,illustration3 ,,colour-,,patch ,,apparatus4 ,,the ,,romance ,,of ,,science4 ,,colour ,,measurement ,,and ,,mixture4 ,with ,numerous ,illustrations4 ,,by ,,captain ,w4 de ,w4 ,,abney1 ,c4,b41 ,r4,e41 ,d4,c4,l41 ,f4,r4,s4 ,,published ,,under ,,the ,,direction ,,of ,,the ,,committee ,,of ,,general ,,literature ,,and ,,education ,,appointed ,,by ,,the ,,society ,,for ,,promoting ,,christian ,,knowledge4 ,,society ,,for ,,promoting ,,christian ,,knowledge4 ,,london3 ,,northumberland ,,avenue1 ,w4,c42 #dc1 ,,queen ,,victoria ,,street1 ,e4,c4 ,,brighton3 #ace1 ,,north ,,street4 ,,new ,,york3 ,e4 ,j4 ,b4 ,,young ,,co4 #ahia4 ,,preface4 ,some ten years ago there were three measurements of the spectrum which ,i set myself to carry out2 the last two1 at all events1 involving new methods of experimenting4 ,the three measurements were3 7#ast7 ,the heating effect2 7#bnd7 the luminosity2 and 7#crd7 the chemical effect on various salts1 of the different rays of the spectrum4 ,the task is now completed1 and it was in carrying out the second part of it that ,general ,festing1 who joined me in the research1 and myself were led into a wider study of colour than at first intended1 as the apparatus we devised enabled us to carry out experiments which1 whilst difficult under ordinary circumstances1 became easy to make4 ,on two occasions1 at the invitation of the ,society of ,arts1 ,i have delivered a short course of lectures on the subject of ,colour1 and naturally ,i chose to treat it from the point of view of our own methods of experimenting2 and these lectures1 expanded and modified1 form the basis of the present volume4 ,as a treatise it must necessarily be incomplete1 as it scarcely touches on the history of the subject--a part which must always be of deep interest4 ,the solely physiological aspect of colour has also been scarcely dealt with2 that part which the physicist can submit to measurement being that which alone was practicable under the circumstances4 ,w4 ,de ,w4 ,abney4 ,south ,kensington1 #ast ,may1 #ahia4 ,,contents4 ,,chapter ,i4 ,sources of ,light--,reflected ,light--,reflection from ,roughened ,surfaces--,colour ,constants p4 #aa ,,chapter ,,ii4 ,a ,standard of ,light--,formation of the ,spectrum by ,prisms and by the ,diffraction ,grating--,wave-lengths of the principal ,fraunhofer ,line--,position of ,colours in the ,spectrum p4 #ag ,,chapter ,,iii4 ,the ,visible and ,invisible ,parts of the ,spectrum--,methods for showing the ,existence of the ,invisible ,portions--,phosphorescence--,photograph y of the ,dark ,rays--,thermo-,electric ,currents p4 #cj ,,chapter ,,iv4 ,description of ,colour ,patch ,apparatus--,rotating ,sectors--,method of making a ,scale for the ,spectrum p4 #da ,,chapter ,v4 ,absorption of the ,spectrum--,analysis of ,colour--,vibrations of ,rays--,absorption by ,pigments--,phosphorescence--,interferen ce p4 #ea ,,chapter ,,vi4 ,scattered ,light--,sunset ,colours--,law of the ,scattering by ,fine ,particles--,sunset ,clouds--,luminosities of ,sunlight at different ,altitudes of the ,sun p4 #fb ,,chapter ,,vii4 ,luminosity of the ,spectrum to ,normal-eyed and ,colour-blind ,persons--,method of determining the ,luminosity of ,pigments--,addition of one ,luminosity to another p4 #gf ,,chapter ,,viii4 ,methods of ,measuring the ,intensity of the ,different ,colours of the ,spectrum1 reflected from ,pigmented ,surfaces--,templates for the ,spectrum p4 #hh ,,chapter ,,ix4 ,colour ,mixtures--,yellow ,spot in the ,eye--,comparison of ,different ,lights--,simple ,colours by ,mixing ,simple ,colours--,yellow and ,blue from ,white p4 #aab ,,chapter ,x4 ,extinction of ,colour by ,white ,light--,extinction of ,white ,light by ,colour p4 #abf ,,chapter ,,xi4 ,primary ,colours--,molecular ,swings--,colour ,sensations--,sensations absent in the ,colour-blind p4 #acc ,,chapter ,,xii4 ,formation of ,colour ,equations--,koenig's ,curves--,maxwell's ,apparatus and ,curves p4 #adg ,,chapter ,,xiii4 ,match of ,compound ,colours with ,simple ,colours--,all ,colours reduced to ,numbers--,method of ,matching a ,colour with a ,spectrum ,colour and ,white ,light p4 #aef ,,chapter ,,xiv4 ,complementary ,colours--,complementary ,pigment ,colours--,measurement of ,complementary ,colours p4 #afg ,,chapter ,,xv4 ,persistence of ,images on the ,retina--,the ,use of ,coloured ,discs p4 #agi ,,chapter ,,xvi4 ,contrast ,colours--,measurement of ,contrast ,colours--,fatigue of the ,eye--,after-,images p4 #aif ,,list ,,of ,,illustrations4 ,,fig4 ,,page ,colour-patch apparatus ,frontispiece #a4 ,spectrum of sunlight #ah #b4 ,carbon poles of an electric light #bj #c4 ,curve for converting prismatic spectrum into wave-lengths #bh #d4 ,the thermopile #ce #e4 ,heating effect of different sources of radiation #ch #f4 ,colour-patch apparatus #db #g4 ,rotating sectors #de #h4 ,spectrum of ,carbon ,sodium and ,lithium #dh #i4 ,interference bands #fj #aj4 ,absorption of rays by the atmosphere #fh #aa4 ,luminosity curve of spectrum of the positive pole of the electric light #gi #ab4 ,rectangles of white and vermilion #hb #ac4 ,arrangement for measuring the luminosities of pigments #hc #ad4 ,measurement of the intensity of rays reflected from white and coloured surfaces #hh #ae4 ,intensity of rays reflected from vermilion1 emerald green1 and ,french ultramarine #ib #af4 ,method of obtaining two patches of identical colour #ie #ag4 ,absorption by red1 blue1 and green glasses #ii #ah4 ,light reflected from metallic surfaces #ajj #ai4 ,intensities of vermilion1 carmine1 mercuric iodide1 and ,indian red #aja #bj4 ,intensities of gamboge1 ,indian yellow1 cadmium yellow1 and yellow ochre #aja #ba4 ,intensities of emerald green1 chromous oxide1 and terre verte #ajc #bb4 ,intensities of indigo1 ,antwerp blue1 cobalt1 and ,french ultramarine #ajd #bc4 ,method of obtaining a colour template #ajd #bd4 ,template of carmine #ajf #be4 ,template of luminosity of white light #ajh #bf4 ,absorption of transmitted and reflected light by ,prussian blue and carmine #ajg #bg4 ,collimator for comparing the intensity of two sources of light #aji #bh4 ,spectrum intensities of sunlight1 gaslight1 and blue sky #aji #bi4 ,comparison of sun and sky lights #aaa #cj4 ,slide with slits to be used in the spectrum #aac #ca4 ,screen on which to match gamboge #aaf #cb4 ,diaphragm in front of prism #abh #cc4 ,curve of sensitiveness of silver bromo-iodide #acf #cd4 ,curves of colour sensations #aci #ce4 ,koenig's curves of colour sensations #aea #cf4 ,maxwell's colour-box #aeb #cg4 ,maxwell's curves of colour sensations #aed #ch4 ,chromatic circle #afh #ci4 ,disc to cause alternate opening and closing of two slits #agi #dj4 ,disc painted blue and red #aha #da4 ,electro-motor with discs attached #ahc #db4 ,method of cutting disc to allow an overlap of a second disc #ahd #dc4 ,arrangement to find value of gamboge in terms of emerald green and vermilion #ahh #dd4 ,disc arranged to give approximately all the spectrum colours #aib #de4 ,method of showing contrast colours #aif ,,colour ,,measurement ,,and ,,mixture4 ,,chapter ,i4 ,sources of ,light--,reflected ,light--,reflection from ,roughened ,surfaces--,colour ,constants4 ,there is nothing1 perhaps1 in our everyday life which appeals more to the mind than colour1 yet so accustomed are the generality of mankind to its influence that but few stop to inquire the why and wherefore of its existence1 or its cause4 ,to those few1 however1 there is a source of endless and boundless enjoyment in its study2 for in the realms of physical and physiological science there is perhaps no other subject in which experiments give results so fascinating and often so beautiful4 ,although its serious study must be undertaken with a clear mind1 a good eye1 and a fair supply of patience1 yet a general idea of the subject may be grasped by those who are possessed of but ordinary intelligence4 ,colour phenomena are encountered nearly every day of one's life1 and the fact that they are so frequently met with1 prevents that attention to them1 or even their remark4 ,who amongst us1 for instance1 has noticed the existence of what are called positive and negative after images1 after looking at some strongly illuminated object1 or would have gauged the fact that a certain portion of the nervous system can be fatigued by a colour1 and give rise to images of its complementary1 had not an enterprising advertiser1 who manufactures a household necessary1 drawn attention to it in a manner that could not be misunderstood4 ,if on an autumn afternoon we pass through a garden whilst it is still perfectly light1 we can notice the gorgeous colouring of the flowers1 and appreciate with the eyes the beauty of each tint4 ,as evening comes on the tints darken1 the darkest-coloured flowers begin to lose their colour1 and only the brightest strike the eye4 ,when night still further closes in every colour goes1 though the outlines of the flowers may still be distinguished2 and it would not be impossible1 in some parts1 to see a tiny speck of pale light upon the ground amongst them4 ,this speck of light we should know from experience to be the light from a glow-worm4 ,why is it that we lose the colour of the flowers and recognize the tiny light from this small worm8 ,the reason for the one is that in order for objects which are not self-luminous to be seen at all1 light must fall on them and illuminate them1 and the light which they reflect may be coloured if they possess the qualities to reflect coloured light4 ,the glow-worm's light is seen1 not because it does not emit light in the day-time1 but because the eye1 being limited in sensitiveness1 is unable to distinguish it when it is flooded with the light of day4 ,the glow-worm1 however1 is self-luminous1 as is shown by the fact that it emits light in the dark1 the light itself being slightly coloured if compared with that of day4 ,that a candle-flame or the sun is self-luminous is an axiom1 and need not be philosophised upon2 but what must be impressed on the reader is1 that though an object which requires to be illuminated to be seen1 is not self-luminous1 yet when illuminated it does in fact become a source of illumination to the eye1 although the light is only light reflected from its surface4 ,it is a point worth remembering that the rougher the surface of an object1 the brighter to the eye it will be4 ,that is1 a coloured object when polished will be a bad secondary source of illumination1 as the light incident upon it will be very nearly reflected from the surface1 according to the ordinary laws of reflection2 but if it be roughened it will become a much better source1 as the roughnesses1 though obeying the laws of reflection1 will reflect light in every direction4 ,a good example of this is an ordinary sheet of glass4 ,light from a source falling on its surface is scarcely reflected in any direction except in that determined by the ordinary laws of reflection1 and it will be scarcely visible to the eye4 ,grind its surface1 however1 and the innumerable facets caused by the grinding will reflect light back to the eye in whatever position it be placed1 and will thus be distinctly seen4 ,we may here premise that even the roughest surface will reflect a greater percentage--varying greatly according to the nature of the surface--of light in the direction which it would do if it were a smooth surface than in any other2 and in taking measurements of the light irregularly reflected from a rough surface1 this fact must be borne in mind4 ,not only must we know how colour is produced1 but we must also be able to refer it to some standard which shall be readily reproduced1 and which shall be unalterable4 ,there are two variable factors which have to be taken into account in colour experiments3 the first is the quality of light which illuminates the object1 and the second is the sensitiveness of the eye which perceives it1 as light is only a sensation which is recognized by the brain through the medium of the eye4 ,we shall1 as we go on1 see that different qualities of light may cause objects to appear of different hues1 and further that eyes may vary in perceptive power1 to an extent of which the large majority of people are not aware4 ,hence it becomes necessary as far as possible to eliminate these variables4 ,the task which we have set ourselves to perform then1 is first to find a suitable light for experimental work1 and next to endeavour to refer colour to an eye which has no abnormal defects4 ,this being accomplished1 we have then to find means to measure the different constants which are involved in colour1 and to refer the measurements to some standard4 ,colour constants are three1 viz4 hue1 luminosity1 and purity2 and it will be seen that if these three are determined1 the measurement of the colour is complete4 ,perhaps the meaning of these terms may require to be explained4 ,the hue of a colour is what in common parlance is often called the colour4 ,thus we talk of rose1 violet1 magenta1 emerald green1 and so on1 but for measuring purposes the hue had best be referred to the spectrum colours as a standard 7the means of doing so will be shortly explained71 for they are simple colours1 which can be expressed by numbers4 ,compound colours1 which it may be said are invariably to be found in nature1 being mixtures of simple colours1 can be just as readily referred to the spectrum4 ,by the luminosity of a colour we mean its brightness1 the standard of reference being the brightness of a white surface when illuminated by the same white light4 ,by the purity of a colour we mean its freedom from admixture with white light4 ,an example of different degrees of purity will be found in washes of water-colours of different tenuity4 ,thus if we wash a sheet of paper with a light tint of carmine1 the whiteness of the paper is not obliterated2 if we pass another wash over it the whiteness of the paper is lessened1 and so on4 ,the lightest tint is that which is most lacking in purity4 ,,chapter ,,ii4 ,a ,standard ,light--,formation of the ,spectrum by ,prisms and by the ,diffraction ,grating--,wave-lengths of the principal ,fraunhofer ,line--,position of ,colours in the ,spectrum4 ,as we have to turn to the spectrum for pure and simple colours1 from which we may produce any compound colour we may wish to deal with1 we will first consider the light with which we shall form it4 ,a spectrum may be produced from any source of light1 such as sunlight1 limelight1 the electric light1 gaslight1 or incandescence electric light1 as also from incandescent vapours1 or gases2 but it is only a solid which is1 or is rendered incandescent1 that will give us a continuous spectrum1 as it is called1 that is1 a spectrum which is unbroken by gaps of non-luminosity1 or sudden change of brightness1 throughout its length4 ,fig4 #a4--,spectrum of ,sunlight4 ,the great desideratum for the study of colour is a light which not only gives a practically continuous spectrum1 but one which is produced by the radiation of matter which is black when cold1 and which can be kept at a constantly high temperature4 ,we have purposely said black in the sentence above1 since it is believed that differently coloured bodies1 when heated to equal temperatures1 might not give the same relative intensities to the different parts of the spectrum1 the variation being dependent on the colour of the heated body4 ,a black body must always give the same visible spectrum when heated to the same temperature4 ,the spectrum of sunlight 7,fig4 #a7 is not continuous1 as we find it crossed by an innumerable number of fine lines of varying breadth and blackness4 ,this want of continuity would not be fatal to its adoption were it possible to use it outside the limits of our atmosphere1 as then1 unless the temperature of the sun itself changed1 the spectrum produced would be invariable2 but unfortunately the relative brightness or luminosity of the different parts of the spectrum varies from day to day1 and hour to hour1 according to the height of the sun above the horizon 7see ,chap4 ,,vi472 and its integral brightness varies according to the clearness of the sky4 ,it is evident then1 that1 as a reference light1 sunlight is most unsuitable1 so we may dismiss it from our possible standards4 ,fig4 #b4--,the ,carbon ,poles of an ,electric ,light4 ,by the process of elimination we may arrive at the light upon which we can rely1 for the purpose we have in view1 viz4 the production of a spectrum of moderate size1 and sufficiently bright to be well viewed when projected upon a screen4 ,for some purposes1 as for instance in becoming acquainted with the general character of the spectrum1 a feebler light1 such as gaslight1 or light from electrical glow lamps1 may be employed1 since the spectrum may be viewed directly by the eye without the intervention of a screen4 ,they have two drawbacks for our object3 one being the want of general intensity1 and the other the feeble luminosity of blue and violet rays in their spectrum 7see page #aaj74 ,the limelight we can also dismiss for want of steadiness4 ,its whiteness and luminosity varies according to the oxygen playing on the lime cylinder1 rendering the relative intensities of the different parts of the spectrum so erratic as to make it unreliable4 ,this leaves the 7electric7 arc-light as the only one which is really available4 ,remember how the arc-light is produced4 ,a current of electricity passes between the ends of two thick black carbon rods1 or poles as they are called1 through an air space of small interval1 and the passage of the current renders the tips of these rods white-hot 7,fig4 #b74 ,the centre of the end of one pole1 called the positive pole1 where a crater-like depression is formed1 is the part which attains the whitest heat1 and its temperature seems to be constant1 and to be that of the volatilization of carbon4 ,numerous experiments have been made by the writer1 and he has found that the light emitted by this crater in the positive pole is1 within the limits of the error of observation1 always of the same whiteness1 and consequently gives a spectrum which is unvarying in the proportionate intensities of the different colours4 ,when the experiments made to determine the luminosity of the spectrum are described1 the method of ascertaining this will be readily understood4 ,in the spectrum produced by this light there are two places in the violet where there are bands of violet lines slightly brighter than the general spectrum4 ,they are principally due to the light emitted from the incandescent vapour of carbon1 which is volatilized and plays between the two poles 7see ,fig4 #b72 but as these bands are of but small visual intensity1 and situated towards the limit of the visible spectrum1 they do not interfere with eye-measures of colours1 though they do1 to a certain extent1 to the analysis of radiation by photography4 ,if we throw the positive pole a little behind the negative pole we can1 however1 considerably mitigate this evil4 ,we can separate the carbon rods to such a degree that the white-hot crater faces the observer1 and a good deal of the arc is hidden4 ,this is well seen in the figure4 ,we have now described the light we have adopted1 and the reasons for adopting it2 and having obtained our light1 we can now consider by what plan we shall form our spectrum4 ,there are two ways open to us--one by glass prisms1 and the other by a diffraction grating4 ,glass prisms separate white light1 or indeed any light1 into its components1 from the fact that the refraction of each coloured ray differs from every other4 ,thus the red rays are least refracted1 and the violet the most1 and the yellow1 green and blue are intermediate between them1 being placed in the order of least refrangibility4 ,between these there is of course every shade of simple colour1 one melting into the other4 ,in order to form a pure and bright spectrum with prisms1 in a room of limited dimensions1 we have to use certain auxiliary apparatus which are not positively essential1 though convenient4 ,the real essentials to form a spectrum are a narrow slit1 a glass prism1 with perfectly plane faces1 and a lens4 ,if this be the only apparatus available1 the slit must be placed at a long distance from the prism1 the beam of light must pass through the slit on to the prism1 and the lens must be placed at such a distance from the slit that it forms a sharp image on a screen4 ,when the light passes through the prism1 the screen will have to be rotated in the arc of a circle1 so that its distance from the slit measured along the line of the ray to the prism1 and from the prism to the screen1 is the same as it would be without the intervening prism4 ,an apparatus of this description is not convenient1 however1 as it requires much more space than is often available4 ,if a lens be placed between the slit and the prism1 at exactly its focal length from the former1 the light entering the slit will1 after passage through the lens1 emerge as parallel rays1 that is1 they will emerge as they would do if the slit were placed at an infinite distance from the observer4 ,the focal length of this collimating lens need not be greater than twelve to eighteen inches1 so that the great space required by the cruder apparatus is very much curtailed4 ,the lens and slit are mounted one at each end of a tube of the necessary length1 and are thus handy to use4 ,instead of one prism two or three may be used1 giving an angular dispersion of the spectrum two or three times respectively greater than that which would be given by only one prism2 consequently to obtain a given length of spectrum with the increased dispersion1 the focal length of the lens used to focus the image on the screen may be diminished4 ,the drawback to the use of prisms is that the dispersion of the red end of the spectrum is much less than that of the blue end1 and is apt to give a false impression as to the relative luminosities of1 and length of spectrum occupied by1 the different colours4 ,in some text-books it is told us that the diffraction grating gives us a dispersion which is in exact relation to the wave-length4 ,this is not true1 however1 as it can only give one small portion in such relationship1 and that only when it is specially set for the purpose4 ,the subject of diffraction is one into which it would be foreign to our purpose to wander4 ,we may say that for measures such as we shall make1 it is handier to employ prisms1 as the prismatic spectrum is more intense than the diffraction spectrum4 ,this can be readily understood when we consider the subject even superficially4 ,if we throw a beam of light on a grating which contains perhaps some #ad1jjj parallel lines in the space of one inch in width1 the lines being ruled on a plane and bright metallic surface1 and receive the reflected beam on a screen1 the appearance that is presented is a white central spot1 together with six or seven spectra of gradually diminishing brightness on each side of it1 all except the first pair overlapping one another4 ,that these different spectra do exist can be readily shown by placing in the beam a piece of red glass1 when symmetrical pairs of the red part of the spectrum will be found1 one of each pair being on opposite sides of what will now be the central red spot4 ,half the light falling on the grating is concentrated in this central spot1 and the remaining half goes to form the spectra2 the pair nearest the central spot being the brightest4 ,we thus are drawn to the conclusion that at the outside we can only have less than one-quarter of the incident light to form the brightest spectrum we can use4 ,with two good prisms we use at last three-fourths of the incident light1 so that for the same length of spectrum we can get at least three times the average brightness that we should get were we to employ a diffraction grating4 ,we must now refresh the reader's memory with a few simple facts about light1 in order that our meaning may be clear when we speak of rays of different wave-lengths4 ,every colour in the spectrum has a different wave-length1 and it is owing to this difference in wave-length that we are able to separate them by refraction1 or diffraction1 and to isolate them4 ,light1 or indeed any radiation1 is caused by a rhythmic oscillation of the impalpable medium which we1 for want of a better term1 call ether1 and the distance between two of these waves which are in the same phase is called the wave-length of the particular radiation4 ,the extent of the oscillation is called the amplitude1 which when squared is in effect a measure of the intensity of the radiation4 ,thus at sea the distance between the crests of two waves is the wave-length1 and the height from trough to crest the amplitude2 and the intensity1 or power of doing work1 of two waves of the same wave-lengths but of different heights1 is as the square of their heights4 ,thus1 if the height of one were one unit1 and of the other two units1 the latter could do four times more work than the former4 ,the waves of radiation which give the sensation of colour in the spectrum vary in length1 not perhaps to the extent that might be imagined1 considering the great difference that is perceived by the eye1 but still they are markedly different4 ,the fact that the spectrum of sunlight is not continuous1 but is broken up by innumerable fine lines1 has already been alluded to4 ,the position of these lines is always the same1 as regards the colour in which they are situated1 and is absolutely fixed directly we know their wave-length2 hence if we know the wave-lengths of these lines1 we can refer the colour in which they lie to them4 ,now some lines of the solar-spectrum are blacker and consequently more marked than others1 and instead of referring the colours to the finer lines1 we can refer them to the distance they are from one or more of these darker lines1 where these latter are absolutely fixed2 in fact they act as mile-stones on a road4 ,in the red we have three lines in the solar spectrum1 which for sake of easy reference are called ,a1 ,b and ,c2 in the orange we have a line called ,d1 in the green a line called ,e1 in the blue ,f1 in the violet ,g1 and in the extreme violet ,h4 ,these lines are our fiducial lines1 and all colours can be referred to them4 ,the following are the wave-lengths of these lines1 on the scale of #a_/aj1jjj1jjj of a millimetre as a unit ,a #geid ,b #fhfg ,c #fefb ,d #ehib ,e #ebfi ,f #dhfa ,g #dcjg ,h #cifh ,when the spectrum is produced by prisms the intervals between these lines are not proportional to the wave-lengths1 and consequently if we measure the distance of a ray in the spectrum from two of these lines1 we have to resort to calculation1 or to a graphically drawn curve1 to ascertain its wave-length4 ,for the purpose of experiments in colour the graphic curve from which the wave-length can immediately be read off is sufficient4 ,the following diagram 7,fig4 #c7 shows how this can be done4 ,the names and range of the principal colours which are seen in the spectrum has been a matter of some controversy4 ,professor ,rood has1 however1 made observations which may be accepted as correct with a moderately bright spectrum4 ,if the spectrum be divided into #ajjj parts between ,a in the red1 and ,h1 the limit of the violet1 he makes the following table of colours4 ---------------------------------------- ------- ,scale4 ,colour4 ---------------------------------------- ------- #j to #adi ,red4 #adi to #aid ,orange red4 #aid to #baj ,orange4 #baj to #bcj ,orange yellow4 #bcj to #bdj ,yellow4 #bdj to #cdd ,yellow green and green yellow4 #cdd to #ddg ,green and blue green4 #ddg to #die ,azure blue4 #die to #hjf ,blue and blue violet4 #hjf to #ajjj ,violet4 ---------------------------------------- ------- ,fig4 #c4--;,curve for converting the ,prismatic ,spectrum into ,wave-lengths4 ,in the above scale 7,fig4 #c7 ,a #j1 ,b #gdj1 ,c #aabg1 ,d #bbjc1 ,e #cfca1 ,f #dicb1 ,g #gecf1 ,h #ajjj4 ,these are the main subdivisions of colour1 but it must be recollected that one melts into the other4 ,when the spectrum is very bright the colours tend to alter in hue2 thus the orange becomes paler1 and the yellow whiter1 and the blue paler4 ,on the other hand1 if the spectrum be diminished in brightness the tendency is for the colours to change in the opposite direction4 ,thus the yellow almost disappears and becomes of a green hue1 whilst the orange becomes redder1 and the spectrum itself becomes shorter to the eye than before4 ,let us strictly guard ourselves1 however1 from the criticism that all eyes see not alike4 ,suffice it to say that the above table is correct for the ordinary or normal eye1 and does not necessarily apply to those who have defective vision as regards colour sensation4 ,,chapter ,,iii4 ,the ,visible and ,invisible ,parts of the ,spectrum--,methods for showing the ,existence of the ,invisible ,portions--,phosphorescence--,photograph y of the ,dark ,rays--,thermo-,electric ,currents4 ,we are apt to forget1 when looking at the spectrum1 that what the eye sees is not all that is to be found in the prismatic analysis of light4 ,the spectrum1 it must be recollected1 is not limited to those rays which the eye perceives4 ,there are rays both beyond the extreme violet and below the extreme