rise to actual splendour when the light becomes intense4 ,shaken in the air the spores produce the same effect4 ,the diffraction phenomena obtained during the artificial precipitation of clouds from the vapours of various liquids in an intensely illuminated tube are1 as ,i have elsewhere shewn1 exceedingly fine4 ,illustration3 ,fig4 #ba4 ,one of the most interesting cases of diffraction by small particles that ever came before me was that of an artist whose vision was disturbed by vividly coloured circles4 ,he was in great dread of losing his sight2 assigning as a cause of his increased fear that the circles were becoming larger and the colours more vivid4 ,i ascribed the colours to minute particles in the humours of the eye1 and ventured to encourage him by the assurance that the increase of size and vividness on the part of the circles indicated that the diffracting particles were becoming smaller1 and that they might finally be altogether absorbed4 ,the prediction was verified4 ,it is needless to say one word on the necessity of optical knowledge in the case of the practical oculist4 ,without breaking ground on the chromatic phenomena presented by crystals1 two other sources of colour may be mentioned here4 ,by interference in the earth's atmosphere1 the light of a star1 as shown by ,arago1 is self-extinguished1 the twinkling of the star and the changes of colour which it undergoes being due to this cause4 ,looking at such a star through an opera-glass1 and shaking the glass so as to cause the image of the star to pass rapidly over the retina1 you produce a row of coloured beads1 the spaces between which correspond to the periods of extinction4 ,fine scratches drawn upon glass or polished metal reflect the waves of light from their sides2 and some1 being reflected from the opposite sides of the same scratch1 interfere with and quench each other4 ,but the obliquity of reflection which extinguishes the shorter waves does not extinguish the longer ones1 hence the phenomena of colours4 ,these are called the colours of striated surfaces4 ,they are beautifully illustrated by mother-of-pearl4 ,this shell is composed of exceedingly thin layers1 which1 when cut across by the polishing of the shell1 expose their edges and furnish the necessary small and regular grooves4 ,the most conclusive proof that the colours are due to the mechanical state of the surface is to be found in the fact1 established by ,brewster1 that by stamping the shell carefully upon black sealing-wax1 we transfer the grooves1 and produce upon the wax the colours of mother-of-pearl4 ,,lecture ,,iii4 ,,relation ,,of ,,theories ,,to ,,experience ,,origin ,,of ,,the ,,notion ,,of ,,the ,,attraction ,,of ,,gravitation ,,notion ,,of ,,polarity1 ,,how ,,generated ,,atomic ,,polarity ,,structural ,,arrangements ,,due ,,to ,,polarity ,,architecture ,,of ,,crystals ,,considered ,,as ,,an ,,introduction ,,to ,,their ,,action ,,upon ,,light ,,notion ,,of ,,atomic ,,polarity ,,applied ,,to ,,crystalline ,,structure ,,experimental ,,illustrations ,,crystallization ,,of ,,water ,,expansion ,,by ,,heat ,,and ,,by ,,cold ,,deportment ,,of ,,water ,,considered ,,and ,,explained ,,bearings ,,of ,,crystallization ,,on ,,optical ,,phenomena ,,refraction ,,double ,,refraction ,,polarization ,,action ,,of ,,tourmaline ,,character ,,of ,,the ,,beams ,,emergent ,,from ,,iceland ,,spar ,,polarization ,,by ,,ordinary ,,refraction ,,and ,,reflection ,,depolarization #a4 ,derivation of ,theoretic ,conceptions from ,experience4 ,one of the objects of our last lecture1 and that not the least important1 was to illustrate the manner in which scientific theories are formed4 ,they1 in the first place1 take their rise in the desire of the mind to penetrate to the sources of phenomena4 ,from its infinitesimal beginnings1 in ages long past1 this desire has grown and strengthened into an imperious demand of man's intellectual nature4 ,it long ago prompted ,csar to say that he would exchange his victories for a glimpse of the sources of the ,nile2 it wrought itself into the atomic theories of ,lucretius2 it impelled ,darwin to those daring speculations which of late years have so agitated the public mind4 ,but in no case1 while framing theories1 does the imagination create its materials4 ,it expands1 diminishes1 moulds1 and refines1 as the case may be1 materials derived from the world of fact and observation4 ,this is more evidently the case in a theory like that of light1 where the motions of a subsensible medium1 the ether1 are presented to the mind4 ,but no theory escapes the condition4 ,newton took care not to encumber the idea of gravitation with unnecessary physical conceptions2 but we know that he indulged in them1 though he did not connect them with his theory4 ,but even the theory1 as it stands1 did not enter the mind as a revelation dissevered from the world of experience4 ,the germ of the conception that the sun and planets are held together by a force of attraction is to be found in the fact that a magnet had been previously seen to attract iron4 ,the notion of matter attracting matter came thus from without1 not from within4 ,in our present lecture the magnetic force must serve as the portal into a new domain2 but in the first place we must master its elementary phenomena4 ,the general facts of magnetism are most simply illustrated by a magnetized bar of steel1 commonly called a bar magnet4 ,placing such a magnet upright upon a table1 and bringing a magnetic needle near its bottom1 one end of the needle is observed to retreat from the magnet1 while the other as promptly approaches4 ,the needle is held quivering there by some invisible influence exerted upon it4 ,raising the needle along the magnet1 but still avoiding contact1 the rapidity of its oscillations decreases1 because the force acting upon it becomes weaker4 ,at the centre the oscillations cease4 ,above the centre1 the end of the needle which had been previously drawn towards the magnet retreats1 and the opposite end approaches4 ,as we ascend higher1 the oscillations become more violent1 because the force becomes stronger4 ,at the upper end of the magnet1 as at the lower1 the force reaches a maximum2 but all the lower half of the magnet1 from ,e to ,s 7fig4 #bb71 attracts one end of the needle1 while all the upper half1 from ,e to ,n1 attracts the opposite end4 ,this doubleness of the magnetic force is called polarity1 and the points near the ends of the magnet in which the forces seem concentrated are called its poles4 ,illustration3 ,fig4 #bb4 ,what1 then1 will occur if we break this magnet in two at the centre ,e8 ,shall we obtain two magnets1 each with a single pole8 ,no2 each half is in itself a perfect magnet1 possessing two poles4 ,this may be proved by breaking something of less value than the magnet--the steel of a lady's stays1 for example1 hardened and magnetized4 ,it acts like the magnet4 ,when broken1 each half acts like the whole2 and when these parts are again broken1 we have still the perfect magnet1 possessing1 as in the first instance1 two poles4 ,push your breaking to its utmost sensible limit--you cannot stop there4 ,the bias derived from observation will infallibly carry you beyond the bourne of the senses1 and compel you to regard this thing that we call magnetic polarity as resident in the ultimate particles of the steel4 ,you come to the conclusion that each molecule of the magnet is endowed with this polar force4 ,like all other forces1 this force of magnetism is amenable to mechanical laws2 and1 knowing the direction and magnitude of the force1 we can predict its action4 ,placing a small magnetic needle near a bar magnet1 it takes a determinate position4 ,that position might be deduced theoretically from the mutual action of the poles4 ,moving the needle round the magnet1 for each point of the surrounding space there is a definite direction of the needle and no other4 ,a needle of iron will answer as well as the magnetic needle2 for the needle of iron is magnetized by the magnet1 and acts exactly like a steel needle independently magnetized4 ,if we place two or more needles of iron near the magnet1 the action becomes more complex1 for then the needles are not only acted on by the magnet1 but they act upon each other4 ,and if we pass to smaller masses of iron--to iron filings1 for example--we find that they act substantially as the needles1 arranging themselves in definite forms1 in obedience to the magnetic action4 ,placing a sheet of paper or glass over a bar magnet and showering iron filings upon the paper1 ,i notice a tendency of the filings to arrange themselves in determinate lines4 ,they cannot freely follow this tendency1 for they are hampered by the friction against the paper4 ,they are helped by tapping the paper2 each tap releasing them for a moment1 and enabling them to follow their tendencies4 ,but this is an experiment which can only be seen by myself4 ,to enable you all to see it1 ,i take a pair of small magnets and by a simple optical arrangement throw the magnified images of the magnets upon the screen4 ,scattering iron filings over the glass plate to which the small magnets are attached1 and tapping the plate1 you see the arrangement of the iron filings in those magnetic curves which have been so long familiar to scientific men 7fig4 #bc74 ,illustration3 ,fig4 #bc4 ,n is the nozzle of the lamp2 ,m a plane mirror1 reflecting the beam upwards4 ,at ,p the magnets and iron filings are placed2 ,l is a lens which forms an image of the magnets and filings2 and ,r is a totally reflecting prism1 which casts the image ,g upon the screen4 7,by a very ingenious device1 ,professor ,mayer1 of ,hoboken1 has succeeded in fixing and photographing the magnetic curves4 ,i am indebted to his kindness for the annexed beautiful illustration1 fig4 #bd47 ,the aspect of these curves so fascinated ,faraday that the greater portion of his intellectual life was devoted to pondering over them4 ,he invested the space through which they run with a kind of materiality2 and the probability is that the progress of science1 by connecting the phenomena of magnetism with the luminiferous ether1 will prove these 'lines of force1' as ,faraday loved to call them1 to represent a condition of this mysterious substratum of all radiant action4 ,it is not1 however1 the magnetic curves1 as such1 but their relationship to theoretic conceptions1 that we have now to consider4 ,by the action of the bar magnet upon the needle we obtain the notion of a polar force2 by the breaking of the strip of magnetized steel we attain the notion that polarity can attach itself to the ultimate particles of matter4 ,the experiment with the iron filings introduces a new idea into the mind2 the idea1 namely1 of structural arrangement4 ,every pair of filings possesses four poles1 two of which are attractive and two repulsive4 ,the attractive poles approach1 the repulsive poles retreat2 the consequence being a certain definite arrangement of the particles with reference to each other4 #b4 ,theory of ,crystallization4 ,now this idea of structure1 as produced by polar force1 opens a way for the intellect into an entirely new region1 and the reason you are asked to accompany me into this region is1 that our next inquiry relates to the action of crystals upon light4 ,prior to speaking of this action1 ,i wish you to realise intellectually the process of crystalline architecture4 ,look then into a granite quarry1 and spend a few minutes in examining the rock4 ,it is not of perfectly uniform texture4 ,it is rather an agglomeration of pieces1 which1 on examination1 present curiously defined forms4 ,you have there what mineralogists call quartz1 you have felspar1 you have mica4 ,in a mineralogical cabinet1 where these substances are preserved separately1 you will obtain some notion of their forms4 ,you will see there1 also1 specimens of beryl1 topaz1 emerald1 tourmaline1 heavy spar1 fluor-spar1 ,iceland spar--possibly a full-formed diamond1 as it quitted the hand of ,nature1 not yet having got into the hands of the lapidary4 ,illustration3 ,fig4 #bd4 ,these crystals1 you will observe1 are put together according to law2 they are not chance productions2 and1 if you care to examine them more minutely1 you will find their architecture capable of being to some extent revealed4 ,they often split in certain directions before a knife-edge1 exposing smooth and shining surfaces1 which are called planes of cleavage2 and by following these planes you sometimes reach an internal form1 disguised beneath the external form of the crystal4 ,ponder these beautiful edifices of a hidden builder4 ,you cannot help asking yourself how they were built2 and familiar as you now are with the notion of a polar force1 and the ability of that force to produce structural arrangement1 your inevitable answer will be1 that those crystals are built by the play of polar forces with which their molecules are endowed4 ,in virtue of these forces1 molecule lays itself to molecule in a perfectly definite way1 the final visible form of the crystal depending upon this play of its ultimate particles4 ,everywhere in ,nature we observe this tendency to run into definite forms1 and nothing is easier than to give scope to this tendency by artificial arrangements4 ,dissolve nitre in water1 and allow the water slowly to evaporate2 the nitre remains and the solution soon becomes so concentrated that the liquid condition can no longer be preserved4 ,the nitre-molecules approach each other1 and come at length within the range of their polar forces4 ,they arrange themselves in obedience to these forces1 a minute crystal of nitre being at first produced4 ,on this crystal the molecules continue to deposit themselves from the surrounding liquid4 ,the crystal grows1 and finally we have large prisms of nitre1 each of a perfectly definite shape4 ,alum crystallizes with the utmost ease in this fashion4 ,the resultant crystal is1 however1 different in shape from that of nitre1 because the poles of the molecules are differently disposed4 ,when they are nursed with proper care1 crystals of these substances may be caused to grow to a great size4 ,the condition of perfect crystallization is1 that the crystallizing force shall act with deliberation4 ,there should be no hurry in its operations2 but every molecule ought to be permitted1 without disturbance from its neighbours1 to exercise its own rights4 ,if the crystallization be too sudden1 the regularity disappears4 ,water may be saturated with sulphate of soda1 dissolved when the water is hot1 and afterwards permitted to cool4 ,when cold the solution is supersaturated2 that is to say1 more solid matter is contained in it than corresponds to its temperature4 ,still the molecules show no sign of building themselves together4 ,this is a very remarkable1 though a very common fact4 ,the molecules in the centre of the liquid are so hampered by the action of their neighbours that freedom to follow their own tendencies is denied to them4 ,fix your mind's eye upon a molecule within the mass4 ,it wishes to unite with its neighbour to the right1 but it wishes equally to unite with its neighbour to the left2 the one tendency neutralizes the other and it unites with neither4 ,but1 if a crystal of sulphate of soda be dropped into the solution1 the molecular indecision ceases4 ,on the crystal the adjacent molecules will immediately precipitate themselves2 on these again others will be precipitated1 and this act of precipitation will continue from the top of the flask to the bottom1 until the solution has1 as far as possible1 assumed the solid form4 ,the crystals here produced are small1 and confusedly arranged4 ,the process has been too hasty to admit of the pure and orderly action of the crystallizing force4 ,it typifies the state of a nation in which natural and healthy change is resisted1 until society becomes1 as it were1 supersaturated with the desire for change1 the change being then effected through confusion and revolution4 ,let me illustrate the action of the crystallizing force by two examples of it3 ,nitre might be employed1 but another well-known substance enables me to make the experiment in a better form4 ,the substance is common sal-ammoniac1 or chloride of ammonium1 dissolved in water4 ,cleansing perfectly a glass plate1 the solution of the chloride is poured over the glass1 to which when the plate is set on edge1 a thin film of the liquid adheres4 ,warming the glass slightly1 evaporation is promoted1 but by evaporation the water only is removed4 ,the plate is then placed in a solar microscope1 and an image of the film is thrown upon a white screen4 ,the warmth of the illuminating beam adds itself to that already imparted to the glass plate1 so that after a moment or two the dissolved salt can no longer exist in the liquid condition4 ,molecule then closes with molecule1 and you have a most impressive display of crystallizing energy overspreading the whole screen4 ,you may produce something similar if you breathe upon the frost ferns which overspread your window-panes in winter1 and then observe through a pocket lens the subsequent recongelation of the film4 ,in this case the crystallizing force is hampered by the adhesion of the film to the glass2 nevertheless1 the play of power is strikingly beautiful4 ,sometimes the crystals start from the edge of the film and run through it from that edge2 for1 the crystallization being once started1 the molecules throw themselves by preference on the crystals already formed4 ,sometimes the crystals start from definite nuclei in the centre of the film1 every small crystalline particle which rests in the film furnishing a starting-point4 ,throughout the process you notice one feature which is perfectly unalterable1 and that is1 angular magnitude4 ,the spicul branch from the trunk1 and from these branches others shoot2 but the angles enclosed by the spicul are unalterable4 ,in like manner you may find alum-crystals1 quartz-crystals1 and all other crystals1 distorted in shape4 ,they are thus far at the mercy of the accidents of crystallization2 but in one particular they assert their superiority over all such accidents--angular magnitude is always rigidly preserved4 ,my second example of the action of crystallizing force is this3 ,by sending a voltaic current through a liquid1 you know that we decompose the liquid1 and if it contains a metal1 we liberate this metal by electrolysis4 ,this small cell contains a solution of acetate of lead1 which is chosen for our present purpose1 because lead lends itself freely to this crystallizing power4 ,into the cell are dipped two very thin platinum wires1 and these are connected by other wires with a small voltaic battery4 ,on sending the voltaic current through the solution1 the lead will be slowly severed from the atoms with which it is now combined2 it will be liberated upon one of the wires1 and at the moment of its liberation it will obey the polar forces of its atoms1 and produce crystalline forms of exquisite beauty4 ,they are now before you1 sprouting like ferns from the wire1 appearing indeed like vegetable growths rendered so rapid as to be plainly visible to the naked eye4 ,on reversing the current1 these wonderful lead-fronds will dissolve1 while from the other wire filaments of lead dart through the liquid4 ,in a moment or two the growth of the lead-trees recommences1 but they now cover the other wire4 ,in the process of crystallization1 ,nature first reveals herself as a builder4 ,where do her operations stop8 ,does she continue by the play of the same forces to form the vegetable1 and afterwards the animal8 ,whatever the answer to these questions may be1 trust me that the notions of the coming generations regarding this mysterious thing1 which some have called 'brute matter1' will be very different from those of the generations past4 ,there is hardly a more beautiful and instructive example of this play of molecular force than that furnished by water4 ,you have seen the exquisite fern-like forms produced by the crystallization of a film of water on a cold window-pane4#ae ,you have also probably noticed the beautiful rosettes tied together by the crystallizing force during the descent of a snow-shower on a very calm day4 ,the slopes and summits of the ,alps are loaded in winter with these blossoms of the frost4 ,they vary infinitely in detail of beauty1 but the same angular magnitude is preserved throughout3 an inflexible power binding spears and spicul to the angle of #fj degrees4 ,the common ice of our lakes is also ruled in its formation by the same angle4 ,you may sometimes see in freezing water small crystals of stellar shapes1 each star consisting of six rays1 with this angle of #fj between every two of them4 ,this structure may be revealed in ordinary ice4 ,in a sunbeam1 or1 failing that1 in our electric beam1 we have an instrument delicate enough to unlock the frozen molecules1 without disturbing the order of their architecture4 ,cutting from clear1 sound1 regularly frozen ice1 a slab parallel to the planes of freezing1 and sending a sunbeam through such a slab1 it liquefies internally at special points1 round each point a six-petalled liquid flower of exquisite beauty being formed4 ,crowds of such flowers are thus produced4 ,from an ice-house we sometimes take blocks of ice presenting misty spaces in the otherwise continuous mass2 and when we inquire into the cause of this mistiness1 we find it to be due to myriads of small six-petalled flowers1 into which the ice has been resolved by the mere heat of conduction4 ,a moment's further devotion to the crystallization of water will be well repaid2 for the sum of qualities which renders this substance fitted to play its part in ,nature may well excite wonder and stimulate thought4 ,like almost all other substances1 water is expanded by heat and contracted by cold4 ,let this expansion and contraction be first illustrated3-- ,a small flask is filled with coloured water1 and stopped with a cork4 ,through the cork passes a glass tube water-tight1 the liquid standing at a certain height in the tube4 ,the flask and its tube resemble the bulb and stem of a thermometer4 ,applying the heat of a spirit-lamp1 the water rises in the tube1 and finally trickles over the top4 ,expansion by heat is thus illustrated4 ,removing the lamp and piling a freezing mixture round the flask1 the liquid column falls1 thus showing the contraction of the water by the cold4 ,but let the freezing mixture continue to act3 the falling of the column continues to a certain point2 it then ceases4 ,the top of the column remains stationary for some seconds1 and afterwards begins to rise4 ,the contraction has ceased1 and expansion by cold sets in4 ,let the expansion continue till the liquid trickles a second time over the top of the tube4 ,the freezing mixture has here produced to all appearance the same effect as the flame4 ,in the case of water1 contraction by cold ceases1 and expansion by cold sets in at the definite temperature of #ci ,fahr4 ,crystallization has virtually here commenced1 the molecules preparing themselves for the subsequent act of solidification1 which occurs at #cb1 and in which the expansion suddenly culminates4 ,in virtue of this expansion1 ice1 as you know1 is lighter than water in the proportion of #h to #i4af ,a molecular problem of great interest is here involved1 and ,i wish now to place before you1 for the satisfaction of your minds1 a possible solution of the problem3-- ,consider1 then1 the ideal case of a number of magnets deprived of weight1 but retaining their polar forces4 ,if we had a mobile liquid of the specific gravity of steel1 we might1 by making the magnets float in it1 realize this state of things1 for in such a liquid the magnets would neither sink nor swim4 ,now1 the principle of gravitation enunciated by ,newton is that every particle of matter1 of every kind1 attracts every other particle with a force varying inversely as the square of the distance4 ,in virtue of the attraction of gravity1 then1 the magnets1 if perfectly free to move1 would slowly approach each other4 ,but besides the unpolar force of gravity1 which belongs to matter in general1 the magnets are endowed with the polar force of magnetism4 ,for a time1 however1 the polar forces do not come sensibly into play4 ,in this condition the magnets resemble our water-molecules at the temperature say of #ej4 ,but the magnets come at length sufficiently near each other to enable their poles to interact4 ,from this point the action ceases to be solely a general attraction of the masses4 ,attractions of special points of the masses and repulsions of other points now come into play2 and it is easy to see that the rearrangement of the magnets consequent upon the introduction of these new forces may be such as to require a greater amount of room4 ,this1 ,i take it1 is the case with our water-molecules4 ,like our ideal magnets1 they approach each other for a time as wholes4 ,previous to reaching the temperature #ci ,fahr41 the polar forces had doubtless begun to act1 but it is at this temperature that their claim to more room exactly balances the contraction due to cold4 ,at lower temperatures1 as regards change of volume1 the polar forces predominate4 ,but they carry on a struggle with the force of contraction until the freezing temperature is attained4 ,the molecules then close up to form solid crystals1 a considerable augmentation of volume being the immediate consequence4 #c4 ,ordinary ,refraction of ,light explained by the ,wave ,theory4 ,we have now to exhibit the bearings of this act of crystallization upon optical phenomena4 ,according to the undulatory theory1 the velocity of light in water and glass is less than in air4 ,consider1 then1 a small portion of a wave issuing from a point of light so distant that the minute area may be regarded as practically plane4 ,moving vertically downwards1 and impinging on a horizontal surface of glass or water1 the wave would go through the medium without change of direction4 ,as1 however1 the velocity in glass or water is less than the velocity in air1 the wave would be retarded on passing into the denser medium4 ,illustration3 ,fig4 #be4 ,but suppose the wave1 before reaching the glass1 to be oblique to the surface2 that end of the wave which first reaches the medium will be the first retarded by it1 the other portions as they enter the glass being retarded in succession4 ,it is easy to see that this retardation of the one end of the wave must cause it to swing round and change its front1 so that when the wave has fully entered the glass its course is oblique to its original direction4 ,according to the undulatory theory1 light is thus refracted4 ,with these considerations to guide us1 let us follow the course of a beam of monochromatic light through our glass prism4 ,the velocity in air is to its velocity in glass as #c3 #b4 ,let ,a ,b ,c 7fig4 #be7 be the section of our prism1 and a b the section of a plane wave approaching it in the direction of the arrow4 ,when it reaches c d1 one end of the wave is on the point of entering the glass4 ,following it still further1 it is obvious that while the portion of the wave still in the air passes over the distance c e1 the wave in the glass will have passed over only two-thirds of this distance1 or d f4 ,the line e f now marks the front of the wave4 ,immersed wholly in the glass it pursues its way to g h1 where the end g of the wave is on the point of escaping into the air4 ,during the time required by the end h of the wave to pass over the distance h k to the surface of the prism1 the other end g1 moving more rapidly1 will have reached the point i4 ,the wave1 therefore1 has again changed its front1 so that after its emergence from the prism it will pass on to l m1 and subsequently in the direction of the arrow4 ,the refraction of the beam is thus completely accounted for2 and it is1 moreover1 based upon actual experiment1 which proves that the ratio of the velocity of light in glass to its velocity in air is that here mentioned4 ,it is plain that if the change of velocity on entering the glass were greater1 the refraction also would be greater4 #d4 ,double ,refraction of ,light explained by the ,wave ,theory4 ,the two elements of rapidity of propagation1 both of sound and light1 in any substance whatever1 are elasticity and density1 the speed increasing with the former and diminishing with the latter4 ,the enormous velocity of light in stellar space is attainable because the ether is at the same time of infinitesimal density and of enormous elasticity4 ,now the ether surrounds the atoms of all bodies1 but it is not independent of them4 ,in ponderable matter it acts as if its density were increased without a proportionate increase of elasticity2 and this accounts for the diminished velocity of light in refracting bodies4 ,we here reach a point of cardinal importance4 ,in virtue of the crystalline architecture that we have been considering1 the ether in many crystals possesses different densities1 and different elasticities1 in different directions2 the consequence is1 that in such crystals light is transmitted with different velocities4 ,and as refraction depends wholly upon the change of velocity on entering the refracting medium1 being greatest where the change of velocity is greatest1 we have in many crystals two different refractions4 ,by such crystals a beam of light is divided into two4 ,this effect is called double refraction4 ,in ordinary water1 for example1 there is nothing in the grouping of the molecules to interfere with the perfect homogeneity of the ether2 but1 when water crystallizes to ice1 the case is different4 ,in a plate of ice the elasticity of the ether in a direction perpendicular to the surface of freezing is different from what it is parallel to the surface of freezing2 ice is1 therefore1 a double refracting substance4 ,double refraction is displayed in a particularly impressive manner by ,iceland spar1 which is crystallized carbonate of lime4 ,the difference of ethereal density in two directions in this crystal is very great1 the separation of the beam into the two halves being1 therefore1 particularly striking4 ,i am unwilling to quit this subject before raising it to unmistakable clearness in your minds4 ,the vibrations of light being transversal1 the elasticity concerned in the propagation of any ray is the elasticity at right angles to the direction of propagation4 ,in ,iceland spar there is one direction round which the crystalline molecules are symmetrically built4 ,this direction is called the axis of the crystal4 ,in consequence of this symmetry the elasticity is the same in all directions perpendicular to the axis1 and hence a ray transmitted along the axis suffers no double refraction4 ,but the elasticity along the axis is greater than the elasticity at right angles to it4 ,consider1 then1 a system of waves crossing