red1 which exist and which exercise a marked effect on the world's economy4 ,thus1 rays beyond the violet are those which with the violet and the blue rays principally affect vegetation1 enabling certain chemical changes to take place which are necessary for its growth and health2 whilst the rays below the red are those possessing the greatest amount of energy1 and if they fall upon bodies which absorb them1 as very nearly all bodies do to a certain extent1 they heat them4 ,the warmth we feel from sunlight is principally due to the dark rays which lie below the red of the spectrum4 ,the existence of both kinds of these dark rays may be demonstrated in a very simple manner by the effect that they produce on certain bodies4 ,for instance1 there is a yellow dye with which cheap ribbon is dyed1 which if placed in the spectrum and beyond the violet causes a visible prolongation of the spectrum4 ,the light in the newly-seen and once invisible part of the spectrum is yellow1 the colour of the ribbon itself4 ,in fact1 the whole of that part of the spectrum1 which on the white screen is seen as blue and violet1 becomes yellow1 the red and green remaining unchanged4 ,this change in colour is due to fluorescence1 a phenomenon of light which ,sir ,g4 ,stokes found was caused by an alteration in the lengths of the waves of light when reflected from certain bodies4 ,it is not meant to imply by this that the wave-length of any ray falling on a body can be altered by reflection1 but only that the body itself on which the rays fall emits rays of light which are not of the same wave-length as those which fall upon it4 ,now it is a fact that the rays that lie beyond the violet1 and which are ordinarily invisible1 are shorter than the violet rays1 and that these are shorter than the yellow rays4 ,it follows therefore that when1 what we may now call1 the ultra-violet rays fall on the yellow dyed ribbon1 the waves emitted by it are so lengthened that they appear yellow to the eye instead of dark1 violet1 or blue4 ,we can also brush a solution of quinine on the screen1 and immediately the place where the ultra-violet rays fall is illuminated by a violet light4 ,we do not see the ultra-violet rays themselves1 but only the rays of increased wave-length1 which are emitted by their effect on the sulphate of quinine4 ,common machine oil as used for engines also emits greenish rays when excited by the ultra-violet rays1 and a very beautiful colour it is4 ,fluorescence then is one means of demonstrating the existence of the ultra-violet rays--or ,ritter's rays as they were formerly called1 after their discoverer--in a very simple manner4 ,the method of rendering the effects of the infra-red rays visible to the eye is also interesting4 ,all1 or at all events most1 of our readers have seen ,balmain's luminous paint4 ,a glass or card coated with this substance1 which is essentially a sulphide of calcium1 when exposed to the light of the sun1 or of the electric arc1 and then taken into comparative darkness1 is seen to shine with a peculiar violet-coloured light4 ,if when thus excited we place it in a bright spectrum for some little time1 we shall find on shutting off the light that where the ultra-violet and blue fell on it1 the violet light is intenser than the light of the main part of the screen2 where the yellow fell there is neither increase or diminution in brightness2 but that in the red it becomes darker1 and also beyond the limit of the visible spectrum1 indicating the existence of rays beyond1 which through their greater length have not the power of affecting the eye4 ,if the spectrum be shut off1 however1 very soon after it falls on the plate1 it has been asserted that the red and infra-red rays have increased the brightness of that particular part of the plate on which they fell4 ,at first these two observations seem to contradict one another2 they do not in reality4 ,we may expose a tablet of ,balmain's paint to light1 and place a heated iron in contact with the back of the plate2 we shall then find that the iron produces a bright image of its surface on a less bright background4 ,this bright image will gradually fade away1 and the same space will eventually become dark compared with the rest of the plate4 ,the reason of this is clear4 ,when light excites the paint a certain amount of energy is poured into it1 which it radiates out slowly as light4 ,when the hot iron is placed in contact with it1 the heat causes the light to radiate more rapidly1 and consequently with greater intensity1 at the part where its surface touches1 and the energy of that particular portion becomes used up4 ,when the energy of radiation of this part becomes less than that of the rest of the tablet1 its light must of necessity be of less brightness than that of the background1 with which the heated iron has had no contact4 ,for this reason the image of the iron subsequently appears dark4 ,we shall see presently1 and as before stated1 that the principal heating effect of the spectrum lies in the red and infra-red1 and it is owing to the heating of the paint by these rays that the image might be at first slightly brighter than the background1 and subsequently darker4 ,there is another way in which the existence of both the ultra-violet and infra-red rays can be demonstrated1 and that is by means of photography4 ,if we place an ordinary photographic plate in the spectrum and develop it1 we shall find that besides being affected by the blue and violet rays1 it is also affected by the rays beyond the violet1 the energy of these rays being capable of causing a decomposition of the sensitive silver salt4 ,if quartz prisms and lenses be used1 and the electric light be the source of illumination1 the ultra-violet spectrum will extend to an enormous extent4 ,a more difficult1 but perhaps even more interesting means of illustrating the existence of the infra-red rays1 and first due to the writer1 can be made by means of photography4 ,it is possible to prepare a photographic plate with bromide of silver1 which is so molecularly arranged that it becomes capable of being decomposed not only by the violet and blue rays1 but also by the red rays1 and by those rays which have wave-lengths of nearly three times that of the red rays4 ,it would be inappropriate to enter into a description of the method of the preparation of these plates4 ,those who are curious as to it will find a description in the ,bakerian lecture published in the ,philosophical ,transactions of the ,royal ,society for #ahha4 ,with plates so prepared it has been found possible to obtain impressions in the dark with the rays coming from a black object1 heated to only a black heat4 ,that these dark rays possess greater energy or capacity for doing work of some kind than any other rays of the spectrum1 can be shown by means of a linear thermopile 7,fig4 #d71 if it be so arranged as to allow only a narrow vertical slice of light to reach its face4 ,fig4 #d4--,the ,thermopile4 ,the principle of the thermopile we need not describe in detail4 ,suffice it to say that the heating of the soldered junctions of two dissimilar metals 7there are ten pairs of antimony and bismuth in the above instrument7 produces a feeble current of electricity1 which1 however1 is sufficient to cause a deflection to the suspended needle of a delicate galvanometer4 ,to the needle is attached a mirror weighing a fraction of a grain1 and the deflections are made visible by the reflection from it of a beam of light issuing from a fixed point along a scale4 ,the greater the heating of the junctions of the thermopile1 within limits which in these cases are never exceeded1 the greater is the current produced1 and consequently the greater is the deflection of the mirror-bearing needle1 and of the beam of light along the scale4 ,in order to get a comparative measure of the energies of the different rays1 it is necessary that they should be completely absorbed4 ,now the junctions themselves of the pile being metal1 and therefore more or less bright1 will not absorb completely1 but if they be coated with a fine layer of lamp-black1 the rays falling on the pile will be absorbed by this substance1 and their absorption will cause a rise in temperature in it1 and the heat will be communicated to the thermopile4 ,if we make a bright spectrum1 and one not too long1 say three inches in length1 and pass the linear thermopile through its length1 we shall find that when the galvanometer is attached1 the galvanometer needle will be differently deflected in its various parts4 ,the deflection will be almost insensible in the violet1 but sensible in the blue1 rather more in the green1 still more in the yellow1 and it will further increase in the red4 ,when1 however1 the slit of the thermopile is placed beyond the limit of the visible spectrum1 the deflection enormously increases1 and will increase till a position is reached as far below the red as the yellow is above it4 ,after this maximum is reached1 by moving the pile still further from the red1 the galvanometer needle will travel towards its zero1 and finally all deflection will cease4 ,at this point we may suppose we have reached the limit of the spectrum1 but if rock-salt prisms and lenses be used1 the limit will be increased4 ,what the real limit of the spectrum is1 is at present unknown2 ,mr4 ,langley with his bolometer1 and rock-salt prisms1 an instrument more sensitive than the thermopile1 must have nearly reached it4 ,fig4 #e4--;,heating effect of different ,sources of ,radiation4 ,the above figure is a graphic representation of the heating effect of the spectrum of the electric light1 sunlight1 and the incandescence electric light1 on the lamp-black coating of the thermopile1 as shown by the galvanometer4 ,the vast difference between the heating effect of the visible rays of the first two sources compared with the last is clearly indicated4 ,since every ray may be taken as totally absorbed1 the heating of the lamp-black is a measure of the energy or the capacity of performing work of some description1 which they possess4 ,waves of the sea do work when they beat against the shore1 and they do work when they lift a vessel4 ,if we notice a ship at anchor we shall find that behind the vessel and towards the shore the waves are lowered in height or amplitude2 the energy which they have expended in raising the vessel of necessity causes this lowering4 ,in the same way the waves of light1 after falling on matter whose molecules or atoms are swinging in unison with them1 are destroyed1 and the energy is spent in either decomposing the matter into a simpler form at first--though the subsequent form may be more complex--or in raising its temperature4 ,as lamp-black or carbon is in its simplest form1 the only work done upon it by the energy of radiation is the raising of its temperature1 and it is for this reason that this material is so excellent for covering the junctions of the pile4 ,the eye evidently does not absorb all rays1 since only a limited part of the spectrum is visible1 and it would be useless to take a measure of the heating effect of lamp-black for the visible part of the spectrum as a measure of its luminosity1 since the latter fades off in the red--the very place in which the heat curve rises rapidly4 ,,chapter ,,iv4 ,description of ,colour ,patch ,apparatus--,rotating ,sectors--,method of making a ,scale for the ,spectrum4 ,before proceeding further we must describe somewhat in detail two or three pieces of apparatus to be used in the experiments we shall make4 ,the first piece was devised by the writer a few years ago1 and has got rid of several objections which existed in older pieces of apparatus4 ,it is not only useful for lecture purposes1 but also for careful laboratory work4 ,the ordinary lecture apparatus for throwing a spectrum on the screen is of too crude a form to be effective for the purpose we have in view2 the purity of the colours seen on the screen is more than doubtful1 and this alone unfits it for our experiments4 ,if we want to form a pure spectrum we must have a narrow slit1 prisms with true1 flat surfaces1 and lenses of proper curvature4 ,as a rule the ordinary lecture apparatus for forming the spectrum lacks all of these requisites4 ,fig4 #f4--;,colour ,patch ,apparatus4 ,the accompanying diagram 7,fig4 #f7 will give an idea of the apparatus we shall employ4 ,on the usual slit ,s#a of a collimator ,c is thrown1 by means of a condensing lens ,l#a1 a beam of light1 which emanates from the intensely white-hot carbon positive pole of the electric light4 ,the focus is so adjusted that an image of the crater is formed on the slit4 ,the collimating lens ,l#b is filled by this beam1 and the rays issue parallel to one another and fall on the prisms ,p#a and ,p#b1 which disperse them4 ,the dispersed beam falls on a corrected photographic lens ,l#c1 attached to a camera in the ordinary way4 ,it is of slightly larger diameter than the height of the prisms1 and a spectrum is formed on the focusing-screen ,d1 which is slewed at a slight angle with the perpendicular to the axis of the lens ,l#c4 ,this is necessary1 because the focus of the least refrangible or red rays is longer than that of the more refrangible or blue rays4 ,by slewing the focusing-screen as shown1 a very good general focus for every ray may be obtained4 ,when the focusing-screen is removed1 the rays form a confused patch of parti-coloured light on a white screen ,f1 placed some four feet off the camera4 ,the rays1 however1 can be collected by a lens ,l#d1 of about two feet focus1 placed near the position of the focusing-screen1 and slightly askew4 ,this forms an image on the screen of the near surface of the last prism ,p#b2 and if correctly adjusted1 the rectangular patch of light should be pure and without any fringes of colour4 ,the card ,d slides into the grooves which ordinarily take the dark slide4 ,in it will be seen a slit ,s#b1 the utility of which will be explained later on4 ,we shall usually require a second patch of white light1 with which to compare the first patch4 ,now1 although the light from the positive pole of the carbons is uniform in quality1 it sometimes varies in quantity1 as it is difficult to keep its image always in exactly the centre of the slit4 ,if we can take one part of the light coming through the slit to form the spectrum1 and another part to form the second patch of white light1 then the brightness of the two will vary together4 ,at first sight this might appear difficult to attain2 but advantage is taken of the fact that from the first surface of the first prism ,p#a a certain amount of light is reflected4 ,placing a lens ,l#e1 and a mirror ,g1 in the path of this reflected beam1 another square patch of light can be thrown on the same screen as that on which the first is thrown1 and this second patch may be made of the same size as the first patch1 if the lens ,l#e be of suitable focus1 and it can be superposed over the first patch if required2 or1 as is useful in some cases1 the two patches may be placed side by side1 just touching each other4 ,we are thus able to secure two square white patches upon the screen ,f1 one from the re-combination of the spectrum1 and one from the reflected beam4 ,if a rod be placed in the path of these two beams when they are superposed1 each beam will throw a shadow of the rod upon the screen4 ,the shadow cast by the integrated spectrum will be illuminated by the reflected beam1 and the shadow cast by the latter will be illuminated by the former4 ,in fact we have an ordinary ,rumford photometer1 and the two shadows may be caused to touch one another by moving the rod towards or from the screen4 ,when the illumination of the two shadows by the white light is equal1 the whole should appear as one unbroken gray patch4 ,to prevent confusion to the eye a black mask is placed on the screen ,f with a square aperture cut out of it1 on which the two shadows are caused to fall4 ,if it be desired to diminish the brightness of either patch1 it can be accomplished by the introduction of rotating sectors ,m1 which can be opened and closed at pleasure during rotation1 in the path of one or other of the beams4 ,fig4 #g4--,rotating ,sectors4 ,the annexed figure 7,fig4 #g7 is a bird's-eye view of the instrument4 ,a ,a are two sectors1 one of which is capable of closing the open aperture by means of a lever arrangement ,c1 which moves a sleeve in which is fixed a pin working in a screw groove1 which allows the aperture in the sectors to be opened and closed at pleasure during their revolution2 ,d is an electro-motor causing the sectors to rotate4 ,to show its efficiency1 if two strips of paper1 one coated with lamp-black and the other white1 are placed side by side on the screen1 and if one shadow from the rod falls on the white strip1 and the other shadow on the black strip of paper1 and the rotating sectors are interposed in the path of the light illuminating the shadow cast on the white strip1 the aperture of the sectors can be closed till the white paper appears absolutely blacker than the black paper4 ,white thus becomes darker than lamp-black1 owing to the want of illumination4 ,this is an interesting experiment1 and we shall see its bearings as we proceed1 as it indicates that even lamp-black reflects a certain amount of white or other light4 ,having thus explained the main part of the apparatus with which we shall work1 we can go on and show how monochromatic light of any degree of purity can be produced on the screen4 ,if the slit in the cardboard slide ,d be passed through the spectrum when it has been focused on the focusing-screen1 only one small strip of practically monochromatic light will reach the screen1 and instead of the white patch on the screen we shall have a succession of coloured patches1 the colour varying according to the position the slit occupies in the spectrum4 ,it should be noted that the purity of the colour depends on two things--the narrowness of the slit ,s#a of the collimator1 and of the slit ,s#b in the card4 ,if two slits be cut in the card ,d1 we shall have two coloured patches overlapping one another1 and if the reflected beam falls on the same space we shall have a mixture of coloured light with white light1 and either the coloured light or the white light can be reduced in brightness by the introduction of the rotating sectors4 ,if the rod be introduced in the path of the rays we shall have two shadows cast1 one illuminated with coloured light1 monochromatic or compound1 and the other with white light1 and these can be placed side by side1 and surrounded by the black mask as before described4 ,fig4 #h4--,spectrum of ,sodium ,lithium and ,carbon4 ,there is one other part of the apparatus which may be mentioned1 and that is the indicator1 which tells us what part of the spectrum is passing through the slit4 ,just outside the camera1 and in a line with the focusing-screen1 is a clip carrying a vertical needle4 ,a small beam of light passes outside the prism ,p#a2 this is caught by a mirror attached to the side of the apparatus1 and is reflected so as to cast a shadow of the needle on to the back of the card ,d1 on which a carefully divided scale of twentieths of an inch is drawn4 ,to fix the position of the slit the poles of the electric light are brushed over with a solution of the carbonates of sodium and lithium in hydrochloric acid1 and the image of the arc is thrown on the slit4 ,this gets rid of the continuous spectrum1 and only the bright lines due to the incandescent vapours appear on the focusing-screen 7,fig4 #h74 ,amongst other lines we have the red and blue lines due to the vapour of lithium2 the orange1 yellow 7,d71 and green lines of sodium1 together with the violet lines of calcium 7these last due to the impurities of the carbons forming the poles74 ,these lines are caused successively to fall on the centre of the slit by moving the card ,d1 which for the nonce is covered with a piece of ground glass1 and the position of the shadow of the needle-point on the scale is registered for each4 ,a further check can be made by taking a photograph of these lines1 or of the solar spectrum1 and having fixed accurately on the scale any one of these lines already named1 the position of the others on the scale may be ascertained by measurement from the photograph4 ,now the wave-lengths of these bright lines have been most accurately ascertained1 in fact as accurately as the dark lines in the solar spectrum4 ,thus the scale on the card is a means of localizing the colour passing through the slit or slits4 ,should more than one slit be used in the spectrum the positions of each can be determined in exactly the same way4 ,the most tedious part of the whole experimental arrangement with this apparatus is what may be called the scaling of the spectrum4 ,a fairly large spectrum may be formed upon the screen without altering any arrangement of the apparatus1 when it has been adjusted to form colour patches4 ,if a lens ,l#f 7see ,fig4 #f7 of short focus be placed in front of ,l#d 7the big combining lens71 an enlarged spectrum will be thrown upon the screen ,f1 and if slits be placed in the spectrum the images of their apertures are formed by the respective coloured rays passing through them1 so that the colours which are combined in the patch can be immediately seen4 ,,chapter ,v4 ,absorption of the ,spectrum--,analysis of ,colour--,vibrations of ,rays--,absorption by ,pigments--,phosphorescence--,interferen ce4 ,we must now briefly consider what is the origin1 or at all events the cause1 of the colour which we see in objects4 ,it is not proposed to enter into this by any means minutely1 but only sufficiently to enable us to understand the subject which is to be brought before you4 ,what for instance is the cause of the colour of this green solution of chlorophyll1 which is an extract of cabbage leaves8 ,if we place it in the front of the spectrum apparatus and throw the spectrum on the screen1 we find that while there is a certain amount of blue transmitted1 the green is strong1 and there are red bands left1 but a good deal of the spectrum is totally absorbed4 ,forming a colour patch of this absorption spectrum on the screen1 we see that it is the same colour as the chlorophyll solution1 and of this we can judge more accurately by using the reflected beam1 and placing the rod in position to cast shadows4 7,the light of the reflected beam is that of the light entering the slit47 ,the colour then of the chlorophyll is due to the absence of certain colours from the spectrum of white light4 ,when white light passes through it1 the material absorbs1 or filters out1 some of the coloured rays1 and allows others to pass more or less unaffected1 and it is the re-combination of these last which makes up the colour of the chlorophyll4 ,we have a green dye which to the eye is very similar in colour to chlorophyll1 but putting a solution of it in front of the spectrum1 we see that it cuts off different rays to the latter4 ,it would be quite possible to mistake one green for the other1 but directly we analyze the white light which has filtered through each by means of the spectrum1 we at once see that they differ4 ,hence the spectrum enables the eye to discriminate by analysis what it would otherwise be unable to do4 ,any coloured solution or transparent body may be analyzed in the same way1 and1 as we shall see subsequently1 the intensity of every ray after passing through it can be accurately compared with the original incident light4 ,there are some cases1 indeed the majority of cases1 in which the colour transmitted through a small thickness of the material is different to that transmitted through a greater thickness4 ,for instance1 a weak solution of litmus in water is blue when a thin layer is examined1 and red when it is a thicker or more concentrated layer4 ,bichromate of potash is more ruddy as the thickness increases4 ,this can be readily understood by a reference to the law of absorption4 ,suppose we have a thin layer of a liquid which gives a purple colour when two simple colours1 red and blue1 pass through it1 and that this thin layer cuts off one-quarter of the red and one-half of the blue incident on it1 another layer of equal thickness will cut off another quarter of the three-quarters of red passing through the first layer1 and half of the one-half left of the blue2 we shall thus have nine-sixteenths of the red passing and only a quarter of the blue4 ,with a third layer we shall have twenty-seven sixty-fourths of red and only one-eighth of blue left1 showing that as the thickness of the liquid is increased the blue rapidly disappears1 leaving the red the dominant colour4 ,now what is true of two simple colours is equally true of any number of them1 where the rates of absorption differ from one another1 and what is true for a solution is true for a transparent solid4 ,in some opaque bodies1 such as rocks1 the reflected colour often differs slightly from that of the same when they are cut into thin and polished slices1 through which the light can pass4 ,the reason is that when opaque1 light penetrates to a very small distance through the surface1 and is reflected back1 whilst in these layers the colour has to struggle through more coloured matter1 and emerges of a different hue4 ,the question why substances transmit some rays and quench others1 brings us into the domain of molecular physics4 ,of all branches of physical science this is perhaps the most fascinating and the most speculative1 yet it is one which is being built up on the solid foundations of experiment and mathematics1 till it has attained an importance which the questions depending on it fully warrants4 ,we have to picture to ourselves1 in the case in point1 molecules1 and the atoms composing them1 of a size which no microscope can bring to view1 vibrating in certain definite periods which are similar to the periods of oscillation of the waves of light4 ,at page #bf we have given the lengths of some of the waves which give the sensation of coloured light4 ,now as light1 of whatever colour it may be1 is practically transmitted with the same velocity through air which has the same density throughout1 it follows that the number of vibrations per second of each ray can be obtained by dividing the velocity of light in any medium by the wave-length4 ,the following table gives roughly the number of vibrations per second of the ether giving rise to the colours fixed by the dark solar lines4 ---------------------------------------- ,name of ,line4 ,millions of ,millions of ,vibrations per ,second4 ---------------------------------------- ,a in the ,red #cie ,b #dcg ,c #deh ,d ,orange #eaj ,e ,green #egj ,f ,blue #fah ,g ,violet #fig ,h ,ultra-,violet #geg ---------------------------------------- ,if we endeavour to gauge what this rate of oscillation means we shall scarcely be able to realize it1 even by a comparison with some physically measurable rate of vibration4 ,a tuning-fork1 for instance1 giving the middle ,c1 vibrates #ebh times per second4 ,compare this with the number of vibrations of the waves of light1 and we still are as far as ever from realizing it1 yet the velocity of light1 and the lengths of the different waves have been accurately determined2 the latter1 although the much smaller quantity1 with even greater accuracy than the first4 ,these rates of vibration must therefore be--cannot help being--at all events approximately true4 ,this being so1 we know that some of the atoms of the molecules at least1 and perhaps in some cases the molecules themselves1 are vibrating at the same rate as those waves of light1 which they refuse to allow to pass4 ,if we have a child's swing beginning to oscillate1 we know that it is only by well-timed blows that the extent of the swing is permanently increased1 and the energy exerted by the person who gives the well-timed blow is expended on producing the increased amplitude4 ,in the same way if the rate of vibration of a wave of light is in accord with that of a molecule or atom1 the amplitude or swing of the atom or molecule is increased1 and the energy of the wave and therefore its amplitude is totally or partially destroyed2 and as the amplitude is a function of the intensity of the light1 the ray fails to be seen at all1 or else is diminished in brightness4 ,in what way the atoms vibrate where more than one ray is absorbed is still a matter of speculation1 but no doubt as experimental methods are more fully developed1 and mathematicians investigate the results of such experiments1 we shall be able to form a picture of the vibrations themselves4 ,at page #acg a speculation as to the reason why solids or liquids can absorb more waves of light than one which are adjacent to each other is put forward1 but it does not deal with the absorptions which occupy various parts of the spectrum4 ,again1 too1 we have the fact that the energy absorbed by these atoms and molecules from the waves of light1 must show itself as work done on them--it may be as heat or as chemical action4 ,we shall see by and by that in some cases1 no doubt1 at least a part is expended in the latter form of work4 ,perhaps this mode of looking at the question of colour in objects may make the