the crystal in a direction perpendicular to the axis4 ,two directions of vibration are open to such waves3 the ether particles can vibrate parallel to the axis or perpendicular to it4 ,they do both1 and hence immediately divide themselves into two systems propagated with different velocities4 ,double refraction is the necessary consequence4 ,illustration3 ,fig4 #bf4 ,by means of ,iceland spar cut in the proper direction1 double refraction is capable of easy illustration4 ,causing the beam which builds the image of our carbon-points to pass through the spar1 the single image is instantly divided into two4 ,projecting 7by the lens ,e1 fig4 #bf7 an image of the aperture 7,l7 through which the light issues from the electric lamp1 and introducing the spar 7,p71 two luminous disks 7,e ,o7 appear immediately upon the screen instead of one4 ,the two beams into which the spar divides the single incident-beam have been subjected to the closest examination4 ,they do not behave alike4 ,one of them obeys the ordinary law of refraction discovered by ,snell1 and is1 therefore1 called the ordinary ray3 its index of refraction is #a4fed4 ,the other does not obey this law4 ,its index of refraction1 for example1 is not constant1 but varies from a maximum of #a4fed to a minimum of #a4dhc2 nor in this case do the incident and refracted rays always lie in the same plane4 ,it is1 therefore1 called the extraordinary ray4 ,in calc-spar1 as just stated1 the ordinary ray is the most refracted4 ,one consequence of this merits a passing notice4 ,pour water and bisulphide of carbon into two cups of the same depth2 the cup that contains the more strongly refracting liquid will appear shallower than the other4 ,place a piece of ,iceland spar over a dot of ink2 two dots are seen1 the one appearing nearer than the other to the eye4 ,the nearest dot belongs to the most strongly refracted ray1 exactly as the nearest cup-bottom belongs to the most highly refracting liquid4 ,when you turn the spar round1 the extraordinary image of the dot rotates round the ordinary one1 which remains fixed4 ,this is also the deportment of our two disks upon the screen4 #e4 ,polarization of ,light explained by the ,wave ,theory4 ,the double refraction of ,iceland spar was first treated in a work published by ,erasmus ,bartholinus1 in #affi4 ,huyghens sought to account for this phenomenon on the principles of the wave theory1 and he succeeded in doing so4 ,he1 moreover1 made highly important observations on the distinctive character of the two beams transmitted by the spar1 admitting1 with resigned candour1 that he had not solved the difficulty1 and leaving the solution to future times4 ,newton1 reflecting on the observations of ,huyghens1 came to the conclusion that each of the beams transmitted by ,iceland spar had two sides2 and from the analogy of this two-sidedness with the two-endedness of a magnet1 wherein consists its polarity1 the two beams came subsequently to be described as polarized4 ,we may begin the study of the polarization of light1 with ease and profit1 by means of a crystal of tourmaline4 ,but we must start with a clear conception of an ordinary beam of light4 ,it has been already explained that the vibrations of the individual ether-particles are executed across the line of propagation4 ,in the case of ordinary light we are to figure the ether-particles as vibrating in all directions1 or azimuths1 as it is sometimes expressed1 across this line4 ,now1 in the case of a plate of tourmaline cut parallel to the axis of the crystal1 a beam of light incident upon the plate is divided into two1 the one vibrating parallel to the axis of the crystal1 the other at right angles to the axis4 ,the grouping of the molecules1 and of the ether associated with the molecules1 reduces all the vibrations incident upon the crystal to these two directions4 ,one of these beams1 namely1 that whose vibrations are perpendicular to the axis1 is quenched with exceeding rapidity by the tourmaline4 ,to such vibrations many specimens of the crystal are highly opaque2 so that1 after having passed through a very small thickness of the tourmaline1 the light emerges with all its vibrations reduced to a single plane4 ,in this condition it is what we call plane polarized light4 ,illustration3 ,fig4 #bg4 ,illustration3 ,fig4 #bh4 ,a moment's reflection will show that1 if what is here stated be correct1 on placing a second plate of tourmaline with its axis parallel to the first1 the light will pass through both2 but that1 if the axes be crossed1 the light that passes through the one plate will be quenched by the other1 a total interception of the light being the consequence4 ,let us test this conclusion by experiment4 ,the image of a plate of tourmaline 7t t1 fig4 #bg7 is now before you4 ,i place parallel to it another plate 7t' t'73 the green of the crystal is a little deepened1 nothing more2 this agrees with our conclusion4 ,by means of an endless screw1 ,i now turn one of the crystals gradually round1 and you observe that as long as the two plates are oblique to each other1 a certain portion of light gets through2 but that when they are at right angles to each other1 the space common to both is a space of darkness 7fig4 #bh74 ,our conclusion1 arrived at prior to experiment1 is thus verified4 ,let us now return to a single plate2 and here let me say that it is on the green light transmitted by the tourmaline that you are to fix your attention4 ,we have to illustrate the two-sidedness of that green light1 in contrast to the all-sidedness of ordinary light4 ,the white light surrounding the green image1 being ordinary light1 is reflected by a plane glass mirror in all directions2 the green light1 on the contrary1 is not so reflected4 ,the image of the tourmaline is now horizontal2 reflected upwards1 it is still green2 reflected sideways1 the image is reduced to blackness1 because of the incompetency of the green light to be reflected in this direction4 ,making the plate of tourmaline vertical1 and reflecting it as before1 it is the light of the upper image that is quenched2 the side image now shows the green4 ,this is a result of the greatest significance4 ,if the vibrations of light were longitudinal1 like those of sound1 you could have no action of this kind2 and this very action compels us to assume that the vibrations are transversal4 ,picture the thing clearly4 ,in the one case the mirror receives1 as it were1 the impact of the edges of the waves1 the green light being then quenched4 ,in the other case the sides of the waves strike the mirror1 and the green light is reflected4 ,to render the extinction complete1 the light must be received upon the mirror at a special angle4 ,what this angle is we shall learn presently4 ,the quality of two-sidedness conferred upon light by bi-refracting crystals may also be conferred upon it by ordinary reflection4 ,malus made this discovery in #ahjh1 while looking through ,iceland spar at the light of the sun reflected from the windows of the ,luxembourg palace in ,paris4 ,i receive upon a plate of window-glass the beam from our lamp2 a great portion of the light reflected from the glass is polarized4 ,the vibrations of this reflected beam are executed1 for the most part1 parallel to the surface of the glass1 and when the glass is held so that the beam shall make an angle of #eh with the perpendicular to the glass1 the whole of the reflected beam is polarized4 ,it was at this angle that the image of the tourmaline was completely quenched in our former experiment4 ,it is called the polarizing angle4 ,sir ,david ,brewster proved the angle of polarization of a medium to be that particular angle at which the refracted and reflected rays inclose a right angle4#ag ,the polarizing angle augments with the index of refraction4 ,for water it is #eb2 for glass1 as already stated1 #eh2 while for diamond it is #fh4 ,and now let us try to make substantially the experiment of ,malus4 ,the beam from the lamp is received at the proper angle upon a plate of glass and reflected through the spar4 ,instead of two images1 you see but one4 ,so that the light1 when polarized1 as it now is by reflection1 can only get through the spar in one direction1 and consequently can produce but one image4 ,why is this8 ,in the ,iceland spar as in the tourmaline1 all the vibrations of the ordinary light are reduced to two planes at right angles to each other2 but1 unlike the tourmaline1 both beams are transmitted with equal facility by the spar4 ,the two beams1 in short1 emergent from the spar1 are polarized1 their directions of vibration being at right angles to each other4 ,when1 therefore1 the light is first polarized by reflection1 the direction of vibration in the spar which coincides with the direction of vibration of the polarized beam1 transmits the beam1 and that direction only4 ,only one image1 therefore1 is possible under the conditions4 ,you will now observe that such logic as connects our experiments is simply a transcript of the logic of ,nature4 ,on the screen before you are two disks of light produced by the double refraction of ,iceland spar4 ,they are1 as you know1 two images of the aperture through which the light issues from the camera4 ,placing the tourmaline in front of the aperture1 two images of the crystal will also be obtained2 but now let us reason out beforehand what is to be expected from this experiment4 ,the light emergent from the tourmaline is polarized4 ,placing the crystal with its axis horizontal1 the vibrations of its transmitted light will be horizontal4 ,now the spar1 as already stated1 has two directions of vibration1 one of which at the present moment is vertical1 the other horizontal4 ,what are we to conclude8 ,that the green light will be transmitted along the latter1 which is parallel to the axis of the tourmaline1 and not along the former1 which is perpendicular to that axis4 ,hence we may infer that one image of the tourmaline will show the ordinary green light of the crystal1 while the other image will be black4 ,tested by experiment1 our reasoning is verified to the letter 7fig4 #bi74 ,illustration3 ,fig4 #bi4 ,illustration2 ,fig4 #cj4 ,let us push our test still further4 ,by means of an endless screw1 the crystal can be turned ninety degrees round4 ,the black image1 as ,i turn1 becomes gradually brighter1 and the bright one gradually darker2 at an angle of forty-five degrees both images are equally bright 7fig4 #cj72 while1 when ninety degrees have been obtained1 the axis of the crystal being then vertical1 the bright and black images have changed places1 exactly as reasoning would have led us to suppose 7fig4 #ca74 ,illustration3 ,fig4 #ca4 ,illustration3 ,fig4 #cb4 ,considering what has been already said 7p4 #aad7 regarding the reflection of light polarized by transmission through tourmaline1 you will readily foresee what must occur when we receive upon a plate of glass1 held at the polarizing angle1 the two beams emergent from our prism of ,iceland spar4 ,i cause both beams to pass side by side through the air1 catch them on a glass plate1 and seek to reflect them upwards4 ,at the polarizing angle one beam only is capable of being thus reflected4 ,which8 ,your prompt answer will be1 ,the beam whose vibrations are horizontal 7fig4 #cb74 ,i now turn the glass plate and try to reflect both beams laterally4 ,one of them only is reflected2 that1 namely1 the vibrations of which are vertical 7fig4 #cc74 ,it is plain that1 by means either of the tourmaline or the reflecting glass1 we can determine in a moment the direction of vibration in any polarized beam4 ,illustration3 ,fig4 #cc4 ,as already stated1 the whole of a beam of ordinary light reflected from glass at the polarizing angle is polarized2 a word must now be added regarding the far larger portion of the light which is transmitted by the glass4 ,the transmitted beam contains a quantity of polarized light equal to the reflected beam2 but this is only a fraction of the whole transmitted light4 ,by taking two plates of glass instead of one1 we augment the quantity of the transmitted polarized light2 and by taking a bundle of plates1 we so increase the quantity as to render the transmitted beam1 for all practical purposes1 perfectly polarized4 ,indeed1 bundles of glass plates are often employed as a means of furnishing polarized light4 ,it is important to note that the plane of vibration of this transmitted light is at right angles to that of the reflected light4 ,one word more4 ,when the tourmalines are crossed1 the space where they cross each other is black4 ,but we have seen that the least obliquity on the part of the crystals permits light to get through both4 ,now suppose1 when the two plates are crossed1 that we interpose a third plate of tourmaline between them1 with its axis oblique to both4 ,a portion of the light transmitted by the first plate will get through this intermediate one4 ,but1 after it has got through1 its plane of vibration is changed3 it is no longer perpendicular to the axis of the crystal in front4 ,hence it will1 in part1 get through that crystal4 ,thus1 by pure reasoning1 we infer that the interposition of a third plate of tourmaline will in part abolish the darkness produced by the perpendicular crossing of the other two plates4 ,i have not a third plate of tourmaline2 but the talc or mica which you employ in your stoves is a more convenient substance1 which acts in the same way4 ,between the crossed tourmalines1 ,i introduce a film of this crystal with its axis oblique to theirs4 ,you see the edge of the film slowly descending1 and1 as it descends1 light takes the place of darkness4 ,the darkness1 in fact1 seems scraped away1 as if it were something material4 ,this effect has been called1 naturally but improperly1 depolarization4 ,its proper meaning will be disclosed in our next lecture4 ,these experiments and reasonings1 if only thoroughly studied and understood1 will form a solid groundwork for the analysis of the splendid optical phenomena next to be considered4 ,,lecture ,,iv4 ,,chromatic ,,phenomena ,,produced ,,by ,,crystals ,,in ,,polarized ,,light ,,the ,,nicol ,,prism ,,polarizer ,,and ,,analyzer ,,action ,,of ,,thick ,,and ,,thin ,,plates ,,of ,,selenite ,,colours ,,dependent ,,on ,,thickness ,,resolution ,,of ,,polarized ,,beam ,,into ,,two ,,others ,,by ,,the ,,selenite ,,one ,,of ,,them ,,more ,,retarded ,,than ,,the ,,other ,,recompounding ,,of ,,the ,,two ,,systems ,,of ,,waves ,,by ,,the ,,analyzer ,,interference ,,thus ,,rendered ,,possible ,,consequent ,,production ,,of ,,colours ,,action ,,of ,,bodies ,,mechanically ,,strained ,,or ,,pressed ,,action ,,of ,,sonorous ,,vibrations ,,action ,,of ,,glass ,,strained ,,or ,,pressed ,,by ,,heat ,,circular ,,polarization ,,chromatic ,,phenomena ,,produced ,,by ,,quartz ,,the ,,magnetization ,,of ,,light ,,rings ,,surrounding ,,the ,,axes ,,of ,,crystals ,,biaxal ,,and ,,uniaxal ,,crystals ,,grasp ,,of ,,the ,,undulatory ,,theory ,,the ,,colour ,,and ,,polarization ,,of ,,sky-,,light ,,generation ,,of ,,artificial ,,skies4 #a4 ,action of ,crystals on ,polarized ,light3 the ,nicol ,prism4 ,we have this evening to examine and illustrate the chromatic phenomena produced by the action of crystals1 and double-refracting bodies generally1 upon polarized light1 and to apply the ,undulatory ,theory to their elucidation4 ,for a long time investigators were compelled to employ plates of tourmaline for this purpose1 and the progress they made with so defective a means of inquiry is astonishing4 ,but these men had their hearts in their work1 and were on this account enabled to extract great results from small instrumental appliances4 ,for our present purpose we need far larger apparatus2 and1 happily1 in these later times this need has been to a great extent satisfied4 ,we have seen and examined the two beams emergent from ,iceland spar1 and have proved them to be polarized4 ,if1 at the sacrifice of half the light1 we could abolish one of these1 the other would place at our disposal a beam of polarized light1 incomparably stronger than any attainable from tourmaline4 ,the beams1 as you know1 are refracted differently1 and from this1 as made plain in #d1 ,lecture ,i41 we are able to infer that the one may be totally reflected1 when the other is not4 ,an able optician1 named ,nicol1 cut a crystal of ,iceland spar in two halves in a certain direction4 ,he polished the severed surfaces1 and reunited them by ,canada balsam1 the surface of union being so inclined to the beam traversing the spar that the ordinary ray1 which is the most highly refracted1 was totally reflected by the balsam1 while the extraordinary ray was permitted to pass on4 ,let b x1 c y 7fig4 #cd7 represent the section of an elongated rhomb of ,iceland spar cloven from the crystal4 ,let this rhomb be cut along the plane b c2 and the two severed surfaces1 after having been polished1 reunited by ,canada balsam4 ,we learned1 in our first lecture1 that total reflection only takes place when a ray seeks to escape from a more refracting to a less refracting medium1 and that it always1 under these circumstances1 takes place when the obliquity is sufficient4 ,now the refractive index of ,iceland spar is1 for the extraordinary ray less1 and for the ordinary greater1 than for ,canada balsam4 ,hence1 in passing from the spar to the balsam1 the extraordinary ray passes from a less refracting to a more refracting medium1 where total reflection cannot occur2 while the ordinary ray passes from a more refracting to a less refracting medium1 where total reflection can occur4 ,the requisite obliquity is secured by making the rhomb of such a length that the plane of which b c is the section shall be perpendicular1 or nearly so1 to the two end surfaces of the rhomb b x1 c y4 ,illustration3 ,fig4 #cd4 ,the invention of the ,nicol prism was a great step in practical optics1 and quite recently such prisms have been constructed of a size and purity which enable audiences like the present to witness the chromatic phenomena of polarized light to a degree altogether unattainable a short time ago4 7,the two prisms employed in these experiments were lent to me by my lamented friend ,mr4 ,william ,spottiswoode1 and they were manufactured by ,mr4 ,ahrens1 an optician of consummate skill47 #b4 ,colours of ,films of ,selenite in ,polarized ,light4 ,two ,nicol prisms play the same part as the two plates of tourmaline4 ,placed with their directions of vibration parallel1 the light passes through both2 while when these directions are crossed the light is quenched4 ,introducing a film of mica between the prisms1 the light1 as in the case of the tourmaline1 is restored4 ,but notice1 when the film of mica is thin you have sometimes not only light1 but coloured light4 ,our work for some time to come will consist of the examination of such colours4 ,with this view1 ,i will take a representative crystal1 one easily dealt with1 because it cleaves with great facility--the crystal gypsum1 or selenite1 which is crystallized sulphate of lime4 ,between the crossed ,nicols ,i place a thick plate of this crystal2 like the mica1 it restores the light1 but it produces no colour4 ,with my penknife ,i take a thin splinter from the crystal and place it between the prisms2 the image of the splinter glows with the richest colours4 ,turning the prism in front1 these colours gradually fade and disappear1 but1 by continuing the rotation until the vibrating sections of the prisms are parallel to each other1 vivid colours again arise1 but these colours are complementary to the former ones4 ,some patches of the splinter appear of one colour1 some of another4 ,these differences are due to the different thicknesses of the film4 ,as in the case of ,hooke's thin plates1 if the thickness be uniform the colour is uniform4 ,here1 for instance1 is a stellar shape1 every lozenge of the star being a film of gypsum of uniform thickness3 each lozenge1 you observe1 shows a brilliant and uniform colour4 ,it is easy1 by shaping our films so as to represent flowers or other objects1 to exhibit such objects in hues unattainable by art4 ,here1 for example1 is a specimen of heart's-ease1 the colours of which you might safely defy the artist to reproduce4 ,by turning the front ,nicol #ij degrees round1 we pass through a colourless phase to a series of colours complementary to the former ones4 ,this change is still more strikingly represented by a rose-tree1 which is now presented in its natural hues--a red flower and green leaves2 turning the prism #ij degrees round1 we obtain a green flower and red leaves4 ,all these wonderful chromatic effects have definite mechanical causes in the motions of the ether4 ,the principle of interference duly applied and interpreted explains them all4 #c4 ,colours of ,crystals in ,polarized ,light explained by the ,undulatory ,theory4 ,by this time you have learned that the word 'light' may be used in two different senses3 it may mean the impression made upon consciousness1 or it may mean the physical cause of the impression4 ,it is with this cause that we have to occupy ourselves at present4 ,the luminiferous ether is a substance which fills all space1 and surrounds the atoms and molecules of bodies4 ,to this inter-stellar and inter-atomic medium definite mechanical properties are ascribed1 and we deal with it in our reasonings and calculations as a body possessed of these properties4 ,in mechanics we have the composition and resolution of forces and of motions1 extending to the composition and resolution of vibrations4 ,we treat the luminiferous ether on mechanical principles1 and1 from the composition and resolution of its vibrations we deduce all the phenomena displayed by crystals in polarized light4 ,illustration3 ,fig4 #ce4 ,let us take1 as an example1 the crystal of tourmaline1 with which we are now so familiar4 ,let a vibration cross this crystal oblique to its axis4 ,experiment has assured us that a portion of the light will pass through4 ,the quantity which passes we determine in this way4 ,let ,a ,b 7fig4 #ce7 be the axis of the tourmaline1 and let a b represent the amplitude of an oblique ethereal vibration before it reaches ,a ,b4 ,from a and b let the two perpendiculars a c and b d be drawn upon the axis3 then c d will be the amplitude of the transmitted vibration4 ,i shall immediately ask you to follow me while ,i endeavour to explain the effects observed when a film of gypsum is placed between the two ,nicol prisms4 ,but1 prior to this1 it will be desirable to establish still further the analogy between the action of the prisms and that of the two plates of tourmaline4 ,the magnified images of these plates1 with their axes at right-angles to each other1 are now before you4 ,introducing between them a film of selenite1 you observe that by turning the film round it may be placed in a position where it has no power to abolish the darkness of the superposed portions of the tourmalines4 ,why is this8 ,the answer is1 that in the gypsum there are two directions1 at right angles to each other1 in which alone vibrations can take place1 and that in our present experiment one of these directions is parallel to one of the axes of the tourmaline1 and the other parallel to the other axis4 ,when this is the case1 the film exercises no sensible action upon the light4 ,but now ,i turn the film so as to render its directions of vibration oblique to the two tourmaline axes2 then1 you see it exercises the power1 demonstrated in the last lecture1 of partially restoring the light4 ,illustration3 ,fig4 #cf4 ,let us now mount our ,nicol prisms1 and cross them as we crossed the tourmaline4 ,introducing our film of gypsum between them1 you notice that in one particular position the film has no power whatever over the field of view4 ,but1 when the film is turned a little way round1 the light passes4 ,we have now to understand the mechanism by which this is effected4 ,first1 then1 we have a prism which receives the light from the electric lamp1 and which is called the polarizer4 ,then we have the plate of gypsum 7supposed to be placed at ,s1 fig4 #cf71 and then the prism in front1 which is called the analyzer4 ,on its emergence from the first prism1 the light is polarized2 and1 in the particular case now before us1 its vibrations are executed in a horizontal plane4 ,we have to examine what occurs when the two directions of vibration in the interposed gypsum are oblique to the horizon4 ,draw a rectangular cross 7,a ,b1 ,c ,d1 fig4 #cg7 to represent these two directions4 ,draw a line 7a b7 to represent the amplitude of the horizontal vibration on the emergence of the light from the first ,nicol4 ,let fall from each end of this line two perpendiculars 7a c1 a f1 b d1 b e7 on the two arms of the cross2 then the distances 7c d1 e f7 between the feet of these perpendiculars represent the amplitudes of two rectangular vibrations1 which are the components of the first single vibration4 ,thus the polarized ray1 when it enters the gypsum1 is resolved into its two equivalents1 which vibrate at right angles to each other4 ,illustration2 ,fig4 #cg4 ,in one of these two rectangular directions the ether within the gypsum is more sluggish than in the other2 and1 as a consequence1 the waves that follow this direction are more retarded than the others4 ,in both cases the undulations are shortened when they enter the gypsum1 but in the one case they are more shortened than in the other4 ,you can readily imagine that in this way the one system of waves may get half a wave-length1 or indeed any number of half wavelengths1 in advance of the other4 ,the possibility of interference here at once flashes upon the mind4 ,a little consideration1 however1 will render it evident that1 as long as the vibrations are executed at right angles to each other1 they cannot quench each other1 no matter what the retardation may be4 ,this brings us at once to the part played by the analyzer4 ,its sole function is to recompound the two vibrations emergent from the gypsum4 ,it reduces them to a single plane1 where1 if one of them be retarded by the proper amount1 extinction will occur4 ,but here1 as in the case of thin films1 the different lengths of the waves of light come into play4 ,red will require a greater thickness to produce the retardation necessary for extinction than blue2 consequently when the longer waves have been withdrawn by interference1 the shorter ones remain1 the film of gypsum shining with the colours which the short waves confer4 ,conversely1 when the shorter waves have been withdrawn1 the thickness is such that the longer waves remain4 ,an elementary consideration suffices to show1 that when the directions of vibration of the prisms and the gypsum enclose an angle of forty-five degrees1 the colours are at their maximum brilliancy4 ,when the film is turned from this direction1 the colours gradually fade1 until1 at the point where the directions of vibration in plate and prisms are parallel1 they disappear altogether4 7,the best way of obtaining a knowledge of these phenomena is to construct a model of thin wood or pasteboard1 representing the plate of gypsum1 its planes of vibration1 and also those of the polarizer and analyzer4 ,two parallel pieces of the board are to be separated by an interval which shall represent the thickness of the film of gypsum4 ,between them two other pieces1 intersecting each other at a right angle1 are to represent the planes of vibration within the film2 while attached to the two parallel surfaces outside are two other pieces of board1 which represent the planes of vibration of the polarizer and analyzer4 ,on the two intersecting planes the waves are to be drawn1 showing the resolution of the first polarized beam into two others1 and then the subsequent reduction of the two systems of vibrations to a common plane by the analyzer4 ,following out rigidly the interaction of the two systems of waves1 we are taught by such a model that all the phenomena of colour obtained by the combination of the waves1 when the planes of vibration of the two ,nicols are parallel1 are displaced by the complementary phenomena1 when the planes of vibration are perpendicular to each other47 ,in considering the next point1 we will operate1 for the sake of simplicity1 with monochromatic light--with red light1 for example1 which is easily obtained pure by red glass4 ,supposing a certain thickness of the gypsum produces a retardation of half a wave-length1 twice this thickness will produce a retardation of two half wave-lengths1 three times this thickness a retardation of three half wave-lengths1 and so on4 ,now1 when the ,nicols are parallel1 the retardation of half a wave-length1 or of any odd number of half wave-lengths1 produces extinction2 at all thicknesses1 on the other hand1 which correspond to a retardation of an even number of half wave-lengths1 the two beams support each other1 when they are brought to a common plane by the analyzer4 ,supposing1 then1 that we take a plate of a wedge form1 which grows gradually thicker from edge to back1 we ought to expect1 in red light1 a series of recurrent bands of light and darkness2 the dark bands occurring at thicknesses which produce retardations of one1 three1 five1 etc41 half wave-lengths1 while the bright bands occur between the dark ones4 ,experiment proves the wedge-shaped film to show these bands4 ,they are also beautifully shown by a circular film1 so worked as to be thinnest at the centre1 and gradually increasing in thickness from the centre outwards4 ,a splendid series of rings of light and darkness is thus produced4 ,when1 instead of employing red light1 we employ blue1 the rings are also seen3 but as they occur at thinner portions of the film1 they are smaller than the rings obtained with the red light4 ,the consequence of employing white light may be now inferred2 inasmuch as the red and the blue fall in different places1 we have iris-coloured rings produced by the white light4 ,some of the chromatic effects of irregular crystallization are beautiful in the extreme4 ,could ,i introduce between our two ,nicols a pane of glass covered by those frost-ferns which your cold weather renders now so frequent1 rich colours would be the result4 ,the beautiful effects of the irregular crystallization of tartaric acid and other substances on glass plates now presented to you1 illustrate what you might expect from the frosted window-pane4 ,and not only do crystalline bodies act thus upon light1 but almost all bodies that possess a definite structure do the same4 ,as a general rule1 organic bodies act thus upon light2 for their architecture implies an arrangement of the molecules1 and of the ether associated with the molecules1 which involves double refraction4 ,a film of horn1 or the section of a shell1 for example1 yields very beautiful colours in polarized light4 ,in a tree1 the ether certainly possesses different degrees of elasticity along and across the fibre2 and1 were wood transparent1 this peculiarity of molecular structure would infallibly reveal itself by chromatic phenomena like those that you have seen4 #d4 ,colours produced by ,strain and ,pressure4 ,not only do natural bodies behave in this way1 but it is possible1 as shown by ,brewster1 to confer1 by artificial strain or pressure1 a temporary double refracting structure upon non-crystalline bodies such as common glass4 ,this is a point worthy of illustration4 ,when ,i place a bar of wood across my knee and seek to break it1 what is the mechanical condition of the bar8 ,it bends1 and its convex surface is strained longitudinally2 its concave surface1 that next my knee1 is longitudinally pressed4 ,both in the strained portion and in the pressed portion of the wood the ether is thrown into a condition which would render the wood1 were it transparent1 double-refracting4 ,for1 in cases like the present1 the drawing of the molecules asunder longitudinally is always accompanied by their approach to each other laterally2 while the longitudinal squeezing is accompanied by lateral retreat4 ,each half of the bar of wood exhibits this antithesis1 and is therefore double-refracting4 ,let us now repeat this experiment with a bar of glass4 ,between the crossed ,nicols ,i introduce such a bar4 ,by the dim residue of light lingering upon the screen1 you see the image of the glass1 but it has no effect upon the light4 ,i simply bend the glass bar with my finger and thumb1 keeping its length oblique to the directions of vibration in the ,nicols4 ,instantly light flashes out upon the screen4 ,the two sides of the bar are illuminated1 the edges most1 for here the strain and pressure are greatest4 ,in passing from longitudinal strain to longitudinal pressure1 we cross a portion of the glass where neither is exerted4 ,this is the so-called neutral axis of the bar of glass1 and along it you see a dark band1 indicating that the glass along this axis exercises no action upon the light4 ,by employing the force of a press1 instead of the force of my finger and thumb1 the brilliancy of the light is greatly augmented4 ,again1 ,i have here a square of glass which can be inserted into a press of another kind4 ,introducing the uncompressed square between the prisms1 its neutrality is declared2 but it can hardly be held sufficiently loosely in the press to prevent its action from manifesting itself4 ,already1 though the pressure is infinitesimal1 you see spots of light at the points where the press is in contact with the glass4 ,on turning a screw1 the image of the square of glass flashes out upon the screen4 ,luminous spaces are seen separated from each other by dark bands4 ,every two adjacent spaces are in opposite mechanical conditions4 ,on one side of the dark band we have strain1 on the other side pressure1 the band marking the neutral axis between both4 ,i now tighten the vice1 and you see colour2 tighten still more1 and the colours appear as rich as those presented by crystals4 ,releasing the vice1 the colours suddenly vanish2 tightening suddenly1 they reappear4 ,from the colours of a soap-bubble ,newton was able to infer the thickness of the bubble1 thus uniting by the bond of thought apparently incongruous things4 ,from the colours here presented to you1 the magnitude of the pressure employed might be inferred4 ,indeed1 the late ,m4 ,wertheim1 of ,paris1 invented an instrument for the determination of strains and pressures1 by the colours of polarized light1 which exceeded in accuracy all previous instruments of the kind4 ,and now we have to push these considerations to a final illustration4 ,polarized light may be turned to account in various ways as an analyzer of molecular condition4 ,it may1 for instance1 be applied to reveal the condition of a solid body when it becomes sonorous4 ,a strip of glass six feet long1 two inches wide and a quarter of an inch thick1 is held at the centre between the finger and thumb4 ,on sweeping a wet woollen rag over one of its halves1 you hear an acute sound due to the vibrations of the glass4 ,what is the condition of the glass while the sound is heard8 ,this3 its two halves lengthen and shorten in quick succession4 ,its two ends1 therefore1 are in a state of quick vibration2 but at the centre the pulses from the two ends alternately meet and retreat from each other4 ,between their opposing actions1 the glass at the centre is kept motionless3 but1 on the other hand1 it is alternately strained and compressed4 ,in fig4 #ch1 ,a ,b may be taken to represent the glass rectangle with its centre condensed2 while ,a' ,b' represents the same rectangle with its centre rarefied4 ,the ends of the strip suffer neither condensation nor rarefaction4 ,illustration3 ,fig4 #ch ,if we introduce the strip of glass 7s s'1 fig4 #ci7 between the crossed ,nicols1 taking care to keep it oblique to the directions of vibration of the ,nicols1 and sweep our wet rubber over the glass1 this is what may be expected to occur3 ,at every moment of compression the light will flash through2 at every moment of strain the light will also flash through2 and these states of strain and pressure will follow each other so rapidly1 that we may expect a permanent luminous impression to be made upon the eye4 ,by pure reasoning1 therefore1 we reach the conclusion that the light will be revived whenever the glass is sounded4 ,that it is so1 experiment testifies3 at every sweep of the rubber 7h1 fig4 #ci7 a fine luminous disk 7,o7 flashes out upon the screen4 ,the experiment may be varied in this way3 ,placing in front of the polarizer a plate of unannealed glass1 you have a series of beautifully coloured rings1 intersected by a black cross4 ,every sweep of the rubber not only abolishes the rings1 but introduces complementary ones1 the black cross being1 for the moment1 supplanted by a white one4 ,this is a modification of a beautiful experiment which we owe to ,biot4 ,his apparatus1 however1 confined the observation of it to a single person at a time4 ,illustration3 ,fig4 #ci4 #e4 ,colours of ,unannealed ,glass4 ,bodies are usually expanded by heat and contracted by cold4 ,if the heat be applied with perfect uniformity1 no local strains or pressures come into play2 but1 if one portion of a solid be heated and another portion not1 the expansion of the heated portion introduces strains and pressures which reveal themselves under the scrutiny of polarized light4 ,when a square of common window-glass is placed between the ,nicols1 you see its dim outline1 but it exerts no action on the polarized light4 ,held for a moment over the flame of a spirit-lamp1 on reintroducing it between the ,nicols1 light flashes out upon the screen4 ,here1 as in the case of mechanical action1 you have luminous spaces of strain divided by dark neutral axes from spaces of pressure4 ,illustration3 ,fig4 #dj4 ,illustration3 ,fig4 #da4 ,let us apply the heat more symmetrically4 ,a small square of glass is perforated at the centre1 and into the orifice a bit of copper wire is introduced4 ,placing the square between the prisms1 and heating the wire1 the heat passes by conduction to the glass1 through which it spreads from the centre outwards4 ,you immediately see four luminous quadrants and a dim cross1 which becomes gradually blacker1 by comparison with the adjacent brightness4 ,and as1 in the case of pressure1 we produced colours1 so here also1 by the proper application of heat1 gorgeous chromatic effects may be evoked4 ,the condition necessary to the production of these colours may be rendered permanent by first heating the glass sufficiently1 and then cooling it1 so that the chilled mass shall remain in a state of permanent strain and pressure4 ,two or three examples will illustrate this point4 ,figs4 #dj and #da represent the figures obtained with two pieces of glass thus prepared2 two rectangular pieces of unannealed glass1 crossed and placed between the polarizer and analyzer1 exhibit the beautiful iris fringes represented in fig4 #db4 ,illustration3 ,fig4 #db4 #f4 ,circular ,polarization4 ,but we have to follow the ether still further into its hiding-places4 ,suspended before you is a pendulum1 which1 when drawn aside and liberated1 oscillates to and fro4 ,if1 when the pendulum is passing the middle point of its excursion1 ,i impart a shock to it tending to drive it at right angles to its present course1 what occurs8 ,the two impulses compound themselves to a vibration oblique in direction to the former one1 but the pendulum still oscillates in a plane4 ,but1 if the rectangular shock be imparted to the pendulum when it is at the limit of its swing1 then the compounding of the two impulses causes the suspended ball to describe1 not a straight line1 but an ellipse2 and1 if the shock be competent of itself to produce a vibration of the same amplitude as the first one1 the ellipse becomes a circle4 ,why do ,i dwell upon these things8 ,simply to make known to you the resemblance of these gross mechanical vibrations to the vibrations of light4 ,i hold in my hand a plate of quartz cut from the crystal perpendicular to its axis4 ,the crystal thus cut possesses the extraordinary power of twisting the plane of vibration of a polarized ray to an extent dependent on the thickness of the crystal4 ,and the more refrangible the light the greater is the amount of twisting2 so that1 when white light is employed1 its constituent colours are thus drawn asunder4 ,placing the quartz plate between the polarizer and analyzer1 this vivid red appears2 and1 turning the analyzer in front from right to left1 the other colours of the spectrum appear in succession4 ,specimens of quartz have been found which require the analyzer to be turned from left to right to obtain the same succession of colours4 ,crystals of the first class are therefore called right-handed1 and of the second class1 left-handed crystals4 ,with profound sagacity1 ,fresnel1 to whose genius we mainly owe the expansion and final triumph of the undulatory theory of light1 reproduced mentally the mechanism of these crystals1 and showed their action to be due to the circumstance that1 in them1 the waves of ether so act upon each other as to produce the condition represented by our rotating pendulum4 ,instead of being plane polarized1 the light in rock crystal is circularly polarized4 ,two such rays1 transmitted along the axis of the crystal1 and rotating in opposite directions1 when brought to interference by the analyzer1 are demonstrably competent to produce all the observed phenomena4 #g4 ,complementary ,colours of ,bi-refracting ,spar in ,circularly ,polarized ,light4 ,proof that ,yellow and ,blue are ,complementary4 ,i now remove the analyzer1 and put in its place the piece of ,iceland spar with which we have already illustrated double refraction4 ,the two images of the carbon-points are now before you1 produced1 as you know1 by two beams vibrating at right angles to each other4 ,introducing a plate of quartz between the polarizer and the spar1 the two images glow with complementary colours4 ,employing the image of an aperture instead of that of the carbon-points1 we have two coloured circles4 ,as the analyzer is caused to rotate1 the colours pass through various changes3 but they are always complementary4 ,when the one is red1 the other is green2 when the one is yellow1 the other is blue4 ,here we have it in our power to demonstrate afresh a statement made in our first lecture1 that although the mixture of blue and yellow pigments produces green1 the mixture of blue and yellow lights produces white4 ,by enlarging our aperture1 the two images produced by the spar are caused to approach each other1 and finally to overlap4 ,the one image is now a vivid yellow1 the other a vivid blue1 and you notice that where these colours are superposed we have a pure white4 7,see fig4 #dc1 where ,n is the end of the polarizer1 ,q the quartz plate1 ,l a lens1 and ,b the bi-refracting spar4 ,the two images overlap at ,o1 and produce white by their mixture47 ,illustration3 ,fig4 #dc4 #h4 ,the ,magnetization of ,light4 ,this brings us to a point of our inquiries which1 though rarely illustrated in lectures1 is nevertheless so likely to affect profoundly the future course of scientific thought that ,i am unwilling to pass it over without reference4 ,i refer to the experiment which ,faraday1 its discoverer1 called the 'magnetization of light4' ,the arrangement for this celebrated experiment is now before you4 ,we have1 first1 our electric lamp1 then a ,nicol prism1 to polarize the beam emergent from the lamp2 then an electro-magnet1 then a second ,nicol1 and finally our screen4 ,at the present moment the prisms are crossed1 and the screen is dark4 ,i place from pole to pole of the electro-magnet a cylinder of a peculiar kind of glass1 first made by ,faraday1 and called ,faraday's heavy glass4 ,through this glass the beam from the polarizer now passes1 being intercepted by the ,nicol in front4 ,on exciting the magnet light instantly appears upon the screen4 ,by the action of the magnet upon the heavy glass the plane of vibration is caused to rotate1 the light being thus enabled to get through the analyzer4 ,the two classes into which quartz-crystals are divided have been already mentioned4 ,in my hand ,i hold a compound plate1 one half of it taken from a right-handed1 and the other from a left-handed crystal4 ,placing the plate in front of the polarizer1 ,i turn one of the ,nicols until the two halves of the plate show a common puce colour4 ,this yields an exceedingly sensitive means of rendering visible the action of a magnet upon light4 ,by turning either the polarizer or the analyzer through the smallest angle1 the uniformity of the colour disappears1 and the two halves of the quartz show different colours4 ,the magnet produces an effect equivalent to this rotation4 ,the puce-coloured circle is now before you on the screen4 7,see fig4 #dd1 where ,n is the nozzle of the lamp1 ,h the first ,nicol1 ,q the biquartz plate1 ,l a lens1 ,m the electro-magnet1 with the heavy glass across its perforated poles1 and ,p the second ,nicol47 ,exciting the magnet1 one half of the image becomes suddenly red1 the other half green4 ,interrupting the current1 the two colours fade away1 and the primitive puce is restored4 ,the action1 moreover1 depends upon the polarity of the magnet1 or1 in other words1 on the direction of the current which surrounds the magnet4 ,reversing the current1 the red and green reappear1 but they have changed places4 ,the red was formerly to the right1 and the green to the left2 the green is now to the right1 and the red to the left4 ,with the most exquisite ingenuity1 ,faraday analyzed all those actions and stated their laws4 ,this experiment1 however1 long remained a scientific curiosity rather than a fruitful germ4 ,that it would bear fruit of the highest importance1 ,faraday felt profoundly convinced1 and present researches are on the way to verify his conviction4 ,illustration3 ,fig4 #dd #i4 ,iris-rings surrounding the ,axes of ,crystals4 ,a few more words are necessary to complete our knowledge of the wonderful interaction between ponderable molecules and the ether interfused among them4 ,symmetry of molecular arrangement implies symmetry on the part of the ether2 atomic dissymmetry1 on the other hand1 involves the dissymmetry of the ether1 and1 as a consequence1 double refraction4 ,in a certain class of crystals the structure is homogeneous1 and such crystals produce no double refraction4 ,in certain other crystals the molecules are ranged symmetrically round a certain line1 and not around others4 ,along the former1 therefore1 the ray is undivided1 while along all the others we have double refraction4 ,ice is a familiar example3 its molecules are built with perfect symmetry around the perpendiculars to the planes of freezing1 and a ray sent through ice in this direction is not doubly refracted2 whereas1 in all other directions1 it is4 ,iceland spar is another example of the same kind3 its molecules are built symmetrically round the line uniting the two blunt angles of the rhomb4 ,in this direction a ray suffers no double refraction1 in all others it does4 ,this direction of no double refraction is called the optic axis of the crystal4 ,hence1 if a plate be cut from a crystal of ,iceland spar perpendicular to the axis1 all rays sent across this plate in the direction of the axis will produce but one image4 ,but1 the moment we deviate from the parallelism with the axis1 double refraction sets in4 ,if1 therefore1 a beam that has been rendered conical by a converging lens be sent through the spar so that the central ray of the cone passes along the axis1 this ray only will escape double refraction4 ,each of the others will be divided into an ordinary and an extraordinary ray1 the one moving more slowly through the crystal than the other2 the one1 therefore1 retarded with reference to the other4 ,here1 then1 we have the conditions for interference1 when the waves are reduced by the analyzer to a common plane4 ,placing the plate of ,iceland spar between the crossed ,nicol prisms1 and employing the conical beam1 we have upon the screen a beautiful system of iris-rings surrounding the end of the optic axis1 the circular bands of colour being intersected by a black cross 7fig4 #de74 ,the arms of this cross are parallel to the two directions of vibration in the polarizer and analyzer4 ,it is easy to see that those rays whose planes of vibration within the spar coincide with the plane of vibration of either prism1 cannot get through both4 ,this complete interception produces the arms of the cross4 ,illustration3 ,fig4 #de4 ,with monochromatic light the rings would be simply bright and black--the bright rings occurring at those thicknesses of the spar which cause the rays to conspire2 the black rings at those thicknesses which cause them to quench each other4 ,turning the analyzer #ij round1 we obtain the complementary phenomena4 ,the black cross gives place to a bright one1 and every dark ring is supplanted also by a bright one 7fig4 #df74 ,here1 as elsewhere1 the different lengths of the light-waves give rise to iris-colours when white light is employed4 ,illustration3 ,fig4 #df4 ,illustration3 ,fig4 #dg4 ,besides the regular crystals which produce double refraction in no direction1 and the uniaxal crystals which produce it in all directions but one1 ,brewster discovered that in a large class of crystals there are two directions in which double refraction does not take place4 ,these are called biaxal crystals4 ,when plates of these crystals1 suitably cut1 are placed between the polarizer and analyzer1 the axes 7,a ,a'1 fig4 #dg7 are seen surrounded1 not by circles1 but by curves of another order and of a perfectly definite mathematical character4 ,each band1 as proved experimentally by ,herschel1 forms a lemniscata2 but the experimental proof was here1 as in numberless other cases1 preceded by the deduction which showed that1 according to the undulatory theory1 the bands must possess this special character4 #aj4 ,power of the ,wave ,theory4 ,i have taken this somewhat wide range over polarization itself1 and over the phenomena exhibited by crystals in polarized light1 in order to give you some notion of the firmness and completeness of the theory which grasps them all4 ,starting from the single assumption of transverse undulations1 we first of all determine the wave-lengths1 and find that on them all the phenomena of colour are dependent4 ,the wavelengths may be determined in many independent ways4 ,newton virtually determined them when he measured the periods of his ,fits3 the length of a fit1 in fact1 is that of a quarter of an undulation4 ,the wave-lengths may be determined by diffraction at the edges of a slit 7as in the ,appendix to these ,lectures72 they may be deduced from the interference fringes produced by reflection2 from the fringes produced by refraction2 also by lines drawn with a diamond upon glass at measured distances asunder4 ,and when the length determined by these independent methods are compared together1 the strictest agreement is found to exist between them4 ,with the wave-lengths once at our disposal1 we follow the ether into the most complicated cases of interaction between it and ordinary matter1 'the theory is equal to them all4 ,it makes not a single new physical hypothesis2 but out of its original stock of principles it educes the counterparts of all that observation shows4 ,it accounts for1 explains1 simplifies the most entangled cases2 corrects known laws and facts2 predicts and discloses unknown ones2 becomes the guide of its former teacher ,observation2 and1 enlightened by mechanical conceptions1 acquires an insight which pierces through shape and colour to force and cause4'#ah ,but1 while ,i have thus endeavoured to illustrate before you the power of the undulatory theory as a solver of all the difficulties of optics1 do ,i therefore wish you to close your eyes to any evidence that may arise against it8 ,by no means4 ,you may urge1 and justly urge1 that a hundred years ago another theory was held by the most eminent men1 and that1 as the theory then held had to yield1 the undulatory theory may have to yield also4 ,this seems reasonable2 but let us understand the precise value of the argument4 ,in similar language a person in the time of ,newton1 or even in our time1 might reason thus3 ,hipparchus and ,ptolemy1 and numbers of great men after them1 believed that the earth was the centre of the solar system4 ,but this deep-set theoretic notion had to give way1 and the helio-centric theory may1 in its turn1 have to give way also4 ,this is just as reasonable as the first argument4 ,wherein consists the strength of the present theory of gravitation8 ,solely in its competence to account for all the phenomena of the solar system4 ,wherein consists the strength of the theory of undulation8 ,solely in its competence to disentangle and explain phenomena a hundred-fold more complex than those of the solar system4 ,accept if you will the scepticism of ,mr4 ,mill#ai regarding the undulatory theory2 but if your scepticism be philosophical1 it will wrap the theory of gravitation in the same or in greater doubt4#bj #aa4 ,the ,blue of the ,sky4 ,i am unwilling to quit these chromatic phenomena without referring to a source of colour which has often come before me of late in the blue of your skies at noon1 and the deep crimson of your horizon after the set of sun4 ,i will here summarize and extend what ,i have elsewhere said upon this subject4 ,proofs of the most cogent description could be adduced to show that the blue light of the firmament is reflected light4 ,that light comes to us across the direction of the solar rays1 and even against the direction of the solar rays2 and this lateral and opposing rush of wave-motion can only be due to the rebound of the waves from the air itself1 or from something suspended in the air4 ,the solar light1 moreover1 is not scattered by the sky in the proportions which produce white4 ,the sky is blue1 which indicates an excess of the smaller waves4 ,the blueness of the air has been given as a reason for the blueness of the sky2 but then the question arises1 ,how1 if the air be blue1 can the light of sunrise and sunset1 which travels through vast distances of air1 be yellow1 orange1 or even red8 ,the passage of the white solar light through a blue medium could by no possibility redden the light2 the hypothesis of a blue atmosphere is therefore untenable4 ,in fact1 the agent1 whatever it be1 which sends us the light of the sky1 exercises in so doing a dichroitic action4 ,the light reflected is blue1 the light transmitted is orange or red1 ,a marked distinction is thus exhibited between reflection from the sky and that from an ordinary cloud1 which exercises no such dichroitic action4 ,the cloud1 in fact1 takes no note of size on the part of the waves of ether1 but reflects them all alike4 ,now the cause of this may be that the cloud-particles are so large in comparison with the size of the waves of ether as to scatter them all indifferently4 ,a broad cliff reflects an ,atlantic roller as easily as it reflects a ripple produced by a sea-bird's wing2 and1 in the presence of large reflecting surfaces1 the existing differences of magnitude among the waves of ether may also disappear4 ,but supposing the reflecting particles1 instead of being very large1 to be very small1 in comparison with the size of the waves4 ,then1 instead of the whole wave being fronted and in great part thrown back1 a small portion only is shivered off by the obstacle4 ,suppose1 then1 such minute foreign particles to be diffused in our atmosphere4 ,waves of all sizes impinge upon them1 and at every collision a portion of the impinging wave is struck off4 ,all the waves of the spectrum1 from the extreme red to the extreme violet1 are thus acted upon2 but in what proportions will they be scattered8 ,largeness is a thing of relation2 and the smaller the wave1 the greater is the relative size of any particle on which the wave impinges1 and the greater also the relative reflection4 ,a small pebble1 placed in the way of the ring-ripples produced by heavy rain-drops on a tranquil pond1 will throw back a large fraction of each ripple incident upon it1 while the fractional part of a larger wave thrown back by the same pebble might be infinitesimal4 ,now to preserve the solar light white1 its constituent proportions must not be altered2 but in the scattering of the light by these very small particles we see that the proportions are altered4 ,the smaller waves are in excess1 and1 as a consequence1 in the scattered light blue will be the predominant colour4 ,the other colours of the spectrum must1 to some extent1 be associated with the blue3 they are not absent1 but deficient4 ,we ought1 in fact1 to have them all1 but in diminishing proportions1 from the violet to the red4 ,we have thus reasoned our way to the conclusion1 that were particles1 small in comparison to the size of the ether waves1 sown in our atmosphere1 the light scattered by those particles would be exactly such as we observe in our azure skies4 ,and1 indeed1 when this light is analyzed1 all the colours of the spectrum are found in the proportions indicated by our conclusion4 ,by its successive collisions with the particles the white light is more and more robbed of its shorter waves2 it therefore loses more and more of its due proportion of blue4 ,the result may be anticipated4 ,the transmitted light1 where moderate distances are involved1 will appear yellowish4 ,but as the sun sinks towards the horizon the atmospheric distance increases1 and consequently the number of the scattering particles4 ,they weaken in succession the violet1 the indigo1 the blue1 and even disturb the proportions of green4 ,the transmitted light under such circumstances must pass from yellow through orange to red4 ,this also is exactly what we find in nature4 ,thus1 while the reflected light gives us1 at noon1 the deep azure of the ,alpine skies1 the transmitted light gives us1 at sunset1 the warm crimson of the ,alpine snows4 ,but can small particles be really proved to act in the manner indicated8 ,no doubt of it4 ,each one of you can submit the question to an experimental test4 ,water will not dissolve resin1 but spirit will2 and when spirit which holds resin in solution is dropped into water1 the resin immediately separates in solid particles1 which render the water milky4 ,the coarseness of this precipitate depends on the quantity of the dissolved resin4 ,professor ,brcke has given us the proportions which produce particles particularly suited to our present purpose4 ,one gramme of clean mastic is dissolved in eighty-seven grammes of absolute alcohol1 and the transparent solution is allowed to drop into a beaker containing clear water briskly stirred4 ,an exceedingly fine precipitate is thus formed1 which declares its presence by its action upon light4 ,placing a dark surface behind the beaker1 and permitting the light to fall into it from the top or front1 the medium is seen to be of a very fair sky-blue4 ,a trace of soap in water gives it a tint of blue4 ,london milk makes an approximation to the same colour1 through the operation of the same cause3 and ,helmholtz has irreverently disclosed the fact that a blue eye is simply a turbid medium4 #ab4 ,artificial ,sky4 ,but we have it in our power to imitate far more closely the natural conditions of this problem4 ,we can generate in air artificial skies1 and prove their perfect identity with the natural one1 as regards the exhibition of a number of wholly unexpected phenomena4 ,it has been recently shown in a great number of instances by myself that waves of ether issuing from a strong source1 such as the sun or the electric light1 are competent to shake asunder the atoms of gaseous molecules4 ,the apparatus used to illustrate this consists of a glass tube about a yard in length1 and from #b to #c inches internal diameter4 ,the gas or vapour to be examined is introduced into this tube1 and upon it the condensed beam of the electric lamp is permitted to act4 ,the vapour is so chosen that one1 at least1 of its products of decomposition1 as soon as it is formed1 shall be precipitated to a kind of cloud4 ,by graduating the quantity of the vapour1 this precipitation may be rendered of any degree of fineness1 forming particles distinguishable by the naked eye1 or particles which are probably far beyond the reach of our highest microscopic powers4 ,i have no reason to doubt that particles may be thus obtained whose diameters constitute but a very small fraction of the length of a wave of violet light4 ,now1 in all such cases when suitable vapours are employed in a sufficiently attenuated state1 no matter what the vapour may be1 the visible action commences with the formation of a blue cloud4 ,let me guard myself at the outset against all misconception as to the use of this term4 ,the blue cloud here referred to is totally invisible in ordinary daylight4 ,to be seen1 it requires to be surrounded by darkness1 it only being illuminated by a powerful beam of light4 ,this cloud differs in many important particulars from the finest ordinary clouds1 and might justly have assigned to it an intermediate position between these clouds and true cloudless vapour4 ,it is possible to make the particles of this actinic cloud grow from an infinitesimal and altogether ultra-microscopic size to particles of sensible magnitude2 and by means of these in a certain stage of their growth1 we produce a blue which rivals1 if it does not transcend1 that of the deepest and purest ,italian sky4 ,introducing into our tube a quantity of mixed air and nitrite of butyl vapour sufficient to depress the mercurial column of an air-pump one-twentieth of an inch1 adding a quantity of air and hydrochloric acid sufficient to depress the mercury half an