subject more interesting to the reader than it at first appears to be deserving4 ,the whole subject is one which enlarges the faculty of making mental pictures1 and this is one of the most useful forms of scientific education4 ,but how can we distinguish between pigments which to the eye are apparently the same8 ,if we dye paper with the green dye referred to1 we can place it in the spectrum1 and we shall see that the dye reflects differently to the white paper4 ,in fact we shall find that it refuses to reflect in those parts of the spectrum which the transparent solution refused to transmit4 ,so long as the light passes through the dye-stuff1 it is indifferent1 as regards the colour produced1 whether the colouring matter be at a distance from the paper or whether the latter be dyed with it1 as we can see at once4 ,if we place the solution of the dye in the reflected beam of the apparatus and form a patch on the screen1 and alongside throw the patch of white light from the integrated or recombined spectrum upon the dyed paper1 it will be found that the two colours are alike2 that is1 the green-coloured light on the white paper1 or the white light on the green paper are the same4 ,similarly we may experiment on other dyes1 such as magenta1 log-wood1 c41 and we shall see that like results are obtained4 ,it should be said1 however1 that when the paper is dyed with the colouring matter a small quantity of white light will be reflected from the surface of the paper itself4 ,we may now say that the general colour is given to a body by its refusal to transmit or reflect1 more or less completely1 certain rays of the spectrum4 ,should the solvent form a compound with the dye1 perhaps this would not be absolutely true1 but in the large majority of cases the statement is correct4 ,when we have bodies which are also fluorescent1 this statement would also have to be modified1 but we need not consider these for the present4 ,another source of colour in objects1 though very rarely met with1 and which for our object we need not stay to explain in detail1 is the interference of light4 ,such is seen in soap-bubbles4 ,briefly it may be said that the colours are due to rays of light reflected from the inner surface of the film1 which quench other rays of light of the same wave-length reflected from the outer surface4 ,if two series of waves of the same wave-length are going in the same direction and from the same source1 each of which has the same intensity as the other1 that is1 having the same amplitude1 and it happens that the one series is exactly half a wave-length behind the other1 then the crest of one wave in the first series will fill up the trough of the other in the second series1 and no motion would result1 and this lack of motion means darkness1 since it is the wave motion which gives the sensation of light4 ,if then we have white light falling on two reflecting surfaces1 such as the front and back of a soap-film1 part of the light will be reflected from each1 and if the film be of such a thickness that the latter reflects light exactly #a_/b wave-length1 #c_/b or #e_/b wave-length1 c41 of some colour behind the former1 the colour due to that particular wave-length will be absent from the reflected white light1 and instead of white light we shall have coloured light1 due to the combination of all the colours less this colour1 which is quenched4 ,a very pretty experiment to make is to throw the image of a soap film on the screen1 and to watch the change in the colours of the film4 ,their brilliancy increases as the film becomes thinner1 and the bands1 which first appear close to each other1 separate1 and then we see a large expanse of changing colour4 ,a soap solution should be made according to almost any of the published formul1 and a piece of flat card be dipped in it1 and be drawn across a ring of wire some inch in diameter1 or--what the writer prefers best--the stop of a photographic lens4 ,a film will form and fill the aperture4 ,the ring or stop may be placed vertically in a clamp1 and a beam of light caused to fall at an angle of about #de degrees on to the film4 ,if a lens be placed in the path of the reflected beam to form an image of the aperture1 the colours which the film shows can be exhibited to an audience1 if the diameter of the image be made four or five feet4 ,instead of this large image1 a small image may be thrown on the slit of the spectroscope1 by using a lens of a greater focal length1 and if the beam be so directed that it falls on the axis of the collimator1 a very fairly bright spectrum may be also thrown on the screen4 ,the appearance of the spectrum is somewhat like that shown in the above diagram 7,fig4 #i74 ,fig4 #i4--;,interference ,bands4 ,if we take a horizontal line across the spectrum1 we shall see what particular colours are missing from the reflected light which falls on the part of the slit corresponding to that line4 ,the colours of some objects1 such as of the opal1 and the lovely colouring of some feathers are due to interference of light4 ,the partial scattering of different rays by small particles will also cause light to be coloured1 as we shall see in the experiments we shall make to imitate the colour of sunlight at various altitudes of the sun4 ,we may1 however1 take it as a rule that the colour of objects is produced by the greater or less absorption of some rays1 and the reflection in the case of opaque bodies1 or the transmission1 in the case of transparent bodies1 of the remainder4 ,,chapter ,,vi4 ,scattered ,light--,sunset ,colours--,law of the ,scattering by ,fine ,particles--,sunset ,clouds--,luminosities of ,sunlight at different ,altitudes of the ,sun4 ,it is probable that we should be able to ascertain approximately the true colour of sunlight 7if we may talk of the colour of white light7 if we could collect all the light from a cloudless sky1 and condense it on a patch of sunlight thrown on a screen4 ,for skylight is1 after all1 only a portion of the light of the sun1 scattered from small particles in the atmosphere1 part of the light being scattered into space1 and part to our earth4 ,the small particles of water and dust--and when we say small we mean small when measured on the same scale as we measure the lengths of waves of light--differentiate between waves of different lengths1 and scatter the blue rays more than the green1 and the green than the red2 consequently what the sun lacks in blue and green is to be found in the light of the sky4 ,the effect that small water particles have upon light passing through them can be very well seen in the streets of ,london at night1 when the atmosphere is at all foggy4 ,gaslights at the far end of a street appear to become ruby red and dim1 and half-way down only orange1 but brighter1 whilst close to they are of the ordinary yellow colour1 and of normal brightness4 ,when no fog is present the gas-lights in the distance and close to are of the same colour and brightness1 showing that their change in appearance is simply due to the misty atmosphere intervening between them and the observer4 ,we can imitate the light from the sun1 after its passage through various thicknesses of atmosphere1 in a very perfect manner in the lecture-room1 using the electric light as a source4 ,a condensing lens is put in front of the lamp1 and in front of that a circular aperture in a plate4 ,beyond that again is a lens which throws an enlarged image of the aperture on the screen1 which we may call our mock sun4 ,if we place a trough of glass1 in which is a dilute solution of hyposulphite of soda1 carefully filtered from motes as far as possible1 in front of the aperture1 we have an image of the aperture unaffected by the insertion of the solution4 ,the white disc on the screen will1 as we have said before1 be a close approximation to sunlight on a ,may-day about noon1 when the sky is clear4 ,by dropping into the trough a little dilute hydrochloric acid1 a change will be found to come over the light of the mock sun2 a pale yellow colour will spread over its surface1 and this will give way to an orange tint1 and at the same time its brightness will diminish4 ,gradually the orange will give place to red1 the luminosity will be very small1 being of the same hue as that seen in the sun when viewed through a ,london fog4 ,finally the last trace of red will so mingle with the scattered white light that the image will disappear1 and then the experiment is over4 ,if we track the cause of this change of colour in our artificial sun1 we shall find that it is due to minute particles of sulphur separating out from the solution of hyposulphite1 and the longer the time that elapses the more turbid the dilute solution will become4 ,this experiment exemplifies the action of small particles on light4 ,examining the trough it will be found that whilst the light which passes through the solution principally loses blue rays1 the light which is scattered from the sides is almost cerulean in blue1 and can well be compared with the light from the sky4 ,we can analyze the transmitted light very readily by focusing the beam from the positive pole of the electric light on to the slit of our colour apparatus1 and placing the lens ,l#f7;,fig4 #f7 in position to form the large spectrum on the screen4 ,we can also show the colour of the light which goes to form the spectrum1 by sending the patch of light reflected from the first surface of the first prism just above it4 ,we thus have the spectrum and the light forming the spectrum to compare with one another4 ,using this apparatus and inserting the trough of dilute hyposulphite in the beam1 the spectrum is of the character usually seen with the electric light2 but on dropping the dilute hydrochloric acid into the solution the same hues fall on the slit of the spectroscope which fell upon the screen to form the mock sun1 and the spectrum is seen to change as the light changes from white to yellow1 and from yellow to red4 ,first the violet will disappear1 the blue and the green being dimmed1 the former most however2 then the blue will vanish to the eye1 the green becoming still less luminous1 and the yellow also fading2 the green and yellow will successively disappear1 leaving finally on the screen a red band alone1 which will be a near match to the colour of the unanalyzed light1 as may be seen by comparing it with the adjacent patch formed from the reflected beam4 ,we have here a proof that the succession of phenomena is caused by a scattering of the shorter wave-lengths of light1 and that the shorter the waves are the more they are scattered4 ,it has been found theoretically by ,lord ,rayleigh that the scattering takes place in inverse proportion to the fourth power of the wave-length2 thus1 if two wave-lengths1 which may be waves in the green and violet1 are in the proportion of three to four1 the former will be scattered as #a_/7cd7 to #a_/7dd71 or as #bef to #ha1 which is approximately as three to one4 ,consequently if the green in passing through a certain thickness of a turbid medium loses one-half the violet in passing through the same thickness will lose five-sixths of its luminosity4 ,the inverse fourth powers of the following wave-lengths1 which are within the limits of the whole visible spectrum1 are shown below4 ----------------------------------- ,lamda #gjjj #fjjj #ejjj #djjj ----------------------------------- #a_/,lamda#d #a #ejd #bfj #ajg ----------------------------------- ,supposing ,lamda#gjjj by the scattering of small particles loses one-tenth of its luminosity1 then ,lamda#fjjj would have #ded of its original brightness2 ,lamda#ejjj1 #bcd2 and ,lamda#djjj1 #jie2 that is1 whilst ,lamda#gjjj would lose one-tenth only of its luminosity1 ,lamda#djjj in the violet would retain not quite one-hundredth of its brightness4 ,during the years #ahhe1 #ahhf1 and #ahhg1 the writer measured the luminosity of the solar spectrum at different times of the year1 and at different hours of the day 7see ,phil4 ,trans4 #ahhg3 ,transmission of ,sunlight through the ,earth's ,atmosphere71 and from the results he found that the smallest coefficient of scattering for one atmosphere at sea-level for each wave-length was #jjac1 when ,lamda-#d was for convenience sake multiplied by #ajag 7thus ,lamda#fjjj-d on this scale was #ggb71 and that the mean was #jjag4 ,the following table shows the loss of light for the rays denoted by the principal lines given at page #bf1 using this last coefficient for different air thicknesses4 ,this is equivalent to giving the intensity of the rays of sunlight when the sun is at different altitudes4 ---------------------------------------- ------------------------- #a ,light after passing through atmospheres of ,line ,wave- - the following thicknesses4 length,lamda-#d------------------------- ------------ x#ajag #j #a #b #c #d #e #f #g #h #cb ---------------------------------------- ---------------- ,a #geid #cj #aieeijhheghaeggegcfgjgffeajg ,b #fhfg #de #aibfhehgiegcefhdfcbehcedbjhf ,c #fefb #ed #aiabhcbgeificfcbegfebfdhjjai ,d #ehib #hc #ahfhgedfeeefididdbhcgbcbcjja ,e #ebfi #abi #ahjcfddeahdbgccdbfhbafagc -- ,f #dhfa #agi #agchedddjbbifbaiafaaaijhh -- ,g #dcjg #bia #afjicfgbbjacgjhdjeajcajai -- ,h #cifh #djc #aejfbedabhjgajccjafjjhjjd -- ---------------------------------------- ---------------- ,the sun traverses the following thicknesses of atmosphere when it is at the angles shown above the horizon4 #a atmosphere #ij #b #cj #c #aicj #d #adcj #e #aacj #f #icj #g #hcj #h #gcj ,fig4 #aj4--;,absorption of ,rays by the ,atmosphere4 ,it traverses thirty-two atmospheres when it is very nearly setting4 ,bougier and ,forbes have calculated that the extreme thickness of the atmosphere1 traversed by its light when the sun is on the horizon1 is approximately #ce-a_/b atmospheres4 ,the absorption shown by #cb atmospheres will therefore be very close to that which would be observed at sunset on an ordinary day1 and it will be seen that practically all rays have been scattered from the light1 except the red1 and a little bit of the orange4 ,as to the luminosity of the sun at these different altitudes1 we can easily find it by reducing the luminosity curve of the sun at some known altitude by the factors in the table just given1 for as many wave-lengths as we please1 and thus construct another curve4 ,the area of the figure thus obtained would be a measure of the total luminosity on the same scale as the area of the luminosity curve from which it was derived4 ,the following are the approximate luminosities of the sun when the light shines through #j atmospheres #a #a #hdj #b #gje #c #eid #d #dif #e #dag #f #cjc #g #bef #h #bae #cb #jjb ,it will thus be seen that the sun is #dbj times less bright just at sunset than it is if it were to shine directly overhead1 and about #cej times brighter than it is for a winter sun in a cloudless and mistless sky at twelve o'clock1 for the altitude of the sun in our latitude is about #cj at that time1 and corresponds with a thickness of two atmospheres1 through which the sun has to shine4 ,we all know that to look at the sun at any time near noon in a cloudless sky dazzles the eyes1 but that near sunset it may be looked at with impunity4 ,the reduction in luminosity explains this fact4 ,the distribution of the scattering particles in the atmosphere is very far from regular4 ,as we ascend1 the particles get more sparse1 as is shown by the less scattering that takes place of the blue rays compared with the red4 ,thus at an altitude of some #hjjj feet the mean coefficient of scattering is about #jjjc1 instead of #jjag1 which it is at sea-level4 ,it must be recollected that there is only about three-fourths of the air above us at #hjjj feet1 and it is less dense4 ,there will therefore be a diminution of particles not only because there is less air1 but because the air itself is less capable of keeping them in suspension4 ,up to #cjjj or #djjj feet there is no very great marked difference in the scattering of light1 as observations carried on during five years have shown2 but above that the scattering rapidly diminishes1 and at #bj1jjj feet it must be very small indeed1 if the diminution increases as rapidly as has been found it does at the altitude of #hjjj feet4 ,we must repeat once more that the blue of the sky is principally if not entirely due to the presence of these particles1 the rays scattered by them1 which are principally the blue rays1 being reflected back from them1 giving the sensation of blue which we know as sky-blue4 ,the greater the number of these fine particles that are encountered by sunlight1 the greater the scattering will be1 and the bluer the sky4 ,it is more than probable that the blue sky of ,italy1 so proverbial for being beautiful1 is due to this cause1 since from its geographical position the small particles of water must be very abundant there4 ,carrying this argument further1 we should expect that as we mount higher the blue would become more fully mixed with the darkness of space1 and this ,alpine travellers will tell you is the case4 ,at heights of #ab1jjj feet or more1 on a clear day1 the sky seems almost black1 and it is no uncommon thing to see this admirably rendered in photographs of ,alpine scenery when taken at a height4 ,many of the late ,mr4 ,donkin's photographs show this in great perfection1 as also ,signor ,sella's4 ,before quitting this subject we may call attention not only to the colour of the sun itself at sunset1 but also to the colouring of the sky which accompanies the sun as it sinks4 ,this colouring is often different to the colour that the sun itself assumes2 but we can easily show that the effects so wonderfully beautiful are entirely dependent on this scattering of light by these small intervening particles in the air4 ,we often see a ruddy sun1 and perhaps nearly in the zenith1 or even further away from the sun1 clouds of a beautiful crimson hue1 lying on a sky which appears almost pea-green1 whilst nearer to the sun the sky is a brilliant orange1 which artists imitate with cadmium yellow4 ,let us fix our attention first on the crimson cloud4 ,the clouds of which the colouring is so gorgeous are often not #ajjj feet above us1 and were we to be at that altitude we should see the sun not quite so ruddy as we see it from the earth1 and the cloud would consequently be illuminated by the sun with a more orange tint2 but the light reflected from the cloud to our eyes has to pass through1 say #ajjj feet of dense atmosphere1 and thus the total atmosphere that the light traverses in the latter case is always greater than the air thickness through which the direct light from the sun has to pass2 hence more orange is cut off1 and the light reflected from the cloud is redder4 ,this red1 however1 will not account for the brilliant crimson and purples which we so often see4 ,it has to be remembered that not sunlight alone illumines the cloud1 but also the blue light of the sky4 ,the feebler the intensity of the red1 the more will the blue of the sky be felt in the mixture of light which reaches our eyes1 and consequently we may have any tint ranging from crimson to purple1 since red and blue make these hues1 according to the proportions in which they are mixed4 ,now let us see how we get the brilliant orange of the sky itself4 ,when the evening is perfectly clear and free from mist and cloud1 the orange in the sky is very feeble1 showing that the intensity depends upon their presence4 ,now a look at the table will show that the sun is very close to the horizon when it becomes ruddy under normal conditions2 but that when the light traverses a thickness of eight atmospheres1 the blue and violet1 and most of the green1 are absent1 leaving a light of yellowish colour4 ,to traverse eight atmospheres the light has only to come from a point some eight degrees above the horizon4 ,when the sun is near the horizon1 it sends its rays not only to us and over us1 but in every direction2 and an eye placed some few thousand feet above the earth would see the sun almost of its midday colour1 for sunset colours of the gorgeous character that we see at sea-level are almost absent at high altitudes4 ,if a cloud or mist were at such an altitude the sunlight would strike it1 and whilst only a small portion would be selectively scattered1 owing to the general grossness of the particles1 the major part would be reflected back to our eyes1 and come from an altitude of over eight to ten degrees1 and would therefore1 after traversing the intervening atmosphere1 reach us as the orange-coloured light of which we have just spoken4 ,the clouds which are orange when near the sun1 are usually higher than those which are simultaneously red or purple4 ,the pea-green colour of the sky is often due to contrast1 for the contrast colour to red is green1 and this would make the blue of the sky appear decidedly greener4 ,sometimes1 however1 it is due to an absolute mixture of the blue of the sky and the orange light which illuminates the same haze4 ,in the high ,alps it is no uncommon occurrence for the snow-clad mountains to be tipped with the same crimson we have described as colouring the clouds1 and this is usually just after sunset1 when the sun has sunk so low beneath the horizon that the light has to traverse a greater thickness of dense air1 and consequently to pass through a larger number of small particles than it has when just above the horizon4 ,in this case the red of the sunlight mixes with blue light of the sky1 and gives us the crimson tints4 ,the deeper and richer tints of the clouds just after sunset are also due to the same cause1 the thickness of air traversed being greater4 ,it is worth while to pause a moment and think what extraordinary sensual pleasure the presence of the small scattering particles floating in the air causes us2 that without them the colouring which impresses itself upon us so strongly would have been a blank1 and that artists would have to rely upon form principally to convey their feelings of art4 ,indeed without these particles there would probably be no sky1 and objects would appear of the same hard definition as do the mountains in the atmosphereless moon4 ,they would be only directly illuminated by sunlight1 and their shadows by the light reflected from the surrounding bright surfaces4 ,,chapter ,,vii4 ,luminosity of the ,spectrum to ,normal-eyed and ,colour-blind ,persons--,method of determining the ,luminosity of ,pigments--,addition of one ,luminosity to another4 ,the determination of the luminosity of a coloured object1 as compared with a colourless surface illuminated by the same light1 is the determination of the second colour constant4 ,we will first take the pure spectrum colours1 and show how their luminosity or relative brightness can be determined4 ,viewing a spectrum on the screen1 there is not much doubt that in the yellow there is the greatest brightness1 and that the brightness diminishes both towards the violet and red4 ,towards the latter the luminosity gradient is evidently more rapid than towards the former4 ,this being the case1 it is evident that1 except at the brightest part there are always two rays1 one on each side of the yellow1 which must be equally luminous4 ,if the spectrum be recombined to form a white patch upon the screen1 and the slide with the slit be passed through it1 patches of equal area of the different colours will successively appear2 but the yellow patch will be the brightest patch4 ,if the patch formed by the reflected beam be superposed over the colour patch1 and the rod be interposed1 we get a coloured stripe alongside a white stripe1 and by placing our rotating sectors in the path of the reflected beam1 the brightness of the latter can be diminished at pleasure4 ,suppose the sectors be set at #de1 which will diminish the reflected beam to one-quarter of its normal intensity1 we shall find some place in the spectrum1 between the yellow and the red1 where the white stripe is evidently less bright than the coloured stripe1 and by a slight shift towards the yellow1 another place will be found where it is more bright4 ,between these two points there must be some place where the brightness to the eye is the same4 ,this can be very readily found by moving the slit rapidly backwards and forwards between these two places of too dark and too light1 and by making the path the slit has to travel less and less1 a spot is finally arrived at which gives equal luminosities4 ,the position that the slit occupies is noted on the scale behind the slide1 as is also the opening of the sectors1 in this case #de4 ,as there is another position in the spectrum between the yellow and the violet1 which is of the same intensity1 this must be found in the same manner1 and be similarly noted4 ,in the same way the luminosities of colours in the spectrum1 equivalent to the white light passing through other apertures of sectors1 can be found1 and the results may then be plotted in the form of a curve4 ,this is done by making the scale of the spectrum the base of the curve1 and setting up at each position the measure of the angular aperture of the sector which was used to give the equal luminosity or brightness to the white4 ,by joining the ends of these ordinates by lines a curve is formed1 which represents graphically the luminosity of the spectrum to the observer4 ,in ,fig4 #aa the maximum luminosity was taken as #ajj1 and the other ordinates reduced to that scale4 ,the outside curve of the figure was plotted from observations made by the writer1 who has colour vision which may be considered to be normal1 as it coincides with observations made by the majority of persons4 ,the inner curve requires a little explanation1 though it will be better understood when the theory of colour vision has been touched upon4 ,fig4 #aa4--,luminosity ,curve of the ,spectrum of the ,positive ,pole of the ,electric ,light4 ,the observer in this case was colour-blind to the red1 that is1 he had no perception of red objects as red1 but only distinguished them by the other colours which were mixed with the red4 ,this being premised1 we should naturally expect that his perception of the spectrum would be shortened1 and this the observations fully prove4 ,if it happened that his perceptions of all other colours were equally acute with a normal-eyed person1 then his illumination value of the part of the spectrum occupied by the violet and green ought to be the same as that of the latter4 ,the diagram shows that it is so1 and the amount of red present in each colour to the normal-eyed observer is shown by the deficiency curve1 which was obtained by subtracting the ordinates of colour-blind curve from those of the normal curve4 ,there are other persons who are defective in the perception of green1 and they again give a different luminosity curve for the spectrum4 ,these variations in the perception of the luminosity of the different colours are very interesting from a physiological point of view1 and this mode of measuring is a very good test as to defective colour vision4 ,we shall allude to the subject of colour-blindness in a subsequent chapter4 ,the following are the luminosities for the colours fixed by the principal lines of the solar spectrum1 and for the red and blue lines of lithium1 to which reference has already been made4 ---------------------------------------- ------------ ,luminosity4 ------------------- ,line4 ,colour4 ,normal ,red ,eye4 ,colour ,blind4 ---------------------------------------- --------- ,a ,very dark ,red -- -- ,b ,red 7,crimson7 #aj #j ,red ,lithium ,red 7,crimson7 #he #e ,c ,red 7,scarlet7 #bjf #ba ,d ,orange #ihe #ecj ,e ,green #ejj #dij ,f ,blue ,green #gj #gj ,blue ,lithium ,blue #ai #ai ,g ,violet #f #f ,h ,faint ,lavender -- -- ---------------------------------------- ------------ ,the failure of the red colour-blind person to perceive red is very well shown from this table4 ,it will for instance be noticed that he perceives about one-tenth of the light at ,c which the normal-eyed person perceives4 ,a modification of this plan can be employed for measuring the luminosity of the spectrum1 and it is excessively useful1 because we can adapt it to the measurement of colours other than these simple ones4 ,in the plan already explained it was the colour in the patch that was altered1 to get an equal luminosity with a certain luminosity of white light4 ,in the modified plan the luminosity of the white light is altered1 for the luminosity of the shadow illuminated by the reflected beam can be altered rapidly at will by opening or closing the apertures of the sectors whilst it is rotating4 ,the slit in the slide is placed in the spectrum at any desired point1 and the aperture of the sectors altered till equal luminosities are secured4 ,the readings by this plan are very accurate1 and give the same results as obtained by the previous method employed4 ,it must be remembered that we have so far dealt with colours which are spectrum colours1 and which are intense because they are colours produced by the spectrum of an intensely bright source of light4 ,by an artifice we can deduce from this curve the luminosity curve of the spectrum of any other source of light4 ,if by any means we can compare1 inter se1 the intensity of the same rays in two different