inch further1 and sending through this compound and highly attenuated atmosphere the beam of the electric light1 within the tube arises gradually a splendid azure1 which strengthens for a time1 reaches a maximum of depth and purity1 and then1 as the particles grow larger1 passes into whitish blue4 ,this experiment is representative1 and it illustrates a general principle4 ,various other colourless substances of the most diverse properties1 optical and chemical1 might be employed for this experiment4 ,the incipient cloud1 in every case1 would exhibit this superb blue2 thus proving to demonstration that particles of infinitesimal size1 without any colour of their own1 and irrespective of those optical properties exhibited by the substance in a massive state1 are competent to produce the blue colour of the sky4 #ac4 ,polarization of ,skylight4 ,but there is another subject connected with our firmament1 of a more subtle and recondite character than even its colour4 ,i mean that 'mysterious and beautiful phenomenon1' as ,sir ,john ,herschel calls it1 the polarization of the light of the sky4 ,looking at various points of the blue firmament through a ,nicol prism1 and turning the prism round its axis1 we soon notice variations of brightness4 ,in certain positions of the prism1 and from certain points of the firmament1 the light appears to be wholly transmitted1 while it is only necessary to turn the prism round its axis through an angle of ninety degrees to materially diminish the intensity of the light4 ,experiments of this kind prove that the blue light sent to us by the firmament is polarized1 and on close scrutiny it is also found that the direction of most perfect polarization is perpendicular to the solar rays4 ,were the heavenly azure like the ordinary light of the sun1 the turning of the prism would have no effect upon it2 it would be transmitted equally during the entire rotation of the prism4 ,the light of the sky may be in great part quenched1 because it is in great part polarized4 ,the same phenomenon is exhibited in perfection by our actinic clouds1 the only condition necessary to its production being the smallness of the particles4 ,in all cases1 and with all substances1 the cloud formed at the commencement1 when the precipitated particles are sufficiently fine1 is blue4 ,in all cases1 moreover1 this fine blue cloud polarizes perfectly the beam which illuminates it1 the direction of polarization enclosing an angle of #ij with the axis of the illuminating beam4 ,it is exceedingly interesting to observe both the growth and the decay of this polarization4 ,for ten or fifteen minutes after its first appearance1 the light from a vividly illuminated incipient cloud1 looked at horizontally1 is absolutely quenched by a ,nicol prism with its longer diagonal vertical4 ,but as the sky-blue is gradually rendered impure by the introduction of particles of too large a size1 in other words1 as real clouds begin to be formed1 the polarization begins to deteriorate1 a portion of the light passing through the prism in all its positions1 as it does in the case of skylight4 ,it is worthy of note that for some time after the cessation of perfect polarization the residual light which passes1 when the ,nicol is in its position of minimum transmission1 is of a gorgeous blue1 the whiter light of the cloud being extinguished4 ,when the cloud-texture has become sufficiently coarse to approximate to that of ordinary clouds1 the rotation of the ,nicol ceases to have any sensible effect on the light discharged at right angles to the beam4 ,the perfection of the polarization in a direction perpendicular to the illuminating beam may be also illustrated by the following experiment1 which has been executed with many vapours4 ,a ,nicol prism large enough to embrace the entire beam of the electric lamp was placed between the lamp and the experimental tube4 ,sending the beam polarized by the ,nicol through the tube1 ,i placed myself in front of it1 the eyes being on a level with its axis1 my assistant occupying a similar position behind the tube4 ,the short diagonal of the large ,nicol was in the first instance vertical1 the plane of vibration of the emergent beam being therefore also vertical4 ,as the light continued to act1 a superb blue cloud visible to both my assistant and myself was slowly formed4 ,but this cloud1 so deep and rich when looked at from the positions mentioned1 utterly disappeared when looked at vertically downwards1 or vertically upwards4 ,reflection from the cloud was not possible in these directions4 ,when the large ,nicol was slowly turned round its axis1 the eye of the observer being on the level of the beam1 and the line of vision perpendicular to it1 entire extinction of the light emitted horizontally occurred when the longer diagonal of the large ,nicol was vertical4 ,but a vivid blue cloud was seen when looked at downwards or upwards4 ,this truly fine experiment1 which ,i should certainly have made without suggestion1 was1 as a matter of fact1 first definitely suggested by a remark addressed to me in a letter by ,professor ,stokes4 ,all the phenomena of colour and of polarization observable in the case of skylight are manifested by those actinic clouds2 and they exhibit additional phenomena which it would be neither convenient to pursue1 nor perhaps possible to detect1 in the actual firmament4 ,they enable us1 for example1 to follow the polarization from its first appearance on the barely visible blue to its final extinction in the coarser cloud4 ,these changes1 as far as it is now necessary to refer to them1 may be thus summed up3-- #a4 ,the actinic cloud1 as long as it continues blue1 discharges polarized light in all directions1 but the direction of maximum polarization1 like that of skylight1 is at right angles to the direction of the illuminating beam4 #b4 ,as long as the cloud remains distinctly blue1 the light discharged from it at right angles to the illuminating beam is perfectly polarized4 ,it may be utterly quenched by a ,nicol prism1 the cloud from which it issues being caused to disappear4 ,any deviation from the perpendicular enables a portion of the light to get through the prism4 #c4 ,the direction of vibration of the polarized light is at right angles to the illuminating beam4 ,hence a plate of tourmaline1 with its axis parallel to the beam1 stops the light1 and with the axis perpendicular to the beam transmits the light4 #d4 ,a plate of selenite placed between the ,nicol and the actinic cloud shows the colours of polarized light2 in fact1 the cloud itself plays the part of a polarizing ,nicol4 #e4 ,the particles of the blue cloud are immeasurably small1 but they increase gradually in size1 and at a certain period of their growth cease to discharge perfectly polarized light4 ,for some time afterwards the light that reaches the eye1 through the ,nicol in its position of least transmission1 is of a magnificent blue1 far exceeding in depth and purity that of the purest sky2 thus the waves that first feel the influence of size1 at both limits of the polarization1 are the shortest waves of the spectrum4 ,these are the first to accept polarization1 and they are the first to escape from it4 ,,lecture ,v4 ,,range ,,of ,,vision ,,not ,,commensurate ,,with ,,range ,,of ,,radiation ,,the ,,ultra-,,violet ,,bays ,,fluorescence ,,the ,,rendering ,,of ,,invisible ,,rays ,,visible ,,vision ,,not ,,the ,,only ,,sense ,,appealed ,,to ,,by ,,the ,,solar ,,and ,,electric ,,beam ,,heat ,,of ,,beam ,,combustion ,,by ,,total ,,beam ,,at ,,the ,,foci ,,of ,,mirrors ,,and ,,lenses ,,combustion ,,through ,,ice-,,lens ,,ignition ,,of ,,diamond ,,search ,,for ,,the ,,rays ,,here ,,effective ,,sir ,,william ,,herschel',s ,,discovery ,,of ,,dark ,,solar ,,rays ,,invisible ,,rays ,,the ,,basis ,,of ,,the ,,visible ,,detachment ,,by ,a ,,ray-,,filter ,,of ,,the ,,invisible ,,rays ,,from ,,the ,,visible ,,combustion ,,at ,,dark ,,foci ,,conversion ,,of ,,heat-,,rays ,,into ,,light-,,rays ,,calorescence ,,part ,,played ,,in ,,nature ,,by ,,dark ,,rays ,,identity ,,of ,,light ,,and ,,radiant ,,heat ,,invisible ,,images ,,reflection1 ,,refraction1 ,,plane ,,polarization1 ,,depolarization1 ,,circular ,,polarization1 ,,double ,,refraction1 ,,and ,,magnetization ,,of ,,radiant ,,heat4 #a4 ,range of ,vision and of ,radiation4 ,the first question that we have to consider to-night is this3 ,is the eye1 as an organ of vision1 commensurate with the whole range of solar radiation--is it capable of receiving visual impressions from all the rays emitted by the sun8 ,the answer is negative4 ,if we allowed ourselves to accept for a moment that notion of gradual growth1 amelioration1 and ascension1 implied by the term evolution1 we might fairly conclude that there are stores of visual impressions awaiting man1 far greater than those now in his possession4 ,ritter discovered in #ahja that beyond the extreme violet of the spectrum there is a vast efflux of rays which are totally useless as regards our present powers of vision4 ,these ultra-violet waves1 however1 though incompetent to awaken the optic nerve1 can shake asunder the molecules of certain compound substances on which they impinge1 thus producing chemical decomposition4 ,but though the blue1 violet1 and ultra-violet rays can act thus upon certain substances1 the fact is hardly sufficient to entitle them to the name of 'chemical rays1' which is usually applied to distinguish them from the other constituents of the spectrum4 ,as regards their action upon the salts of silver1 and many other substances1 they may perhaps merit this title2 but in the case of the grandest example of the chemical action of light--the decomposition of carbonic acid in the leaves of plants1 with which my eminent friend ,dr4 ,draper 7now no more7 has so indissolubly associated his name--the yellow rays are found to be the most active4 ,there are substances1 however1 on which the violet and ultra-violet waves exert a special decomposing power2 and1 by permitting the invisible spectrum to fall upon surfaces prepared with such substances1 we reveal both the existence and the extent of the ultraviolet spectrum4 #b4 ,ultra-violet ,rays3 ,fluorescence4 ,the method of exhibiting the action of the ultraviolet rays by their chemical action has been long known2 indeed1 ,thomas ,young photographed the ultra-violet rings of ,newton4 ,we have now to demonstrate their presence in another way4 ,as a general rule1 bodies either transmit light or absorb it2 but there is a third case in which the light falling upon the body is neither transmitted nor absorbed1 but converted into light of another kind4 ,professor ,stokes1 the occupant of the chair of ,newton in the ,university of ,cambridge1 has demonstrated this change of one kind of light into another1 and has pushed his experiments so far as to render the invisible rays visible4 ,a large number of substances examined by ,stokes1 when excited by the invisible ultra-violet waves1 have been proved to emit light4 ,you know the rate of vibration corresponding to the extreme violet of the spectrum2 you are aware that to produce the impression of this colour1 the retina is struck #ghi millions of millions of times in a second4 ,at this point1 the retina ceases to be useful as an organ of vision2 for1 though struck by waves of more rapid recurrence1 they are incompetent to awaken the sensation of light4 ,but when such non-visual waves are caused to impinge upon the molecules of certain substances--on those of sulphate of quinine1 for example--they compel those molecules1 or their constituent atoms1 to vibrate2 and the peculiarity is1 that the vibrations thus set up are of slower period than those of the exciting waves4 ,by this lowering of the rate of vibration through the intermediation of the sulphate of quinine1 the invisible rays are brought within the range of vision4 ,we shall subsequently have abundant opportunity for learning that transparency to the visible by no means involves transparency to the invisible rays4 ,our bisulphide of carbon1 for example1 which1 employed in prisms1 is so eminently suitable for experiments on the visual rays1 is by no means so suitable for these ultra-violet rays4 ,flint glass is better1 and rock crystal is better than flint glass4 ,a glass prism1 however1 will suit our present purpose4 ,casting by means of such a prism a spectrum1 not upon the white surface of our screen1 but upon a sheet of paper which has been wetted with a saturated solution of the sulphate of quinine and afterwards dried1 an obvious extension of the spectrum is revealed4 ,we have1 in the first instance1 a portion of the violet rendered whiter and more brilliant2 but1 besides this1 we have the gleaming of the colour where1 in the case of unprepared paper1 nothing is seen4 ,other substances produce a similar effect4 ,a substance1 for example1 recently discovered by ,president ,morton1 and named by him ,thallene1 produces a very striking elongation of the spectrum1 the new light generated being of peculiar brilliancy4 ,fluor spar1 and some other substances1 when raised to a temperature still under redness1 emit light4 ,during the ages which have elapsed since their formation1 this capacity of shaking the ether into visual tremors appears to have been enjoyed by these substances4 ,light has been potential within them all this time2 and1 as well explained by ,draper1 the heat1 though not itself of visual intensity1 can unlock the molecules so as to enable them to exert their long-latent power of vibration4 ,this deportment of fluor spar determined ,stokes in his choice of a name for his great discovery3 he called this rendering visible of the ultra-violet rays ,fluorescence4 ,by means of a deeply coloured violet glass1 we cut off almost the whole of the light of our electric beam2 but this glass is peculiarly transparent to the violet and ultra-violet rays4 ,the violet beam now crosses a large jar filled with water1 into which ,i pour a solution of sulphate of quinine4 ,clouds1 to all appearance opaque1 instantly tumble downwards4 ,fragments of horse-chestnut bark thrown upon the water also send down beautiful cloud-like strife4 ,but these are not clouds3 there is nothing precipitated here3 the observed action is an action of molecules1 not of particles4 ,the medium before you is not a turbid medium1 for when you look through it at a luminous surface it is perfectly clear4 ,if we paint upon a piece of paper a flower or a bouquet with the sulphate of quinine1 and expose it to the full beam1 scarcely anything is seen4 ,but on interposing the violet glass1 the design instantly flashes forth in strong contrast with the deep surrounding violet4 ,president ,morton has prepared for me a most beautiful example of such a design which1 when placed in the violet light1 exhibits a peculiarly brilliant fluorescence4 ,from the experiments of ,drs4 ,bence ,jones and ,dupr1 it would seem that there is some substance in the human body resembling the sulphate of quinine1 which causes all the tissues of the body to be more or less fluorescent4 ,all animal infusions show this fluorescence4 ,the crystalline lens of the eye exhibits the effect in a very striking manner4 ,when1 for example1 ,i plunge my eye into this violet beam1 ,i am conscious of a whitish-blue shimmer filling the space before me4 ,this is caused by fluorescent light generated in the eye itself4 ,looked at from without1 the crystalline lens at the same time is seen to gleam vividly4 ,long before its physical origin was understood this fluorescent light attracted attention4 ,boyle describes it with great fulness and exactness4 ',we have sometimes1' he says1 'found in the shops of our druggists certain wood which is there called ,lignum ,nephriticum1 because the inhabitants of the country where it grows are wont to use the infusion of it1 made in fair water1 against the stone in the kidneys4 ,this wood may afford us an experiment which1 besides the singularity of it1 may give no small assistance to an attentive considerer towards the detection of the nature of colours4 ,take ,lignum1 ,nephriticum1 and with a knife cut it into thin slices3 put about a handful of these slices into two or three or four pounds of the purest spring water4 ,decant this impregnated water into a glass phial2 and if you hold it directly between the light and your eye1 you shall see it wholly tinted with an almost golden colour4 ,but if you hold this phial from the light1 so that your eye be placed betwixt the window and the phial1 the liquid will appear of a deep and lovely ceruleous colour4' ',these1' he continues1 'and other phenomena which ,i have observed in this delightful experiment1 divers of my friends have looked upon1 not without some wonder2 and ,i remember an excellent oculist1 finding by accident in a friend's chamber a phial full of this liquor1 which ,i had given that friend1 and having never heard anything of the experiment1 nor having anybody near him who could tell him what this strange liquor might be1 was a great while apprehensive1 as he presently afterwards told me1 that some strange new distemper was invading his eyes4 ,and ,i confess that the unusualness of the phenomenon made me very solicitous to find out the cause of this experiment2 and though ,i am far from pretending to have found it1 yet my enquiries have1 ,i suppose1 enabled me to give such hints as may lead your greater sagacity to the discovery of the cause of this wonder4'#ba ,goethe in his ',farbenlehre' thus describes the fluorescence of horse-chestnut bark3--',let a strip of fresh horse-chestnut bark be taken and clipped into a glass of water2 the most perfect sky-blue will be immediately produced4'#bb ,sir ,john ,herschel first noticed and described the fluorescence of the sulphate of quinine1 and showed that the light proceeded from a thin stratum of the solution adjacent to the surface where the light enters it4 ,he showed1 moreover1 that the incident beam1 although not sensibly weakened in luminous intensity1 lost1 in its transmission through the solution of sulphate of quinine1 the power of producing the blue fluorescent light4 ,sir ,david ,brewster also worked at the subject2 but to ,professor ,stokes we are indebted not only for its expansion1 but for its full and final explanation4 #c4 ,the ,heat of the ,electric ,beam4 ,ignition through a ,lens of ,ice4 ,possible ,cometary ,temperature4 ,but the waves from our incandescent carbon-points appeal to another sense than that of vision4 ,they not only produce light1 but heat1 as a sensation4 ,the magnified image of the carbon-points is now upon the screen2 and with a suitable instrument the heating power of the rays which form that image might be readily demonstrated4 ,in this case1 however1 the heat is spread over too large an area to be very intense4 ,drawing out the camera lens1 and causing a movable screen to approach the lamp1 the image is seen to become smaller and smaller2 the rays at the same time becoming more and more concentrated1 until finally they are able to pierce black paper with a burning ring4 ,pushing back the lens so as to render the rays parallel1 and receiving them upon a concave mirror1 they are brought to a focus2 paper placed at that focus is caused to smoke and burn4 ,heat of this intensity may be obtained with our ordinary camera and lens1 and a concave mirror of very moderate power4 ,illustration3 ,fig4 #dh4 ,we will now adopt stronger measures with the radiation4 ,in this larger camera of blackened tin is placed a lamp1 in all particulars similar to those already employed4 ,but instead of gathering up the rays from the carbon-points by a condensing lens1 we gather them up by a concave mirror 7m m'1 fig4 #dh71 silvered in front and placed behind the carbons 7,p74 ,by this mirror we can cause the rays to issue through the orifice in front of the camera1 either parallel or convergent4 ,they are now parallel1 and therefore to a certain extent diffused4 ,we place a convex lens 7,l7 in the path of the beam2 the light is converged to a focus 7,c71 and at that focus paper is not only pierced1 but it is instantly set ablaze4 ,many metals may be burned up in the same way4 ,in our first lecture the combustibility of zinc was mentioned4 ,placing a strip of sheet-zinc at this focus1 it is instantly ignited1 burning with its characteristic purple flame4 ,and now ,i will substitute for our glass lens 7,l7 one of a more novel character4 ,in a smooth iron mould a lens of pellucid ice has been formed4 ,placing it in the position occupied a moment ago by the glass lens1 ,i can see the beam brought to a sharp focus4 ,at the focus ,i place1 a bit of black paper1 with a little gun-cotton folded up within it4 ,the paper immediately ignites and the cotton explodes4 ,strange1 is it not1 that the beam should possess such heating power after having passed through so cold a substance8 ,in his arctic expeditions ,dr4 ,scoresby succeeded in exploding gunpowder by the sun's rays1 converged by large lenses of ice2 here we have succeeded in producing the effect with a small lens1 and with a terrestrial source of heat4 ,in this experiment1 you observe that1 before the beam reaches the ice-lens1 it has passed through a glass cell containing water4 ,the beam is thus sifted of constituents1 which1 if permitted to fall upon the lens1 would injure its surface1 and blur the focus4 ,and this leads me to say an anticipatory word regarding transparency4 ,in our first lecture we entered fully into the production of colours by absorption1 and we spoke repeatedly of the quenching of the rays of light4 ,did this mean that the light was altogether annihilated8 ,by no means4 ,it was simply so lowered in refrangibility as to escape the visual range4 ,it was converted into heat4 ,our red ribbon in the green of the spectrum quenched the green1 but if suitably examined its temperature would have been found raised4 ,our green ribbon in the red of the spectrum quenched the red1 but its temperature at the same time was augmented to a degree exactly equivalent to the light extinguished4 ,our black ribbon1 when passed through the spectrum1 was found competent to quench all its colours2 but at every stage of its progress an amount of heat was generated in the ribbon exactly equivalent to the light lost4 ,it is only when absorption takes place that heat is thus produced3 and heat is always a result of absorption4 ,examine the water1 then1 in front of the lamp after the beam has passed through it3 it is sensibly warm1 and1 if permitted to remain there long enough1 it might be made to boil4 ,this is due to the absorption1 by the water1 of a certain portion of the electric beam4 ,but a portion passes through unabsorbed1 and does not at all contribute to the heating of the water4 ,now1 ice is also in great part transparent to these latter rays1 and therefore is but little melted by them4 ,hence1 by employing the portion of the beam transmitted by water1 we are able to keep our lens intact1 and to produce by means of it a sharply defined focus4 ,placed at that focus1 white paper is not ignited1 because it fails to absorb the rays emergent from the ice-lens4 ,at the same place1 however1 black paper instantly burns1 because it absorbs the transmitted light4 ,and here it may be useful to refer to an estimate by ,newton1 based upon doubtful data1 but repeated by various astronomers of eminence since his time4 ,the comet of #afhj1 when nearest to the sun1 was only a sixth of the sun's diameter from his surface4 ,newton estimated its temperature1 in this position1 to be more than two thousand times that of molted iron4 ,now it is clear from the foregoing experiments that the temperature of the comet could not be inferred from its nearness to the sun4 ,if its power of absorption were sufficiently low1 the comet might carry into the sun's neighbourhood the chill of stellar space4 #d4 ,combustion of a ,diamond by ,radiant ,heat4 ,the experiment of burning a diamond in oxygen by the concentrated rays of the sun was repeated at ,florence1 in presence of ,sir ,humphry ,davy1 on ,tuesday1 the #bgth of ,march1 #ahad4 ,it is thus described by ,faraday3--',to-day we made the grand experiment of burning the diamond1 and certainly the phenomena presented were extremely beautiful and interesting4 ,a glass globe containing about #bb cubical inches was exhausted of air1 and filled with pure oxygen4 ,the diamond was supported in the centre of this globe4 ,the ,duke's burning-glass was the instrument used to apply heat to the diamond4 ,it consists of two double convex lenses1 distant from each other about #c feet2 the large lens is about #ad or #ae inches in diameter1 the smaller one about #c inches in diameter4 ,by means of the second lens the focus is very much reduced1 and the heat1 when the sun shines brightly1 rendered very intense4 ,the diamond was placed in the focus and anxiously watched4 ,on a sudden ,sir ,h4 ,davy observed the diamond to burn visibly1 and when removed from the focus it was found to be in a state of active and rapid combustion4' ,the combustion of the diamond had never been effected by radiant heat from a terrestrial source4 ,i tried to accomplish this before crossing the ,atlantic1 and succeeded in doing so4 ,the small diamond now in my hand is held by a loop of platinum wire4 ,to protect it as far as possible from air currents1 and also to concentrate the heat upon it1 it is surrounded by a hood of sheet platinum4 ,bringing a jar of oxygen underneath1 ,i cause the focus of the electric beam to fall upon the diamond4 ,a small fraction of the time expended in the experiment described by ,faraday suffices to raise the diamond to a brilliant red4 ,plunging it then into the oxygen1 it glows like a little white star2 and it would continue to burn and glow until wholly consumed4 ,the focus can also be made to fall upon the diamond in oxygen1 as in the ,florentine experiment3 the result is the same4 ,it was simply to secure more complete mastery over the position of the focus1 so as to cause it to fall accurately upon the diamond1 that the mode of experiment here described was resorted to4 #e4 ,ultra-red ,rays3 ,calorescence4 ,in the path of the beam issuing from our lamp ,i now place a cell with glass sides containing a solution of alum4 ,all the light of the beam passes through this solution4 ,this light is received on a powerfully converging mirror silvered in front1 and brought to a focus by the mirror4 ,you can see the conical beam of reflected light tracking itself through the dust of the room4 ,a scrap of white paper placed at the focus shines there with dazzling brightness1 but it is not even charred4 ,on removing the alum cell1 however1 the paper instantly inflames4 ,there must1 therefore1 be something in this beam besides its light4 ,the light is not absorbed by the white paper1 and therefore does not burn the paper2 but there is something over and above the light which is absorbed1 and which provokes combustion4 ,what is this something8 ,in the year #ahjj ,sir ,william ,herschel passed a thermometer through the various colours of the solar spectrum1 and marked the rise of temperature corresponding to each colour4 ,he found the heating effect to augment from the violet to the red2 he did not1 however1 stop at the red1 but pushed his thermometer into the dark space beyond it4 ,here he found the temperature actually higher than in any part of the visible spectrum4 ,by this important observation1 he proved that the sun emitted heat-rays which are entirely unfit for the purposes of vision4 ,the subject was subsequently taken up by ,seebeck1 ,melloni1 ,mller1 and others1 and within the last few years it has been found capable of unexpected expansions and applications4 ,i have devised a method whereby the solar or electric beam can be so filtered as to detach from it1 and preserve intact1 this invisible ultra-red emission1 while the visible and ultra-violet emissions are wholly intercepted4 ,we are thus enabled to operate at will upon the purely ultra-red waves4 ,in the heating of solid bodies to incandescence1 this non-visual emission is the necessary basis of the visual4 ,a platinum wire is stretched in front of the table1 and through it an electric current flows4 ,it is warmed by the current1 and may be felt to be warm by the hand4 ,it emits waves of heat1 but no light4 ,augmenting the strength of the current1 the wire becomes hotter2 it finally glows with a sober red light4 ,at this point ,dr4 ,draper many years ago began an interesting investigation4 ,he employed a voltaic current to heat his platinum1 and he studied1 by means of a prism1 the successive introduction of the colours of the spectrum4 ,his first colour1 as here1 was red2 then came orange1 then yellow1 then green1 and lastly all the shades of blue4 ,as the temperature of the platinum was gradually augmented1 the atoms were caused to vibrate more rapidly2 shorter waves were thus introduced1 until finally waves were obtained corresponding to the entire spectrum4 ,as each successive colour was introduced1 the colours preceding it became more vivid4 ,now the vividness or intensity of light1 like that of sound1 depends not upon the length of the wave1 but on the amplitude of the vibration4 ,hence1 as the less refrangible colours grew more intense when the more refrangible ones were introduced1 we are forced to conclude that side by side with the introduction of the shorter waves we had an augmentation of the amplitude of the longer ones4 ,these remarks apply not only to the visible emission examined by ,dr4 ,draper1 but to the invisible emission which precedes the appearance of any light4 ,in the emission from the white-hot platinum wire now before you1 the lightless waves exist with which we started1 only their intensity has been increased a thousand-fold by the augmentation of temperature necessary to the production of this white light4 ,both effects are bound up together3 in an incandescent solid1 or in a molten solid1 you cannot have the shorter waves without this intensification of the longer ones4 ,a sun is possible only on these conditions2 hence ,sir ,william ,herschel's discovery of the invisible ultra-red solar emission4 ,the invisible heat1 emitted both by dark bodies and by luminous ones1 flies through space with the velosity of light1 and is called radiant heat4 ,now1 radiant heat may be made a subtle and powerful explorer of molecular condition1 and1 of late years1 it has given a new significance to the act of chemical combination4 ,take1 for example1 the air we breathe4 ,it is a mixture of oxygen and nitrogen2 and it behaves towards radiant heat like a vacuum1 being incompetent to absorb it in any sensible degree4 ,but permit the same two gases to unite chemically2 then1 without any augmentation of the quantity of matter1 without altering the gaseous condition1 without interfering in any way with the transparency of the gas1 the act of chemical union