sources of light1 one being the electric light1 we can evidently from the above figure deduce the luminosity curve of the spectrum of the other source of light 7see p4 #aji74 ,we can now show how we can adapt the last method to the measurement of the luminosity of the light reflected from pigments4 ,fig4 #ab4--,rectangles of ,white and ,vermilion4 ,fig4 #ac4--;,arrangement for measuring the ,luminosities of ,pigments4 ,suppose the luminosity of a vermilion-coloured surface had to be compared with a white surface when both were illuminated1 say by gaslight1 the following procedure is adopted4 ,a rectangular space is cut out of black paper 7,fig4 #ab7 of a size such that its side is rather less than twice the breadth of the rod used to cast a shadow3 a convenient size is about one inch broad by three-quarters of an inch in height4 ,one-half of the aperture is filled with a white surface1 and the other half with the vermilion-coloured surface4 ,the light ,l 7,fig4 #ac7 illuminates the whole1 and the rod ,r1 a little over half an inch in breadth1 is placed in such a position that it casts a shadow on the white surface1 the edge of the shadow being placed accurately at the junction of the vermilion and white surface4 ,a flat silvered mirror ,m is placed at such a distance and at such an angle that the light it reflects casts a second shadow on the vermilion surface4 ,between ,r and ,l are placed the rotating sectors ,a4 ,the white strip is caused to be evidently too dark and then too light by altering the aperture of the sectors1 and an oscillation of diminishing extent is rapidly made till the two shadows appear equally luminous4 ,a white screen is next substituted for the vermilion and again a comparison made4 ,the mean of the two sets of readings of angular apertures gives the relative value of the two luminosities4 ,it must be stated1 however1 that any diffused light which might be in the room would relatively illuminate the white surface more than the coloured one4 ,to obviate this the receiving screen is placed in a box1 in the front of which a narrow aperture is cut just wide enough to allow the two beams to reach the screen4 ,an aperture is also cut at the front angle of the box1 through which the observer can see the screen4 ,when this apparatus is adopted1 its efficiency is seen from the fact that when the apertures of the rotating sectors are closed the shadow on the white surface appears quite black1 which it would not have done had there been diffused light in any measurable quantity present within the box4 ,the box1 it may be stated1 is blackened inside1 and is used in a darkened room4 ,the mirror arrangement is useful1 as any variation in the direct light also shows itself in the reflected light4 ,instead of gaslight1 reflected skylight or sunlight can be employed by very obvious artifices1 in some cases a gaslight taking the place of the reflected beam4 ,when we wish to measure luminosities in our standard light1 viz4 the light emitted from the crater of the positive pole of the arc-light1 all we have to do is to place the pigment in the white patch of the recombined spectrum1 and illuminate the white surface by the reflected beam1 using of course the rod to cast shadows1 as just described4 ,the rotating sectors must be placed in either one beam or the other1 according to the luminosity of the pigment4 ,the luminosities of the following colours were taken by the above method1 and subsequently we shall have to use their values4 ,electric ,light4 ,white #ajj ,vermilion #cf ,emerald ,green #cj ,ultramarine #dd ,orange #cia ,black #cd ,black 7different surface7 #ea ,suppose we have two or more colours of the spectrum whose luminosities have been found1 the question immediately arises1 as to whether1 when these two colours are combined1 the luminosity of the compound colour is the sum of the luminosities of each separately4 ,thus suppose we have a slide with two slits placed in the spectrum1 and form a colour patch of the mixture of the two colours and measure its luminosity1 and then measure the luminosity of the patch first when one slit is covered up1 and then the other4 ,will the sum of the two latter luminosities be equal to the measure of the luminosity of the compounded colour patch8 ,one would naturally assume that it would1 but the physicist is bound not to make any assumptions which are not capable of proof2 and the truth or otherwise is perfectly easy to ascertain1 by employing the method of measurement last indicated4 ,let us get our answer from such an experiment4 ---------------------------- ,colours ,observed ,measured4 ,luminosity4 ---------------------------- ,r #bjcj ,g #che ,v #he 7,r ,g7 #bdb 7,g ,v7 #de 7,r ,v7 #bad 7,r ,g ,v7 #bej ---------------------------- ,three apertures were employed1 one in the red1 another in the green1 and the third in the violet1 and the luminosity was taken of each separately1 next two together1 and then all three combined1 with the results given above4 ,the accuracy of the measurements will perhaps be best shown by adding the single colours together1 the pairs and the single colours1 and comparing these values with that obtained when the three colours were combined4 ,when the pairs are shown they will be placed in brackets2 thus 7,r ,g7 means that the luminosity of the compound colour made by red and green are being considered4 ,r ,g ,v #bejj 7,r ,g7 ,v #beje 7,r ,v7 ,g #bebe 7,g ,v7 ,r #bdhj 7,r ,g ,v7 #bejj ,the mean of the first four is #bejbe1 which is only #a_/aj different from the value of #bej obtained from the measurement of 7,r ,g ,v7 combined4 ,other measures fully bore out the fact that the luminosity of the mixed light is equal to the sum of the luminosities of its components4 ,it is true that we have here only been dealing with spectrum colours1 but we shall see when we come to deal with the mixture of colours reflected from pigments that the same law is universally true4 ,it will be proved by and by that a mixture of three colours1 and sometimes of only two colours1 be they of the spectrum or of pigments1 can produce the impression of white light4 ,if then we measure all the components but one1 and also the white light produced by all1 then the luminosity of the remaining component can be obtained by deducting the first measures from the last4 ,for instance1 red1 green and violet were mixed to form white light4 ,the luminosity of the white being taken as #ajj1 the red and violet were measured and found to have a luminosity of #dde and #c respectively4 ,this should give the green as having a luminosity of #ebe4 ,the green was measured and found to be #ec1 whilst a measurement of the red and green together gave a luminosity of #ife instead of #ig4 ,,chapter ,,viii4 ,methods of ,measuring the ,intensity of the ,different ,colours of the ,spectrum1 reflected from ,pigmented ,surfaces--,templates for the ,spectrum4 ,fig4 #ad4--,measurement of the ,intensity of ,rays reflected from white and coloured surfaces4 ,we will now proceed to demonstrate how we can measure the amount of spectral light reflected by different pigments4 ,let us take a strip of card painted with a paste of vermilion1 leaving half the breadth white2 and similarly one with emerald green4 ,if we place the first in the spectrum so that half its breadth falls on the red1 and the other half on the white card1 we shall see that apparently the red and orange rays are undiminished in intensity by reflection from the vermilion1 but that in the green and beyond but very little of the spectrum is reflected4 ,with the emerald green placed similarly in the spectrum1 the red rays will be found to be absorbed1 but in the green rays the full intensity of colour is found1 fading off in the blue4 ,what we now have to do is to find a method of comparing the intensities of the different rays reflected from the pigments1 with those from the white surface4 ,we will commence with the second of the two methods which the writer devised with this object1 and then describe the first1 which is more complex4 ,suppose we have1 say a card disc three inches in diameter1 painted with the pigment whose reflective power has to be measured1 and place it on a rotating apparatus with black and white sectors of say five inches diameter1 and capable of overlapping so as to show different proportions of black to white 7see ,fig4 #db74 ,if we throw a colour patch 7shown in ,fig4 #ad as the area inside the dotted square7 on the combination of black and white1 and at the same time on the pigmented disc1 it is probable that either one or other will be the brighter4 ,by moving the slit along the spectrum it is evident1 however1 that a colour can be found which is equally reflected from them both whilst rotating4 ,take as an example the sectors as set at two parts white1 to one part black1 the centre disc being vermilion1 the slit is moved along the spectrum until such a point is reached that the colour reflected from the ring and the disc appears of the same brightness1 for it must be recollected that they cannot differ in hue1 as the light is monochromatic4 ,it will be found that the place where they match in brightness is in the red1 the exact position being fixed by the scale at the back of the slide4 ,taking the proportion of black to white as three to one1 the match will be found to take place in the orange4 ,increasing the proportion of black more and more1 a point will be reached where the reflection takes place uniformly along the blue end of the spectrum1 this will be from the green to the end of the violet4 ,by sufficiently increasing the number of matches made1 a curve of reflection can be made showing the exact proportion of each ray of the spectrum that is reflected4 ,the uniform reflection along the blue end of the spectrum shows that a certain amount of white light is reflected from the pigment4 ,next taking the emerald green disc1 if we adopt the same procedure it will be found that for some shades of the ring there are two places in the spectrum from which the colours reflected give the same brightness4 ,by plotting curves in exactly the same way as that shown for the curve of luminosity at page #gh1 substituting for the open aperture of the sector the angular value of the white used1 we can show graphically the correct reflection for each part of the spectrum4 ,sometimes three places in the spectrum will be read1 as giving equal reflections from the coloured disc and the grey ring4 ,the accompanying figures show the results obtained for reflection from vermilion1 emerald green1 and ,french blue1 after having made a correction for the white by adding the amount which the black reflects4 ,the scale is that of the prismatic spectrum employed4 ,on page #df we stated that a white surface could be made to appear darker than a black surface1 by illuminating the latter and cutting off the light from the former4 ,by placing the black surface in place of one of the coloured ones1 as shown in page #hb1 the luminosity of the black surface can be ascertained4 ,in this case it was found that almost exactly #e of the white light from the crater of the positive pole was reflected4 ,in the table the original measures are shown1 and also the corrected measures1 and for convenience sake the intensity of every ray throughout the length of the spectrum reflected from white1 has been taken as #ajj4 ,the position of the reference lines on the scale 7,fig4 #ae7 are as follows-- ,fig4 #ae4--;,intensity of ,rays reflected from ,vermilion1 ,emerald ,green1 and ,french ,ultramarine4 ,b#aja1 ,c#ifbe1 ,d#hi1 ,e#gii1 ,f#gae1 ,g#ece4 ,,vermilion4 ---------------------------------------- ------- ,white ,sectors4 -----------------------------------,read ing of ,original ,white ,cor-,corrected ,spectrum ,setting4 rected ,for ,white ,scale4 -------------- ,black4 #ajj4 ,white4,black4 ---------------------------------------- --- #aj #cej #bge #gfe #ga-a_/b #bj #cdj #cgj #ajae #hd #cj #ccj #dfe #abie #hfb #ej #caj #fee #ahaj #hhj #gj #bij #hde #bcej #hhg #ij #bgj #ajce #big #hie #abj #bdj #acbj #cgb #ijc #aej #baj #afje #dej #ia #ahj #ahj #ahij #ebe #iaf #baj #aej #bage #fjb #ibe #bbj #adj #bbgj #fcb #ice #bcj #acj #bcfe #ffb #ide #bdj #abj #bdfj #fhe #if #bcj #acj #bcfe #ffb #igg #baj #aej #bage #fjb #ajjj ---------------------------------------- --- ,,emerald ,,green4 ---------------------------------------- ----------- ,white ,sectors -------------------------------------- ,reading of ,original ,setting4,white ,cor-,corrected ,spectrum -----------------rected ,for ,white ,scale4 ,white4 ,black4 ,black4 #ajj4 ---------------------------------------- -------- #aj #cej #bge #gfe #ej #bj #cdj #cgj #ajae #ed #cj #ccj #dfe #abie #ee #ej #caj #fee #ahaj #ege #gj #bij #hde #bce #fjj #ij #bgj #ajce #big #fce #aaj #bej #abbe #cdg #fee #acj #bcj #adae #cie #fge #aej #baj #afje #dej #fhe #agj #aij #agie #ejj #ga #aij #agj #aiee #edg #gce #baj #aej #bage #fjb #gej #bbj #adj #bbg #fcb #gf #bbj #adj #bbg #fcb #gh #baj #aej #bage #fjb #hj #aij #agj #aihe #edg #hb #agj #aij #agie #ejj #hc #aej #baj #afje #dej #hd #acj #bcj #adae #cie #he #aaj #bej #abbe #cdg #hfe #ij #bgj #ajce #big #hge #gj #bij #hde #bce #hhe #ej #caj #fee #ahaj #ijj #cj #ccj #dfe #abie #ib #bj #cdj #cgj #ajae #id #aj #cej #bge #gfe #ih ---------------------------------------- -------- ,,french ,,ultramarine ,,blue4 ---------------------------------------- ------------- ,white ,sectors4 --------------------------------------- ,reading of ,original ,setting4 ,white ,corrected ,spectrum ---------------- corrected ,white ,scale4 ,white4 ,black4 for black4 #ajj4 ---------------------------------------- ---------- #j #cfj #ahj #ej #hd #aj #cej #bge #gfe #hj #bj #cdj #cgj #ajae #gg #cj #ccj #dfe #abie #ge #dj #cbj #efj #aef #gd #fj #cjj #gej #bjg #gbe #hj #bhj #idj #bee #gje #ajj #bfj #aacj #cbe #fh #abj #bdj #acbj #cgb #ffe #adj #bbj #aeaj #dbc #fbe #afj #bjj #agjj #dgd #eie #agj #aij #agie #ejj #ee #afj #bjj #agjj #dgd #ea #adj #bbj #aeaj #dbc #df #j #cfj #ahj #ej #ie #aj #cej #bge #gfe #ih #bj #cdj #cgj #ajae #ii #cj #ccj #dfe #abie #aaj ---------------------------------------- ---------- ,these three measurements have been given in full1 since they will be useful for reference when other experiments are described4 ,fig4 #af4--,method of obtaining two ,patches of identical ,colour4 ,when we have to measure the colour transmitted through coloured bodies1 we have to adopt a slightly different plan1 which is extremely accurate4 ,the first thing necessary is to make some arrangement whereby two beams of identical colour--that is1 of the same wave-length--reach the screen1 one of which passes through the transparent body to be measured1 and the other unabsorbed4 ,if we in addition have some means of equalizing the intensity of the two beams1 we can then tell the amount cut off by the body through which one beam passes4 ,the method that would be first thought of would be to use two spectra1 from two sources of light2 but should we adopt that plan there would be no guarantee that the spectra would not vary in intensity from time to time4 ,the point then that had to be aimed at was to form two spectra from the same source of light1 and with the same beam that passes through the slit of the collimator4 ,here we are helped by the property of ,iceland spar1 which is able to split up a ray into two divergent rays4 ,by placing what is called a double-image prism of ,iceland spar at the end of the collimator1 we get two divergent beams of light falling on the prisms1 and by turning the double-image prism we are able to obtain two spectra on the screen of the camera one above the other1 and if the slit of the slide be sufficiently long two beams would issue through it of identical colour1 and separated from one another by a dark space1 the breadth of which depends on the length of the slit of the collimator4 ,it is to be observed that by this arrangement we have exactly what we require3 a light from one source passes through the same slit1 is decomposed by the same prisms1 and as the beams diverge in a plane passing through the slit of the collimator1 the length of spectrum is the same4 ,the problem to solve is how to utilize these two spectra now we have got them4 ,we can make the light from the top spectrum pass through the coloured body by the following artifice4 ,let us place a right-angled prism in front of the top slit1 reflecting say the beam to the right1 and after it has travelled a certain distance1 catch it by another right-angled prism1 and thus reflect it on to the screen4 ,already in the path of the ray1 issuing through the slit from the bottom spectrum1 the lens ,l#d is placed1 forming a square patch on the screen4 ,by placing a similar lens in the path of the other ray after reflection from the second right-angled prism1 we can superpose a second patch of the same colour over the first patch1 and by putting a rod in the path of the two beams we can have as before two shadows side by side1 but this time each illuminated by the same colour4 ,one shadow will be more strongly illuminated than the other1 owing to the different intensities of beams into which the double-image prism splits up the primary ray4 ,the two1 however1 can be equalized by placing a rotating apparatus in the path of one of the beams4 ,when equalized the sector is read off1 and tells us how much brighter one spectrum is than the other4 ,thus suppose in the direct beam the sectors had to be closed to an angle of #hj1 to effect this1 the bottom spectrum would be #ahj_/hj1 or #bbe times brighter than the bottom spectrum4 ,it should be noted that as the two spectra are formed by the identical quality of light1 this same ratio will hold good throughout their length4 ,if it does not1 it shows that the double-image prism is not in adjustment1 and that the same rays are not coming through the slit in the slide1 and it must be rotated till the readings throughout are the same4 ,one of the most sensitive tests for adjustment is to form a patch with orange light1 when the slightest deviation from adjustment will be seen by the two patches differing in hue4 ,we can now place the coloured transparent object in the path of the beam which is most convenient1 and by again equalizing the shadows1 measure the amount it cuts off2 this we can do for any ray we choose4 ,as both right-angled prisms can be attached to the card or slide which moves across the spectrum1 nothing besides the card need be moved4 ,in the following diagram we have the proportion of rays transmitted by the three different glasses1 red1 green1 and blue1 in terms of the unabsorbed spectrum4 ,take for instance on the scale of the spectrum the number #aa4 ,the curve shows that at that particular part of the spectrum which lies in the blue1 the blue glass only allowed #d_/ajj or #a_/be of the ray to pass1 whilst the green glass allowed #aj_/ajj or #a_/aj to pass4 ,so at scale ,no4 #d in the orange1 through the blue only #b was transmitted1 through the green glass #d1 and through the red #bj4 ,fig4 #ag4--;,absorption by ,red1 ,blue1 and ,green ,glasses4 ,fig4 #ah4--,light reflected from ,metallic ,surfaces4 ,fig4 #ai4--a4 ,vermilion #b4 ,carmine4 #c4 ,mercuric ,iodide4 #d4 ,indian ,red4 ,from such curves as these we can readily derive the luminosity curves of the spectrum1 after the white light has passed through the coloured object4 ,all we have to do is to alter the ordinates of the luminosity curve of white light in the proportion to the intensities of the rays before and after passing through the object4 ,it will be seen that when the luminosity curve of the spectrum of any source is known1 this method holds good4 ,fig4 #bj4--a4 ,gamboge4 #b4 ,indian ,yellow4 #c4 ,cadmium ,yellow4 #d4 ,yellow ,ochre4 ,the intensity of the different rays of the spectrum reflected from metallic surfaces can also be measured1 if for the first or second right-angled prism a small piece of the metal is substituted1 using it as a reflecting surface1 as can also the rays reflected from any surface which is bright and polished4 ,in ,fig4 #ah the dotted curves show the luminosity of the spectrum reflected from the different metals1 curve ,v being that of white light4 ,these curves are derived by reducing the ordinates of curve ,v proportionately to the intensity curves4 ,thus at #di brass reflects #gg of the light1 and the luminosity of the white is #hj4 ,the luminosity of the light from the brass is therefore #gg_/ajj of #hj1 or #fa4 ,this shows the method which is adopted1 of deducing luminosities from intensities4 ,fig4 #ba4--a4 ,emerald ,green4 #b4 ,chromous ,oxide4 #c4 ,terre ,verte4 ,the light reflected from pigments can also be measured by the same plan4 ,the procedure adopted is that carried out when measuring their luminosities1 viz4 to cause the ray from one spectrum to fall on a strip of a white surface1 and that from the other on a strip of the coloured surface 7see page #hb74 ,this is a more convenient method than that just described1 when the coloured surface is small4 ,the annexed figures 7,figs4 #ai1 #bj1 #ba1 #bb7 show the results obtained from various pigments4 ,fig4 #bb4--a4 ,indigo4 #b4 ,antwerp ,blue4 #c4 ,cobalt4 #d4 ,french ,ultramarine4 ,fig4 #bc4--,method of obtaining a ,colour ,template4 ,from curves such as these we are able to produce the colour of the pigment on the screen from the spectrum itself4 ,this is a useful proof of the truth of the measurements made4 ,to do this we must mark off on a card 7,fig4 #bc7 the absolute scale of the spectrum along the radius of a circle1 and draw circles at the various points of the scale from its centre4 ,from the same centre we must draw lines at angles to the fixed radius corresponding to the various apertures of the sectors required at the various points of the scale to measure the light reflected from a pigment4 ,where each radial line cuts the circle drawn through the particular point of the scale to which its angle has reference1 gives us points which joined give a curved figure4 ,such a figure1 when cut out and rotated in front of the spectrum in the proper position 7as for instance by making the ,d sodium line correspond with that on the scale71 will cut off exactly the same proportion of each colour that the pigment absorbs4 ,the spectrum1 when recombined1 should give a patch of the exact colour of that measured4 ,the spectrum must be made narrow1 as the template is only theoretically correct for a spectrum of the width of a line1 as can be readily seen4 ,templates like these will always enable any colour to be reproduced on the screen1 and if the light be used for the spectrum in which the colour has to be viewed1 be it sunlight1 gaslight1 starlight--whatever light it is--the colour obtained will be that which the pigment would reflect if it were viewed in that light4 ,the identity of the colour produced on the screen by this plan with that measured1 can be readily seen by placing the latter in the reflected beam of white light alongside the coloured patch formed on the white surface4 ,fig4 #bd4--,template of ,carmine4 ,in ,fig4 #bd we have a mask or template of carmine1 which was used for determining if the measurements were right4 ,the black fingerlike-looking space on the right was the amount of red reflected light1 and the other that of the blue and violet2 scarcely any light at all was reflected from the green part of the spectrum4 ,fig4 #bf4--;,absorption of transmitted and reflected ,light by ,prussian ,blue and ,carmine4 ,on page #ajh we have given the diagram of the luminosity of the spectrum in reference to a standard white light4 ,it will bring this luminosity more home if1 in a similar manner to that described above1 we make a template of this curve 7,fig4 #be74 ,we can place a narrow slit horizontally in front of the condensing lens of the optical lantern1 and throw an image of it on to the screen4 ,if in close contact with this slit we rotate the template1 we shall have on the screen a graduated strip of white light1 giving in black and white the apparent luminosity of the spectrum as seen by the eye4 ,fig4 #be4--,template of ,luminosity of ,white ,light4 ,it has been stated in chapter ,v41 that it is generally immaterial whether a pigment is in contact with the paper or away from it1 so long as the light passes through the pigment4 ,the above figure 7,fig4 #bf7 shows the truth of this assertion4 ,i4 and ,,ii4 are the curves taken of the light transmitted by ,prussian blue and carmine respectively1 and ,,iii4 and ,,iv41 from the light reflected from these colours on paper4 ,fig4 #bg4--;,collimator for comparing the intensity of two sources of ,light4 ,to measure the difference in the intensities of the rays of different sources of light we can use a spectroscopic arrangement with two slits 7,s7 7,fig4 #bg7 placed in a line at right angles to the axis of the collimator4 ,one slit is a little below the other1 the rays being reflected to the collimating lens ,l1 by means of two right-angled prisms ,p1 and two spectra are formed1 one above the other4 ,by placing the rotating sectors in front of one of the sources1 the intensities of the different parts of the spectrum can be equalized and measured4 ,fig4 #bh4--,spectrum ,intensities of ,sunlight1 ,gaslight1 and ,blue ,sky4 ,the curves for the annexed figure 7,fig4 #bh7 were derived from measures taken in this manner4 ,if the rays of a ,may-day sun are taken at #ajj1 it will be seen what a rapid diminution there is in the green and the blue rays in gaslight4 ,gaslight only possesses about #bj of the green rays1 whilst of the violet hardly #e4 ,on the other hand the light which comes to us from the sky shows a very marked falling off in the yellow and red rays4 ,a very easy experiment will convince us of the difference in colour between skylight and gaslight4 ,if we let a beam of daylight fall on a sheet of paper at the end of a blackened box1 and cast a shadow with a rod by such a beam1 and then bring a lighted candle or gas-flame so that it casts another shadow of the rod alongside1 one shadow will be illuminated by the artificial light1 and the other by the daylight4 ,the difference in colour will be most marked3 the blue of the latter light and the yellow of the former being intensified by the contrast 7see page #aih74 ,fig4 #bi4--;,comparison of ,sun and ,sky ,lights4 ,by a little trouble the blue light from the sky may be compared with sunlight4 ,a beam of light ,b 7,fig4 #bi7 is reflected by a silvered glass mirror from the blue sky into the box ,,hh1 at the end of which is a screen ,e4 ,another mirror ,a1 which is preferably of plain glass1 reflects light from the sun on to a second unsilvered mirror ,g 7shown in the figure as a prism71 which again reflects it on to the screen1 and each of these lights casts a shadow from the rod ,d2 ,k are rotating sectors to diminish the sunlight1 and we can make two equally bright shadows alongside one another4 ,the bluer colour of the sky will be very evident4 ,,chapter ,,ix4 ,colour ,mixtures--,yellow ,spot in the ,eye--,comparison of ,different ,lights--,simple ,colours by mixing ,simple ,colours--,yellow and ,blue form ,white4 ,the colour of an object in nature1 without exception we might almost say1 is due1 not to one simple spectrum colour1 or even to a mixture of two or three of them1 but to the whole of white light1 from which bands of colour are more or less abstracted1 the absorption taking place over a considerable portion or portions of the spectrum4 ,notwithstanding this we shall now experimentally show that every colour can be formed by the simple admixture of not more than three simple colours1 if they be rightly chosen1 and from this we shall make a deduction regarding vision itself4 ,we are in a position to obtain three simple colours by means of a slide containing three slits4 ,now for our purpose we require that the three slits can be placed in any part of the spectrum1 and that they can be narrowed or widened at pleasure4 ,instead of a card the writer uses a metal slide1 as shown in ,fig4 #cj4 ,fig4 #cj4--,slide with slits to be used in the ,spectrum4 ,it will be seen that the three slits can be closed or opened from the centre by a parallel motion4 ,they also slide in a couple of grooves1 so that they can be moved along the frame into any position4 ,the position they occupy is indicated by a scale engraved on the front of the slide4 ,behind the grooves in which the slits move are another pair of grooves1 into which small pieces of card ,,cccc can slide1 and thus close the apertures between the slits4 ,by this arrangement all rays except those coming through the slits themselves are cut off4 ,the metal frame fits on to an outer wooden frame1 which slides in the grooves used with the card in the apparatus as already described4 ,it is convenient always to keep the scale on the back of this wooden slide in the same position as regards the shadow of the needle-point used for registering the position1 and to move the slits along their grooves when a change in position is required4 ,using these three slits three different colours can be thrown on the same square patch on the screen4 ,a very crucial experiment is to see if we can make white light by the admixture of three colours1 for if this can be done it almost follows that any