is accompanied by an enormous diminution of its diathermancy1 or perviousness to radiant heat4 ,the researches which established this result also proved the elementary gases1 generally1 to be highly transparent to radiant heat4 ,this1 again1 led to the proof of the diathermancy of elementary liquids1 like bromine1 and of solutions of the solid elements sulphur1 phosphorus1 and iodine4 ,a spectrum is now before you1 and you notice that the transparent bisulphide of carbon has no effect upon the colours4 ,dropping into the liquid a few flakes of iodine1 you see the middle of the spectrum cut away4 ,by augmenting the quantity of iodine1 we invade the entire spectrum1 and finally cut it off altogether4 ,now1 the iodine1 which proves itself thus hostile to the light1 is perfectly transparent to the ultra-red emission with which we have now to deal4 ,it1 therefore1 is to be our ray-filter4 ,placing the alum-cell again in front of the electric lamp1 we assure ourselves1 as before1 of the utter inability of the concentrated light to fire white paper-,introducing a cell containing the solution of iodine1 the light is entirely cut off2 and then1 on removing the alum-cell1 the white paper at the dark focus is instantly set on fire4 ,black paper is more absorbent than white for these rays2 and the consequence is1 that with it the suddenness and vigour of the combustion are augmented4 ,zinc is burnt up at the same place1 magnesium bursts into vivid combustion1 while a sheet of platinized platinum1 placed at the focus1 is heated to whiteness4 ,looked at through a prism1 the white-hot platinum yields all the colours of the spectrum4 ,before impinging upon the platinum1 the waves were of too slow recurrence to awaken vision2 by the atoms of the platinum1 these long and sluggish waves are broken up into shorter ones1 being thus brought within the visual range4 ,at the other end of the spectrum1 by the interposition of suitable substances1 ,professor ,stokes lowered the refrangibility1 so as to render the non-visual rays visual1 and to this change he gave the name of ,fluorescence4 ,here1 by the intervention of the platinum1 the refrangibility is raised1 so as to render the non-visual visual1 and to this change ,i have given the name of ,calorescence4 ,at the perfectly invisible focus where these effects are produced1 the air may be as cold as ice4 ,air1 as already stated1 does not absorb radiant heat1 and is therefore not warmed by it4 ,nothing could more forcibly illustrate the isolation1 if ,i may use the term1 of the luminiferous ether from the air4 ,the wave-motion of the one is heaped up to an extraordinary degree of intensity1 without producing any sensible effect upon the other4 ,i may add that1 with suitable precautions1 the eye may be placed in a focus competent to heat platinum to vivid redness1 without experiencing any damage1 or the slightest sensation either of light or heat4 ,the important part played by these ultra-red rays in ,nature may be thus illustrated3 ,i remove the iodine filter1 and concentrate the total beam upon a test tube containing water4 ,it immediately begins to splutter1 and in a minute or two it boils4 ,what boils it8 ,placing the alum solution in front of the lamp1 the boiling instantly ceases4 ,now1 the alum is pervious to all the luminous rays2 hence it cannot be these rays that caused the boiling4 ,i now introduce the iodine1 and remove the alum3 vigorous ebullition immediately recommences at the invisible focus4 ,so that we here fix upon the invisible ultra-red rays the heating of the water4 ,we are thus enabled to understand the momentous part played by these rays in ,nature4 ,it is to them that we owe the warming and the consequent evaporation of the tropical ocean2 it is to them1 therefore1 that we owe our rains and snows4 ,they are absorbed close to the surface of the ocean1 and warm the superficial water1 while the luminous rays plunge to great depths without producing any sensible effect4 ,but we can proceed further than this4 ,here is a large flask containing a freezing mixture1 which has so chilled the flask1 that the aqueous vapour of the air of this room has been condensed and frozen upon it to a white fur4 ,introducing the alum-cell1 and placing the coating of hoar-frost at the intensely luminous focus of the electric lamp1 not a spicula of the dazzling frost is melted4 ,introducing the iodine-cell1 and removing the alum1 a broad space of the frozen coating is instantly melted away4 ,hence we infer that the snow and ice1 which feed the ,rhone1 the ,rhine1 and other rivers with glaciers for their sources1 are released from their imprisonment upon the mountains by the invisible ultra-red rays of the sun4 #f4 ,identity of ,light and ,radiant ,heat4 ,reflection from ,plane and ,curved ,surfaces4 ,total ,reflection of ,heat4 ,the growth of science is organic4 ,that which today is an end becomes to-morrow a means to a remoter end4 ,every new discovery in science is immediately made the basis of other discoveries1 or of new methods of investigation4 ,thus about fifty years ago ,o,ersted1 of ,copenhagen1 discovered the deflection of a magnetic needle by an electric current2 and about the same time ,thomas ,seebeck1 of ,berlin1 discovered thermoelectricity4 ,these great discoveries were soon afterwards turned to account1 by ,nobili and ,melloni1 in the construction of an instrument which has vastly augmented our knowledge of radiant heat4 ,this instrument1 which is called a thermo-electric pile1 or more briefly a thermo-pile1 consists of thin bars of bismuth and antimony1 soldered alternately together at their ends1 but separated from each other elsewhere4 ,from the ends of this 'thermo-pile' wires pass to a galvanometer1 which consists of a coil of covered wire1 within and above which are suspended two magnetic needles1 joined to a rigid system1 and carefully defended from currents of air4 ,the action of the arrangement is this3 the heat1 falling on the pile1 produces an electric current2 the current1 passing through the coil1 deflects the needles1 and the magnitude of the deflection may be made a measure of the heat4 ,the upper needle moves over a graduated dial far too small to be directly seen4 ,it is now1 however1 strongly illuminated2 and above it is a lens which1 if permitted1 would form an image of the needle and dial upon the ceiling4 ,there1 however1 it could not be conveniently viewed4 ,the beam is therefore received upon a looking-glass1 placed at the proper angle1 which throws the image upon a screen4 ,in this way the motions of this small needle may be made visible to you all4 ,the delicacy of this apparatus is such that in a room filled1 as this room now is1 with an audience physically warm1 it is exceedingly difficult to work with it4 ,my assistant stands several feet off4 ,i turn the pile towards him3 the heat radiated from his face1 even at this distance1 produces a deflection of #ij4 ,i turn the instrument towards a distant wall1 a little below the average temperature of the room4 ,the needle descends and passes to the other side of zero1 declaring by this negative deflection that the pile has lost its warmth by radiation against the cold wall4 ,possessed of this instrument1 of our ray-filter1 and of our large ,nicol prisms1 we are in a condition to investigate a subject of great philosophical interest2 one which long engaged the attention of some of our foremost scientific workers--the substantial identity of light and radiant heat4 ,that they are identical in all respects cannot of course be the case1 for if they were they would act in the same manner upon all instruments1 the eye included4 ,the identity meant is such as subsists between one colour and another1 causing them to behave alike as regards reflection1 refraction1 double refraction1 and polarization4 ,let us here run rapidly over the resemblances of light and heat4 ,as regards reflection from plane surfaces1 we may employ a looking-glass to reflect the light4 ,marking any point in the track of the reflected beam1 cutting off the light by the dissolved iodine1 and placing the pile at the marked point1 the needle immediately starts aside1 showing that the heat is reflected in the same direction as the light4 ,this is true for every position of the mirror4 ,recurring1 for example1 to the simple apparatus employed in our first lecture 7fig4 #c1 p4 #aa72 moving the index attached to the mirror along the divisions of our graduated arc 7m n71 and determining by the pile the positions of the invisible reflected beam1 we prove that the angular velocity of the heat-beam1 like that of the light-beam1 is twice that of the mirror4 ,illustration3 ,fig4 #di4 ,as regards reflection from curved surfaces1 the identity also holds good4 ,receiving the beam from our electric lamp on a concave mirror 7m m1 fig4 #di71 it is gathered up into a cone of reflected light rendered visible by the floating dust of the air2 marking the apex of the cone by a pointer1 and cutting off the light by the iodine solution 7,t71 a moment's exposure of the pile 7,p7 at the marked point produces a violent deflection of the needle4 ,the common reflection and the total reflection of a beam of radiant heat may be simultaneously demonstrated4 ,from the nozzle of the lamp 7,l1 fig4 #ej7 a beam impinges upon a plane mirror 7,m ,n71 is reflected upwards1 and enters a right-angled prism1 of which a b c is the section4 ,it meets the hypothenuse at an obliquity greater than the limiting angle1#bc and is therefore totally reflected4 ,quenching the light by the ray-filter at ,f1 and placing the pile at ,p1 the totally reflected heat-beam is immediately felt by the pile1 and declared by the galvanometric deflection4 ,illustration3 ,fig4 #ej4 #g4 ,invisible ,images formed by ,radiant ,heat4 ,perhaps no experiment proves more conclusively the substantial identity of light and radiant heat1 than the formation of invisible heat-images4 ,employing the mirror already used to raise the beam to its highest state of concentration1 we obtain1 as is well known1 an inverted image of the carbon points1 formed by the light rays at the focus4 ,cutting off the light by the ray-filter1 and placing at the focus a thin sheet of platinized platinum1 the invisible rays declare their presence and distribution1 by stamping upon the platinum a white-hot image of the carbons4 7,see fig4 #ea47 ,illustration3 ,fig4 #ea4 #h4 ,polarization of ,heat4 ,whether radiant heat be capable of polarization or not was for a long time a subject of discussion4 ,brard had announced affirmative results1 but ,powell and ,lloyd failed to verify them4 ,the doubts thus thrown upon the question were removed by the experiments of ,forbes1 who first established the polarization and 'depolarization' of heat4 ,the subject was subsequently followed up by ,melloni1 an investigator of consummate ability1 who sagaciously turned to account his own discovery1 that the obscure rays of luminous sources are in part transmitted by black glass4 ,intercepting by a plate of this glass the light from an oil flame1 and operating upon the transmitted invisible heat1 he obtained effects of polarization1 far exceeding in magnitude those which could be obtained with non-luminous sources4 ,at present the possession of our more perfect ray-filter1 and more powerful source of heat1 enables us to pursue this identity question to its utmost practical limits4 ,illustration3 ,fig4 #eb4 ,mounting our two ,nicols 7,b and ,c1 fig4 #eb7 in front of the electric lamp1 with their principal sections crossed1 no light reaches the screen4 ,placing our thermo-electric pile 7,d7 behind the prisms1 with its face turned towards the source1 no deflection of the galvanometer is observed4 ,interposing between the lamp 7,a7 and the first prism 7,b7 our ray-filter1 the light previously transmitted through the first ,nicol is quenched2 and now the slightest turning of either ,nicol opens a way for the transmission of the heat1 a very small rotation sufficing to send the needle up to #ij4 ,when the ,nicol is turned back to its first position1 the needle again sinks to zero1 thus demonstrating1 in the plainest manner1 the polarization of the heat4 ,when the ,nicols are crossed and the field is dark1 you have seen1 in the case of light1 the effect of introducing a plate of mica between the polarizer and analyzer4 ,in two positions the mica exerts no sensible influence2 in all others it does4 ,a precisely analogous deportment is observed as regards radiant heat4 ,introducing our ray-filter1 the thermo-pile1 playing the part of an eye as regards the invisible radiation1 receives no heat when the eye receives no light2 but when the mica is so turned as to make its planes of vibration oblique to those of the polarizer and analyzer1 the heat immediately passes through4 ,so strong does the action become1 that the momentary plunging of the film of mica into the dark space between the ,nicols suffices to send the needle up to #ij4 ,this is the effect to which the term 'depolarization' has been applied2 the experiment really proving that with both light and heat we have the same resolution by the plate of mica1 and recompounding by the analyzer1 of the ethereal vibrations4 ,removing the mica and restoring the needle once more to #j1 ,i introduce between the ,nicols a plate of quartz cut perpendicular to the axis2 the immediate deflection of the needle declares the transmission of the heat1 and when the transmitted beam is properly examined1 it is found to be circularly polarized1 exactly as a beam of light is polarized under the same conditions4 #i4 ,double ,refraction of ,heat4 ,i will now abandon the ,nicols1 and send through the piece of ,iceland spar 7,b1 fig4 #ec71 already employed 7in ,lecture ,,iii47 to illustrate the double refraction of light1 our sifted beam of invisible heat4 ,to determine the positions of the two images1 let us first operate upon the luminous beam4 ,marking the places of the light-images1 we introduce between ,n and ,l our ray-filter 7not in the figure7 and quench the light4 ,causing the pile to approach one of the marked places1 the needle remains unmoved until the place has been attained2 here the pile at once detects the heat4 ,pushing the pile across the interval separating the two marks1 the needle first falls to #j1 and then rises again to #ij in the second position4 ,this proves the double refraction of the heat4 ,illustration3 ,fig4 #ec4 ,i now turn the ,iceland spar3 the needle remains fixed2 there is no alteration of the deflection4 ,passing the pile rapidly across to the other mark1 the deflection is maintained4 ,once more ,i turn the spar1 but now the needle falls to #j1 rising1 however1 again to #ij after a rotation of #cfj4 ,we know that in the case of light the extraordinary beam rotates round the ordinary one2 and we have here been operating on the extraordinary heat-beam1 which1 as regards double refraction1 behaves exactly like a beam of light4 #aj4 ,magnetization of ,heat4 ,to render our series of comparisons complete1 we must demonstrate the magnetization of heat4 ,but here a slight modification of our arrangement will be necessary4 ,in repeating ,faraday's experiment on the magnetization of light1 we had1 in the first instance1 our ,nicols crossed and the field rendered dark1 a flash of light appearing upon the screen when the magnet was excited4 ,now the quantity of light transmitted in this case is really very small1 its effect being rendered striking through contrast with the preceding darkness4 ,when we so place the ,nicols that their principal sections enclose an angle of #de1 the excitement of the magnet causes a far greater positive augmentation of the light1 though the augmentation is not so well seen through lack of contrast1 because here1 at starting1 the field is illuminated4 ,in trying to magnetize our beam of heat1 we will adopt this arrangement4 ,here1 however1 at the outset1 a considerable amount of heat falls upon one face of the pile4 ,this it is necessary to neutralize1 by permitting rays from another source to fall upon the opposite face of the pile4 ,the needle is thus brought to zero4 ,cutting off the light by our ray-filter1 and exciting the magnet1 the needle is instantly deflected1 proving that the magnet has opened a door for the heat1 exactly as in ,faraday's experiment it opened a door for the light4 ,thus1 in every case brought under our notice1 the substantial identity of light and radiant heat has been demonstrated4 ,by the refined experiments of ,knoblauch1 who worked long and successfully at this question1 the double refraction of heat1 by ,iceland spar1 was first demonstrated2 but1 though he employed the luminous heat of the sun1 the observed deflections were exceedingly small4 ,so1 likewise1 those eminent investigators ,de la ,povostaye and ,desains succeeded in magnetizing a beam of heat2 but though1 in their case also1 the luminous solar heat was employed1 the deflection obtained did not amount to more than two or three degrees4 ,with obscure radiant heat the effect1 prior to the experiments now brought before you1 had not been obtained2 but1 with the arrangement here described1 we obtain deflections from purely invisible heat1 equal to #aej of the lower degrees of the galvanometer4 #aa4 ,distribution of ,heat in the ,electric ,spectrum4 ,we have finally to determine the position and magnitude of the invisible radiation which produces these results4 ,for this purpose we employ a particular form of the thermo-pile4 ,its face is a rectangle1 which by movable side-pieces can be rendered as narrow as desirable4 ,throwing a small and concentrated spectrum upon a screen1 by means of an endless screw we move the rectangular pile through the entire spectrum1 and determine in succession the thermal power of all its colours4 ,illustration3 ,,spectrum ,,of ,,electric ,,light4 ,when this instrument is brought to the violet end of the spectrum1 the heat is found to be almost insensible4 ,as the pile gradually moves from the violet towards the red1 it encounters a gradually augmenting heat4 ,the red itself possesses the highest heating power of all the colours of the spectrum4 ,pushing the pile into the dark space beyond the red1 the heat rises suddenly in intensity1 and at some distance beyond the red it attains a maximum4 ,from this point the heat falls somewhat more rapidly than it rose1 and afterwards gradually fades away4 ,drawing a horizontal line to represent the length of the spectrum1 and erecting along it1 at various points1 perpendiculars proportional in length to the heat existing at those points1 we obtain a curve which exhibits the distribution of heat in the prismatic spectrum4 ,it is represented in the adjacent figure4 ,beginning at the blue1 the curve rises1 at first very gradually2 towards the red it rises more rapidly1 the line ,c ,d 7fig4 #ed1 opposite page7 representing the strength of the extreme red radiation4 ,beyond the red it shoots upwards in a steep and massive peak to ,b2 whence it falls1 rapidly for a time1 and afterwards gradually fades from the perception of the pile4 ,this figure is the result of more than twelve careful series of measurements1 from each of which the curve was constructed4 ,on superposing all these curves1 a satisfactory agreement was found to exist between them4 ,so that it may safely be concluded that the areas of the dark and white spaces1 respectively1 represent the relative energies of the visible and invisible radiation4 ,the one is #g4g times the other4 ,but in verification1 as already stated1 consists the strength of science4 ,determining in the first place the total emission from the electric lamp1 and then1 by means of the iodine filter1 determining the ultra-red emission2 the difference between both gives the luminous emission4 ,in this way1 it is found that the energy of the invisible emission is eight times that of the visible4 ,no two methods could be more opposed to each other1 and hardly any two results could better harmonize4 ,i think1 therefore1 you may rely upon the accuracy of the distribution of heat here assigned to the prismatic spectrum of the electric light4 ,there is nothing vague in the mode of investigation1 or doubtful in its conclusions4 ,spectra are1 however1 formed by diffraction1 wherein the distribution of both heat and light is different from that produced by the prism4 ,these diffractive spectra have been examined with great skill by ,draper and ,langley4 ,in the prismatic spectrum the less refrangible rays are compressed into a much smaller space than in the diffraction spectrum4 ,,lecture ,,vi4 ,,principles ,,of ,,spectrum ,,analysis ,,prismatic ,,analysis ,,of ,,the ,,light ,,of ,,incandescent ,,vapours ,,discontinuous ,,spectra ,,spectrum ,,bands ,,proved ,,by ,,bunsen ,,and ,,kirchhoff ,,to ,,be ,,characteristic ,,of ,,the ,,vapour ,,discovery ,,of ,,rubidium1 ,c,,sium1 ,,and ,,thallium ,,relation ,,of ,,emission ,,to ,,absorption ,,the ,,lines ,,of ,,fraunhofer ,,their ,,explanation ,,by ,,kirchhoff ,,solar ,,chemistry ,,involved ,,in ,,this ,,explanation ,,foucault',s ,,experiment ,,principles ,,of ,,absorption ,,analogy ,,of ,,sound ,,and ,,light ,,experimental ,,demonstration ,,of ,,this ,,analogy ,,recent ,,applications ,,of ,,the ,,spectroscope ,,summary ,,and ,,conclusion4 ,we have employed as our source of light in these lectures the ends of two rods of coke rendered incandescent by electricity4 ,coke is particularly suitable for this purpose1 because it can bear intense heat without fusion or vaporization4 ,it is also black1 which helps the light2 for1 other circumstances being equal1 as shown experimentally by ,professor ,balfour ,stewart1 the blacker the body the brighter will be its light when incandescent4 ,still1 refractory as carbon is1 if we closely examined our voltaic arc1 or stream of light between the carbon-points1 we should find there incandescent carbon-vapour4 ,and if we could detach the light of this vapour from the more dazzling light of the solid points1 we should find its spectrum not only less brilliant1 but of a totally different character from the spectra that we have already seen4 ,instead of being an unbroken succession of colours from red to violet1 the carbon-vapour would yield a few bands of colour with spaces of darkness between them4 ,what is true of the carbon is true in a still more striking degree of the metals1 the most refractory of which can be fused1 boiled1 and reduced to vapour by the electric current4 ,from the incandescent vapour the light1 as a general rule1 flashes in groups of rays of definite degrees of refrangibility1 spaces existing between group and group1 which are unfilled by rays of any kind4 ,but the contemplation of the facts will render this subject more intelligible than words can make it4 ,within the camera is now placed a cylinder of carbon hollowed out at the top2 in the hollow is placed a fragment of the metal thallium4 ,down upon this we bring the upper carbon-point1 and then separate the one from the other4 ,a stream of incandescent thallium-vapour passes between them1 the magnified image of which is now seen upon the screen4 ,it is of a beautiful green colour4 ,what is the meaning of that green8 ,we answer the question by subjecting the light to prismatic analysis4 ,sent through the prism1 its spectrum is seen to consist of a single refracted band4 ,light of one degree of refrangibility--that corresponding to this particular green--is emitted by the thallium-vapour4 ,we will now remove the thallium and put a bit of silver in its place4 ,the are of silver is not to be distinguished from that of thallium2 it is not only green1 but the same shade of green4 ,are they then alike8 ,prismatic analysis enables us to answer the question4 ,however impossible it is to distinguish the one colour from the other1 it is equally impossible to confound the spectrum of incandescent silver-vapour with that of thallium4 ,in the case of silver1 we have two green bands instead of one4 ,if we add to the silver in our camera a bit of thallium1 we shall obtain the light of both metals4 ,after waiting a little1 we see that the green of the thallium lies midway between the two greens of the silver4 ,hence this similarity of colour4 ,but why have we to 'wait a little' before we see this effect8 ,the thallium band at first almost masks the silver bands by its superior brightness4 ,indeed1 the silver bands have wonderfully degenerated since the bit of thallium was put in1 and for a reason worth knowing4 ,it is the resistance offered to the passage of the electric current from carbon to carbon1 that calls forth the power of the current to produce heat4 ,if the resistance were materially lessened1 the heat would be materially lessened2 and if all resistance were abolished1 there would be no heat at all4 ,now1 thallium is a much more fusible and vaporizable metal than silver2 and its vapour facilitates the passage of the electricity to such a degree1 as to render the current almost incompetent to vaporize the more refractory silver4 ,but the thallium is gradually consumed2 its vapour diminishes1 the resistance rises1 until finally you see the two silver bands as brilliant as they were at first4#bd ,we have in these bands a perfectly unalterable characteristic of the two metals4 ,you never get other bands than these two green ones from the silver1 never other than the single green band from the thallium1 never other than the three green bands from the mixture of both metals4 ,every known metal has its own particular bands1 and in no known case are the bands of two different metals alike in refrangibility4 ,it follows1 therefore1 that these spectra may be made a sure test for the presence or absence of any particular metal4 ,if we pass from the metals to their alloys1 we find no confusion4 ,copper gives green bands2 zinc gives blue and red bands2 brass--an alloy of copper and zinc--gives the bands of both metals1 perfectly unaltered in position or character4 ,but we are not confined to the metals themselves2 the salts of these metals yield the bands of the metals4 ,chemical union is ruptured by a sufficiently high heat2 the vapour of the metal is set free1 and it yields its characteristic bands4 ,the chlorides of the metals are particularly suitable for experiments of this character4 ,common salt1 for example1 is a compound of chlorine and sodium2 in the electric lamp it yields the spectrum of the metal sodium4 ,the chlorides of copper1 lithium1 and strontium yield1 in like manner1 the bands of these metals4 ,when1 therefore1 ,bunsen and ,kirchhoff1 the illustrious founders of spectrum analysis1 after having established by an exhaustive examination the spectra of all known substances1 discovered a spectrum containing bands different from any known bands1 they immediately inferred the existence of a new metal4 ,they were operating at the time upon a residue1 obtained by evaporating one of the mineral waters of ,germany4 ,in that water they knew the unknown metal was concealed1 but vast quantities of it had to be evaporated before a residue could be obtained sufficiently large to enable ordinary chemistry to grapple with the metal4 ,they1 however1 hunted it down1 and it now stands among chemical substances as the metal ,rubidium4 ,they subsequently discovered a second metal1 which they called ,csium4 ,thus1 having first placed spectrum analysis on a sure foundation1 they demonstrated its capacity as an agent of discovery4 ,soon afterwards ,mr4 ,crookes1 pursuing the same method1 discovered the bright green band of ,thallium1 and obtained the salts of the metal which yielded it4 ,the metal itself was first isolated in ingots by ,m4 ,lamy1 a ,french chemist4 ,all this relates to chemical discovery upon earth1 where the materials are in our own hands4 ,but it was soon shown how spectrum analysis might be applied to the investigation of the sun and stars2 and this result was reached through the solution of a problem which had been long an enigma to natural philosophers4 ,the scope and conquest of this problem we must now endeavour to comprehend4 ,a spectrum is pure in which the colours do not overlap each other4 ,we purify the spectrum by making our beam narrow1 and by augmenting the number of our prisms4 ,when a pure spectrum of the sun has been obtained in this way1 it is found to be furrowed by innumerable dark lines4 ,four of them were first seen by ,dr4 ,wollaston1 but they were afterwards multiplied and measured by ,fraunhofer with such masterly skill1 that they are now universally known as ,fraunhofer's lines4 ,to give an explanation of these lines was1 as ,i have said1 a problem which long challenged the attention of philosophers1 and to ,professor ,kirchhoff belongs the honour of having first conquered this problem4 7,the positions of the principal lines1 lettered according to ,fraunhofer1 are shown in the annexed sketch 7fig4 #ee7 of the solar spectrum4 ,a is supposed to stand near the extreme red1 and ,j near the extreme violet47 ,illustration3 ,fig4 #ee4 ,the brief memoir of two pages1 in which this immortal discovery is recorded1 was communicated to the ,berlin ,academy on ,october #bg1 #ahei4 ,fraunhofer had remarked in the spectrum of a candle flame two bright lines1 which coincide accurately1 as to position1 with the double dark line ,d of the solar spectrum4 ,these bright lines are produced with particular intensity by the yellow flame derived from a mixture of salt and alcohol4 ,they are in fact the lines of sodium vapour4 ,kirchhoff produced a spectrum by permitting the sunlight to enter his telescope by a slit and prism1 and in front of the slit he placed the yellow sodium flame4 ,as long as the spectrum remained feeble1 there always appeared two bright lines1 derived from the flame1 in the place of the two dark lines ,d of the spectrum4 ,in this case1 such absorption as the flame exerted upon the sunlight was more than atoned for by the radiation from the flame4 ,when1 however1 the solar spectrum was rendered sufficiently intense1 the bright bands vanished1 and the two dark ,fraunhofer lines appeared with much greater sharpness and distinctness than when the flame was not employed4 ,this result1 be it noted1 was not due to any real quenching of the bright lines of the flame1 but to the augmentation of the intensity of the adjacent spectrum4 ,the experiment proved to demonstration1 that when the white light sent through the flame was sufficiently intense1 the quantity which the flame absorbed was far in excess of that which it radiated4 ,here then is a result of the utmost significance4 ,kirchhoff immediately inferred from it that the salt flame1 which could intensify so remarkably the dark lines of ,fraunhofer1 ought also to be able to produce them4 ,the spectrum of the ,drummond light is known to exhibit the two bright lines of sodium1 which1 however1 gradually disappear as the modicum of sodium1 contained as an impurity in the incandescent lime1 is exhausted4 ,kirchhoff formed a spectrum of the limelight1 and after the two bright lines had vanished1 he placed his salt flame in front of the slit4 ,the two dark lines immediately started forth4 ,thus1 in the continuous spectrum of the lime-light1 he evoked1 artificially1 the lines ,d of ,fraunhofer4 ,kirchhoff knew that this was an action not peculiar to the sodium flame1 and he immediately extended his generalisation to all coloured flames which yield sharply defined bright bands in their spectra4 ,white light1 with all its constituents complete1 sent through such flames1 would1 he inferred1 have those precise constituents absorbed1 whose refrangibilities are the same as those of the bright bands2 so that after passing through such flames1 the white light1 if sufficiently intense1 would have its spectrum furrowed by bands of darkness4 ,on the occasion here referred to ,kirchhoff also succeeded in reversing a bright band of lithium4 ,the long-standing difficulty of ,fraunhofer's lines fell to pieces in the presence of facts and reflections like these1 which also carried with them an immeasurable extension of the chemist's power4 ,kirchhoff saw that from the agreement of the lines in the spectra of terrestrial substances with ,fraunhofer's lines1 the presence of these substances in the sun and fixed stars might be immediately inferred4 ,thus the dark lines ,d in the solar spectrum proved the existence of sodium in the solar atmosphere2 while the bright lines discovered by ,brewster in a nitre flame1 which had been proved to coincide exactly with certain dark lines between ,a and ,b in the solar spectrum1 proved the existence of potassium in the sun4 ,all subsequent research verified the accuracy of these first daring conclusions4 ,in his second paper1 communicated to the ,berlin ,academy before the close of #ahei1 ,kirchhoff proved the existence of iron in the sun4 ,the bright lines of the spectrum of iron vapour are exceedingly numerous1 and #fe of them were subsequently proved by ,kirchhoff to be absolutely identical in position with #fe dark ,fraunhofer's lines4 ngstrm and ,thaln pushed the coincidences to #dej for iron1 while1 according to the same excellent investigators1 the following numbers express the coincidences1 in the case of the respective metals to which they are attached3-- ,calcium #ge ,barium #aa ,magnesium #d ,manganese #eg ,titanium #aah ,chromium #ah ,nickel #cc ,cobalt #ai ,hydrogen #d ,aluminium #b ,zinc #b ,copper #g ,the probability is overwhelming that all these substances exist in the atmosphere of the sun4 ,kirchhoff's discovery profoundly modified the conceptions previously entertained regarding the constitution of the sun1 leading him to views which1 though they may be modified in detail1 will1 ,i believe1 remain substantially valid to the end of time4 ,the sun1 according to ,kirchhoff1 consists of a molten nucleus which is surrounded by a flaming atmosphere of lower temperature4 ,the nucleus may1 in part1 be clouds1 mixed with1 or underlying true vapour4 ,the light of the nucleus would give us a continuous spectrum1 like that of the ,drummond light2 but having to pass through the photosphere1 as ,kirchhoff's beam passed through the sodium flame1 those rays of the nucleus which the photosphere emit are absorbed1 and shaded lines1 corresponding to the rays absorbed1 occur in the spectrum4 ,abolish the solar nucleus1 and we should have a spectrum showing a bright line in the place of every dark line of ,fraunhofer1 just as1 in the case of ,kirchhoff's second experiment1 we should have the bright sodium lines of the flame if the lime-light were withdrawn4 ,these lines of ,fraunhofer are therefore not absolutely dark1 but dark by an amount corresponding to the difference between the light intercepted and the light emitted by the photosphere4 ,almost every great scientific discovery is approached contemporaneously by many minds1 the fact that one mind usually confers upon it the distinctness of demonstration being an illustration1 not of genius isolated1 but of genius in advance4 ,thus ,foucault1 in #ahdi1 came to the verge of ,kirchhoff's discovery4 ,by converging an image of the sun upon a voltaic arc1 and thus obtaining the spectra of both sun and arc superposed1 he found that the two bright lines which1 owing to the presence of a little sodium in the carbons or in the air1 are seen in the spectrum of the arc1 coincide with the dark lines ,d of the solar spectrum4 ,the lines ,d he found to he considerably strengthened by the passage of the solar light through the voltaic arc4 ,instead of the image of the sun1 ,foucault then projected upon the arc the image of one of the solid incandescent carbon points1 which of itself would give a continuous spectrum2 and he found that the lines ,d were thus generated in that spectrum4 ,foucault's conclusion from this admirable experiment was 'that the arc is a medium which emits the rays ,d on its own account1 and at the same time absorbs them when they come from another quarter4' ,here he stopped4 ,he did not extend his observations beyond the voltaic arc2 he did not offer any explanation of the lines of ,fraunhofer2 he did not arrive at any conception of solar chemistry1 or of the constitution of the sun4 ,his beautiful experiment remained a germ without fruit1 until the discernment1 ten years subsequently1 of the whole class of phenomena to which it belongs1 enabled ,kirchhoff to solve these great problems4 ,soon after the publication of ,kirchhoff's discovery1 ,professor ,stokes1 who also1 ten years prior to the discovery1 had nearly anticipated it1 borrowed an illustration from sound1 to explain the reciprocity of radiation and absorption4 ,a stretched string responds to arial vibrations which synchronize with its own4 ,a great number of such strings stretched in space would roughly represent a medium2 and if the note common to them all were sounded at a distance they would take up or absorb its vibrations4 ,when a violin-bow is drawn across this tuning-fork1 the room is immediately filled with a musical sound1 which may be regarded as the radiation or emission of sound from the fork4 ,a few days ago1 on sounding this fork1 ,i noticed that when its vibrations were quenched1 the sound seemed to be continued1 though more feebly4 ,it appeared1 moreover1 to come from under a distant table1 where stood a number of tuning-forks of different sizes and rates of vibration4 ,one of these1 and one only1 had been started by the sounding fork1 and it was the one whose rate of vibration was the same as that of the fork which started it4 ,this is an instance of the absorption of the sound of one fork by another4 ,placing two unisonant forks near each other1 sweeping the bow over one of them1 and then quenching the agitated fork1 the other continues to sound2 this other can re-excite the former1 and several transfers of sound between the two forks can be thus effected4 ,placing a cent-piece on each prong of one of the forks1 we destroy its perfect synchronism with the other1 and no such communication of sound from the one to the other is then possible4 ,i have now to bring before you1 on a suitable scale1 the demonstration that we can do with light what has been here done with sound4 ,for several days in #ahfa ,i endeavoured to accomplish this1 with only partial success4 ,in iron dishes a mixture of dilute alcohol and salt was placed1 and warmed so as to promote vaporization4 ,the vapour was ignited1 and through the yellow flame thus produced the beam from the electric lamp was sent2 but a faint darkening only of the yellow band of a projected spectrum could be obtained4 ,a trough was then made which1 when fed with the salt and alcohol1 yielded a flame ten feet thick2 but the result of sending the light through this depth of flame was still unsatisfactory4 ,remembering that the direct combustion of sodium in a ,bunsen's flame produces a yellow far more intense than that of the salt flame1 and inferring that the intensity of the colour indicated the copiousness of the incandescent vapour1 ,i sent through the flame from metallic sodium the beam of the electric lamp4 ,the success was complete2 and this experiment ,i wish now to repeat in your presence4#be ,firstly then you notice1 when a fragment of sodium is placed in a platinum spoon and introduced into a ,bunsen's flame1 an intensely yellow light is produced4 ,it corresponds in refrangibility with the yellow band of the spectrum4 ,like our tuning-fork1 it emits waves of a special period4 ,when the white light from the electric lamp is sent through that flame1 you will have ocular proof that the yellow flame intercepts the yellow of the spectrum2 in other words1 that it absorbs waves of the same period as its own1 thus producing1 to all intents and purposes1 a dark ,fraunhofer's band in the place of the yellow4 ,in front of the slit 7at ,l1 fig4 #ef7 through which the beam issues is placed a ,bunsen's burner 7b7 protected by a chimney 7,c74 ,this beam1 after passing through a lens1 traverses the prism 7,p7 7in the real experiment there was a pair of prisms71 is there decomposed1 and forms a vivid continuous spectrum 7,s ,s7 upon the screen4 ,introducing a platinum spoon with its pellet of sodium into the ,bunsen's flame1 the pellet first fuses1 colours the flame intensely yellow1 and at length bursts into violent combustion4 ,at the same moment the spectrum is furrowed by an intensely dark band 7,d71 two inches wide and two feet long4 ,introducing and withdrawing the sodium flame in rapid succession1 the sudden appearance and disappearance of the band of darkness is shown in a most striking manner4 ,in contrast with the adjacent brightness this band appears absolutely black1 so vigorous is the absorption4 ,the blackness1 however1 is but relative1 for upon the dark space falls a portion of the light of the sodium flame4 ,illustration3 ,fig4 #ef4 ,i have already referred to the experiment of ,foucault2 but other workers also had been engaged on the borders of this subject before it was taken up by ,bunsen and ,kirchhoff4 ,with some modification ,i have on a former occasion used the following words regarding the precursors of the discovery of spectrum analysis1 and solar chemistry3--',mr4 ,talbot had observed the bright lines in the spectra of coloured flames1 and both he and ,sir ,john ,herschel pointed out the possibility of making prismatic analysis a chemical test of exceeding delicacy1 though not of entire certainty4 ,more than a quarter of a century ago ,dr4 ,miller gave drawings and descriptions of the spectra of various coloured flames4 ,wheatstone1 with his accustomed acuteness1 analyzed the light of the electric spark1 and proved that the metals between which the spark passed determined the bright bands in its spectrum4 ,in an investigation described by ,kirchhoff as classical1 ,swan had shown that #a_/b1ejj1jjj of a grain of sodium in a ,bunsen's flame could be detected by its spectrum4 ,he also proved the constancy of the bright lines in the spectra of hydrocarbon flames4 ,masson published a prize essay on the bands of the induction spark2 while ,van der ,willigen1 and more recently ,plcker1 have also given us beautiful drawings of spectra obtained from the same source4 ',but none of these distinguished men betrayed the least knowledge of the connexion between the bright bands of the metals and the dark lines of the solar spectrum2 nor could spectrum analysis be said to be placed upon anything like a safe foundation prior to the researches of ,bunsen and ,kirchhoff4 ,the man who1 in a published paper1 came nearest to the philosophy of the subject was ngstrm4 ,in that paper1 translated by myself1 and published in the ,philosophical ,magazine for #ahee1 he indicates that the rays which a body absorbs are precisely those which1 when luminous1 it can emit4 ,in another place1 he speaks of one of his spectra giving the general impression of the reversal of the solar spectrum4 ,but his memoir1 philosophical as it is1 is distinctly marked by the uncertainty of his time4 ,foucault1 ,thomson1 and ,balfour ,stewart have all been near the discovery1 while1 as already stated1 it was almost hit by the acute but unpublished conjecture of ,stokes4' ,mentally1 as well as physically1 every year of the world's age is the outgrowth and offspring of all preceding years4 ,science proves itself to be a genuine product of ,nature by growing according to this law4 ,we have no solution of continuity here4 ,all great discoveries are duly prepared for in two ways2 first1 by other discoveries which form their prelude2 and1 secondly1 by the sharpening of the inquiring intellect4 ,thus ,ptolemy grew out of ,hipparchus1 ,copernicus out of both1 ,kepler out of all three1 and ,newton out of all the four4 ,newton did not rise suddenly from the sea-level of the intellect to his amazing elevation4 ,at the time that he appeared1 the table-land of knowledge was already high4 ,he juts1 it is true1 above the table-land1 as a massive peak2 still he is supported by the plateau1 and a great part of his absolute height is the height of humanity in his time4 ,it is thus with the discoveries of ,kirchhoff4 ,much had been previously accomplished2 this he mastered1 and then by the force of individual genius went beyond it4 ,he replaced uncertainty by certainty1 vagueness by definiteness1 confusion by order2 and ,i do not think that ,newton has a surer claim to the discoveries that have made his name immortal1 than ,kirchhoff has to the credit of gathering up the fragmentary knowledge of his time1 of vastly extending it1 and of infusing into it the life of great principles4 ,with one additional point we will wind up our illustrations of the principles of solar chemistry4 ,owing to the scattering of light by matter floating mechanically in the earth's atmosphere1 the sun is seen not sharply defined1 but surrounded by a luminous glare4 ,now1 a loud noise will drown a whisper1 an intense light will overpower a feeble one1 and so this circumsolar glare prevents us from seeing many striking appearances round the border of the sun4 ,the glare is abolished in total eclipses1 when the moon comes between the earth and the sun1 and there are then seen a series of rose-coloured protuberances1 stretching sometimes tens of thousands of miles beyond the dark edge of the moon4 ,they are described by ,vassenius in the ',philosophical ,transactions' for #agcc2 and were probably observed even earlier than this4 ,in #ahdb they attracted great attention1 and were then compared to ,alpine snow-peaks reddened by the evening sun4 ,that these prominences are flaming gas1 and principally hydrogen gas1 was first proved by ,m4 ,janssen during an eclipse observed in ,india1 on the #ahth of ,august1 #ahfh4 ,but the prominences may be rendered visible in sunshine2 and for a reason easily understood4 ,you have seen in these lectures a single prism employed to produce a spectrum1 and you have seen a pair of prisms employed4 ,in the latter case1 the dispersed white light1 being diffused over about twice the area1 had all its colours proportionately diluted4 ,you have also seen one prism and a pair of prisms employed to produce the bands of incandescent vapours2 but here the light of each band1 being absolutely monochromatic1 was incapable of further dispersion by the second prism1 and could not therefore be weakened by such dispersion4 ,apply these considerations to the circumsolar region4 ,the glare of white light round the sun can be dispersed and weakened to any extent1 by augmenting the number of prisms2 while a monochromatic light1 mixed with this glare1 and masked by it1 would retain its intensity unenfeebled by dispersion4 ,upon this consideration has been founded a method of observation1 applied independently by ,m4 ,janssen in ,india and by ,mr4 ,lockyer in ,england1 by which the monochromatic bands of the prominences are caused to obtain the mastery1 and to appear in broad daylight4 ,by searching carefully and skilfully round the sun's rim1 ,mr4 ,lockyer has proved these prominences to be mere local juttings from a fiery envelope which entirely clasps the sun1 and which he has called the ,chromosphere4 ,it would lead us far beyond the object of these lectures to dwell upon the numerous interesting and important results obtained by ,secchi1 ,respighi1 ,young1 and other distinguished men who have worked at the chemistry of the sun and its appendages4 ,nor can ,i do more at present than make a passing reference to the excellent labours of ,dr4 ,huggins in connexion with the fixed stars1 nebulae1 and comets4 ,they1 more than any others1 illustrate the literal truth of the statement1 that the establishment of spectrum analysis1 and the explanation of ,fraunhofer's lines1 carried with them an immeasurable extension of the chemist's range4 ,the truly powerful experiments of ,professor ,dewar are daily adding to our knowledge1 while the refined researches of ,capt4 ,abney and others are opening new fields of inquiry4 ,but my object here is to make principles plain1 rather than to follow out the details of their illustration4 ,,summary ,,and ,,conclusion4 ,my desire in these lectures has been to show you1 with as little breach of continuity as possible1 something of the past growth and present aspect of a department of science1 in which have laboured some of the greatest intellects the world has ever seen4 ,i have sought to confer upon each experiment a distinct intellectual value1 for experiments ought to be the representatives and expositors of thought--a language addressed to the eye as spoken words are to the ear4 ,in association with its context1 nothing is more impressive or instructive than a fit experiment2 but1 apart from its context1 it rather suits the conjurer's purpose of surprise1 than the purpose of education which ought to be the ruling motive of the scientific man4 ,and now a brief summary of our work will not be out of place4 ,our present mastery over the laws and phenomena of light has its origin in the desire of man to know4 ,we have seen the ancients busy with this problem1 but1 like a child who uses his arms aimlessly1 for want of the necessary muscular training1 so these early men speculated vaguely and confusedly regarding natural phenomena1 not having had the discipline needed to give clearness to their insight1 and firmness to their grasp of principles4 ,they assured themselves of the rectilineal propagation of light1 and that the angle of incidence was equal to the angle of reflection4 ,for more than a thousand years--,i might say1 indeed1 for more than fifteen hundred years--the scientific intellect appears as if smitten with paralysis1 the fact being that1 during this time1 the mental force1 which might have run in the direction of science1 was diverted into other directions4 ,the course of investigation1 as regards light1 was resumed in #aajj by an ,arabian philosopher named ,alhazen4 ,then it was taken up in succession by ,roger ,bacon1 ,vitellio1 and ,kepler4 ,these men1 though failing to detect the principles which ruled the facts1 kept the fire of investigation constantly burning4 ,then came the fundamental discovery of ,snell1 that cornerstone of optics1 as ,i have already called it1 and immediately afterwards we have the application1 by ,descartes1 of ,snell's discovery to the explanation of the rainbow4 ,following this we have the overthrow1 by ,roemer1 of the notion of ,descartes1 that light was transmitted instantaneously through space4 ,then came ,newton's crowning experiments on the analysis and synthesis of white light1 by which it was proved to be compounded of various kinds of light of different degrees of refrangibility4 ,up to his demonstration of the composition of white light1 ,newton had been everywhere triumphant--triumphant in the heavens1 triumphant on the earth1 and his subsequent experimental work is1 for the most part1 of immortal value4 ,but infallibility is not an attribute of man1 and1 soon after his discovery of the nature of white light1 ,newton proved himself human4 ,he supposed that refraction and chromatic dispersion went hand in hand1 and that you could not abolish the one without at the same time abolishing the other4 ,here ,dollond corrected him4 ,but ,newton committed a graver error than this4 ,science1 as ,i sought to make clear to you in our second lecture1 is only in part a thing of the senses4 ,the roots of phenomena are embedded in a region beyond the reach of the senses1 and less than the root of the matter will never satisfy the scientific mind4 ,we find1 accordingly1 in this career of optics the greatest minds constantly yearning to break the bounds of the senses1 and to trace phenomena to their subsensible foundation4 ,thus impelled1 they entered the region of theory1 and here ,newton1 though drawn from time to time towards truth1 was drawn still more strongly towards error2 and he made error his substantial choice4 ,his experiments are imperishable1 but his theory has passed away4 ,for a century it stood like a dam across the course of discovery2 but1 as with all barriers that rest upon authority1 and not upon truth1 the pressure from behind increased1 and eventually swept the barrier away4 ,in #ahjh ,malus1 looking through ,iceland spar at the sun1 reflected from the window of the ,luxembourg ,palace in ,paris1 discovered the polarization of light by reflection4 ,as stated at the time1 this discovery ushered in the darkest hour in the fortunes of the wave theory4 ,but the darkness did not continue4 ,in #ahaa ,arago discovered the splendid chromatic phenomena which we have had illustrated by the deportment of plates of gypsum in polarized light2 he also discovered the rotation of the plane of polarization by quartz-crystals4 ,in #ahac ,seebeck discovered the polarization of light by tourmaline4 ,that same year ,brewster discovered those magnificent bands of colour that surround the axes of biaxal crystals4 ,in #ahad ,wollaston discovered the rings of ,iceland spar4 ,all these effects1 which1 without a theoretic clue1 would leave the human mind in a jungle of phenomena without harmony or relation1 were organically connected by the theory of undulation4 ,the wave theory was applied and verified in all directions1 ,airy being especially conspicuous for the severity and conclusiveness of his proofs4 ,a most remarkable verification fell to the lot of the late ,sir ,william ,hamilton1 of ,dublin1 who1 taking up the theory where ,fresnel had left it1 arrived at the conclusion that at four special points of the 'wave-surface' in double-refracting crystals1 the ray was divided1 not into two parts but into an infinite number of parts2 forming at these points a continuous conical envelope instead of two images4 ,no human eye had ever seen this envelope when ,sir ,william ,hamilton inferred its existence4 ,he asked ,dr4 ,lloyd to test experimentally the truth of his theoretic conclusion4 ,lloyd1 taking a crystal of arragonite1 and following with the most scrupulous exactness the indications of theory1 cutting the crystal where theory said it ought to be cut1 observing it where theory said it ought to be observed1 discovered the luminous envelope which had previously been a mere idea in the mind of the mathematician4 ,nevertheless this great theory of undulation1 like many another truth1 which in the long run has proved a blessing to humanity1 had to establish1 by hot conflict1 its right to existence4 ,illustrious names were arrayed against it4 ,it had been enunciated by ,hooke1 it had been expounded and applied by ,huyghens1 it had been defended by ,euler4 ,but they made no impression4 ,and1 indeed1 the theory in their hands lacked the strength of a demonstration4 ,it first took the form of a demonstrated verity in the hands of ,thomas ,young4 ,he brought the waves of light to bear upon each other1 causing them to support each other1 and to extinguish each other at will4 ,from their mutual actions he determined their lengths1 and applied his knowledge in all directions4 ,he finally showed that the difficulty of polarization yielded to the grasp of theory4 ,after him came ,fresnel1 whose transcendent mathematical abilities enabled him to give the theory a generality unattained by ,young4 ,he seized it in its entirety2 followed the ether into the hearts of crystals of the most complicated structure1 and into bodies subjected to strain and pressure4 ,he showed that the facts discovered by ,malus1 ,arago1 ,brewster1 and ,biot were so many ganglia1 so to speak1 of his theoretic organism1 deriving from it sustenance and explanation4 ,with a mind too strong for the body with which it was associated1 that body became a wreck long before it had become old1 and ,fresnel died1 leaving1 however1 behind him a name immortal in the annals of science4 ,one word more ,i should like to say regarding ,fresnel4 ,there are things better even than science4 ,character is higher than ,intellect1 but it is especially pleasant to those who wish to think well of human nature when high intellect and upright character are found combined4 ,they were combined in this young ,frenchman4 ,in those hot conflicts of the undulatory theory1 he stood forth as a man of integrity1 claiming no more than his right1 and ready to concede their rights to others4 ,he at once recognized and acknowledged the merits of ,thomas ,young4 ,indeed1 it was he1 and his fellow-countryman ,arago1 who first startled ,england into the consciousness of the injustice done to ,young in the ',edinburgh ,review4' ,i should like to read to you a brief extract from a letter written by ,fresnel to ,young in #ahbd1 as it throws a pleasant light upon the character of the ,french philosopher4 ',for a long time1' says ,fresnel1 'that sensibility1 or that vanity1 which people call love of glory has been much blunted in me4 ,i labour much less to catch the suffrages of the public1 than to obtain that inward approval which has always been the sweetest reward of my efforts4 ,without doubt1 in moments of disgust and discouragement1 ,i have often needed the spur of vanity to excite me to pursue my researches4 ,but all the compliments ,i have received from ,arago1 ,de la ,place1 and ,biot never gave me so much pleasure as the discovery of a theoretic truth or the confirmation of a calculation by experiment4' 99 99 99 99 99 ,this1 then1 is the core of the whole matter as regards science4 ,it must be cultivated for its own sake1 for the pure love of truth1 rather than for the applause or profit that it brings4 ,and now my occupation in ,america is well-nigh gone4 ,still ,i will bespeak your tolerance for a few concluding remarks1 in reference to the men who have bequeathed to us the vast body of knowledge of which ,i have sought to give you some faint idea in these lectures4 ,what was the motive that spurred them on8 ,what urged them to those battles and those victories over reticent ,nature1 which have become the heritage of the human race8 ,it is never to be forgotten that not one of those great investigators1 from ,aristotle down to ,stokes and ,kirchhoff1 had any practical end in view1 according to the ordinary definition of the word 'practical4' ,they did not propose to themselves money as an end1 and knowledge as a means of obtaining it4 ,for the most part1 they nobly reversed this process1 made knowledge their end1 and such money as they possessed the means of obtaining it4 ,we see to-day the issues of their work in a thousand practical forms1 and this may be thought sufficient to justify1 if not ennoble1 their efforts4 ,but they did not work for such issues2 their reward was of a totally different kind4 ,in what way different8 ,we love clothes1 we love luxuries1 we love fine equipages1 we love money1 and any man who can point to these as the result of his efforts in life1 justifies these results before all the world4 ,in ,america and ,england1 more especially1 he is a 'practical' man4 ,but ,i would appeal confidently to this assembly whether such things exhaust the demands of human nature8 ,the very presence here for six inclement nights of this great audience1 embodying so much of the mental force and refinement of this vast city1#bf is an answer to my question4 ,i need not tell such an assembly that there are joys of the intellect as well as joys of the body1 or that these pleasures of the spirit constituted the reward of our great investigators4 ,led on by the whisperings of natural truth1 through pain and self-denial1 they often pursued their work4 ,with the ruling passion strong in death1 some of them1 when no longer able to hold a pen1 dictated to their friends the last results of their labours1 and then rested from them for ever4 ,could we have seen these men at work1 without any knowledge of the consequences of their work1 what should we have thought of them8 ,to the uninitiated1 in their day1 they might often appear as big children playing with soap-bubbles and other trifles4 ,it is so to this hour4 ,could you watch the true investigator--your ,henry or your ,draper1 for example--in his laboratory1 unless animated by his spirit1 you could hardly understand what keeps him there4 ,many of the objects which rivet his attention might appear to you utterly trivial2 and if you were to ask him what is the use of his work1 the chances are that you would confound him4 ,he might not be able to express the use of it in intelligible terms4 ,he might not be able to assure you that it will put a dollar into the pocket of any human being present or to come4 ,that scientific discovery may put not only dollars into the pockets of individuals1 but millions into the exchequers of nations1 the history of science amply proves2 but the hope of its doing so never was1 and it never can be1 the motive power of the investigator4 ,i know that some risk is run in speaking thus before practical men4 ,i know what ,de ,tocqueville says of you4 ',the man of the ,north1' he says1 'has not only experience1 but knowledge4 ,he1 however1 does not care for science as a pleasure1 and only embraces it with avidity when it leads to useful applications4' ,but what1 ,i would ask1 are the hopes of useful applications which have caused you so many times to fill this place1 in spite of snow-drifts and biting cold8 ,what1 ,i may ask1 is the origin of that kindness which drew me from my work in ,london to address you here1 and which1 if ,i permitted it1 would send me home a millionaire8 ,not because ,i had taught you to make a single cent by science am ,i here to-night1 but because ,i tried to the best of my ability to present science to the world as an intellectual good4 ,surely no two terms were ever so distorted and misapplied with reference to man1 in his higher relations1 as these terms useful and practical4 ,let us expand our definitions until they embrace all the needs of man1 his highest intellectual needs inclusive4 ,it is specially on this ground of its administering to