colour can be formed4 ,we must use the colour patch apparatus1 and begin with placing one slit in the violet near the line ,g1 another between ,e and ,f1 and a third between ,b and ,c of the solar spectrum1 and fill up the gaps between them with cards as shown in the figure4 ,for our present purpose it is better to make the colour patch and the white patch touch each other1 not using the rod1 as by this means we avoid fringes of colour4 ,we shall find that the aperture of the slits can be so altered that we can produce a perfect match with the white reflected light4 ,by placing the rotating sectors in front of the reflected beam we can reduce its intensity1 so that the two patches are equally bright4 ,by a tapering wedge we can measure the width of the slits1 and thus get the proportions of these three different colours which must be used to give the white4 ,this is a sample of the method that we employ when we match any other colour4 ,suppose1 for instance1 it be wished to measure the colour of a solution of bichromate of potash2 it is placed in the path of the reflected light1 and we have an orange strip of light which we have to match4 ,in this case it will be found that the slit in the blue has to be closed entirely1 and only the green and red slits opened4 ,the intensities of the two lights are equalized by the rotating sectors as before4 ,so again with a solution of permanganate of potash4 ,in this instance no green light will be required 7or if any of it but a trifle71 and the colour of the permanganate will be formed by the rays coming through the blue and red slits4 ,this plan is a very useful one for measuring all kinds of transparent colours in terms of three rays4 ,the method of finding the intensity of any ray of the spectrum transmitted by any such medium has already been explained4 ,the latter has one advantage over the former1 in that the measurements by it are exact1 whatever source of light be used to form the spectrum4 ,by the method now described this is not the case4 ,for instance1 the colour of permanganate of potash may be matched in the electric light with the red and blue slits4 ,if the limelight were substituted for the electric light1 it would be found that the slits would require other apertures1 not proportional to those already formed1 to match the colour of this substance4 ,fig4 #ca4--,screen on which to match ,gamboge4 ,if we wish to register the tint of any pigment1 we have to slightly alter our mode of procedure4 ,suppose1 for instance1 we wish to register the colour of gamboge4 ,in such a case we paint a small bit of card 7,fig4 #ca7 with the pigment1 and divide the white space on which the colour patches are thrown into two parts1 and cover one-half with the pigmented card1 leaving the other half white4 ,the reflected beam illuminates the pigment1 and the spectrum patch the white4 ,the widths of the three slits are then altered till the two tints agree1 and the brightness matched by means of the rotating sectors4 ,there are certain sad and sthetic colours which it might be considered cannot be matched by a mixture of three colours4 ,a brown colour1 or eau de nil1 might appear to come out of the range of matching4 ,these colours1 however1 can be matched in precisely the same manner as the brighter colours are matched4 ,thus a brown pigment will be found to require red and a little green1 and a trifle of blue2 and the only difference between it and a brighter shade of the same colour1 is that more total light has to be cut off from it to give the sombreness4 ,a sad colour only means a pigment or dye which reflects but little light1 and if that be so it can naturally be matched by using but very small quantities of the compounding colours4 ,there is one curious phenomenon to which attention may be called in this matching1 which is worthy of remark4 ,the match will be found to differ according as the patches are compared from a distance of a couple of feet1 or from a considerable distance4 ,more green will be required in the latter case than in the former4 ,if matched at a distance of about six feet1 and the eyes be then turned so that the edge of the patch falls on their centres1 it will be noticed that the colour mixture appears of a green hue4 ,this last experiment indicates that the retina is not equally sensitive for all colours throughout its area4 ,physiologists tell us that what is known as the yellow spot occupies a central position in the retina1 and that it absorbs a part of the spectrum lying in the green4 ,now when the eyes are close to the patch1 its image occupies a considerable part of the retina1 and the colour is compounded as it were of the colour as seen on the yellow spot1 and of that beyond it1 for the yellow spot will take in an image of from six to eight degrees in angular measurement4 ,when viewed at a distance we have the image of the patch falling almost entirely on the yellow spot1 and hence a greater quantity of green is required1 as it has to make up the deficiency caused by the absorption4 ,when the eyes are turned a little on one side the image falls on the outside of the yellow spot1 and the patch illuminated by the mixed light appears green1 compared with the patch illuminated with the white reflected beam4 ,it is thus evident that when colour matches have to be made1 the distance of the eye from the screen should always be stated1 as also the dimensions of the patches viewed4 ,it may be fairly asked why1 if the half patch illuminated by the mixed colours appears greener when the eye is turned1 the other should not equally do so4 ,this is a very fair question to ask4 ,it must be remembered that one strip is illuminated with white light1 in which every coloured ray of light is compounded1 whilst in the other only three rays are blended4 ,the green ray chosen happens to be taken from that part of the spectrum which is absorbed by the yellow spot2 but all of the green rays of the spectrum are not so much absorbed1 hence in ordinary white light1 in which all the green rays are present1 only a small percentage of the total green in the spectrum is absorbed1 compared with that absorbed from the single green ray with which the match is made4 ,no doubt both patches are really greener when the eye receives the impression of their images outside the yellow spot1 but one is much greener than the other1 and it is thus comparatively green4 ,it is possible to make a match with some colours with a blue-green in which the phenomenon described does not appear2 but in cases where a match has to be made with colours in which but little blue is required1 it would be impossible to make it1 owing to the blue existent in such a green-blue ray4 ,we will now return to our compounding of three colours to make white4 ,why have we chosen the positions of the slits which we did in the spectrum for its formation8 ,would not other positions answer as well8 ,let us give our answer by experiment4 ,let us move the slit which is now in the green towards the red2 we shall find that as we do so--and keeping the blue slit of the same width--that we shall have to close the red slit1 and alter the aperture of the green slit itself4 ,if we reason on this point we shall be forced to the conclusion that the green slit lets through more red light of some description1 as less red from the red slit is required to make the match4 ,if we move the green slit almost into the yellowish green1 we shall find that the red slit has to be entirely closed1 and that white light is formed of the two colours1 yellowish green and violet4 ,this shows us that the yellowish green colour here used is formed by a mixture of the red and green rays which passed through the two slits in their original positions4 ,if we replace the slits in these positions and close the violet slit1 we are at once able to verify it4 ,if we again form white light with the slits in their original positions1 and move the green slit towards the blue1 we shall find that1 keeping the red slit at a constant aperture1 the blue slit will have to be closed1 and the green slit altered in width4 ,the necessity of lessening the aperture of the blue slit shows that there is a certain amount of blue light coming through the green slit4 ,at one point1 when the slit has travelled into the blue-green1 the blue slit may be entirely closed1 and white light be formed of this and the red1 showing that the blue-green colour is composed of the same proportions of blue and green which passed through the blue and green slits in their original position4 ,the positions chosen were arrived at by the writer from experiments made in this manner1 moving first one slit and then the others1 and the position of the green slit was confirmed by a consideration of the neutral point which exists in a green colour-blind person's spectrum4 ,the method of mixing three colours together gives us a means of imitating all kinds of white light1 as it does of coloured light4 ,at page #aaj we have already given a diagram of the relative amounts of spectrum colours in sunlight1 skylight and gaslight4 ,if we by any means throw a patch of the light which we wish to match on the patch formed by the colour patch apparatus1 and interpose the rod1 we can measure the apertures of the three slits1 and thus arrive at the relative proportions of each colour present4 ,in an experiment carried out1 sunlight1 the electric arc-light1 and gaslight were compared in this manner4 ,the following are the results1 the red being near the ,c line1 the green near the ,e line1 and the violet near the ,g line of the solar spectrum4 ---------------------------------------- ----------- ,sunlight4 ,electric ,gaslight4 ,skylight4 ---------------------------------------- ----------- ,red #ajj #ajj #ajj #ajj ,green #aic #bjc #ie #bef ,violet #bbh #bej #bg #gfj ---------------------------------------- ----------- ,now from the above it might seem that as three simple spectrum colours will give us the colour of any pigment1 that therefore two colours ought to give us the same colour as any intermediate simple colours in the spectrum which lie between them2 for instance1 that the simple blue-green ought to be obtained by mixing spectral green and spectral violet together4 ,this can be ascertained with a single colour patch apparatus1 by cutting a slit in the card that fills up the aperture between the two adjustable slits1 and deflecting the beam transmitted through it by a right-angled prism1 and back on to the screen through another similar prism1 as described in chapter ,,viii4 ,it is more convenient1 however1 to use a duplicate apparatus precisely similar to the first1 with the exception that no collimator is required1 placing them side by side1 and mirrors making the reflected beam from the first traverse the second set of prisms4 ,there will be a reflected beam from the second apparatus1 which can be utilized in the same way as was that from the first apparatus1 and the two spectra will vary together in brightness1 as will also the new reflected beam1 since they all are formed by the light coming through one slit4 ,a patch of the colour intermediate between the two is thrown on the screen from the second apparatus1 and the second patch from the first apparatus overlaps it4 ,a rod placed in the usual manner throws two shadows1 which are illuminated by the two different beams4 ,if blue-green be a colour it is wished to match1 it will be found that no matter in what part of the violet and green the slits are placed1 no match can be effected4 ,but if some very small quantity of red light be mixed with simple blue-green1 that then a colour identical in every respect as regards the eye can be obtained from the violet and green of the first apparatus4 ,it must be remembered that a mixture of red1 green and violet form white1 and that they are mixed in definite proportions4 ,no matter how feeble in intensity the white may be1 the same proportions will still obtain4 ,in the above experiment1 as the blue-green must contain violet and green1 the small quantity of red must combine with the proper proportion of violet and green1 and will form white light1 so that the match is obtained by the residues of the violet and green mixed with the small quantity of white light1 of which the red is the indicator4 ,we can test the truth of this argument in a very simple way4 ,if we add to the colour with which the match has to be made a small quantity of white light from the reflected beam1 cutting off more or less by the rotating sectors1 we can get the exact hue of the impure blue-green made by the mixture of the colours coming through the two slits2 and further we shall find that the amount of white added corresponds with the amount of red which would be required when the components of the white light in the terms of the three colours are taken into account4 ,for spectrum colours between the violet and the green it may therefore safely be said that no match can be effected by the mixture of violet and green light2 but that it always gives the intermediate colour diluted with white light4 ,for colours between the green and the red of the spectrum1 a very close1 if indeed not an exact match1 can be made with the red and green slits1 without the addition of white4 ,if we take from the second apparatus light from above the position of the violet slit in the first apparatus1 that is1 nearer the limit of visibility1 it will be found that a match is made1 for at all events a very considerable way with the violet slit alone1 by merely reducing the aperture1 thus showing that the colour is the same1 only less intense4 ,in the same way it will be seen that the rays coming from any point between the lower limit of the spectrum to a little below the ,c line are identical in colour4 ,as we have arrived at the fact that in colour mixtures of violet and green1 white light is to be found in the colour produced1 it follows that either the violet or the green1 or both1 must themselves contain some small proportion of white4 ,it might perhaps be said that violet is really a mixture of red and blue1 and hence the white in the mixture with the green2 but if in the first apparatus we place one slit in the purest blue we can find1 and the other in the red1 and throw a violet patch on the screen from the second apparatus1 we shall be unable to form the same hue of violet by any means2 it will always be diluted with white4 ,now as the very blue we are using1 if matched as above by green and violet1 requires white light to be added to it1 and as to match the violet with the same blue and red1 white light has also to be added to it1 it follows that the violet must be freer from white light at all events than the blue4 ,there is one other experiment that must be mentioned before leaving for a time this part of our subject1 viz4 the formation of white by a mixture of yellow and blue4 ,if one of the slits be placed in the yellow of the spectrum1 a position will be found in the blue where1 if a second slit be placed1 and the apertures are adjusted1 an absolute match with the reflected white of the apparatus can be secured4 ,this experiment will be referred to later on1 when considering the question of primary colours4 ,the above experiments have a great bearing on the theory of colour vision1 and should be considered very carefully in connection with the shortened spectrum which we have shown exists when red colour-blind people are observing its luminosity4 ,there is one point to be recollected in relation to the mixtures of the three or two different colours which make white light4 ,if different coloured pigments be illuminated by the made white light1 they will not appear of the same hues1 as a rule1 as when viewed by ordinary white light4 ,they will vary not only in colour1 but in brightness4 ,this might be expected when the spectral light which they reflect is taken into account4 ,,chapter ,x4 ,extinction of ,colour by ,white ,light--,extinction of ,white ,light by ,colour4 ,in the last chapter we have shown the impossibility of matching the hue of the simple colours between the violet and the green1 unless a certain and appreciable quantity of white light be added to them4 ,we will now turn to a phase of colour measurement which will materially help us to see why1 in some cases1 the addition of white light to the simple spectrum colours1 between the red and green1 does not appear necessary in order to make a match with a mixture of red and green4 ,we will ask ourselves two questions3 one is1 whether any colour1 and if so how much1 can be added to white without appearing to the eye8 and the other1 if any1 and if so how much1 white light can be added to a colour without its being perceived8 ,perhaps one of the readiest methods of explaining exactly what we mean is by a rotating disc4 ,suppose we have a red disc1 of nine or ten inches in diameter1 and at every one inch from the centre paste on it a white wafer about one-eighth of an inch in diameter1 and cause it to rapidly rotate4 ,on examination we shall find that pink rings will be formed by the combination of the white and red near the centre1 but that towards the margins no rings will be visible1 owing of course to more red being combined with the same amount of white4 ,this shows that the eye is only sensitive to a certain degree1 and cannot distinguish a very small diminution in colour purity4 ,the intensity of the light has something to do with the number of these pink rings which are visible1 as may readily be tested in a room4 ,if the rotating disc be placed near a window1 and the number of rings visible be counted1 a different number will be visible when it is placed in a dark corner4 ,a kindred experiment is to place red circular wafers upon a white disc1 and note the rings visible4 ,this gives the sensitiveness of the eye for the diminution in intensity at the other end of the scale4 ,it will be found that there is a marked difference between the two4 ,fig4 #cb4--;,diaphragm in front of ,prism4 ,it is more instructive if we experiment with pure colours1 and so we must resort to our colour patch apparatus described in ,fig4 #f4 ,if a small circular aperture about quarter of an inch in diameter be cut in a card1 and placed in front of the prism nearest the camera lens 7,fig4 #cb71 the colour patch1 instead of being an image of the face of the prism1 will be an image of the circular hole1 and when the slit is passed through the spectrum we shall have a coloured spot on the screen1 on which we can superpose a patch of white light from the reflected beam4 ,there are two ways in which we can reduce the intensity of the spot1 by narrowing the slit through which the spectral ray passes or by placing the rotating sectors in front of the coloured beam4 ,this last1 perhaps1 is the readiest plan1 as it only involves the reading of the sector4 ,we can then diminish the intensity of the coloured spot to such a degree that by its dilution with white light it will entirely disappear4 ,it will be found that red disappears at a different aperture of sector to that required for the green1 and the green to that for the blue4 ,from our previous experiments in chapter ,,vii4 we know the luminosity of the spectrum to the eye1 and it will be of interest to see what relation the luminosity at which the spots of different colour disappear1 when they are so diluted with white light1 bear to the total luminosity of these rays4 ,in a set of measurements made it was found that the reduced angular apertures required for the colours indicated by the following were3 ,b required #cjj99 of aperture4 ,c #ef ,d #ad ,e #bb ,f #aej ,g #bajj99 ,the large numbers marked with an asterisk were obtained by placing the rotating sectors in front of the white reflected beam4 ,the light of ,d had to be reduced to #ad before it was extinguished2 therefore to extinguish the original light of this colour in the spectrum would require #ahj_/ad1 or #abi times the intensity of the white light of the reflected beam4 ,with the ,e light it would take #ahj_/bb1 or #hb times the white light to extinguish it1 and so on4 ,if we tabulate the results in this manner1 and take the white light necessary to extinguish the ,d light empirically as #ihe1 which is its percentage luminosity in the spectrum of the electric light1 we can then compare the extinguishing factor with the luminosity in each case4 ---------------------------------------- --------------- ,white required ,white required to extinguish ,luminosity ,colour4 to ,extinguish the ,spectrum1 of the ,spectrum4with #ej as ,that ,spectrum4 required at ,e4 ---------------------------------------- ------------- near line ,b #f #ci #di ,c #cb #aie #bjf ,d #abi #gh #ihe ,e #hb #ej #ej ,f #ab #ge #ge ,g #jhg #ef #f ---------------------------------------- ---------------- ,the very close resemblance between the last two columns indicates that the same luminosity of white light is necessary to extinguish the same luminosity of most colours1 within the limits of observation that is to say4 ,indeed the method of extinction was a plan which ,draper and ,vierordt essayed1 but the results1 tabulated from experiments made by them with the apparatus they employed1 give a curve of intensity very unlike that given in ,chapter ,,vii4 ,in these experiments the luminosity of the orange light corresponding to the ,d line coming through the slit was measured1 and it was found to be #cge_/ahj of the white light4 ,now according to the last table but one #ad_/ahj of this light was extinguished by the full white light1 consequently #cge_/ahj x #ad_/ahj1 or #a_/fb of the orange light was extinguished by the white light4 ,in other words1 if white light be sixty-two times brighter than the orange light1 the colour of the latter when the two are mixed will be invisible4 ,the extinction of all colours requires somewhat more light than this1 and a calculation shows that the extinction of every colour is effected by white light1 which is seventy-five times brighter than the colour4 ,artists are well aware that a pale wash of a pigment may be washed over drawing paper1 and when dry is invisible to the eye4 ,the above experiments fully account for it4 ,the other experiment which was to be tried was to see how much white light could be extinguished by a colour4 ,there are several ways by which this can be effected4 ,for instance we may superpose a white dot on the colour patch by placing a card1 in which a circular hole is cut1 in the reflected beam near the prism1 from which the reflection takes place2 or by putting a black circular disc of small dimensions pasted on a glass in the same position1 by which means the white light is superposed over the whole of the colour patch1 with the exception of what1 when the colour is cut off1 is a black spot2 or again by placing a rod to shade half the patch from the white light1 but leaving the whole of it exposed to the coloured beam4 ,all these methods have been tried1 and it appears that the size of the piece of the patch over which the white light is thrown may have some effect on the resulting curve1 but of one thing there is evidence1 viz4 that a great deal more white light can be mixed unperceived with orange light1 than can be with the green1 blue1 or violet4 ,from one experiment it was found that #a_/cf part of white light of the same luminosity as the orange could be mixed with the orange and not be perceived2 but that with the green light at ,e #a_/ij would just be visible1 whilst at ,f in the blue-green the #a_/abj could be distinguished4 ,looking at these results1 and applying them in elucidating the experiments in which it was attempted1 but without success1 to match the intermediate colours between violet and green 7of which the light at ,f is a case in point71 by mixing them together1 unless white light were added to the simple colour2 and the success of the other experiment1 in which orange light could be obtained of the same hue as that at ,d by a mixture of the red and green1 it will be noticed that #cc times more white light can be added to the orange than to the green light at ,f1 without its perception4 ,the white light produced by the mixture in the first case might well show when mixed with the green1 but might pass wholly unperceived when mixed with the orange4 ,,chapter ,,xi4 ,primary ,colours--,molecular ,swings--,colour ,sensations--,sensations absent in the ,colour-blind4 ,for some purposes it is advantageous to show experiments before indicating the deductions from them which may lead to a theory4 ,those described in ,chapter ,,ix4 will enable us to treat the theory of colour perception from a standpoint of some advantage4 ,how is it that the combination of three colours suffices to form white1 or to match any colours we wish1 be they spectrum colours to which a little white is added1 or the colours of pigments8 ,the most plausible theory that can be advanced is that it is only necessary for the eye to be furnished with a three-colour-perceiving apparatus to give the impression of every colour1 and yet this would be somewhat difficult to believe had we not had the experiments narrated in that chapter before us4 ,we should have almost expected some machinery in the eye to exist1 which would answer to the rhythmic swing of the rays of every wave-length which together make up white light4 ,but now we have to stand face to face with the results of experiment1 and we find that at the most only three colours are necessary to make up white light1 and that from these three spectrum colours we can form any others1 with the limitation already mentioned1 when some simple colours are in question4 ,we must here digress for a moment1 and notice the fact that from our experiments we have derived the three primary colours as they are called1 viz4 red1 violet1 and green2 the definition of a primary colour being that it cannot be formed by the mixture of any other colours4 ,we have ascertained that yellow and blue make white4 ,it is therefore evident that blue1 yellow1 and red cannot be primary colours1 since two of them form white2 and we have moreover shown that yellow can be made from green and red2 hence it might be fair to assume that the three primary colours are red1 green1 and blue4 ,but blue1 when mixed with a very small percentage of white light1 can be made by green and violet4 ,hence1 in the white light formed by the two colours yellow and blue1 we have the first made by green and red1 and the second by green and violet2 hence the three colours which really make the white light are red1 green1 and violet4 ,the approximate positions of these three colours in the spectrum are those already indicated2 though1 as we shall presently see1 it is highly improbable that any person whose eyes are what are called normal1 has ever experienced the fundamental green sensation4 ,the fact that red1 yellow1 and blue cannot be primary colours has been mentioned1 as even now it is sometimes taught that they are so4 ,as long as the theory of colour principally lay with artists there was reasonable ground for their assumption1 since they worked with impure colours1 viz4 those of pigments2 and as we shall see later on the truth of the assumption agreed with such experiments as they would make4 ,when1 however1 the question was taken up by the physicist with more exact methods of experimenting1 and with pure colours1 the falsity of the old triad was soon capable of proof4 ,to return from our digression3 how it is that three mixed colours can give the sensation of white light is at first sight hard to understand2 but a reference to the action of light on a photographic salt helps us in some degree4 ,in the case of a sensitive salt1 such as the bromo-iodide of silver1 we find that a chemical decomposition is caused by the violet end of the spectrum1 and is only feebly affected by any other part1 though with prolonged exposure even the red will cause it4 ,the annexed figure 7,fig4 #cc7 gives the idea of the relative action of different parts of this violet portion4 ,fig4 #cc4--;,curve of ,sensitiveness of ,silver ,bromo-iodide4 ,the height of the curve shows the relative effects produced4 ,now this curve is not symmetrical1 but has a maximum effect nearer to the violet end of the spectrum than to the red4 ,the atomic composition of the silver bromo-iodide is probably two atoms of silver and one of bromine and one of iodine oscillating together1 and we can conceive of some one atom1 the period of whose swings in its molecule is isochronous with some wave-length of light4 ,further1 we can conceive that1 like a pendulum whose vibrations are increased in magnitude by well-timed blows1 the swing of the atom is also increased1 and that eventually it gets beyond the sphere of the attraction of its parent molecule1 leaves it1 and is attracted to some neighbouring molecule of different constitution1 and that thus a chemical change is induced4 ,this we can conceive1 but how can other waves1 which are not isochronous with the rhythmic swing of the atoms1 alter the composition of the molecule8 ,if we have an impulse given to a pendulum exactly timed with the period of oscillation1 there is no doubt that the swing is increased4 ,if we have one nearly in accord1 it will be found that though the swings are not increased in amplitude so greatly as when there is perfect accord1 yet an increased swing is given1 and as exact accord is removed further and further1 so the increase in the swing of the pendulum gets smaller and smaller4 ,in somewhat the same manner it is possible that many series of waves1 differing in wave-length1 and therefore in periods of oscillation1 may be capable of increasing the amplitude of a swing1 and with the photographic salt this probably occurs1 with the result which we see in the above figure4 ,suppose in the eye we have three such sensitive pendulums which are capable of responding to the beats of waves of light1 it requires no great imagination to see that one such pendulum will respond not only to that wave of light which is isochronous with it1 but also with waves shorter and longer than that particular wave4 ,the same pendulum indeed may respond to the whole of the visible spectrum1 but when far off from the maximum the response would be very small indeed4 ,we may therefore assume that though each pendulum may have its maximum increase of oscillation at one part of the spectrum1 yet at other parts not only it alone answers to the beating of the waves1 but that the other pendulums are also affected by the same1 and thus the whole spectrum is recognized by the swings more or less long1 of either one1 two1 or of all three4 ,to ,thomas ,young is usually attributed the three-colour theory1 though it seems to have been promulgated in an incomplete state some time before2 ,clark-,maxwell and ,helmholtz revived it in later years1 and it is usually known as the ,young-,helmholtz theory4 ,it should be remarked that the three fundamental colour sensations are not of necessity the same sensations as are given by the three primary colours1 as we shall see further on4 ,the following figure 7,fig4 #cd7 is taken from ,helmholtz's physiological optics1 as diagrammatic of the three sensations4 ,fig4 #cd4--;,curves of ,colour ,sensations4 ,to this diagram there is an objection1 in one respect1 viz4 that it gives the same luminosity-value to the blue of the spectrum as it does to the red and green4 ,it has been seen that if we call the luminosity of the yellow #ajj1 that of the blue is about #e4 ,the objection does not hold if it is remembered that the three maxima of impressions are taken as equal4 ,if the ordinates were increased1 so that the maxima were of the same height as that of the photographic curve1 the resemblance between them and this last would be very marked4 ,it will be noticed that each of the three colour sensations is not only excited by a limited portion of the spectrum1 but by all of it1 the height of the curves being a measure of their response4 ,now assuming that this is the case1 since a certain degree of stimulation given simultaneously to the three sensations causes an integral sensation of white light1 it follows that the colour perceived in every part of the spectrum is due to the excess of stimulation of either one or two of the fundamental sensations1 together with the sensation of white light4 ,if this diagram were correct1 at no point in the spectrum is one fundamental sensation excited alone1 but we believe that the diagram obtained by ,koenig 7,fig4 #ce71 from colour equations 7which will be explained in our next chapter71 is more exact1 and that it is probable that in the extreme violet and extreme red of the spectrum the only sensations which are stimulated are the violet and red respectively4 ,our measures in the red and violet of the spectrum make it appear that each of the two sensations can be perceived unaccompanied by any others1 and the fact that the red colour blind person perceives a shortened spectrum in the red end1 is a further proof of this deduction1 so far as the red is concerned4 ,the colour which the fundamental green sensation excites in the normal eye has probably never been seen1 nor can be seen4 ,this is due to the fact that all three sensations overlap in the green2 that is1 that the pendulum which answers to the green colour in the spectrum also affects1 but with much less energy1 the other two pendulums1 which respond to the red and violet sensations4 ,the word pendulum has been used advisedly1 for it may equally as well apply to a molecular aggregation as to one which is visible and measurable4 ,without entering into the physiological structure of the eye1 we may say that it has usually been assumed that the pendulums are the ends of nerves which vibrate with the waves of light2 but this seems rather doubtful4 ,gross matter1 such as these ends are1 compared with the molecules of which they are built up1 cannot1 as a rule1 vibrate with waves of light1 and there seems to be no reason why there should be an exception in the case of the eye4 ,it seems much more probable that a chemical decomposition takes place in some substance attached to them1 and where such decomposition takes place electricity of some kind must be produced4 ,in other sensations of the body the nerves act as telegraph wires1 carrying messages to the brain1 and it is not improbable that the nerves of the eye are employed in somewhat the same manner4 ,professor ,dewar has shown that when light acts on an extirpated eye1 a current of electricity does traverse the nerves1 and of such an amount that it can be shown to a large audience4 ,this experiment is not1 however1 conclusive1 as the effect may be mistaken for the cause4 ,this idea1 however1 is only hypothetical1 as is indeed the hypothesis of the mechanical action of light on the gross matter of which the rods and cones attached to the retina are composed4 ,we have in a previous chapter stated that there are some eyes in which the sensation of some colour is altogether absent1 and in others in which it is more or less deficient4 ,thus some eyes appear to be lacking wholly in the sensation of red1 others of green1 and some very few of violet2 and there have been cases known in which two sensations1 the red and violet1 have been totally absent4 ,in the first case1 where the sensation of red is entirely absent1 what is known to the normal-eyed as white can be matched with a mixture of blue and green1 and there is a place in the spectrum that is recognized as white4 ,similarly white can be matched by a green blind person with a mixture of red and blue4 ,to those who may be curious to see the colour which red and green blind persons would call white1 a very simple means is at hand to demonstrate it4 ,using the colour patch apparatus with the three slits inserted in the slide1 and in the positions we have indicated in the violet1 green1 and red1 and forming white light for ourselves on the screen1 if we cover up the red slit entirely we shall have a patch of sea-green colour1 which a red blind person would call white2 and if we cover the green slit1 uncovering of course the red1 we shall have a brilliant purple1 which to a green blind person would be white4 ,they both would call white what the normal-eyed person sees as white1 for the simple reason that either the red or the green mixed with the remaining colours would be unperceived4 ,the examination of colour-blind people is of prime importance for testing any theory of colour vision4 ,for instance1 if it were asserted that the fundamental sensations did not overlap as shown in the diagram above1 then it would follow that at some place in the spectrum there would be a dark point4 ,if they do overlap1 it must follow that both for the red and for the green colour blind person there must be some place in the spectrum where what is white light to them is produced4 ,colour-blind people were tested with the colour apparatus4 ,the reflected beam and the colour patch were made to cast shadows as before1 and the rotating sectors placed in the path of the former4 ,a slide with one slit was passed across the spectrum1 and the position noted where it was said that the two shadows were illuminated with white light2 to the normal-eyed person one shadow of course appeared illuminated with the sea-green colour1 or bluish green1 according as the observer was red or green colour blind4 ,the ray in the spectrum which to the red colour blind is white1 has a wave-length of about #dijj1 and that for the green colour blind a wave-length of #ejbj1 which corresponds to the position in which we usually place the green slit when a normal-eyed person is making colour matches4 ,it may be further remarked1 that if the maxima of all the three colour sensations are taken1 as in the diagram1 as of equal value1 that the place in the spectrum where the white light is perceived by the colour-blind is where the two sensations are of equal strength1 that is1 where the two curves cut one another1 and are of equal height4 ,by obtaining the proportions of the different colours with colour-blind persons which make up what to them is white light1 the curves for the two sensations can be worked out in the form of simple equations4 ,the experiments carried out with colour-blind people are of the most interesting character1 and a good deal remains to be done with the data already obtained from them4 ,to the popular mind a colour-blind person is usually thought a strange creature1 and it is a matter of wonderment1 if not of amusement1 that they cannot distinguish between the red of cherries and the leaves of the cherry tree4 ,the physicist1 studying the theory of colour1 views the matter quite differently1 and he looks upon an intelligent observer of this class as a boon4 ,it may be remarked that both the red-blind and the green-blind persons would be unable to distinguish between the cherries and the leaves4 ,the red-blind person would see the cherries as green1 as also the leaves2 whilst the green-blind person would see both as red4 ,without regarding form it is probable that the red-blind would see the leaves as a bright green1 whilst the green-blind would see them as darker red than the cherries4 ,failure to distinguish between the two is more likely to occur with the green of leaves1 and the red of such fruits as cherries1 since the former contains a marked proportion of red in it1 and the latter a small proportion of green4 ,one highly-educated gentleman was led to know his deficiency in colour sense1 by hearing a companion on a tour going into raptures over a sunset4 ,he saw but little difference between it and that to be seen at midday4 ,testing his vision it appeared that he was totally blind to the sensation of green1 and that white and purple would consequently be mistaken by him for one another4 ,the crimson on the clouds1 illuminated by the setting sun1 would appear to him as only slightly different to the white clouds which he would see at midday2 in fact he would be always seeing what to us would be a sunset4 ,for this gentleman to mix spectrum colours to match others would evidently be no guide to normal-eyed persons4 ,we believe that amongst us in our daily life we have many persons who are blind to some colour1 but who are not aware of it1 or if they are aware of it1 hide their defect as far as possible4 ,that some are ignorant of it to a late period of their life we know4 ,we have said that there are cases in which persons are only defective in colour perceptions1 and not wanting in them altogether4 ,the former are more common than the latter1 and to the experimenter are by no means so interesting4 ,they are only alluded to here to indicate that there are degrees in the defectiveness of eyes to colour4 ,one point which must be remembered here is that all colour production for registration by the mixture of three colours is delusive1 unless the eye of the operator is tested for its colour sense4 ,,chapter ,,xii4 ,formation of ,colour ,equations--,koenig's ,curves--,maxwell's ,apparatus and ,curves4 ,the plan of obtaining colour equations will by this time have become fairly evident4 ,and we may as well illustrate it by equations obtained with the apparatus we have been using in our previous experiments4 ,let us suppose we have an individual who is desirous of having his eye-sight for colour tested1 and that we have the slide with the three slits in situ4 ,it will be found that when we alter their width and form white light with them1 matching in purity the white light of the reflected beam1 that we shall have to reduce the intensity of the latter very considerably1 by means of the rotating sectors4 ,the aperture may sometimes be as small as #d1 and at other times perhaps somewhere between #d and #e4 ,now the variation in aperture between #d1 and say #dg1 is very considerable1 but it is highly probable that the latter might be estimated as #df1 since only degrees are marked on the sectors4 ,it therefore becomes essential to use a less brilliant reflected beam for the comparison1 and this is secured by using as a mirror a plain unsilvered glass4 ,what before read #d will perhaps read #fj1 and #dg will be #gj-a_/b1 whilst #df would be #fi1 a difference easily read4 ,we can now commence operations4 ,let us then place the red slit at say 7#ce7 of the scale1 the green at 7#bh71 and the violet at 7#ag71 and make white light of the same intensity by altering the apertures of the slits4 ,let us do the same with the slits at 7#cd71 7#bh71 and 7#ag71 instead of at 7#ce71 7#bh71 and 7#ag72 and again make white light1 and similarly with the slits at 7#ce71 7#bh71 and 7#ah72 and let the following be the results-- 7#a7 #bj7ce7 #fj7bh7 #dj7ag7 #ajj ,w 7#b7 #aj7cd7 #ee7bh7 #dj7ag7 #ajj ,w 7#c7 #bj7ce7 #ei7bh7 #aj7ah7 #ajj ,w ,subtracting 7#a7 from 7#b7 we get-- #aj7cd7 #bj7ce7 #e7bh7 or 7#cd7 #b7ce7 #a_/d7bh7 which means that the colour sensation at 7#cd7 is made up of two parts of the sensation of 7#ce71 together with #a_/d part of the sensation of 7#bh74 ,in the same way we find that the colour sensation of 7#ah7 is made up of the sensations of 7#ag7 and 7#bh74 7#ah7 #d7ag7 #a_/aj7bh74 ,in this way all the different colour sensations can be referred to the sensations which we may happen to consider as best representing the fundamental sensations4 ,what these are is a matter still unsettled2 though from the equations formed by colour-blind people1 who only require really two colours to form equations1 their places are approximately known2 evidently as before said1 the ray in the spectrum which the green colour-blind person sees as white light1 is that where to the normal eye the green fundamental sensation is purest1 being free from predominance of either of the other two sensations1 and might be taken as a standard colour4 ,now if our luminosity curve is correct1 and if the sum of the luminosities of each colour separately is equal to the luminosity of the colours when mixed 7which we have shown to be the case in chapter ,,vii471 it follows that the correctness of the measures can be checked by using the widths of the slits as multipliers of the luminosities4 ,these luminosities can then be added together1 and they should equal in luminosity the white light with which the comparison was made4 ,the results can be compared together by reducing the equations to the same standard of white light4 ,the following is a set of observations which bear this out4 ,the red and violet slits in this case were kept at #ce and #agh on the scale1 and the position of the green slit altered4 ---------------------------------------- ------------ ,position of ,aperture of ,luminosity ,sum of the ,slits4 ,slits4 of ,colour4 ,luminosity -------------------------------- of each ,colour ,r ,g ,v ,r ,g ,v ,r ,g ,v multiplied by the ,aperture4 ---------------------------------------- ------ #ce #bhe #aghaae #chaabahagc #fe #dicj #ce #bhj #aghaai #deajjahafaefe #dihi #ce #bggeaghabb #eb #heahaeb #fe #difj #ce #bgceaghabe #fe #gdahadj #fe #dijg #ce #bgj #aghabh #gh #fgahaccbfe #died #ce #bfc #aghaccabe #djahabjcfe #dihg #ce #bfj #aghacdaej #ajahaafgfe #dieb #ce #beheaghaceagj #jahaaejfe #diic -------------- ,mean #diei ---------------------------------------- ------- ,the red slit was at a point in the spectrum between ,c and the red lithium line1 and excited probably the fundamental sensation of red alone4 ,the violet slit was close to ,g1 and probably in this case the fundamental sensation of violet was almost excited alone4 ,with the green slit the reverse was the case1 all three fundamental sensations being excited4 ,at #bfc the green sensation was probably the fundamental sensation mixed with white light alone1 as at that point the green blind person saw white light in the spectrum1 on the red side of it there being what he describes as a warm colour1 and on the violet side a cold colour4 ,an inspection of the table will show how very closely the sum of the luminosities agree amongst themselves1 the white light formed by them in each case being of equal intensities4 ,it must be recollected that white light is not necessary to form colour equations2 colours may be mixed to form any other colour1 which may be taken as a standard4 ,this is often useful in the case of the light between the violet and the blue1 where the luminosities are small compared with the luminosity in the green1 yellow1 and red4 ,fig4 #ce4--,koenig's ,curves of ,colour ,sensations4 ,by taking a large number of colour equations1 ,koenig1 who works in ,helmholtz's laboratory1 has derived what he considers curves of the three fundamental sensations in a normal-eyed person1 and also those of the colour-blind4 ,it may be said that with the colour-blind only two of the fundamental sensations are seen1 and therefore only two curves are found1 and that these agree in the main with some two of the curves of the three belonging to the normal-eyed4 ,fig4 #cf4 ,maxwell's ,colour-box4 ,maxwell was the first to make a definite piece of apparatus for the purpose of obtaining colour equations1 and we reproduce from his paper in the ,philosophical ,transactions of the ,royal ,society for #ah--1 a somewhat modified diagram of it4 ,this apparatus is often known as ,maxwell's colour-box1 and is in fact a spectroscope reversed4 ,with a collimator and prisms we form a spectrum on the focusing-screen of the camera 7,fig4 #f71 by light coming through the slit1 and we can obtain light on the distant screen1 a patch of any colour1 by placing in the spectrum slits as given at ,fig4 #cj4 ,if we were to illuminate the slits so placed with white light1 and look through the slit of the collimator1 we should see the front surface of the first prism illuminated by the mixture of the colours which would1 when the light illuminated the collimator slit1 have formed one colour patch on the screen4 ,in ,maxwell's apparatus1 the slits ,s#a1 ,s#b1 ,s#c are illuminated by the light reflected from a white card ,c1 placed in the sunshine1 the rays passing through them fall on two prisms ,p#a1 ,p#b1 are reflected back again through these prisms by a concave mirror ,m#c1 are received on another mirror ,m1 and fall at ,e on to the eye4 ,at ,a is an aperture in the box1 letting through white light on to a mirror ,m#a1 which reflects it through a lens ,l on to ,m#b1 which again reflects it on to ,m1 and so to the eye at ,e4 ,thus at ,e an image of the prisms1 and an image of the aperture are seen1 and the white light of the latter can be compared with the mixture of the colours formed by the prism passing through ,s#a1 ,s#b1 and ,s#c4 ,suppose we have one slit ,s#a1 the white light will be decomposed by the prisms1 and will be seen at ,e as light of the same colour as would be seen at ,s#a1 if the light were sent from ,e to ,s#a1 and so with the other slits4 ,thus when two or three of the slits are uncovered1 the light falling on the eye at ,e will be a mixture of two or three colours4 ,there are two drawbacks to the mode of illumination used1 one being that the quality of sunlight varies1 and therefore colour equations will not be accurately comparable one with the other2 and the second is that the light reflected from the card is not absolutely the same in all directions1 and it cannot be perpendicularly placed to each of the rays which strike the prisms1 after passing through the different slits4 ,this latter is a small objection1 and is not of much account1 but the first drawback is a more serious one4 ,fig4 #cg4--,maxwell's ,curves of ,colour ,sensations4 ,with this apparatus1 then1 ,maxwell formed his colour equations1 but he fixed as the colours which may be called his standard colours1 portions of the spectrum which are certainly not pure1 and hence he got curves which are not as perfect as those of ,koenig4 ,it will be seen1 for instance1 that his red and violet curves do not overlap1 but touch each other near ,e4 ,were this true1 the green colour-blind person should see a dark space in the spectrum1 since the green sensation is missing in such eyes4 ,as a matter of fact the luminosity of the spectrum is very considerable to such a person at this point4 ,it will also be seen that some of his curves are negative curves lying below the base4 ,this shows that the three standard colours he took are somewhat wrong4 ,the dotted curve gives the combination of his three sensations at every point1 and should be the luminosity curve2 but owing to his having taken empirically certain standards of luminosity for his three colours1 it does not represent the truth1 as may be seen on comparison with ,fig4 #aa1 page #gi4 ,it must be recollected that since ,maxwell's observations the subject has been largely experimented upon1 and naturally improved appliances and greater knowledge have enabled more nearly correct views to be entertained regarding it4 ,,chapter ,,xiii4 ,match of ,compound ,colours with ,simple ,colours--,all ,colours reduced to ,numbers--,method of matching a ,colour with a ,spectrum ,colour and ,white ,light4 ,if we place the solution of bichromate of potassium in front of the slit of the collimator1 we shall see that on producing a spectrum on the screen1 all rays from the red to the yellow-green pass2 hence bichromate of potash transmits a colour which is a compound colour4 ,it has been shown that this orange colour and the spectral yellow can be matched by mixing the simple colours of red and green together2 but it will be instructive to see if a simple colour in the spectrum itself can be found which can match such a compound colour as that of the bichromate4 ,if we place the bichromate in the reflected beam of the colour patch apparatus and illuminate one shadow cast by the rod with the light transmitted by it1 and pass a slit along the spectrum1 to produce monochromatic light1 with which the other shadow of the rod is illuminated1 a position will be found near the orange sodium line ,d1 where the two colours apparently match in every respect2 when the intensities of the two illuminated shadows are equalized as before by the rotating sectors4 ,in the same way by filling the part of the square with the pigment on which the shadow illuminated by the reflected beam falls1 we can see if we can match emerald green1 cyanine blue1 and other coloured pigments4 ,it will often be--more often than not--necessary1 however1 to dilute the spectrum colour thrown on the white half of the patch with a trace of white light4 ,by reference to our previous experiments we arrive at what may appear an unlooked-for result1 that no matter what the colour may be1 we can refer it to one ray of the spectrum1 together with a percentage of added white light4 ,it is worthy of remark1 that the place in the spectrum where the simple and the compound colours match1 varies according to the kind of light with which the pigment is illuminated4 ,this we can show in a very simple way4 ,to persons who are totally colour-blind to one sensation1 viz4 the green or the red1 the matching of a compound colour with a simple one in the spectrum should possess no difficulties4 ,taking the trichromic theory of three sensations for the normal-eyed person1 it is evident that only the following classes of sensations are possible in the normal-eyed1 the green colour-blind and the red colour-blind-- ,normal-eye4 ,green colour-blind4 ,red colour-blind4 ,red ,red -- ,green -- ,green4 ,violet ,violet ,violet4 ,mixtures of red -- -- and green ,mixtures of red ,mixtures of red -- and violet and violet ,mixtures of green ,mixtures of green and violet and violet4 ,mixtures of red1 -- green and violet ,if we take as a type of colour-blindness the green colour-blind person1 we see that every colour in the spectrum must be either pure red or violet1 or else these colours mixed with more or less white light1 since these two sensations when excited in certain proportions give the sensation of white4 ,at one place1 which is commonly called the neutral point1 the proportions of the two colours are such that the impression there given is only white2 hence it follows that1 between this neutral point and each end of the spectrum1 the rays are mixtures of violet and white1 or red and white1 the dilution of the colours varying from no white to all white4 ,as every compound colour must be a mixture of the same two colours in certain proportions1 it follows that the green colour-blind person can match every compound colour with some one ray of the spectrum1 and that every colour must to him be either red or violet1 diluted with different proportions of white light4 ,in the same way1 a person who is colour-blind to the red can also match any colour with a single spectrum colour1 and he will see it as green or violet diluted with more or less white light4 ,this can be readily understood1 but it is not quite so plain how any colour sensation felt by the normal eye can be referred to the spectrum4 ,if we take three rays in the spectrum--one in the red between ,c and the red ,lithium line which we will call ,r1 another in the green between ,f and b which we will call ,g1 and a third in the violet near ,g but on the ,h side of it1 and which we may call ,v--then by varying their intensities 7which is equivalent to varying the luminosities7 and mixing them1 we can give the same impression to the eye that any compound colour gives2 and that any intermediate simple spectrum colour gives1 if very slightly diluted with white light4 ,with these same three colours1 but in different proportions1 we can also give the impression of white light to the eye4 ,the intermediate spectrum colours between the green and the violet rays selected when slightly diluted are imitated by mixing these rays together in different proportions1 and similarly those lying between the red and the green by mixing together these rays in different proportions--and there is some ray present in the spectrum which1 when very slightly diluted with white light1 has the same colorific effect on the eye as the mixtures of the pairs v and b1 and ,g and ,r1 in any proportions whatever4 ,let the luminosities of the rays ,r1 ,g and ,v1 which give the impression of white light1 be a1 b and c units respectively1 and p1 q and r those which give that of the colour which has to be registered and reproduced4 ,we then get the following equations--where ,w is white1 w its luminosity1 ,z the colour1 and z its luminosity-- a,r b,g c,v w,w--7i472 p,r q,g r,v z,z--7ii472 ,then evidently-- 7a b c7 w2 and 7p q r7 z4 ,let p ,alphaa1 q ,betab1 r ,gammac1 ,then we may write 7ii47 as-- ,alphaa,r ,betab,g ,gammac,v z,z--7iii474 ,now either ,alpha1 ,beta1 or ,gamma must be smaller than the other two4 ,as an example1 if ,alpha be the smallest1 we multiply 7i47 by ,alpha when we get-- ,alphaa,r ,alphab,g ,alphac,v ,alphaw,w--7iv47 ,subtracting 7iv47 from 7iii47 and we get-- 7,beta-,alpha7b,g 7,gamma-,alpha7c,v z,z - ,alphaw,w4 ,now it has already been stated that between ,v and ,g there is some ray which gives the same sensation of colour1 mixed with a very small quantity of white light1 as the above mixture of ,v and ,g--let us call it ,x and its luminosity x x being evidently equal to 7,beta-,alpha7b 7,gamma-,alpha7c1 and ,mu the luminosity of the small quantity of white added4 ,we then get z,z x,x 7,mu ,alpha7 ,w4 ,here we have the colour ,z in terms of a single ray1 and of white light4 ,this same holds good when in 7ii47 ,gamma is smaller than ,alpha and ,beta2 but it does not do so should it happen that ,beta is the smallest1 for there is no part of the spectrum which contains simple colours giving the same sensation to the eye as mixtures of red and blue4 ,there is1 however1 a very simple way in which the registration of such a colour 7which it must be remarked must be of a purple tone7 can be effected4 ,it can be fixed by its complementary4 ,to do this we must add to 7ii47 a certain amount of ,r and ,v1 which will make the whole white4 ,thus1 suppose in 7iii47 ,alpha to be larger than ,gamma and ,gamma than ,beta1 then we must add ,phph,phi ,pi mu ,phib,g ,thetac,v and we have ,alphaa,r 7,beta ,phi7b,g 7,gamma ,theta7c,v n,w ,z ,phib,g ,thetac,v2 but 7,beta ,phi71 and 7,gamma ,theta7 each equal ,alpha ,therefore n ,alphaw4 ,therefore ,z ,phib,g ,thetac,v ,alphaw,w4 ,now between ,v and ,g in the spectrum there is some single colour which gives the sensation of the mixture of ,g and ,v4 ,let it be ,x with luminosity x1 together with white whose luminosity is ,mu1 which must equal 7,phib ,thetac74 ,therefore ,z x,x ,mu,w ,alphaw,w ,z 7,alphaw - ,mu7,w - x,x which again is the colour expressed in terms of white light less the