the higher needs of the intellect2 it is mainly because ,i believe it to be wholesome1 not only as a source of knowledge but as a means of discipline1 that ,i urge the claims of science upon your attention4 ,but with reference to material needs and joys1 surely pure science has also a word to say4 ,people sometimes speak as if steam had not been studied before ,james ,watt1 or electricity before ,wheatstone and ,morse2 whereas1 in point of fact1 ,watt and ,wheatstone and ,morse1 with all their practicality1 were the mere outcome of antecedent forces1 which acted without reference to practical ends4 ,this also1 ,i think1 merits a moment's attention4 ,you are delighted1 and with good reason1 with your electric telegraphs1 proud of your steam-engines and your factories1 and charmed with the productions of photography4 ,you see daily1 with just elation1 the creation of new forms of industry--new powers of adding to the wealth and comfort of society4 ,industrial ,england is heaving with forces tending to this end2 and the pulse of industry beats still stronger in the ,united ,states4 ,and yet1 when analyzed1 what are industrial ,america and industrial ,england8 ,if you can tolerate freedom of speech on my part1 ,i will answer this question by an illustration4 ,strip a strong arm1 and regard the knotted muscles when the hand is clenched and the arm bent4 ,is this exhibition of energy the work of the muscle alone8 ,by no means4 ,the muscle is the channel of an influence1 without which it would be as powerless as a lump of plastic dough4 ,it is the delicate unseen nerve that unlocks the power of the muscle4 ,and without those filaments of genius1 which have been shot like nerves through the body of society by the original discoverer1 industrial ,america1 and industrial ,england1 would be very much in the condition of that plastic dough4 ,at the present time there is a cry in ,england for technical education1 and it is a cry in which the most commonplace intellect can join1 its necessity is so obvious4 ,but there is no such cry for original investigation4 ,still1 without this1 as surely as the stream dwindles when the spring dies1 so surely will 'technical education' lose all force of growth1 all power of reproduction4 ,our great investigators have given us sufficient work for a time2 but if their spirit die out1 we shall find ourselves eventually in the condition of those ,chinese mentioned by ,de ,tocqueville1 who1 having forgotten the scientific origin of what they did1 were at length compelled to copy without variation the inventions of an ancestry wiser than themselves1 who had drawn their inspiration direct from ,nature4 ,both ,england and ,america have reason to bear those things in mind1 for the largeness and nearness of material results are only too likely to cause both countries to forget the small spiritual beginnings of such results1 in the mind of the scientific discoverer4 ,you multiply1 but he creates4 ,and if you starve him1 or otherwise kill him--nay1 if you fail to secure for him free scope and encouragement--you not only lose the motive power of intellectual progress1 but infallibly sever yourselves from the springs of industrial life4 ,what has been said of technical operations holds equally good for education1 for here also the original investigator constitutes the fountain-head of knowledge4 ,it belongs to the teacher to give this knowledge the requisite form2 an honourable and often a difficult task4 ,but it is a task which receives its final sanctification1 when the teacher himself honestly tries to add a rill to the great stream of scientific discovery4 ,indeed1 it may be doubted whether the real life of science can be fully felt and communicated by the man who has not himself been taught by direct communion with ,nature4 ,we may1 it is true1 have good and instructive lectures from men of ability1 the whole of whose knowledge is second-hand1 just as we may have good and instructive sermons from intellectually able and unregenerate men4 ,but for that power of science1 which corresponds to what the ,puritan fathers would call experimental religion in the heart1 you must ascend to the original investigator4 ,to keep society as regards science in healthy play1 three classes of workers are necessary3 ,firstly1 the investigator of natural truth1 whose vocation it is to pursue that truth1 and extend the field of discovery for the truth's own sake and without reference to practical ends4 ,secondly1 the teacher of natural truth1 whose vocation it is to give public diffusion to the knowledge already won by the discoverer4 ,thirdly1 the applier of natural truth1 whose vocation it is to make scientific knowledge available for the needs1 comforts1 and luxuries of civilized life4 ,these three classes ought to co-exist and interact4 ,now1 the popular notion of science1 both in this country and in ,england1 often relates not to science strictly so called1 but to the applications of science4 ,such applications1 especially on this continent1 are so astounding--they spread themselves so largely and umbrageously before the public eye--that they often shut out from view those workers who are engaged in the quieter and profounder business of original investigation4 ,take the electric telegraph as an example1 which has been repeatedly forced upon my attention of late4 ,i am not here to attenuate in the slightest degree the services of those who1 in ,england and ,america1 have given the telegraph a form so wonderfully fitted for public use4 ,they earned a great reward1 and they have received it4 ,but ,i should be untrue to you and to myself if ,i failed to tell you that1 however high in particular respects their claims and qualities may be1 your practical men did not discover the electric telegraph4 ,the discovery of the electric telegraph implies the discovery of electricity itself1 and the development of its laws and phenomena4 ,such discoveries are not made by practical men1 and they never will be made by them1 because their minds are beset by ideas which1 though of the highest value from one point of view1 are not those which stimulate the original discoverer4 ,the ancients discovered the electricity of amber2 and ,gilbert1 in the year #afjj1 extended the discovery to other bodies4 ,then followed ,boyle1 ,von ,guericke1 ,gray1 ,canton1 ,du ,fay1 ,kleist1 ,cunus1 and your own ,franklin4 ,but their form of electricity1 though tried1 did not come into use for telegraphic purposes4 ,then appeared the great ,italian ,volta1 who discovered the source of electricity which bears his name1 and applied the most profound insight1 and the most delicate experimental skill to its development4 ,then arose the man who added to the powers of his intellect all the graces of the human heart1 ,michael ,faraday1 the discoverer of the great domain of magneto-electricity4 ,o,ersted discovered the deflection of the magnetic needle1 and ,arago and ,sturgeon the magnetization of iron by the electric current4 ,the voltaic circuit finally found its theoretic ,newton in ,ohm2 while ,henry1 of ,princeton1 who had the sagacity to recognize the merits of ,ohm while they were still decried in his own country1 was at this time in the van of experimental inquiry4 ,in the works of these men you have all the materials employed at this hour1 in all the forms of the electric telegraph4 ,nay1 more2 ,gauss1 the illustrious astronomer1 and ,weber1 the illustrious natural philosopher1 both professors in the ,university of ,gttingen1 wishing to establish a rapid mode of communication between the observatory and the physical cabinet of the university1 did this by means of an electric telegraph4 ,thus1 before your practical men appeared upon the scene1 the force had been discovered1 its laws investigated and made sure1 the most complete mastery of its phenomena had been attained--nay1 its applicability to telegraphic purposes demonstrated--by men whose sole reward for their labours was the noble excitement of research1 and the joy attendant on the discovery of natural truth4 ,are we to ignore all this8 ,we do so at our peril4 ,for ,i say again that1 behind all our practical applications1 there is a region of intellectual action to which practical men have rarely contributed1 but from which they draw all their supplies4 ,cut them off from this region1 and they become eventually helpless4 ,in no case is the adage truer1 ',other men laboured1 but ye are entered into their labours1' than in the case of the discoverer and applier of natural truth4 ,but now a word on the other side4 ,while practical men are not the men to make the necessary antecedent discoveries1 the cases are rare1 though1 in our day1 not absent1 in which the discoverer knows how to turn his labours to practical account4 ,different qualities of mind and habits of thought are usually needed in the two cases2 and while ,i wish to give emphatic utterance to the claims of those whose position1 owing to the simple fact of their intellectual elevation1 is often misunderstood1 ,i am not here to exalt the one class of workers at the expense of the other4 ,they are the necessary complements of each other4 ,but remember that one class is sure to be taken care of4 ,all the material rewards of society are already within their reach1 while that same society habitually ascribes to them intellectual achievements which were never theirs4 ,this cannot but act to the detriment of those studies out of which1 not only our knowledge of nature1 but our present industrial arts themselves1 have sprung1 and from which the rising genius of the country is incessantly tempted away4 ,pasteur1 one of the most illustrious members of the ,institute of ,france1 in accounting for the disastrous overthrow of his country1 and the predominance of ,germany in the late war1 expresses himself thus3 ',few persons comprehend the real origin of the marvels of industry and the wealth of nations4 ,i need no further proof of this than the employment1 more and more frequent1 in official language1 and in writings of all sorts1 of the erroneous expression applied science4 ,the abandonment of scientific careers by men capable of pursuing them with distinction1 was recently deplored in the presence of a minister of the greatest talent4 ,the statesman endeavoured to show that we ought not to be surprised at this result1 because in our day the reign of theoretic science yielded place to that of applied science4 ,nothing could be more erroneous than this opinion1 nothing1 ,i venture to say1 more dangerous1 even to practical life1 than the consequences which might flow from these words4 ,they have rested in my mind as a proof of the imperious necessity of reform in our superior education4 ,there exists no category of the sciences1 to which the name of applied science could be rightly given4 ,we have science1 and the applications of science1 which are united together as the tree and its fruit4' ,and ,cuvier1 the great comparative anatomist1 writes thus upon the same theme3 ',these grand practical innovations are the mere applications of truths of a higher order1 not sought with a practical intent1 but pursued for their own sake1 and solely through an ardour for knowledge4 ,those who applied them could not have discovered them2 but those who discovered them had no inclination to pursue them to a practical end4 ,engaged in the high regions whither their thoughts had carried them1 they hardly perceived these practical issues though born of their own deeds4 ,these rising workshops1 these peopled colonies1 those ships which furrow the seas--this abundance1 this luxury1 this tumult--all this comes from discoveries in science1 and it all remains strange to the discoverers4 ,at the point where science merges into practice they abandon it2 it concerns them no more4' ,when the ,pilgrim ,fathers landed at ,plymouth ,rock1 and when ,penn made his treaty with the ,indians1 the new-comers had to build their houses1 to cultivate the earth1 and to take care of their souls4 ,in such a community science1 in its more abstract forms1 was not to be thought of4 ,and at the present hour1 when your hardy ,western pioneers stand face to face with stubborn ,nature1 piercing the mountains and subduing the forest and the prairie1 the pursuit of science1 for its own sake1 is not to be expected4 ,the first need of man is food and shelter2 but a vast portion of this continent is already raised far beyond this need4 ,the gentlemen of ,new ,york1 ,brooklyn1 ,boston1 ,philadelphia1 ,baltimore1 and ,washington have already built their houses1 and very beautiful they are2 they have also secured their dinners1 to the excellence of which ,i can also bear testimony4 ,they have1 in fact1 reached that precise condition of well-being and independence when a culture1 as high as humanity has yet reached1 may be justly demanded at their hands4 ,they have reached that maturity1 as possessors of wealth and leisure1 when the investigator of natural truth1 for the truth's own sake1 ought to find among them promoters and protectors4 ,among the many problems before them they have this to solve1 whether a republic is able to foster the highest forms of genius4 ,you are familiar with the writings of ,de ,tocqueville1 and must be aware of the intense sympathy which he felt for your institutions2 and this sympathy is all the more valuable from the philosophic candour with which he points out not only your merits1 but your defects and dangers4 ,now if ,i come here to speak of science in ,america in a critical and captious spirit1 an invisible radiation from my words and manner will enable you to find me out1 and will guide your treatment of me to-night4 ,but if ,i in no unfriendly spirit--in a spirit1 indeed1 the reverse of unfriendly--venture to repeat before you what this great historian and analyst of democratic institutions said of ,america1 ,i am persuaded that you will hear me out4 ,he wrote some three and twenty years ago1 and1 perhaps1 would not write the same to-day2 but it will do nobody any harm to have his words repeated1 and1 if necessary1 laid to heart4 ,in a work published in #ahej1 ,de ,tocqueville says3 ',it must be confessed that1 among the civilized peoples of our age1 there are few in which the highest sciences have made so little progress as in the ,united ,states4'#bg ,he declares his conviction that1 had you been alone in the universe1 you would soon have discovered that you cannot long make progress in practical science without cultivating theoretic science at the same time4 ,but1 according to ,de ,tocqueville1 you are not thus alone4 ,he refuses to separate ,america from its ancestral home2 and it is there1 he contends1 that you collect the treasures of the intellect1 without taking the trouble to create them4 ,de ,tocqueville evidently doubts the capacity of a democracy to foster genius as it was fostered in the ancient aristocracies4 ',the future1' he says1 'will prove whether the passion for profound knowledge1 so rare and so fruitful1 can be born and developed as readily in democratic societies as in aristocracies4 ,for my part1' he continues1 ',i can hardly believe it4' ,he speaks of the unquiet feverishness of democratic communities1 not in times of great excitement1 for such times may give an extraordinary impetus to ideas1 but in times of peace4 ,there is then1 he says1 'a small and uncomfortable agitation1 a sort of incessant attrition of man against man1 which troubles and distracts the mind without imparting to it either loftiness or animation4' ,it rests with you to prove whether these things are necessarily so--whether scientific genius cannot find1 in the midst of you1 a tranquil home4 ,i should be loth to gainsay so keen an observer and so profound a political writer1 but1 since my arrival in this country1 ,i have been unable to see anything in the constitution of society1 to prevent a student1 with the root of the matter in him1 from bestowing the most steadfast devotion on pure science4 ,if great scientific results are not achieved in ,america1 it is not to the small agitations of society that ,i should be disposed to ascribe the defect1 but to the fact that the men among you who possess the endowments necessary for profound scientific inquiry1 are laden with duties of administration1 or tuition1 so heavy as to be utterly incompatible with the continuous and tranquil meditation which original investigation demands4 ,it may well be asked whether ,henry would have been transformed into an administrator1 or whether ,draper would have forsaken science to write history1 if the original investigator had been honoured as he ought to be in this land4 ,i hardly think they would4 ,still ,i do not imagine this state of things likely to last4 ,in ,america there is a willingness on the part of individuals to devote their fortunes1 in the matter of education1 to the service of the commonwealth1 which is probably without a parallel elsewhere2 and this willingness requires but wise direction to enable you effectually to wipe away the reproach of ,de ,tocqueville4 ,your most difficult problem will be1 not to build institutions1 but to discover men4 ,you may erect laboratories and endow them2 you may furnish them with all the appliances needed for inquiry2 in so doing you are but creating opportunity for the exercise of powers which come from sources entirely beyond your reach4 ,you cannot create genius by bidding for it4 ,in biblical language1 it is the gift of ,god2 and the most you could do1 were your wealth1 and your willingness to apply it1 a million-fold what they are1 would be to make sure that this glorious plant shall have the freedom1 light1 and warmth necessary for its development4 ,we see from time to time a noble tree dragged down by parasitic runners4 ,these the gardener can remove1 though the vital force of the tree itself may lie beyond him3 and so1 in many a case you men of wealth can liberate genius from the hampering toils which the struggle for existence often casts around it4 ,drawn by your kindness1 ,i have come here to give these lectures1 and now that my visit to ,america has become almost a thing of the past1 ,i look back upon it as a memory without a single stain4 ,no lecturer was ever rewarded as ,i have been4 ,from this vantage-ground1 however1 let me remind you that the work of the lecturer is not the highest work2 that in science1 the lecturer is usually the distributor of intellectual wealth amassed by better men4 ,and though lecturing and teaching1 in moderation1 will in general promote their moral health1 it is not solely or even chiefly1 as lecturers1 but as investigators1 that your highest men ought to be employed4 ,you have scientific genius amongst you--not sown broadcast1 believe me1 it is sown thus nowhere--but still scattered here and there4 ,take all unnecessary impediments out of its way4 ,keep your sympathetic eye upon the originator of knowledge4 ,give him the freedom necessary for his researches1 not overloading him1 either with the duties of tuition or of administration1 nor demanding from him so-called practical results--above all things1 avoiding that question which ignorance so often addresses to genius3 ',what is the use of your work8' ,let him make truth his object1 however unpractical for the time being it may appear4 ,if you cast your bread thus upon the waters1 be assured it will return to you1 though it be after many days4 ,,appendix4 ,,on ,,the ,,spectra ,,of ,,polarized ,,light4 ,mr4 ,william ,spottiswoode introduced some years ago to the members of the ,royal ,institution1 in a very striking form1 a series of experiments on the spectra of polarized light4 ,with his large ,nicol prisms he in the first place repeated and explained the experiments of ,foucault and ,fizeau1 and subsequently enriched the subject by very beautiful additions of his own4 ,i here append a portion of the abstract of his discourse3-- ',it is well known that if a plate of selenite sufficiently thin be placed between two ,nicol's prisms1 or1 more technically speaking1 between a polarizer and analyzer1 colour will be produced4 ,and the question proposed is1 ,what is the nature of that colour8 is it simply a pure colour of the spectrum1 or is it a compound1 and if so1 what are its component parts8 ,the answer given by the wave theory is in brief this3 ,in its passage through the selenite plate the rays have been so separated in the direction of their vibrations and in the velocity of their transmission1 that1 when re-compounded by means of the analyzer1 they have in some instances neutralized one another4 ,if this be the case1 the fact ought to be visible when the beam emerging from the analyzer is dispersed by the prism2 for then we have the rays of all the different colours ranged side by side1 and1 if any be wanting1 their absence will be shown by the appearance of a dark band in their place in the spectrum4 ,but not only so2 the spectrum ought also to give an account of the other phenomena exhibited by the selenite when the analyzer is turned round1 viz4 that when the angle of turning amounts to #de1 all trace of colour disappears2 and also that when the angle amounts to #ij1 colour reappears1 not1 however1 the original colour1 but one complementary to it4 ',you see in the spectrum of the reddish light produced by the selenite a broad but dark band in the blue2 when the analyzer is turned round the band becomes less and less dark1 until when the angle of turning amounts to #de it has entirely disappeared4 ,at this stage each part of the spectrum has its own proportional intensity1 and the whole produces the colourless image seen without the spectroscope4 ,lastly1 as the turning of the analyzer is continued1 a dark band appears in the red1 the part of the spectrum complementary to that occupied by the first band2 and the darkness is most complete when the turning amounts to #ij4 ,thus we have from the spectroscope a complete account of what has taken place to produce the original colour and its changes4 ',it is further well known that the colour produced by a selenite1 or other crystal plate1 is dependent upon the thickness of the plate4 ,and1 in fact1 if a series of plates be taken1 giving different colours1 their spectra are found to show bands arranged in different positions4 ,the thinner plates show bands in the parts of the spectrum nearest to the violet1 where the waves are shorter1 and consequently give rise to redder colours2 while the thicker show bands nearer to the red1 where the waves are longer and consequently supply bluer tints4 ',when the thickness of the plate is continually increased1 so that the colour produced has gone through the complete cycle of the spectrum1 a further increase of thickness causes a reproduction of the colours in the same order2 but it will be noticed that at each recurrence of the cycle the tints become paler1 until when a number of cycles have been performed1 and the thickness of the plate is considerable1 all trace of colour is lost4 ,let us now take a series of plates1 the first two of which1 as you see1 give colours2 with the others which are successively of greater thickness the tints are so feeble that they can scarcely be distinguished4 ,the spectrum of the first shows a single band2 that of the second1 two2 showing that the second series of tints is not identical with the first1 but that it is produced by the extinction of two colours from the components of white light4 ,the spectra of the others show series of bands more and more numerous in proportion to the thickness of the plate1 an array which may be increased indefinitely4 ,the total light1 then1 of which the spectrum is deprived by the thicker plates is taken from a greater number of its parts2 or1 in other words1 the light which still remains is distributed more and more evenly over the spectrum2 and in the same proportion the sum total of it approaches more and more nearly to white light4 ',these experiments were made more than thirty years ago by the ,french philosophers1 ,,mm4 ,foucault and ,fizeau4 ',if instead of selenite1 ,iceland spar1 or other ordinary crystals1 we use plates of quartz cut perpendicularly to the axis1 and turn the analyzer round as before1 the light1 instead of exhibiting only one colour and its complementary with an intermediate stage in which colour is absent1 changes continuously in tint2 and the order of the colour depends partly upon the direction in which the analyzer is turned1 and partly upon the character of the crystal1 i4e4 whether it is right-handed or left-handed4 ,if we examine the spectrum in this case we find that the dark band never disappears1 but marches from one end of the spectrum to another1 or vice vers1 precisely in such a direction as to give rise to the tints seen by direct projection4 ',the kind of polarization effected by the quartz plates is called circular1 while that effected by the other class of crystals is called plane1 on account of the form of the vibrations executed by the molecules of ther2 and this leads us to examine a little more closely the nature of the polarization of different parts of these spectra of polarized light4 ',now1 two things are clear3 first1 that if the light be plane-polarized--that is1 if all the vibrations throughout the entire ray are rectilinear and in one plane--they must in all their bearings have reference to a particular direction in space1 so that they will be differently affected by different positions of the analyzer4 ,secondly1 that if the vibrations be circular1 they will be affected in precisely the same way 7whatever that may be7 in all positions of the analyzer4 ,this statement merely recapitulates a fundamental point in polarization4 ,in fact1 plane-polarized light is alternately transmitted and extinguished by the analyzer as it is turned through #ij2 while circularly polarized light if we could get a single ray remains to all appearance unchanged4 ,and if we examine carefully the spectrum of light which has passed through a selenite1 or other ordinary crystal1 we shall find that1 commencing with two consecutive bands in position1 the parts occupied by the bands and those midway between them are plane-polarized1 for they become alternately dark and bright2 while the intermediate parts1 i4e4 the parts at one-fourth of the distance from one band to the next1 remain permanently bright4 ,these are1 in fact1 circularly polarized4 ,but it would be incorrect to conclude from this experiment alone that such is really the case1 because the same appearance would be seen if those parts were unpolarized1 i4e4 in the condition of ordinary lights4 ,and on such a supposition we should conclude with equal justice that the parts on either side of the parts last mentioned 7e4g4 the parts separated by eighth parts of the interval between two bands7 were partially polarized4 ,but there is an instrument of very simple construction1 called a quarter-undulation plate1 a plate usually of mica1 whose thickness is an odd multiple of a quarter of a wave-length1 which enables us to discriminate between light unpolarized and circularly polarized4 ,the exact mechanical effect produced upon the ray could hardly be explained in detail within our present limits of time2 but suffice it for the present to say that1 when placed in a proper position1 the plate transforms plane into circular and circular into plane polarization4 ,that being so1 the parts which were originally banded ought to remain bright1 and those which originally remained bright ought to become banded during the rotation of the analyzer4 ,the general effect to the eye will consequently be a general shifting of the bands through one-fourth of the space which separates each pair4 ',circular polarization1 like circular motion generally1 may of course be of two kinds1 which differ only in the direction of the motion4 ,and1 in fact1 to convert the circular polarization produced by this plate from one of these kinds to the other 7say from right-handed to left-handed1 or vice vers71 we have only to turn the plate round through #ij4 ,conversely1 right-handed circular polarization will be changed by the plate into plane-polarization in one direction1 while left-handed will be changed into plane at right angles to the first4 ,hence if the plate be turned round through #ij we shall see that the bands are shifted in a direction opposite to that in which they were moved at first4 ,in this therefore we have evidence not only that the polarization immediately on either side of a band is circular2 but also that that immediately on the one side is right-handed1 while that immediately on the other is left-handed#bh4 ',if time permitted1 ,i might enter still further into detail1 and show that the polarization between the plane and the circular is elliptical1 and even the positions of the longer and shorter axes and the direction of motion in each case4 ,but sufficient has1 perhaps1 been said for our present purpose4 ',before proceeding to the more varied forms of spectral bands1 which ,i hope presently to bring under your notice1 ,i should like to ask your attention for a few minutes to the peculiar phenomena exhibited when two plates of selenite giving complementary colours are used4 ,the appearance of the spectrum varies with the relative position of the plates4 ,if they are similarly placed--that is1 as if they were one plate of crystal--they will behave as a single plate1 whose thickness is the sum of the thicknesses of each1 and will produce double the number of bands which one alone would give2 and when the analyzer is turned1 the bands will disappear and re-appear in their complementary positions1 as usual in the case of plane-polarization4 ,if one of them be turned round through #de1 a single band will be seen at a particular position in the spectrum4 ,this breaks into two1 which recede from one another towards the red and violet ends respectively1 or advance towards one another according to the direction in which the analyzer is turned4 ,if the plate be turned through #de in the opposite direction1 the effects will be reversed4 ,the darkness of the bands is1 however1 not equally complete during their whole passage4 ,lastly1 if one of the plates be turned through #ij1 no bands will be seen1 and the spectrum will be alternately bright and dark1 as if no plates were used1 except only that the polarization is itself turned through #ij4 ',if a wedge-shaped crystal be used1 the bands1 instead of being straight1 will cross the spectrum diagonally1 the direction of the diagonal 7dexter or sinister7 being determined by the position of the thicker end of the wedge4 ,if two similar wedges be used with their thickest ends together1 they will act as a wedge whose angle and whose thickness is double of the first4 ,if they be placed in the reverse position they will act as a flat plate1 and the bands will again cross the spectrum in straight lines at right angles to its length4 ',if a concave plate be used the bands