complementary colour4 ,we have thus arrived at the very simple deduction that the hue and luminosity of any colour1 however compounded1 may be registered by a reference to white light and a single ray of the spectrum4 ,in practice this dominant ray is very easy to find4 ,suppose we wish to determine numerically the colour of a signal-green glass in the electric light1 we should proceed as follows-- ,the colour patch apparatus 7described in chapter ,,iv47 is employed1 and the coloured glass is placed between the silvered mirror which reflects the beam already reflected from the first surface of the first prism of the spectrum apparatus1 and the screen1 and a square image of that surface of the prism showing the tint of the glass is formed on the screen by means of the lens4 ,touching this image is a square patch of white light formed by the re-combination of the spectrum by means of another lens4 ,an opaque slide containing an adjustable slit is moved across the spectrum in the manner described in the chapter referred to until the colour of this last patch is approximately the same hue as that of the glass4 ,in the path of the reflected beam1 but between the prism and the silvered mirror1 is inserted a piece of plain glass which can be made to reflect part of the beam into the spectrum patch of light1 a square patch of the white light being formed by means of a third lens4 ,we thus have monochromatic light mixed with white light4 ,the requisite intensity of the added white light can be adjusted by means of the rotating sectors1 as described in the same chapter1 which open and close at will during rotation1 and the total luminosity of the mixed beams can be altered by this1 together with the adjustable slit in the slide4 ,the slit may probably have to be moved in the spectrum to make the hue of these mixed lights the same as that of the glass1 but by trial the position of the ray whose colour when diluted with white makes the match is readily found4 ,the position of the slit in the spectrum is noted1 as also the aperture of the sectors4 ,the relative luminosities of the beam reflected from the plain glass mirror and of the coloured ray is next measured by placing a rod in the path of the two beams1 and equalizing by the sectors the luminosity of the shadows which are illuminated1 the one by the spectral ray1 and the other by the white light4 ,when the sector aperture is noted the registration is complete1 as far as hue is concerned1 but the luminosity of the ray transmitted through the glass should be compared with that of the reflected beam1 and then the luminosity is also recorded4 ,should the colour of a pigment be in question1 the ray reflected from the silvered mirror is made to fall on the pigmented surface and the same procedure adopted4 ,if a purple glass 7say7 has to be registered1 we proceed in a slightly different manner4 ,the patch of coloured light passing through the purple glass is superposed over the spectrum patch1 and the slit in the slide is moved till a ray is found which will make white light when superposed on the colour of the glass4 ,the luminosities of this white light1 of the reflected beam1 and of the spectral colour are compared inter se1 and there are then sufficient data with which to make numerical registration4 ,coloured glasses to be used at night with oil or gas1 or pigments to be viewed by these lights1 must be registered in these lights4 ,as the spectrum colours are always the same1 it is convenient to use the electric light spectrum1 and the only alteration in the apparatus is to use two gas-lights to illuminate two square apertures1 in front of one of which the glass whose colour has to be measured is placed4 ,the images of these apertures are thrown on the screen1 the coloured image touching the square image of the spectral colour patch1 and the naked image over the latter4 ,the same determinations are gone through as those just described4 ,the following are the determinations of some glasses-- ---------------------------------------- -------- ,percentage of ,luminosity ,wave- of ,light ,glasses lengths of,percentage ,transmitted ,measured4 ,dominant of ,white through ,ray4 ,light4 the ,glass4 ---------------------------------------- ------- ,ruby #fbbj #b #aca ,canary #ehej #bf #hbj ,bottle ,green #eeaj #ca #ajf ,no4 #a ,signal ,green #dibe #cb #fi ,no4 #b ,signal ,green #eajj #fa #aid ,cobalt #dfge #db #cge ---------------------------------------- ------- ,the following are determinations of some coloured pigments-- ---------------------------------------- ----------- ,percentage ,percentageof ,luminosity1 ,wave-lengths of ,white ,coloured of ,dominant ,white ,paper ,papers4 ,ray4 ,light4 being #ajj4 ---------------------------------------- ----------- ,vermilion #fajj #be #adh ,emerald ,green #ebbj #eij #bbg ,french ,ultra- marine ,blue #dgbj #faj #dd ,brown ,paper #eidj #ejj #bej #ehgj #fgj #aie ,orange #eiae #dj #fbe ,chrome ,yellow #ehce #bfj #ggg ,blue ,green #ejje #dbe #adh ,eosin ,dye #fdjj #gbj #ddg 7,sporting ,times7 ,cobalt #dhbj #eee #ade ---------------------------------------- ----------- ,,chapter ,,xiv4 ,complementary ,colours--,complementary ,pigment ,colours--,measurement of ,complementary ,colours4 ,we are now in a position to enter into the question of complementary colours1 which is one of supreme interest to artists4 ,a complementary colour1 in its strictest sense1 may be described as the colour which1 combined with the colour whose complement is required1 makes up white4 ,in this definition we have three characteristics to take into account1 viz4 hue and luminosity1 and dilution with white light4 ,as an example of what we mean we refer to an experiment which was made and described at page #abe4 ,it was said that if the violet slit was placed in a certain position in the blue of the spectrum1 it was possible to move the green slit into a part of the yellow1 so that the two colours when mixed together would form white4 ,in that case the blue is complementary to the yellow1 and the yellow to the blue1 so long as the intensities are those which make up white light4 ,again1 if it requires the light coming through the three slits to make up white light1 be it the white of the electric light or that of gaslight1 we can obtain the complementary colour of the light issuing through any one of them by covering that slit up4 ,thus suppose the slits to be in the normal position the complementary colour of the red is a green-blue1 formed by the mixture of the violet and green rays1 the complementary colour of the green is a purple1 formed by the mixture of the red and the violet light1 whilst the complementary colour of the violet is greenish yellow1 formed by the mixture of the red and green rays4 ,it will be evident that as the intensities of the three rays respectively will be different according as the white light matched is the electric light or gaslight1 the complementary colours in the former will be different in hue and intensity to those in the latter4 ,fig4 #ch4--;,chromatic ,circle4 ,another couple of striking experiments which the writer devised to show these colours can be made with the colour patch apparatus1 and on the same principle as that used for obtaining the intensity of the rays reflected from pigments1 and transmitted through coloured transparent bodies4 ,instead of the small slit with a right-angled prism in front to deflect the beam from the top spectrum1 where two spectra are produced 7see ,fig4 #af1 p4 #ie71 a single spectrum is used1 with a right-angled prism of such a size that it deflects half of it1 which is again reflected on to the screen by a mirror1 and through a lens to form a second patch of equal size as the undeflected beam4 ,a rod can be so placed in the path of the beams that two coloured stripes are formed1 together with a white stripe caused by their overlapping4 ,the two coloured stripes are complementary one to the other4 ,by moving the prism along the spectrum various coloured stripes can be formed1 in some cases one being much less luminous than the other1 and yet they are complementary4 ,if instead of the large right-angled prism a smaller one be used1 the complementary colour due to a small part of the spectrum can be shown in the same manner4 ,it is customary to show the complementary colours diagrammatically by what is known as the chromatic circle4 ,roughly it is drawn as in the above figure 7,fig4 #ch74 ,the three colours1 red1 green and blue1 which are taken for primary colours1 are placed at #abj apart in a circle1 and lines drawn from them through the centre1 at which white is supposed to be situated4 ,where these lines cut the circumference is placed the complementary colour4 ,other colours can be placed round the circle with their complementary colours opposite1 and so a fairly complete diagram of the spectrum can be made4 ,but it must be remembered that this is really of no scientific value1 as it conveys no idea of the luminosity of the spectrum colours1 nor of the quantities which have to be mixed together to form the complementaries4 ,such a circle is1 however1 convenient as a sort of memoria technica1 and can be filled up according to the fancy of the observer4 ,the following are pairs of most carefully selected complementary colours of pigments1 as adopted by ,professor ,church4 ,complementaries4 ,pigments4 ,red ,madder red or crimson vermilion4 and ,green blue ,viridian1 the emerald oxide of chromium with a little cobalt4 ,orange ,cadmium yellow1 of full orange hue4 and ,greenish blue ,cobalt green4 ,orange yellow ,cadmium yellow1 or deep chrome4 and ,turquoise ,coerulium1 or cobalt blue1 with a little emerald green4 ,yellow ,lemon yellow1 pale chrome1 or aureolin4 and ,blue ,ultramarine from lapis-lazuli4 ,greenish yellow ,aureolin with a little viridian4 and ,violet blue ,french ultramarine4 ,green yellow ,lemon yellow1 with some emerald green4 and ,violet ,french ultramarine with madder carmine4 ,yellowish green ,lemon yellow with much emerald green4 and ,purplish violet ,madder carmine with ,french ultramarine4 ,green ,emerald green with lemon yellow4 and ,purple ,madder carmine with ,french ultramarine4 ,emerald green ,emerald green alone4 and ,reddish purple ,madder carmine with a little ,french ultramarine4 ,as these pairs of pigments are complementary1 it follows that if rotated together in proper proportions1 they should make a grey which will be indistinguishable from a grey formed by rotating black and white sectors together4 7,see chap4 ,,xv47 ,it will probably happen that a good deal more of one of the pairs of the colours is required in the disc than of the other1 and supposing that the two are each used of the full brightness which the pigments are capable of giving1 it follows that in a diagram where equal areas are filled with the pigments as complementary1 some means must be adopted to give the true depth of tone to each4 ,the mixture of white will heighten the luminosity of either1 or the admixture of black will lower it1 but often alters the hue4 ,one of the most beautiful methods of observing complementary colours is by means of the polarization of light1 which we need not describe in detail4 ,what is known as ,brcke's schistoscope is perhaps one of the most convenient4 ,dove's ,iceland spar prism is also useful1 when two pigments have to be worked on to paper1 so as to be complementary4 ,the two squares of pigmented paper are placed side by side1 and two images of each are formed4 ,one image of one colour can be caused to overlap the second of the other1 and if the two when superposed appear of a grey they are complementary one to the other4 ,if too much of one colour appears1 it must be toned down till the grey is formed4 ,this is a very simple piece of apparatus1 and for experiments with pigments will be found to be very handy4 ,when the right tint of each is secured in this manner1 a further test may be made by making the pigmented surfaces into sectors1 and rotating them together1 when if the double-image prism gives correct results1 the angular aperture of the sectors should be #ahj each1 to match a grey produced by a mixture by rotation of black and white4 ,we have already shown how the complementaries of the spectrum colours can be found2 the question is can we find the complementaries of pigments by the spectrum8 ,there is one very self-evident way4 ,we can place the three slits in the spectrum as given in chapter ,,ix41 and match in intensity the white light of the reflected beam1 and note the apertures of the slits4 ,we must then in the reflected beam place the pigment whose complementary colour is required1 and match its colour with the light from the three slits1 keeping1 for the sake of convenience1 the white light falling on the pigmented surface of unaltered intensity1 and again note the apertures4 ,if we deduct the last measures from the first1 the difference of aperture will give the complementary colour4 ,thus it was found that with slits in a certain position in the spectrum1 to make white light the following apertures in hundredths of a millimetre were required3 ,red #afe 7#a7 ,green #fj ,violet #ajj ,emerald green was placed in the patch and was matched by the light from the three slits1 when it was found that it required ,red #d 7#b7 ,green #ce ,violet #be ,deducting one from the other we get as the complementary colour1 ,red #abe 7#c7 ,green #be ,violet #ge ,this is a complementary colour1 but like the green itself it is mixed with white light2 but we can easily deduce what is the simplest complementary colour2 for we have only to deduct the possible white light from the second measure4 ,now evidently the greatest amount of white light is when the whole of the green is taken as forming part of it1 with the proper proportions of red and violet1 and these we can obtain by taking the proportions of the colours in 7#a72 therefore deduct-- ,red #fi 7#d7 ,green #be ,violet #dae and this would leave as the complementary colour without any admixture of white-- 7#e7 ,red #ef ,violet #cce which is a purple as would be expected4 ,now to give the same dilution of white to the complementary that the emerald green has1 we must take away from the emerald green all the white mixed with it1 and add that quantity to the complementary4 ,the white in the emerald green can be found by treating the whole of the red as going to form the white2 we then have from 7#a7-- ,red #dj 7#f7 ,green #add ,violet #bd ,deducting these from 7#b71 we find that the colour of emerald green1 less the white light1 is #bjf of green mixed with #a of violet4 ,to find the proper dilution of the complementary colour we must add the above proportions of the three colours1 and as our final result we find the complementary colour1 of equal impurity1 is a mixture of-- ,red #if 7#g7 ,green #add ,violet #ege ,the slits may be set at these apertures and a colour patch thrown on the screen1 and we shall find it of a delicate pink4 ,the truth of this can be seen by using a double-image prism to view the pigmented surface1 illuminated by the same white light as that in which it was measured1 and the colour patch on the screen by its side4 ,the two colours may be caused to overlap1 when it will be seen that white is produced4 ,another example was an orange pigment1 and this we will work out in the form of colour equation4 ,the same mixture gave white1 viz43 #afe ,r #fj ,g #ajj ,v ,w #afe ,r #db ,g ,o ,therefore the complementary colour1 which is ,w - ,o #ah ,g #ajj ,v1 or a dark-blue colour4 ,in this case there was apparently no white light reflected from the orange4 ,it was slightly glossy1 and as polarized light was used for the reflected beam1 it was probably somewhat quenched2 but what is more probable is that the green contains some violet as well as red1 for the reasons given in chapter ,,xi4 ,the reason we have been particular in showing to what extent complementary colours must be diluted with white to the same proportion that the colour itself is diluted1 will be apparent if considered for a moment4 ,a deep brown is in reality orange1 much degraded in tone1 and can be produced as a colour patch on the screen if a bright orange pigment be placed in the reflected beam of the colour patch1 and the light nearly shut off by the rotating sectors4 ,now the same complementary colour will be found for both1 but if we were to use the bright complementary colour which we obtained with the orange for the brown1 and endeavoured to obtain a white with it by means of the double-image prism we should fail1 as the complementary colour would predominate4 ,complementary colours can always be formed by a mixture of only two rays1 and although the overlapping images may form white1 yet when the two are placed side by side1 it often will be found that the complementary1 unless diluted with white1 is evidently too dark to be satisfactory1 but the luminosity may be increased by adding white to it1 as any amount of white may be added to the mixture of the two rays which form the complementary1 and of course white will still be formed with the original colour4 ,it is thus quite feasible to give the complementary the same luminosity as the latter by adding white light to it4 ,like the colour itself1 the complementary colour can always be expressed either by a single ray of the spectrum1 or by white light from which a single ray is deducted4 7,see chapter ,,xiii47 ,,chapter ,,xv4 ,persistence of ,images on the ,retina--,the ,use of ,coloured ,discs4 ,fig4 #ci4--;,disc to cause alternate opening and closing of two ,slits4 ,by this time we must be thoroughly convinced that by throwing one coloured patch over another a compound colour can be formed2 our next business is to demonstrate that the same effect can be produced by successive images of these same colours4 ,thus we can show that as a mixture of red and blue produces purple1 when the two lights are superposed1 so precisely the same purple can be produced by allowing the same two colours to strike the eye alternately1 and in very rapid succession4 ,we can make a match of the beautiful purple of permanganate of potash as before upon the screen1 by placing one adjustable slit in the red and the other in the violet4 ,if we place in front of the slits a disc cut out with equal angular apertures 7,fig4 #ci71 the slit ,s#a will be covered when the slit ,s#b is open1 and vice vers1 and the two will never be uncovered at the same time when the card is turning round its centre4 ,when this disc is caused to rotate rapidly1 we shall have first a patch formed by the light coming through one slit1 and then another formed by that coming through the other slit1 thrown on the screen on the same place in rapid succession1 and the effect on the eye should be precisely the same as if the disc was not there1 save in the matter of intensity4 ,applying this artifice experimentally to the two slits which were used to give the colour of permanganate1 the experiment tells us that such is the case4 ,it would be going away from the intention of this work were the physiological aspect of this experiment dwelt upon2 it need only be stated that an impression on the retina lasts an appreciable time1 though short1 and that the impression made by the blue patch has not had time to disappear before there is an impression made by the red patch1 and so on4 ,as the retina retains these two impressions together1 they produce the impression of purple4 ,fig4 #dj4--;,disc painted ,blue and ,red4 ,for experiments in colour this duration of impressions is of great value1 for we can take advantage of it to compound the colours of pigments together in a very simple manner4 ,for instance1 we can take a circular disc painted in sectors with blue and red 7,fig4 #dj71 and produce a purple by causing it to rotate round its centre4 ,small discs of two inches in diameter may be painted with different coloured sectors1 and if a pin be passed through the centre1 a smart movement of a finger at the periphery will cause it to rotate sufficiently quickly to make the colours blend4 ,a more convenient plan for exact work is1 however1 to have an electro-motor similar to that which moves the rotating movable sectors 7,fig4 #da71 and at the end of the spindle to fix a cap with a screw and nut attached4 ,the disc1 perforated at the centre with a clean-cut hole1 can be slipt over the screw1 and fastened by the circular nut4 ,when the armature rotates1 the disc also rotates at the same speed1 and the colours thus blend without any exertion on the part of the observer4 ,ordinary tops can also be used1 but it is somewhat fatiguing to have to wind them up and start them afresh for each experiment4 ,the motor shown in the figure rotates sufficiently rapidly1 with discs of eight inches in diameter1 to blend colours4 ,it may here be remarked that the stronger the light in which such sectors rotate1 the quicker the rotation should be4 ,too slow a rotation allows a scintillation which is destructive of accuracy of reading4 ,to blend some colours together also requires more rapid rotation than with others4 ,the brighter the colour the more rapid it should be4 ,we learn from this that the diminution of the more intense impressions on the retina is more rapid at first than of the feebler4 ,fig4 #da4--;,electro-motor with ,discs attached4 ,fig4 #db4--,method of cutting ,disc to allow an overlap of a second ,disc4 ,very convenient discs for producing colours by rotation of sectors may be made by the following3 vermilion 7,v71 emerald green 7,e71 ,french ultramarine blue 7,u71 chrome yellow 7,y71 lamp-black 7,x71 and 7zinc7 white 7,w74 ,with these nearly every colour can be produced1 or its value derived4 ,the chrome yellow disc is somewhat superfluous1 but is sometimes useful4 ,the alteration in the proportions of the colours can be readily made by ,clark-,maxwell's plan4 ,from the circumference to the centre he cut the discs open1 as at ab 7,fig4 #db74 ,any moderate number of discs1 similarly cut1 may be slipt over one another1 and only a sector of each is left visible4 ,it should be remarked that this necessitates the rotating apparatus being viewed with a direct light1 as in the case of two or three overlapping discs it is impossible to keep them entirely flat1 and shades are apt to be introduced4 ,if we wish to produce a white1 or rather a grey1 from three colours1 we can take three small discs of ,v1 ,e and ,u1 of equal diameter1 and behind them place discs of black and white1 of larger diameter1 rotating the whole five on a common centre4 ,we shall find that by altering the proportions of the three first we can get a grey which can be exactly matched by a mixture of black and white1 ,x and ,w4 ,it has already been shown that even lamp-black reflects a certain amount of white light1 so this amount of reflected white light has to be added to the white in the outside sectors4 ,in the sectors used in the following experiments it was found that the following proportions of the three colours were required-- ,v #abd ,e #adc ,u #ic ---- #cfj and to make the same grey it required ,x #bgh ,w #hb ---- #cfj ,now the black reflected #cd of white light1 so that really the proportions of black and white were ,x #bfhf ,w #iad ----- #cfjj ,these matches were made in the light emitted by the crater of the positive pole of the electric light1 and are correct only for this light4 ,the greys here are dark greys1 and such greys can be matched exactly by throwing the white light in which the comparisons were made on a white card1 and reducing the intensity by means of the rotating sectors4 ,we can prove whether our matches are fairly correct from our previous measures of the luminosity of these three colours1 in comparison with that of white4 ,the luminosities of ,v1 ,e1 and ,u1 as found from the measures 7pp4 #ic-ie71 are #cf1 #cj1 and #dd1 white being #ajj2 #abd of ,v would have a luminosity of 7#abdx#cf7_/cfj1 or #abd2 #adc of ,e would have #aaib2 and #ic of ,u would have #aad2 which1 added to either1 give a luminosity of #bedf4 ,the luminosity of #iad_/cfj of white1 which is that of the mixture of black and white1 comes to #beci1 so that we may assume our observations have been fairly correct4 ,the influence of the kind of light in which the match was made is well exemplified by taking the matched discs whilst rotating into a room illuminated by the light from the sky1 when it is seen that the grey of the outer discs is bluish2 or again1 if the matched discs be examined in gaslight1 the inner grey will be found too blue4 ,the match of grey in this last light was found to be ,v #aai ,e #adh ,u #ic ---- #cfj which matched with ,x #bdd ,w #aaf 7,in this case the black and white are the corrected black and white47 ,the importance of making matches in a uniform light is fairly demonstrated by this experiment1 and we cannot be wrong in asserting that as skylight and sunlight and cloudlight 7the last being often a mixture of the two first71 are so variable no measures made on one day can be fairly compared with those made on another1 more especially if the observers are different4 ,with an emerald green1 a vermilion1 an ultramarine1 a white1 and a black disc any colour may be reproduced in the rotation apparatus1 the three first nearly matching what we have already stated to be the three primary colours4 ,it may seem curious that both black and white may have to be mixed with the colours1 to produce a pigment colour2 but a little reflection will show how it is4 ,for instance1 suppose we want to know the colour composition of gamboge 7,y7 in terms of vermilion 7,v71 emerald green 7,e71 and ultramarine blue 7,u74 ,we must make a disc painted with gamboge1 and also a black and a white disc of the same diameter1 but rather larger than the other three discs1 and place them on the spindle of the electro-motor 7,fig4 #dc74 ,we shall soon see on rotating them that no blue is required in the inner disc1 and that all that remains to do is to use the red and the green4 ,mix these two1 however1 in whatever proportions we may1 the mixture will never attain the same luminosity1 consequently we must darken the yellow with black4 ,even then we shall find that1 add what black we may1 the rotating red and green sectors will always be a little less saturated with colour2 which means that on rotation they produce a certain quantity of white light mixed with the yellow4 ,this we might expect1 for as emerald green1 besides green and red1 also contains a fair proportion of blue1 and as red1 green and blue when mixed give white1 it follows that when ,v and ,e are rotated together1 a grey or subdued white light must be mixed with the colour produced4 ,turning back to ,chapter ,,xiii4 we also see that as the emerald green is expressible by a single ray of the spectrum1 mixed with white light this result might have been foretold4 ,fig4 #dc4--;,arrangement to find value of ,gamboge in terms of ,emerald ,green and ,vermilion4 ,this necessitates adding some white to the rotating sectors of the yellow and black1 as the yellow reflects but little white light1 and finally we shall get an absolute match1 of which the final results are #agb ,v #ahh ,e #ge ,y #de ,w #bdj ,x4 ,this equation is full of meaning4 ,it tells us in the first place what we have already known1 that ,v and ,e are one or both impure colours1 and that when rotated together in the proportions indicated1 they produce at least a luminosity of white equal to #ec_/cfj of a white disc 7as the black used reflected just #cd of white light74 ,further1 it tells us that we can obtain the luminosity of ,y1 when we know the luminosities of ,v and ,e4 ,at page #ahf1 the luminosities of these colours are given as #cf and #cj respectively1 white being #ajj4 ,this makes the luminosity of the colours on the left hand of the equation #agb #aefg1 or #cbhg1 and on the right #ge_/cfj ,y #adgf1 and consequently the luminosity of ,y #hfi4 ,in the same way we can obtain any other colour in terms of these standards4 ,we may here show how we can obtain the luminosity of any colour by means of the three inner discs1 and the black and white outer discs4 ,we have already shown that any colour may be matched by the combination of not more than two simple colours1 after deducting white from it2 and from this we deduce that any coloured pigment will form a grey with some two of the three coloured discs1 ,v1 ,e1 and ,u2 and this being done we can then calculate the luminosity4 ,for instance1 with an orange-coloured pigment we should proceed to make a disc of the same diameter as that of the three above2 an inspection would show us that in this colour red predominates1 and therefore we could do without the red disc4 ,we should then alter the proportions of ,v1 ,u1 and ,o1 till they gave a match which was the same as that of a grey given by the rotating black and white sectors4 ,in an experiment with an orange of this kind1 the following results were obtained-- ,e #aae ,u #aej ,w #he ,o #ie ,x #bge ,we can now from these deduce the luminosity of the orange employed in this case4 ,the luminosities of ,e and ,u1 as already found1 were #cj and #dd1 whilst the black 7,x7 reflected #cd of white light2 we thus get the following equations-- #aae x #cj #aej x #dd #ie ,o 7#he #cd x #bge7 #ajj4 ,this gives #ie ,o #idce - 