will dispose themselves in a fanlike arrangement1 their divergence depending upon the distance of the slit from the centre of concavity4 ',if two quartz wedges1 one of which has the optic axis parallel to the edge of the refractory angle1 and the other perpendicular to it1 but in one of the planes containing the angle 7,babinet's ,compensator71 the appearances of the bands are very various4 ',the diagonal bands1 besides sometimes doubling themselves as with ordinary wedges1 sometimes combine so as to form longitudinal 7instead of transverse7 bands2 and sometimes cross one another so as to form a diaper pattern with bright compartments in a dark framework1 and vice vers1 according to the position of the plates4 ',the effects of different dispositions of the interposed crystals might be varied indefinitely2 but enough has perhaps been said to show the delicacy of the method of spectrum analysis as applied to the examination of polarized light4' 99 99 99 99 99 ,the singular and beautiful effect obtained with a circular plate of selenite1 thin at the centre1 and gradually thickening towards the circumference1 is easily connected with a similar effect obtained with ,newton's rings4 ,let a thin slice of light fall upon the glasses which show the rings1 so as to cover a narrow central vertical zone passing through them all4 ,the image of this zone upon the screen is crossed by portions of the iris-rings4 ,subjecting the reflected beam to prismatic analysis1 the resultant spectrum may be regarded as an indefinite number of images of the zone placed side by side4 ,in the image before dispersion we have iris-rings1 the extinction of the light being nowhere complete2 but when the different colours are separated by dispersion1 each colour is crossed transversely by its own system of dark interference bands1 which become gradually closer with the increasing refrangibility of the light4 ,the complete spectrum1 therefore1 appears furrowed by a system of continuous dark bands1 crossing the colours transversely1 and approaching each other as they pass from red to blue4 ,in the case of the plate of selenite1 a slit is placed in front of the polarizer1 and the film of selenite is held close to the slit1 so that the light passes through the central zone of the film4 ,as in the case of ,newton's rings1 the image of the zone is crossed by iris-coloured bands2 but when subjected to prismatic dispersion1 the light of the zone yields a spectrum furrowed by bands of complete darkness exactly as in the case of ,newton's rings and for a similar reason4 ,this is the beautiful effect described by ,mr4 ,spottiswoode as the fanlike arrangement of the bands--the fan opening out at the red end of the spectrum4 99 99 99 99 99 ,,measurement ,,of ,,the ,,waves ,,of ,,light4 ,the diffraction fringes described in ,lecture ,,ii41 instead of being formed on the retina1 may be formed on a screen1 or upon ground glass1 when they can be looked at through a magnifying lens from behind1 or they can be observed in the air when the ground glass is removed4 ,instead of permitting them to form on the retina1 we will suppose them formed on a screen4 ,this places us in a condition to understand1 even without trigonometry1 the solution of the important problem of measuring the length of a wave of light4 ,we will suppose the screen so distant that the rays falling upon it from the two margins of the slit are sensibly parallel4 ,we have learned in ,lecture ,,ii4 that the first of the dark bands corresponds to a difference of marginal path of one undulation2 the second dark band to a difference of path of two undulations2 the third dark band to a difference of three undulations1 and so on4 ,now the angular distance of the bands from the centre is capable of exact measurement2 this distance depending1 as already stated1 on the width of the slit4 ,with a slit #a4ce millimeter wide1#bi ,schwerd found the angular distance of the first dark band from the centre of the field to be #a'ch2 the angular distances of the second1 third1 fourth dark bands being twice1 three times1 four times this quantity4 ,illustration3 ,fig4 #eg4 ,let ,a ,b1 fig4 #eg1 be the plate in which the slit is cut1 and ,c ,d the grossly exaggerated width of the slit1 with the beam of red light proceeding from it at the obliquity corresponding to the first dark band4 ,let fall a perpendicular from one edge1 ,d1 of the slit on the marginal ray of the other edge at d4 ,the distance1 ,c d1 between the foot of this perpendicular and the other edge is the length of a wave of the light4 ,the angle ,c ,d d1 moreover1 being equal to ,r ,c ,r'1 is1 in the case now under consideration1 #a'ch4 ,from the centre ,d1 with the width ,d ,c as radius1 describe a semicircle2 its radius ,d ,c being #a4ce millimeter1 the length of this semicircle is found by an easy calculation to be #d4bdh millimeters4 ,the length ,c d is so small that it sensibly coincides with the arc of the circle4 ,hence the length of the semicircle is to the length ,c d of the wave as #ahj to #a'ch1 or1 reducing all to seconds1 as #fdh1jjj to #ih4 ,thus1 we have the proportion-- #fdh1jjj 3 #ih 33 #d4bdh to the wave-length ,c d4 ,making the calculation1 we find the wave-length for this particular kind of light to be #j4jjjfdc of a millimeter1 or #j4jjjjbf of an inch4 ,,footnotes3 ,footnote #a3 ,among whom may be especially mentioned the late ,sir ,edmund ,head1 ,bart41 with whom ,i had many conversations on this subject4 ,footnote #b3 ,at whose hands it gives me pleasure to state ,i have always experienced honourable and liberal treatment4 ,footnote #c3 ,one of the earliest of these came from ,mr4 ,john ,amory ,lowell of ,boston4 ,footnote #d3 ,it will be subsequently shown how this simple apparatus may be employed to determine the 'polarizing angle' of a liquid4 ,footnote #e3 ,from this principle ,sir ,john ,herschel deduces in a simple and elegant manner the fundamental law of reflection4--,see ,familiar ,lectures1 p4 #bcf4 ,footnote #f3 ,the low dispersive power of water masks1 as ,helmholtz has remarked1 the imperfect achromatism of the eye4 ,with the naked eye ,i can see a distant blue disk sharply defined1 but not a red one4 ,i can also see the lines which mark the upper and lower boundaries of a horizontally refracted spectrum sharp at the blue end1 but ill-defined at the red end4 ,projecting a luminous disk upon a screen1 and covering one semicircle of the aperture with a red and the other with a blue or green glass1 the difference between the apparent sizes of the two semicircles is in my case1 and in numerous other cases1 extraordinary4 ,many persons1 however1 see the apparent sizes of the two semicircles reversed4 ,if with a spectacle glass ,i correct the dispersion of the red light over the retina1 then the blue ceases to give a sharply defined image4 ,thus examined1 the departure of the eye from achromatism appears very gross indeed4 ,footnote #g3 ,both in foliage and in flowers there are striking differences of absorption4 ,the copper beech and the green beech1 for example1 take in different rays4 ,but the very growth of the tree is due to some of the rays thus taken in4 ,are the chemical rays1 then1 the same in the copper and the green beech8 ,in two such flowers as the primrose and the violet1 where the absorptions1 to judge by the colours1 are almost complementary1 are the chemically active rays the same8 ,the general relation of colour to chemical action is worthy of the application of the method by which ,dr4 ,draper proved so conclusively the chemical potency of the yellow rays of the sun4 ,footnote #h3 ,young1 ,helmholtz1 and ,maxwell reduce all differences of hue to combinations in different proportions of three primary colours4 ,it is demonstrable by experiment that from the red1 green1 and violet all the other colours of the spectrum may be obtained4 ,some years ago ,sir ,charles ,wheatstone drew my attention to a work by ,christian ,ernst ,wnsch1 ,leipzig #agib1 in which the author announces the proposition that there are neither five nor seven1 but only three simple colours in white light4 ,wnsch produced five spectra1 with five prisms and five small apertures1 and he mixed the colours first in pairs1 and afterwards in other ways and proportions4 ,his result is that red is a simple colour incapable of being decomposed2 that orange is compounded of intense red and weak green2 that yellow is a mixture of intense red and intense green2 that green is a simple colour2 that blue is compounded of saturated green and saturated violet2 that indigo is a mixture of saturated violet and weak green2 while violet is a pure simple colour4 ,he also finds that yellow and indigo blue produce white by their mixture4 ,yellow mixed with bright blue 7,hochblau7 also produces white1 which seems1 however1 to have a tinge of green1 while the pigments of these two colours when mixed always give a more or less beautiful green1 ,wnsch very emphatically distinguishes the mixture of pigments from that of lights4 ,speaking of the generation of yellow1 he says1 ',i say expressly red and green light1 because ,i am speaking about light-colours 7,lichtfarben71 and not about pigments4' ,however faulty his theories may be1 ,wnsch's experiments appear in the main to be precise and conclusive4 ,nearly ten years subsequently1 ,young adopted red1 green1 and violet as the three primary colours1 each of them capable of producing three sensations1 one of which1 however1 predominates over the two others4 ,helmholtz adopts1 elucidates1 and enriches this notion4 7,popular ,lectures1 p4 #bdi4 ,the paper of ,helmholtz on the mixture of colours1 translated by myself1 is published in the ,philosophical ,magazine for #aheb4 ,maxwell's memoir on the ,theory of ,compound ,colours is published in the ,philosophical ,transactions1 vol4 #aej1 p4 #fg47 ,footnote #i3 ,the following charming extract1 bearing upon this point1 was discovered and written out for me by my deeply lamented friend ,dr4 ,bence ,jones1 when ,hon4 ,secretary to the ,royal ,institution3-- ',in every kind of magnitude there is a degree or sort to which our sense is proportioned1 the perception and knowledge of which is of the greatest use to mankind4 ,the same is the groundwork of philosophy2 for1 though all sorts and degrees are equally the object of philosophical speculation1 yet it is from those which are proportioned to sense that a philosopher must set out in his inquiries1 ascending or descending afterwards as his pursuits may require4 ,he does well indeed to take his views from many points of sight1 and supply the defects of sense by a well-regulated imagination2 nor is he to be confined by any limit in space or time2 but1 as his knowledge of ,nature is founded on the observation of sensible things1 he must begin with these1 and must often return to them to examine his progress by them4 ,here is his secure hold3 and as he sets out from thence1 so if he likewise trace not often his steps backwards with caution1 he will be in hazard of losing his way in the labyrinths of ,nature4'--7,maclaurin3 ,an ,account of ,sir ,i4 ,newton's ,philosophical ,discoveries4 ,written #agbh2 second edition1 #agej2 pp4 #ah1 #ai47 ,footnote #aj3 ,i do not wish to encumber the conception here with the details of the motion1 but ,i may draw attention to the beautiful model of ,prof4 ,lyman1 wherein waves are shown to be produced by the circular motion of the particles4 ,this1 as proved by the brothers ,weber1 is the real motion in the case of water-waves4 ,footnote #aa3 ,copied from ,weber's ,wellenlehre4 ,footnote #ab3 ,see ,lectures on ,sound1 #ast and #bnd ed41 ,lecture ,,vii42 and #crd ed41 ,chap4 ,,viii4 ,longmans4 ,footnote #ac3 ,boyle's ,works1 ,birch's edition1 p4 #fge4 ,footnote #ad3 ,page #gdc4 ,footnote #ae3 ,the beautiful plumes produced by water-crystallization have been successfully photographed by ,professor ,lockett4 ,footnote #af3 ,in a little volume entitled ',forms of ,water1' ,i have mentioned that cold iron floats upon molten iron4 ,in company with my friend ,sir ,william ,armstrong1 ,i had repeated opportunities of witnessing this fact in his works at ,elswick1 #ahfc4 ,faraday1 ,i remember1 spoke to me subsequently of the perfection of iron castings as probably due to the swelling of the metal on solidification4 ,beyond this1 ,i have given the subject no special attention2 and ,i know that many intelligent iron-founders doubt the fact of expansion4 ,it is quite possible that the solid floats because it is not wetted by the molten iron1 its volume being virtually augmented by capillary repulsion4 ,certain flies walk freely upon water in virtue of an action of this kind4 ,with bismuth1 however1 it is easy to burst iron bottles by the force of solidification4 ,footnote #ag3 ,this beautiful law is usually thus expressed3 ,the index of refraction of any substance is the tangent of its polarizing angle4 ,with the aid of this law and an apparatus similar to that figured at page #ae1 we can readily determine the index of refraction of any liquid4 ,the refracted and reflected beams being visible1 they can readily be caused to inclose a right angle4 ,the polarizing angle of the liquid may be thus found with the sharpest precision4 ,it is then only necessary to seek out its natural tangent to obtain the index of refraction4 ,footnote #ah3 ,whewell4 ,footnote #ai3 ,removed from us since these words were written4 ,footnote #bj3 ,the only essay known to me on the ,undulatory ,theory1 from the pen of an ,american writer1 is an excellent one by ,president ,barnard1 published in the ,smithsonian ,report for #ahfb4 ,footnote #ba3 ,boyle's ,works1 ,birch's edition1 vol4 i4 pp1 #gbi and #gcj4 ,footnote #bb3 ,werke1 ,b4 xxix4 p4 #bd4 ,footnote #bc3 ,defined in ,lecture ,i4 ,footnote #bd3 ,this circumstance ought not to be lost sight of in the examination of compound spectra4 ,other similar instances might be cited4 ,footnote #be3 ,the dark band produced when the sodium is placed within the lamp was observed on the same occasion4 ,then was also observed for the first time the magnificent blue band of lithium which the ,bunsen's flame fails to bring out4 ,footnote #bf3 ,new ,york3 for more than a decade no such weather had been experienced4 ,the snow was so deep that the ordinary means of locomotion were for a time suspended4 ,footnote #bg3 ',il faut reconnatre que parmi les peuples civiliss de nos jours il en est pen chez qui les hautes sciences aient fait moins de progrs qu'aux tats-,unis1 ou qui aient fourni moins de grands artistes1 de potes illustres et de clbres crivains4' 7,de la ,dmocratie en ,amrique1 etc4 tome ii4 p4 #cf47 ,footnote #bh3 ,at these points the two rectangular vibrations into which the original polarized ray is resolved by the plates of gypsum1 act upon each other like the two rectangular impulses imparted to our pendulum in ,lecture ,,iv41 one being given when the pendulum is at the limit of its swing4 ,vibration is thus converted into rotation4 ,footnote #bi3 ,the millimeter is about #a_/beth of an inch4 ,,index4 ,absorption1 principles of1 #aii ,airy1 ,sir ,george1 severity and conclusiveness of his proofs1 #bji ,alhazen1 his inquiry respecting light1 #ad1 #bjg ,analyzer1 polarizer and1 #abg ----recompounding of the two systems of waves by the analyzer1 #abi ngstrm1 his paper on spectrum analysis1 #bjb ,arago1 ,franois1 and ,dr4 ,young1 #ej ----his discoveries respecting light1 #bjh ,atomic polarity1 #ic-if ,bacon1 ,roger1 his inquiry respecting light1 #ad1 #bjg ,bartholinus1 ,erasmus1 on ,iceland spar1 #aab ,brard on polarization of heat1 #ahj ,blackness1 meaning of1 #cb ,boyle1 ,robert1 his observations on colours1 #fe1 #ff ----his remarks on fluorescence1 #afc1 #afd ,bradley1 ,james1 discovers the aberration of light1 #ba1 #bb ,brewster1 ,sir ,david1 his chief objection to the undulatory theory of light1 #dg ,brewster1 ,sir ,david1 his discovery in biaxal crystals1 #bji ,brougham1 ,mr4 7afterwards ,lord71 ridicules ,dr4 ,t4 ,young's speculations1 #ej1 #ea ,csium1 discovery of1 #aic ,calorescence1 #agd ,clouds1 actinic1 #aeb-aed ----polarization of1 #aee ,colours of thin plates1 #fd ----,boyle's observations on1 #fe1 #ff ----,hooke on the colours of thin plates1 #fg ----of striated surfaces1 #hi1 #ij ,comet of #afhj1 ,newton's estimate of the temperature of1 #afh ,crookes1 ,mr41 his discovery of thallium1 #aic ,crystals1 action of1 upon light1 #ih ----built by polar force1 #ih ----illustrations of crystallization1 #ii ----architecture of1 considered as an introduction to their action upon light1 #ih ----bearings of crystallization upon optical phenomena1 #ajf ,crystals1 rings surrounding the axes of1 uniaxal and biaxal1 #ade ,cuvier on ardour for knowledge1 #bbj ,de ,tocqueville1 writings of1 #bae1 #bbb1 #bbc ,descartes1 his explanation of the rainbow1 #bd1 #be ----his ideas respecting the transmission of light1 #dc ----his notion of light1 #bjg ,diamond1 ignition of a1 in oxygen1 #afi ,diathermancy1 #agc ,diffraction of light1 phenomena of1 #gh ----bands1 #gh1 #gi ----explanation of1 #hj ----colours produced by1 #hi ,dollond1 his experiments on achromatism1 #bh ,draper1 ,dr41 his investigation on heat1 #agb ,drummond light1 spectrum of1 #aie ,earth1 daily orbit of1 #gd ,electric beam1 heat of the1 #afh ,electricity1 discoveries in1 #bag1 #bah ,emission theory of light1 bases of the1 #de ----,newton espouses the theory1 and the results of this espousal1 #gg ,ether1 ,huyghens and ,euler advocate and defend the conception of an1 #dh1 #eh ----objected to by ,newton1 #eh ,euler espouses and defends the conception of an ether1 #dh1 #eh ,eusebius on the natural philosophers of his time1 #ac ,expansion by cold1 #ajd ,experiment1 uses of1 #c ,eye1 the1 its imperfections1 grown for ages towards perfection1 #h ----imperfect achromatism of the1 #bi1 note ,faraday1 ,michael1 his discovery of magneto-electricity1 #bah ',fits1' theory of1 #gc ----its explanation of ,newton's rings1 #gd ----overthrow of the theory1 #gg ,fizeau determines the velocity of light1 #bb ,fluorescence1 ,stokes's discovery of1 #afa ----the name1 #agd ,forbes1 ,professor1 polarizes and depolarizes heat1 #ahj ,foucault1 determines the velocity of light1 #bb ----his experiments on absorption1 #aig1 #aih ,fraunhofer1 his theoretical calculations respecting diffraction1 #hg ----his lines1 #aic ------their explanation by ,kirchhoff1 #aic ,fresnel1 and ,dr4 ,young1 #ej ----his theoretical calculations respecting diffraction1 #hg ----his mathematical abilities and immortal name1 #baj ,goethe on fluorescence1 #afe ,gravitation1 origin of the notion of the attraction of1 #ib ----strength of the theory of1 #adh ,grimaldi1 his discovery with respect to light1 #ef ----,young's generalizations of1 #ef ,hamilton1 ,sir ,william1 of ,dublin1 his discovery of conical refraction1 #bji ,heat1 generation of1 #f ----,dr4 ,draper's investigation respecting1 #aga ,helmholtz1 his estimate of the genius of ,young1 #ej ----on the imperfect achromatism of the eye1 #bi note1 #ca ----reveals the cause of green in the case of pigments1 #cg ,henry1 ,professor ,joseph1 his invitation1 #b ,herschel1 ,sir ,john1 his theoretical calculations respecting diffraction1 #hg ----first notices and describes the fluorescence of sulphate of quinine1 #afe ----his experiments on spectra1 #bja ,herschel1 ,sir ,william1 his experiments on the heat of the various colours of the solar spectrum1 #aga ,hooke1 ,robert1 on the colours of thin plates1 #fg ----his remarks on the idea that light and heat are modes of motion1 #fh ,horse-chestnut bark1 fluorescence of1 #afe ,huggins1 ,dr41 his labours1 #bje ,huyghens advocates the conception of ether1 #dh1 #eh ----his celebrated principle1 #hc ,huyghens on the double refraction of ,iceland spar1 #aab ,iceland spar1 #aji ----double refraction caused by1 #aaj ----this double refraction first treated by ,erasmus ,bartholinus1 #aab ----character of the beams emergent from1 #aad ----tested by tourmaline1 #aaf ----,knoblauch's demonstration of the double refraction of1 #ahe ,ice-lens1 combustion through1 #afg ,imagination1 scope of the1 #db ----note by ,maclaurin on this point1 #dc note ,janssen1 ,m41 on the rose-coloured solar prominences1 #bjd ,jupiter1 ,roemer's observations of the moons of1 #bj ,jupiter's distance from the sun1 #bj ,kepler1 his investigations on the refraction of light1 #ad1 #bjg ,kirchhoff1 ,professor1 his explanation of ,fraunhofer's lines1 #aic ----his precursors1 #bja ----his claims1 #bjc ,knoblauch1 his demonstration of the double refraction of heat of ,iceland spar1 #ahe ,lactantius1 on the natural philosophers of his time1 #ac ,lamy1 ,m41 isolates thallium in ingots1 #aic ,lesley1 ,professor1 his invitation1 #b ,light familiar to the ancients1 #e ----generation of1 #f1 #g ----spherical aberration of1 #h ----the rectilineal propagation of1 and mode of producing it1 #i ----illustration showing that the angle of incidence is equal to the angle of reflection1 #aj1 #aa ----sterility of the ,middle ,ages1 #ac ----history of refraction1 #ad ----demonstration of the fact of refraction1 #ad ----partial and total reflection of1 #af-bj ----velocity of1 #bj ----,bradley's discovery of the aberration of light1 #ba1 #bb ----principle of least time1 #bc ----,descartes and the rainbow1 #bd ----,newton's analysis of1 #bf1 #bg ----synthesis of white light1 #cj ----complementary colours1 #ca ----yellow and blue lights produce white by their mixture1 #ca ----what is the meaning of blackness8 #cb ----analysis of the action of pigments upon1 #cc ----absorption1 #cd ----mixture of pigments contrasted with mixture of lights1 #cg ----,wnsch on three simple colours in white light1 #ci note ----,newton arrives at the emission theory1 #de ----,young's discovery of the undulatory theory1 #di ----illustrations of wave-motion1 #eh ----interference of sound-waves1 #eh ----velocity of1 #fj ----principle of interference of waves of1 #fa ----phenomena which first suggested the undulatory theory #fb-fi ----soap-bubbles and their colours1 #fb-fe ----,newton's rings1 #fi-gg ----his espousal of the emission theory1 and the results of this espousal1 #gg ----transmitted light1 #gg ----diffraction1 #gg1 #hi ----origin of the notion of the attraction of gravitation1 #ib ----polarity1 how generated1 #ic ----action of crystals upon1 #ih ----refraction of1 #ajf ----elasticity and density1 #ajh ----double refraction1 #aji ----chromatic phenomena produced by crystals in polarized1 #aba ----the ,nicol prism1 #abb ----mechanism of1 #abe ----vibrations1 #abe ----composition and resolution of vibrations1 #abh ----polarizer and analyzer1 #abg ----recompounding the two systems of waves by the analyzer1 #abi ----interference thus rendered possible1 #aca ----chromatic phenomena produced by quartz1 #aci ----magnetization1 of1 #ada ----rings surrounding the axes of crystals1 #adc ----colour and polarization of sky1 #adi1 #aed ----range of vision incommensurate with range of radiation1 #aei ----effect of thallene on the spectrum1 #afb ----fluorescence1 #afb ----transparency1 #afg ----the ultra-red rays1 #agj ----part played in ,nature by these rays1 #age ----conversion of heat-rays into light-rays1 #agf ----identity of radiant heat and1 #agg ----polarization of heat1 #ahj ----principles of spectrum analysis1 #ahi ----spectra of incandescent vapours1 #aij ----,fraunhofer's lines1 and ,kirchhoff's explanation of them1 #aic ----solar chemistry1 #aie-aig ----demonstration of analogy between sound and1 #aih1 #aii ----,kirchhoff and his precursors1 #bja ----rose-coloured solar prominences1 #bjd ----results obtained by various workers1 #bje ----summary and conclusion1 #bjf ----polarized1 the spectra of1 #bbg ----measurement of the waves of1 #bcd ,lignum ,nephriticum1 fluorescence of1 #afd ,lloyd1 ,dr41 on polarization of heat1 #ahj1 #bji ,lockyer1 ,mr41 on the rose-coloured solar prominences1 #bje ,lycopodium1 diffraction effects caused by the spores of1 #hh ,magnetization of light1 #ada ,malus1 his discovery respecting reflected light through ,iceland spar1 #aae ----discovers the polarization of light by reflection1 #bjh ,masson1 his essay on the bands of the induction spark1 #bjb ,melloni1 on the polarization of heat1 #ahj ,metals1 combustion of1 #e1 #f ----spectrum analysis of1 #aij ----spectrum bands proved by ,bunsen and ,kirchhoff to be characteristic of the vapour of1 #aib ,mill1 ,john ,stuart1 his scepticism regarding the undulatory theory1 #adi ,miller1 ,dr41 his drawings and descriptions of the spectra of various coloured flames1 #bja ,morton1 ,professor1 his discovery of thallene1 #afb ,mother-of-pearl1 colours of1 #ij ,nature1 a savage's interpretation of1 #d ,newton1 ,sir ,isaac1 his experiments on the composition of solar light1 #bf ----his spectrum1 #bg ----dispersion1 #bg ----arrives at the emission theory of light1 #de ----his objection to the conception of an ether espoused and defended by ,huyghens and ,euler1 #eh ----his optical career1 #gj ----his rings1 #fi-gg ----his rings explained by the theory of 'fits1' #gc ----espouses the emission theory1 #gg ----effects of this espousal1 #gg ----his idea of gravitation1 #ib ----his errors1 #bjh ,nicol prism1 the1 #abb ,ocean1 colour of the1 #ce ,o,ersted1 discovers the deflection of a magnetic needle by an electric current1 #agf ,optics1 science of1 #d ,pasteur referred to1 #bai ,physical theories1 origin of1 #da-dd ,pigments1 analysis of the action of1 upon light1 #cc ----mixture of1 contrasted with mixture of lights1 #cg ----,helmholtz reveals the cause of the green in the case of mixed blue and yellow pigments1 #cg ----impurity of natural colours1 #cg ,pitch of sound1 #ei ,plcker1 his drawings of spectra1 #bjb ,polariscope1 stained glass in the1 #acj1aca ----unannealed glass in the1 #acf ,polarity1 notion of1 how generated1 #ic ----atomic1 #ic-if ----structural arrangements due to1 #if ----polarization of light1 #aab ----tested by tourmaline1 #aaf ----and by reflection and refraction1 #aai ----depolarization1 #abj ,polarization of light1 #aab ----circular1 #adj ----sky-light1 #adi1 #aeg ----of artificial sky1 #aef ----of radiant heat1 #ahj ,polarizer and analyzer1 #abg ,poles of a magnet1 #ic ,powell1 ,professor1 on polarization of heat1 #ahj ,prism1 the ,nicol1 #abb ,quartz1 chromatic phenomena produced by1 #aci ,radiant heat1 #agb ----diathermancy1 or perviousness to radiant heat1 #agc ----conversion of heat-rays into light rays1 #agd ----formation of invisible heat-images1 #agi ----polarization of1 #ahj ----double refraction1 #ahb ----magnetization of1 #ahd ,rainbow1 ,descartes' explanation of the1 #bd ,refraction1 demonstration of1 #ad ,refraction of light1 #ajf ----double1 #aji ,reflection1 partial and total1 #af-bj ,respighi1 results obtained by1 #bje ,ritter1 his discovery of the ultraviolet rays of the sun1 #aei ,roemer1 ,olav1 his observations of ,jupiter's moons1 #bj ----his determination of the velocity of light1 #ba ,rubidium1 discovery of1 #aic ,rusting of iron1 what it is1 #e ,schwerd1 his observations respecting diffraction1 #hg ,science1 growth of1 #agf1 #bjc ,scoresby1 ,dr41 succeeds in exploding gunpowder by the sun's rays conveyed by large lenses of ice1 #afg ,secchi1 results obtained by1 #bje ,seebeck1 ,thomas1 discovers thermo-electricity1 #agf ----discovers the polarization of light by tourmaline1 #bjh ,selenite1 experiments with thick and thin plates of1 #abd ,silver spectrum1 analysis of1 #aij1 #aia ,sky-light1 colour and polarization of1 #adi1 #aed ----generation of artificial skies1 #aeb ,snell1 ,willebrord1 his discovery1 #ad ----his law1 #ae1 #bd ,soap-bubbles and their colours1 #fc1 #fe ,sound1 early notions of the ancients respecting1 #ea ----interference of waves of1 #eh ----pitch of1 #ei ----analogies of light and1 #ef ----demonstration of analogy between1 and light1 #aih1 #aii ,sonorous vibrations1 action of1 #acd ,spectrum analysis1 principles of1 #ahi ,spectra of incandescent vapours1 #aij ----discontinuous1 #aia1 #aib ----of polarized light1 #bbg ,spectrum bands proved by ,bunsen and ,kirchhoff to be characteristic of the vapour1 #aib ----its capacity as an agent of discovery1 #aic ----analysis of the sun and stars1 #aic ,spottiswoode1 ,mr4 ,william1 #abc1 #bbg ,stewart1 ,professor ,balfour1 #bjb ,stokes1 ,professor1 results of his examination of substances excited by the ultra-violet waves1 #afa ----his discovery of fluorescence1 #afb ----on fluorescence1 #afe ----nearly anticipates ,kirchhoff's discovery1 #aih1 #bjb ,striated surfaces1 colours of1 #hi ,sulphate of quinine first noticed and described by ,sir ,john ,herschel1 #afe ,sun1 chemistry of the1 #aie ,sun1 rose-coloured solar prominences1 #bjd ,talbot1 ,mr41 his experiments1 #bja ,tartaric acid1 irregular crystallization of1 and its effects1 #aca ,thallene1 its effect on the spectrum1 #afb ,thallium1 spectrum analysis of1 #aij1 #aia ----discovery of1 #aic ----isolated in ingots by ,m4 ,lamy1 #aic ,theory1 relation of1 to experience1 #ia ,thermo-electric pile1 #agf ,thermo-electricity1 discovery of1 #agf ,tombeline1 ,mont1 inverted image of1 #ai ,tourmaline1 polarization of light by means of1 #aab ,transmitted light1 reason for1 #gg ,transparency1 remarks on1 #afg ,ultra-violet sun-rays1 discovered by ,ritter1 #aei ----effects of1 #afj ,ultra-red rays of the solar spectrum1 #aga ----part played by the1 #agc ,undulatory theory of light1 bases of the1 #dg ----,sir ,david ,brewster's chief objection to the1 #dg ,undulatory theory of light1 ,young's foundation of the1 #di ----phenomena which first suggested the1 #fb1 #fi ----,mr4 ,mill's scepticism regarding the1 #adc ----a demonstrated verity in the hands of ,young1 #baj ,vassenius describes the rose-coloured solar prominences in #agcc1 #bjd ,vitellio1 his skill and conscientiousness1 #ad ----his investigations respecting light1 #bjg ,voltaic battery1 use of1 and its production of heat1 #f1 #g ,water1 deportment of1 considered and explained1 #aje1 #ajf ,waves of water1 #ea ----length of a wave1 #eb ----interference of waves1 #ec-ee ,wertheim1 ,m41 his instrument for the determination of strains and pressures by the colours of polarized light1 #acd ,wheatstone1 ,sir ,charles1 his analysis of the light of the electric spark1 #bjb ,whirlpool ,rapids1 illustration of the principle of the interference of waves at the1 #ee ,willigen1 ,van der1 his drawings of spectra1 #bjb ,wollaston1 ,dr41 first observes lines in solar spectrum1 #aic ----discovers the rings of ,iceland spar1 #bji ,woodbury1 ,mr41 on the impurity of natural colours1 #cg ,wnsch1 ,christian ,ernst1 on the three simple colours in white lights1 #ci note ----his experiments1 #ci note ,young1 ,dr4 ,thomas1 his discovery of ,egyptian hieroglyphics1 #di2 ----and the undulatory theory of light1 #di ----,helmholtz's estimate of him1 #ej ----ridiculed by ,brougham in the ',edinburgh ,review1' #ej ----generalizes ,grimaldi's observation on light1 #ef1 #eg ----photographs the ultra-violet rings of ,newton1 #afj