7#cdej #ffj74 ,o #ef4 ,that is1 the luminosity of the orange is #ef that of white2 by direct measurement it was #eg4 ,in a similar way the luminosity of chrome yellow 7,y7 is found4 ,in this case-- ,e #ce ,u #bjd ,w #aja ,y #aba ,x #bei ,similar equations were formed as the above4 #ce x #cj #bjd x #dd #aba ,y 7#aja #cd x #bei7 #ajj whence ,y #ggf4 ,that is1 the luminosity of the chrome yellow is #gh2 the same as was obtained by direct measurement4 ,in the same manner the luminosity of any colour can be found4 ,thus that of a purple1 or of green1 can be ascertained2 of the former by using the green disc with either the red or the blue disc1 and the latter by the red and blue disc4 ,from this it is apparent that we can check the luminosities derived from other means by this plan4 ,a taking experiment can be made with colour discs to imitate all the colours of the spectrum in their proper order1 though diluted more or less by white light4 ,this can be done by rotating ,v1 ,e1 and ,u together2 but in order to get additional luminosity in the yellow1 we can use chrome yellow as well4 ,if a disc be made as in the figure 7,fig4 #dd71 it will on rotating give a fair imitation of the spectrum1 if it be viewed through a slit held in front of the disc4 ,fig4 #dd4--;,disc arranged to give approximately all the ,spectrum ,colours4 ,the mixture of colours by means of rotating sectors is one which the artist cannot use for artistic purposes1 and it might seem that for him any deductions made from this method are useless2 but it is not so4 ,suppose we take black lines ruled closely together on paper1 and examine the surface from such a distance that the lines are no longer distinguishable it will appear of a grey2 and if we take the amount of black on the paper and amount of white1 and prepare two sectors of black and white1 whose angles are in these proportions1 and rotate them alongside the ruled surface1 it will be found that the grey of one matches the grey of the other4 ,if instead of lines of black and white we have them of light yellow and cobalt blue1 a grey is also produced when the surface covered by the blue is to that covered by the yellow in correct proportions1 and may be matched by rotating sectors containing merely black and white4 ,now some artists employ stippling1 filling up cross-hatching of one colour with dots of a totally different colour1 or they place dots side by side4 ,when seen from the distance at which the picture should be viewed1 these various colours blend one into another1 and form a tint which is the same as that which would be obtained by rotating these colours together in the proportion in which they cover the ground4 ,artists1 however1 generally mix their pigments together on the palette1 and the resulting mixtures are often totally unlike those which are obtained by rotating the same colours together1 a noteworthy example is that of yellow and blue4 ,by rotation1 and when in proper proportion1 these two give a white1 but when mixed on the palette a green results4 ,what causes this difference8 ,experimental proof is always the most satisfactory proof1 so let us have recourse to the spectrum apparatus to obtain an answer4 ,let a spectrum be thrown on the screen1 and in it place a strip of paper painted with the yellow1 and then another with the blue4 ,with the first it will be seen that the blue rays are not reflected1 but only the green and yellow and red1 taking the spectrum as roughly made up of these four colours4 ,with the latter the yellow is not reflected1 and but very little red1 but the blue and the green are reflected strongly4 ,now we have already said that the reflection of colour from a surface is indicative of the colours the particles of pigments when taken thin enough to be transparent would transmit2 hence we may take it that the yellow pigment transmits the red1 yellow1 and green1 and the blue pigment scarcely anything but blue and green4 ,when we have a mixture of these fine particles of pigment on paper1 some will underlie the others4 ,but let us pay attention to what would happen if a yellow particle were at the top1 and a blue one beneath it4 ,white light would impinge on the yellow particle1 but only red1 yellow1 and green would pass out or be reflected from it4 ,this sifted light would next fall on the blue particle and--as we have seen--only blue and green can pass through or be reflected from it2 but as the yellow particle has already deprived the white light of its blue component1 the green light alone would pass to the paper1 and be reflected either direct from the surface of the paper1 or through the particles themselves to the eye4 ,if the blue particle were on the top1 precisely the same effect would be produced2 it would only allow blue and green to pass to the yellow particle1 and as the yellow is opaque to the blue1 only green light again would pass4 ,similarly if side by side the same phenomena would occur1 since the light reflected from one on to the other would be deprived of all colour except the green4 ,a very pretty experimental proof of this is to place a yellow solution of dye in front of the slit of the colour apparatus1 and having formed the yellow colour patch to place in it a piece of paper covered with a blue pigment3 the latter becomes green4 ,by placing a blue solution in front of the slit1 and using a piece of yellow pigmented paper1 the same result is obtained4 ,the artist therefore in mixing his pigments calls into play the law of absorption1 and from his mixtures very naturally assumes that blue and yellow make green4 ,he makes a neutral tint of blue1 red1 and yellow1 and as the red cuts off the green1 this naturally follows from the above4 ,such experiments as these led him to the conclusion that red1 yellow1 and blue are the three primary colours1 an assumption which had he used simple spectrum colours instead of compound colours1 such as pigments1 he would not have ventured to make4 ,,chapter ,,xvi4 ,contrast ,colours--,measurement of ,contrast ,colours--,fatigue of the ,eye--,after-,images4 ,fig4 #de4--,method of showing ,contrast ,colours4 ,there is a phenomenon in colour which must be alluded to1 and which possesses more than a passing interest to the art world1 and that is colour contrast4 ,perhaps one of the best methods of showing this is by our colour patch apparatus4 ,if we throw the reflected beam and the colour patch on a square as before1 and place a rather thinner rod in front1 so that the two shadows lie on a background of the combined white light and spectral colours1 on passing a slit through the spectrum1 the shadow which is illuminated by white light will appear anything but white4 ,thus if we allow yellow spectral light to illuminate one shadow1 the other will appear decidedly of a blue hue2 if a green ray it will be of a ruddy hue2 if a blue ray of a yellow hue2 that is1 all the contrast hues will appear to the eye to tend towards a complementary tone to the spectral light4 ,the kind of white light illuminating the shadow has a marked effect on the tone1 as might be expected4 ,the following table shows the contrast colour of the white illuminated shadow when the white light used was that of a candle4 ---------------------------------------- --------------------------- ,contrast ,contrast ,spectrum ,colours in ,spectrum ,colours in ,colour4 ,electric light4 ,colour4 ,gaslight4 ---------------------------------------- --------------------------- ,cherry red ,green gray ,cherry red ,green gray ,scarlet ,bluish green gray ,scarlet ,sap green ,terra-cotta ,blue gray ,light red ,green gray ,raw sienna ,light blue gray ,olive green ,pink gray ,olive green ,umber ,apple green ,mauve black ,emerald green ,pinkish lavender ,emerald green ,pink terra-cotta ,grass green ,light pink ,emerald green ,pink terra-cotta ,bluish green ,dark pink ,bluish green ,pinker terra-cotta ,signal green ,salmon ,peacock blue ,salmon ,cyanine blue ,yellow ochre ,prussian blue ,reddish yellow ,ultramarine ,raw sienna ,ultramarine ,raw sienna ,violet blue ,brownish yellow ,violet blue ,brownish ,orange ,blue violet ,green yellow brown ,blue violet ,brownish yellow ,violet ,burnt sienna ,violet ,yellow ochre ---------------------------------------- --------------------------- ,the contrasts here shown are not so visible when the two shadows of the rod occupy the whole of the white square1 but are decidedly increased by the shadows occupying only a part of the field1 the margins being illuminated with a mixture of the two lights4 ,not only are there contrasts with coloured light and white1 but the relative position of one colour to another may alter the hue of each to the eye4 ,the following experiments indicate what change can be expected in contrasted colours4 ,the double colour apparatus was used as described at page #abb1 and a slit was placed in four different positions in the spectrum1 viz4 in the red1 orange1 green1 and violet1 to form patches1 and another slit was placed in the same four positions in the other spectrum1 and the contrasts noted4 ---------------------------------------- ----------------------- ,original ,colours4 ,change due to ,contrast4 ---------------------------------------- --------------------- ,red ,orange ,red became yellower ,orange became green grey ,green unaltered1 but ,green unaltered1 but brighter brighter ,blue became more ,blue became greener orange ,violet became orange ,violet1 no marked change ,green ,orange ,green became bluer ,orange became yellower ,blue became olive ,blue became more violet ,violet became yellower ,violet became bluer ,orange ,blue ,orange became redder ,blue became bluer ,violet became greener ,violet became bluer ,violet ,blue ,hardly altered ,hardly altered ---------------------------------------- --------------------- ,these contrasts were in most cases very marked1 as would be seen by causing the same colours to fall on a different part of the screen1 outside that on which the comparisons were made4 ,this phenomenon of contrast is one which is most valuable for artistic purposes1 for it gives a power of increasing the value of the colour of pigments which is used by the artist almost intuitively4 ,thus he can heighten the tone of his orange pigment1 with which he makes a sunset sky1 by placing in juxtaposition with it some bit of blue coloured space4 ,the blue becomes bluer1 and the orange more orange1 by this artifice4 ,all these artifices--or rather we should say intuitive applications of science--are most necessary when the small range of luminosity of colours with which he has to deal is taken into account4 ,for instance1 in a picture of a sun-lighted snow mountain and deep pine forests1 the utmost luminosity he can give to the former is that of white paper when seen in the shade1 which1 in comparison with what he sees1 is really a mixture of #ij of black with the light from the snow1 so that his range of luminosity is only nine-tenths of that which occurs in nature4 ,it is in adapting this low scale to his picture that true genius of the artist is seen4 ,it might seem that these contrast colours being only a physiological effect1 could not be accurately measured1 but such is not the case1 if a little artifice be employed4 ,if we use the second colour patch apparatus side by side with the first1 we can very readily and with very close approximation determine the contrast colours we see4 ,suppose by the second apparatus we form a colour patch of say red1 and place a thin rod in the beam of this ray and of the reflected beam1 and about six inches from it form another patch with the first apparatus1 using the three slits to make colour mixtures2 by first noting the contrast colour1 and then approximating in the second patch to what the eye perceives1 we can little by little get a fairly exact match to the contrast colour1 and can definitely note it4 ,we now give the results of three measures made for the contrast colours which presented themselves to the eye when they were caused by a red ray near the lithium line1 another near the ,e line in the green1 and the third near the ,g line in the violet4 ,to make white light and the contrast colours1 the slits had to be of the following apertures-- ---------------------------------------- - ,colour4 ,red4 ,green4 ,violet4 ---------------------------------------- - ,white light #aeg #fe #ih ,contrast to ,red #ace #aah #bbe ,green #aeh #ea #dh ,violet #aei #gb #db ---------------------------------------- - ,thus to form the contrast to red took #ace of red1 #aah of green1 and #bbe of violet4 ,now from each of these there can be deducted the amount of white light1 which will leave only two colours mixed4 ,calculating this out we find that the contrasts are-- ---------------------------------------- - ,contrast ,colour ,red4 ,green4 ,violet4 to ---------------------------------------- - ,red -- #ce #afg ,green #aeg #cb -- ,violet #aid #ie -- ---------------------------------------- - ,if the contrasts were exactly complementary colours1 the proportions of the two colours left should be the same as those of the same colours as given1 which with the original colour make white light4 ,it will be seen that such is not the case4 ,a very simple way of testing this is to form a patch of white light with the three slits in the first apparatus1 and then to obtain the contrasts by the other apparatus1 with the same colours one after the other that pass through the three slits4 ,if now we cover up the slit in the first apparatus through which the colour whose contrast in the second apparatus is sought passes1 we may dilute it with white light as we will1 but in no case has the writer found that an exact match to the contrast colour can be obtained in this way4 ,thus1 supposing we wanted to try the experiment with the same red light as that which comes through the red slit1 we should use that same light in the second apparatus1 and form the contrast colour with the white beam1 and then in the first apparatus cover up the red slit1 leaving the violet and green to form a patch on the screen4 ,we should then dilute the colour of this patch with white light1 and note if it appeared the same as the contrast colour4 ,another phenomenon which presents itself is the fatigue of the colour-sensation apparatus of the eye1 induced by looking at a bright object4 ,for instance1 if we look at a crimson wafer or spot for some time1 and then turn the eye so that it rests on a grey surface1 an image of the spot will still be seen1 but as of a greenish-blue colour4 ,this is due to the fact that the red-seeing apparatus is fatigued and exhausted1 whilst the green and violet-seeing machinery has not been largely exercised4 ,consequently when looking at grey paper the grey of the paper is seen in the retina at all parts as grey1 except in the small part of the retina which has got diminished power of perceiving a red sensation2 hence a sea-green image will be seen until the fatigue has passed away4 ,this colour can be reproduced with very fair accuracy by allowing only one eye to be fatigued1 and then using the other to obtain a colour mixture corresponding to it4 ,it will then be found that the colour is the same as the complementary colour1 much diluted with white light4 ,to the same cause may be traced positive and negative after-images1 as they are called4 ,if we look at a strongly-illuminated coloured form1 such as a church window1 and close the eyes1 the window will still be seen1 at first of its original colour 7a positive after-image71 and it will then fade and be seen in its complementary colours 7a negative after-image74 ,the positive image is due to the persistence of what we may call nerve irritation1 whilst the negative image is due to the physiological excitation of all the nerve fibrils1 which ordinarily speaking give the sensation of a very dull white light4 ,the previous fatigue of one set of fibrils1 however1 prevents them being excited to the same degree as the others1 hence we get a complementary image4 ,it would be out of place to pursue this subject further1 as we have only dealt with the physical measurement of colour-sensations1 and these are beyond it4 ,,index4 ,absorption by red1 blue1 and green glasses1 #ec ,absorption of light in the earth's atmosphere1 #fg ,absorption1 reference to law of1 #ec ,after-glow1 #gd ,arc light1 #bj ,artists and colours1 #aie ,balmain's paint1 #cc ,black body1 #ah ,blindness to green1 #adb ,blindness to red1 #gi-adb ,bromo-iodide of silver1 #acf ,carbon poles1 #bj ,carmine1 light reflected from1 #ajg template1 #ajf ,chlorophyll1 green solution of1 #ea ,collimating lens1 focal length of1 #bb ,colour1 analysis of1 #eb ,colour-blind1 red and green1 #gi1 #hj ,colour-blindness1 #adb-adf1 #aeg1 #aei ,colour constants1 #ae ,colour equations1 formation of1 #adg1 #adh ,colour1 extinction of1 by white light1 #abf ,colour mixtures1 #aac ,colour patch apparatus1 #da-eb ,colour sensation of the eye1 #bjb ,coloured discs1 use of1 #ahi ,coloured glasses1 measurement of1 #afb ,colours1 complementary of pigments1 #agj-agb ,colours1 complementary of spectrum1 #afg ,colours1 how matched1 #aef1 #aeg ,complementary colours1 measurement of1 #agc-agh ,compound colours1 definition of1 #af ,continuous spectrum1 #ag ,contrast colours1 #aif-bjj ,diffraction gratings1 #bc spectra1 #bd ,dimness and brightness of spectrum1 #bi ,discs1 spinning1 #ahb ,dust1 particles of1 #fb ,electric light1 contrast colours in1 #aig ,electric light1 crater of positive pole of1 #bj ,emerald green1 light reflected from1 #id ,equations1 colour1 #adg ,essentials of spectrum1 #bb ,extraction of colour by white light1 #abf ,extraction of white light by colour1 #aca ,eye1 sensitiveness of1 #ae ,fatigue of the retina1 #bjb ,fluorescence1 #ca ,fundamental sensations1 #adj ,gamboge1 matching1 #ahi ,glass1 light from sheet of1 #ad ,glass prisms1 #ba1 #bb ,glow-worm1 #ac ,green colour-blindness1 #adb ,heating effect of radiation1 #ch ,hue1 #ae ,images1 after1 #bjb ,images1 persistence of1 on retina1 #agi ,impurity of simple colours1 #abd ,indicator of sectors1 #dh ,infra-red rays1 #cb photography with1 #cd ,insensitiveness of the yellow spot to green1 #aah ,intensities of limelight1 gaslight1 and blue sky compared1 #aaj1 #aba ,interference1 #eh1 #ei ,interference bands on soap film1 #fj ,invisible spectrum1 methods for showing existence of1 #cb1 #cc ,koenig's curves1 #aea ,koenig's experiments1 #adj ,law of the scattering by fine particles1 #ff ,light from sun1 imitation of1 #fc ,light1 quality of1 illumining object1 #ad ,light scattered1 #fb ,limelight1 #ai ,lines in solar spectrum1 #bf ,luminosity1 #ac ,luminosity1 addition of one to another1 #he-hg ,luminosity of colour1 #af ,luminosity of pigments1 methods of determining1 #ha1 #hb ,luminosity of spectrum to normal-eyed and colour-blind persons1 #gf-gh ,luminosity of sun at different altitudes1 #fi-ga ,maxwell's colour-box1 #aeb1 #aec ,maxwell's discs1 #ahd-ahf ,measurement of amount of light reflected by different pigments1 #hh-ib ,metals1 light reflected from1 #ajj ,mock suns1 cause of change of colour in1 #fd ,molecular physics1 #ed ,molecular swings1 #acf1 #acg ,monochromatic light1 #dg ,negative images1 #bjc ,normal vision1 #gg ,orange1 finding luminosity of1 #aij ,percentages of skylight1 sunlight1 and gaslight1 #aaj1 #aaa ,phosphorescence1 #cb1 #ef ,pigments1 absorption by1 #eg1 #eh ,plan of forming spectrum1 #ba ,polished and uneven surfaces1 #ac ,primary colours1 definition of1 #acc-ace ,prism1 ,iceland spar1 #if ,prismatic spectrum into wave-lengths1 conversion of1 #bh ,prisms1 drawback to use of1 #bc ,prussian blue template1 #ajg light reflected from1 #ajg ,purity of colour1 #af ,rays1 infra-red1 #cd ,rays1 photography of dark1 #cd ,rays1 ultra-violet1 #cd ,registering tint of pigments1 #aaf colours1 #aef ,retina1 persistence of images on1 #agi ,ritter's rays1 #cb ,rood's colour scale1 #bf ,rotating sectors1 #df ,scaling of spectrum1 #di ,sectors1 rotating1 #df ,simple colours1 how obtained1 #aab1 #aac ,slits placed in spectrum1 #aac ,soap-bubbles1 #eh1 #ei ,soap-films1 #ei ,spectrum1 absorption of1 #ea1 #eb ,spectrum of sunlight1 #ah ,sun1 mock1 #fd ,sunset clouds1 #fh1 #fi1 #gb1 #gc ,sunset sky1 #gb1 #gc ,thermopile1 heating effects of1 #cf ,thermopile1 principle of1 #ce ,ultramarine1 light reflected from1 #ie ,ultra-violet rays1 #ca ,vermilion1 light reflected from1 #ic ,vibrations of rays per second1 #ee ,violet bands1 brightness of1 #ba ,visible and invisible parts of spectrum1 #cj ,water1 particles of1 #fb ,wave-length of lines in solar spectrum1 #bf ,white light and contrast colours1 #bjj-bjb ,white light1 extinction of by colour1 #aca ,white light1 formation of by mixture of yellow and blue1 #abe ,white light1 how made1 #aad1 #aae1 #aai-abc ,white light1 impression of1 #ha ,yellow and blue make white1 #abe ,yellow1 chrome1 luminosity of1 #aia ,yellow spot1 #aag ,young-,helmholtz theory1 #ach ,,the ,,end4 ,richard ,clay ,sons1 ,limited1 ,london ,bungay4 ,,publications ,,of ,,the ,society for ,promoting ,christian ,knowledge4 ,,the ,,romance ,,of ,,science4 ,a series of books which shows that science has for the masses as great interest as1 and more edification than1 the romances of the day4 ,small ,post #hvo1 ,cloth boards4 ,coal1 and what we get from it4 ,expanded from the ,notes of a ,lecture delivered at the ,london ,institution4 ,by ,professor ,raphael ,meldola1 ,f4,r4,s41 ,f4,i4,c4 ,with several ,illustrations4 #bs4 #f;d4 ,colour ,measurement and ,mixture4 ,by ,captain ,w4 de ,w4 ,abney1 ,l4,b41 ,r4,e41 ,f4,r4,s4 ,with ,numerous ,illustrations4 #bs4 #f;d4 ,the ,making of ,flowers4 ,by the ,rev4 ,professor ,george ,henslow1 ,m4,a41 ,f4,l4,s41 ,f4,g4,s4 ,with ,several ,illustrations4 #bs4 #f;d4 ,the ,birth and ,growth of ,worlds4 ,a ,lecture by ,professor ,a4 ,h4 ,green1 ,m4,a41 ,f4,r4,s4 #as4 ,soap-,bubbles1 and the ,forces which ,mould ,them4 ,a course of ,lectures by ,c4 ,v4 ,boys1 ,a4,r4,s4,m41 ,f4,r4,s4 ,with numerous diagrams4 #bs4 #f;d4 ,spinning ,tops4 ,by ,professor ,j4 ,perry1 ,m4,e41 ,d4,sc41 ,f4,r4,s4 ,with numerous diagrams4 #bs4 #f;d4 ,diseases of ,plants4 ,by ,professor ,marshall ,ward4 ,with ,numerous ,illustrations4 #bs4 #f;d4 ,the ,story of a ,tinder-,box4 ,a course of ,lectures by ,charles ,meymott ,tidy1 ,m4,b41 ,m4,s41 ,f4,c4,s4 ,with ,numerous ,illustrations4 #bs4 ,time and ,tide4 ,a ,romance of the ,moon4 ,by ,sir ,robert ,s4 ,ball1 ,,ll4,d41 ,royal ,astronomer of ,ireland4 ,with ,illustrations4 #bs4 #f;d4 ,,manuals ,,of ,,health4 ,fcap4 #hvo1 #abh pp41 limp cloth1 price #as4 each4 ,health and ,occupation4 ,by ,b4 ,w4 ,richardson1 ,esq41 ,f4,r4,s41 ,m4,d4 ,habitation in ,relation to ,health 7,the74 ,by ,f4 ,s4 ,b4 ,chaumont1 ,m4,d41 ,f4,r4,s4 ,on ,personal ,care of ,health4 ,by the late ,e4 ,a4 ,parkes1 ,m4,d41 ,f4,r4,s4 ,water1 ,air1 and ,disinfectant4 ,by ,w4 ,noel ,hartley1 ,esq41 ,king's ,college4 ,,manuals ,,of ,,elementary ,,science4 ,fcap4 #hvo1 #abh pp41 with ,illustrations1 limp cloth1 #as4 each4 ,physiology4 ,by ,f4 le ,gros ,clarke1 ,f4,r4,s41 ,st4 ,thomas's ,hospital4 ,geology4 ,by the ,rev4 ,t4 ,g4 ,bonney1 ,m4,a41 ,f4,g4,s41 ,fellow and late ,tutor of ,st4 ,john's ,college1 ,cambridge4 ,chemistry4 ,by ,albert ,j4 ,bernays4 ,astronomy4 ,by ,w4 ,h4 ,m4 ,christie1 ,m4,a41 the ,royal ,observatory1 ,greenwich4 ,botany4 ,by ,robert ,bentley1 ,professor of ,botany in ,king's ,college1 ,london4 ,zoology4 ,by ,alfred ,newton1 ,m4,a41 ,f4,r4,s41 ,professor of ,zoology and ,comparative ,anatomy in the ,university of ,cambridge4 ,matter and ,motion4 ,by the late ,j4 ,clerk ,maxwell1 ,m4,a41 ,trinity ,college1 ,cambridge4 ,spectroscope and its ,work 7,the74 ,by the late ,richard ,a4 ,proctor4 ,crystallography4 ,by ,henry ,palin ,gurney1 ,m4,a41 ,clare ,college1 ,cambridge4 ,electricity4 ,by the late ,professor ,fleeming ,jenkin4 ,the ,fathers for ,english ,readers4 ,a series of ,monograms on the ,chief ,fathers of the ,church1 the ,fathers selected being centres of influence at important periods of ,church ,history and in important spheres of action4 ,fcap4 #hvo1 cloth1 boards1 #bs4 each4 ,leo the ,great4 ,by the ,rev4 ,charles ,gore1 ,m4,a4 ,gregory the ,great4 ,by the ,rev4 ,j4 ,barmby1 ,b4,d4 ,saint ,ambrose3 his ,life1 ,times1 and ,teaching4 ,by the ,rev4 ,robinson ,thornton1 ,d4,d4 ,saint ,athanasius3 his ,life and ,times4 ,by the ,rev4 ,r4 ,wheler ,bush4 7#bs4 #f;d47 ,saint ,augustine4 ,by the ,rev4 ,e4 ,l4 ,cutts1 ,b4,a4 ,saint ,basil the ,great4 ,by the ,rev4 ,richard ,t4 ,smith1 ,b4,d4 ,saint ,bernard3 ,abbot of ,clairvaux1 ,a4,d4 #ajia-aaec4 ,by the ,rev4 ,s4 ,j4 ,eales1 ,m4,a41 ,d4,c4,l4 7#bs4 #f;d47 ,saint ,hilary of ,poitiers1 and ,saint ,martin of ,tours4 ,by the ,rev4 ,j4 ,gibson ,cazenove1 ,d4,d4 ,saint ,jerome4 ,by the ,rev4 ,edward ,l4 ,cutts1 ,b4,a4 ,saint ,john of ,damascus4 ,by the ,rev4 ,j4 ,h4 ,lupton1 ,m4,a4 ,saint ,patrick3 his ,life and ,teaching4 ,by the ,rev4 ,e4 ,j4 ,newell1 ,m4,a4 7#bs4 #f;d47 ,synesius of ,cyrene1 ,philosopher and ,bishop4 ,by ,alice ,gardner4 ,the ,apostolic ,fathers4 ,by the ,rev4 ,h4 ,s4 ,holland4 ,the ,defenders of the ,faith2 or1 ,the ,christian ,apologists of the ,second and ,third ,centuries4 ,by the ,rev4 ,f4 ,watson1 ,m4,a4 ,the ,venerable ,bede4 ,by the ,rev4 ,g4 ,f4 ,browne4 ,,miscellaneous ,,publications4 s4 d4 ,animal ,creation 7,the74 ,a popular ,introduction to ,zoology4 ,by the late ,thomas ,rymer ,jones1 ,f4,r4,s4 ,with #dhh ,woodcuts4 ,post #hvo4 ,cloth boards #g #f ,beauty in ,common ,things4 ,illustrated by #ab ,drawings from ,nature1 by ,mrs4 ,j4 ,w4 ,whymper1 and printed in ,colours1 with descriptions by the ,author of ,life ,underground1 c4 #dto4 ,cloth boards #aj #f ,birds' ,nests and ,eggs4 ,with #bb coloured plates of ,eggs4 ,square #afmo4 ,cloth boards #c #j ,british ,birds in their ,haunts4 ,by the late ,rev4 ,c4 ,a4 ,johns1 ,b4,a41 ,f4,l4,s4 ,with #aij engravings by ,wolf and ,whymper4 ,post #hvo4 ,cloth boards #f #j ,evenings at the ,microscope2 or1 ,researches among the ,minuter ,organs and ,forms of ,animal ,life4 ,by ,philip ,h4 ,gosse1 ,f4,r4,s4 ,with #aab woodcuts4 ,post #hvo4 ,cloth boards #d #j ,fern ,portfolio 7,the74 ,by ,francis ,g4 ,heath1 ,author of ,where to find ,ferns1 c4 ,with #ae plates1 elaborately drawn life-size1 exquisitely coloured from ,nature1 and accompanied with descriptive text4 ,cloth boards #h #j ,fishes1 ,natural ,history of ,british3 their ,structure1 ,economic ,uses1 and ,capture by ,net and ,rod4 ,by the late ,frank ,buckland4 ,with numerous illustrations4 ,crown #hvo4 ,cloth boards #e #j ,flowers of the ,field4 ,by the late ,rev4 ,c4 ,a4 ,johns1 ,b4,a41 ,f4,l4,s4 ,with numerous woodcuts4 ,post #hvo4 ,cloth boards #e #j ,forest ,trees 7,the7 of ,great ,britain4 ,by the late ,rev4 ,c4 ,a4 ,johns1 ,b4,a41 ,f4,l4,s4 ,with #aej woodcuts4 ,post #hvo4 ,cloth boards #e #j ,freaks and ,marvels of ,plant ,life2 or1 ,curiosities of ,vegetation4 ,by ,m4 ,c4 ,cooke1 ,m4,a41 ,,ll4,d4 ,with numerous illustrations4 ,post #hvo4 ,cloth boards #f #j ,man and his ,handiwork4 ,by the late ,rev4 ,j4 ,g4 ,wood1 ,author of ,lane and ,field1 c4 ,with about #ejj illustrations4 ,large ,post #hvo4 ,cloth boards #aj #f ,natural ,history of the ,bible 7,the74 ,by the ,rev4 ,canon ,tristram1 ,author of ,the ,land of ,israel1 c4 ,with numerous illustrations4 ,crown #hvo4 ,cloth boards #e #j ,nature and her ,servants2 or1 ,sketches of the ,animal ,kingdom4 ,by the ,rev4 ,theodore ,wood4 ,with numerous woodcuts4 ,large ,post #hvo4 ,cloth boards #e #j ,ocean 7,the74 ,by ,philip ,henry ,gosse1 ,f4,r4,s41 ,author of ,evenings at the ,microscope4 ,with #ea illustrations and woodcuts4 ,post #hvo4 ,cloth boards #c #j ,our ,bird ,allies4 ,by the ,rev4 ,theodore ,wood4 ,with numerous illustrations4 ,fcap4 #hvo4 ,cloth boards #b #f ,our ,insect ,allies4 ,by the ,rev4 ,theodore ,wood4 ,with numerous illustrations4 ,fcap4 #hvo4 ,cloth boards #b #f ,our ,insect ,enemies4 ,by the ,rev4 ,theodore ,wood4 ,with numerous illustrations4 ,fcap4 #hvo4 ,cloth boards #b #f ,our ,island ,continent4 ,a ,naturalist's ,holiday in ,australia4 ,by ,j4 ,e4 ,taylor1 ,f4,l4,s41 ,f4,g4,s4 ,with ,map4 ,fcap4 #hvo4 ,cloth boards #b #f ,our ,native ,songsters4 ,by ,anne ,pratt1 ,author of ,wild ,flowers4 ,with #gb coloured plates4 #afmo4 ,cloth boards #f #j ,selborne 7,the ,natural ,history of74 ,by the ,rev4 ,gilbert ,white4 ,with ,frontispiece1 ,map1 and #ej woodcuts4 ,post #hvo4 ,cloth boards #b #f ,toilers in the ,sea4 ,by ,m4 ,c4 ,cooke1 ,m4,a41 ,,ll4,d4 ,post #hvo4 ,with numerous illustrations4 ,cloth boards #e #j ,wayside ,sketches4 ,by ,f4 ,edward ,hulme1 ,f4,l4,s41 ,f4,s4,a4 ,with numerous illustrations4 ,crown #hvo4 ,cloth boards #e #j ,where to find ,ferns4 ,by ,francis ,g4 ,heath1 ,author of ,the ,fern ,portfolio1 c4 ,with numerous illustrations4 ,fcap4 #hvo4 ,cloth boards #a #f ,wild ,flowers4 ,by ,anne ,pratt1 ,author of ,our ,native ,songsters1 c4 ,with #aib coloured plates4 ,in two volumes4 #afmo4 ,cloth boards #ab #j ,,london3 ,northumberland ,avenue1 ,charing ,cross1 ,w4,c42 #dc1 ,queen ,victoria ,street1 ,e4,c4 ,,brighton3 #ace1 ,north ,street4 ,transcribers ,note3 ,page #afb ,the following equation3 ,therefore ,z x,x ,mu,w ,alphaw,w ,z 7,alphaw - ,mu7,w - x,x ,is printed as ,therefore ,z x#a,x ,mu,w ,alphaw,w ,z 7,alphaw - ,mu7,w - x,x in the original4