LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the following, mainly the light waves, that is, the second or high frequency range of radiation, will be discussed. The elec- tric waves are usually of importance only in their relation to the radiator or oscillator which produces them, or to the receiver on which they impinge, and thus are treated in connection with the radiator or receiver, that is, the electric conductor, in the theory of transient electric phenomena and oscillations.* The radiation may be of a single frequency, that is, a single wave; or a mixture of different frequencies, that is, a mixture of different and frequently of an infinite number of waves. Electric radiation usually is of a single frequency, that is, of the frequency or wave length determined by the constants of the electric circuit which produces the radiation, mainly the induct- ance L and the capacity C. They may, however, have different wave shapes, that is, comprise, in adolition to the fundamental wave, higher harmonics or multiples thereof, just as the sound waves which represent the same tone with different musical instruments are of the same frequency but of different wave shapes, that is, contain different higher harmonics. Light radiations usually are a mixture of a number of waves of different frequencies, and very commonly a mixture of an infinite number of frequencies, as is, for instance, the case with the * "Theory and Calculation of Transient Electric Phenomena and Oscilla- tions. " RELATION OF BODIES TO RADIATION. 21 radiation of an incandescent body as a lamp filament, which contains all the frequencies from long ultra-red waves over visible light waves to ultra-violet waves. In the action of vibrations on our senses there is a characteristic difference between the perception of sound waves by the ear and that of light waves by the eye : the ear is analytic, that is, can separate the individual waves in a mixture of different sound waves, as an accord on the piano, and distinguish the individual components of the mixed sound which reaches the ear. Thus we can hear and distinguish an individual voice amongst a mass of other noises. The eye, however, perceives only the resultant of all -the visible radiations which reach it, but cannot separate their components, and very different mixtures of radiations thus make the same impression upon the eye: thus, for instance, numerous mixtures of blue and yellow light appear alike to the eye and the same as green light, that is, appear green, while physically, it is obvious that mixtures of blue and yellow light are essentially different from green light. It is interesting to imagine how nature would look to us if the eye were analytic, that is, could separate the different component radiations, and if it could perceive waves over as great a range of frequency as the ear, about nine octaves instead of less than one octave as is now the case. The information given to us by the sense of sight would be infinitely increased, and we would see many differences and changes which now escape us. 10. However, while the eye cannot distinguish the different component radiations but sees only their resultant, the specific effects of the component radiations, as the physiologically harm- ful action of an ultra-violet component of light, still remain, even if the eye does not see the components, and in the study of radia- tion for the purpose of its engineering use for illumination it is therefore necessary to analyze the mixed radiation given by a source as a lamp, by resolving it into its component waves. This is done by using some feature of the radiation which varies with the frequency. Such is the case with the velocity of propagation. The velocity of light in empty space is 3 X 1010 cm. per sec. It is practically the same in air and other gases. In denser bodies, however, as water, glass, etc., the velocity of light is less and, as will be seen, is different for different frequencies. 22 RADIATION, LIGHT, AND ILLUMINATION. Assume then, in Fig. 15, a beam of light B striking under an angle the boundary between two media, as air A and water W, the vibration of the ether particles in the beam of light is at right angles to the direction of propagation BC, and successively the waves thus reach at blf a2 bz . . . As soon, however, as the back edge of the beam reaches the boundary at D its speed changes FIG. 15. by entering the medium W — decreases in the present instance. Let then Sl = speed of propagation in medium A, S2 = speed of propagation in medium W. Then, while the center of the beam moves the distance EC, the back edge, in the denser medium, a moves only the distance DI = -^EC, and the wave front of the »i back half of the beam thus changes to CI while that of the front half of the beam, which is still in the medium A, remains GC. Then, while the front edge of the beam moves from G to H, the center and the whole back half of the beam moves in the denser o medium TF, only the distance CK = — 2 GH, and the wave front «i of the beam, in the medium TF, now is EL. That is, due to the difference in velocity in the two media A and W, the wave front of the beam, and thereby its direction of propagation, is changed RELATION OF BODIES TO RADIATION. 23 when traversing the boundary between the two media, and the beam EC continues its motion in the direction CM. Let then o^ = angle of incidence, that is, the angle between the incident beam BC and the perpendicular CN on the boundary, and a2 = angle of refraction, that is, the angle between the out- going or refracted beam CM and the perpendicular CP on the boundary. It is then : FDH = a, and LHD = a2 ; hence, FH = DH sin a, and DL = DH sin av (1) The front edge of the beam moves the distance FH in medium A, while the back edge moves the distance DL in medium W; that is, FH + DL = S, - S3; (2) hence, substituting (1) into (2), gives: sin «1 Sl sn (3) That is, the ratio of the sines of the angle of incidence and the angle of refraction equals the ratio of the speed of propagation in the two media, hence the ratio of the sines of these two angles is constant. This is the law of refraction, and this ratio of sines is called the refractive index between the two media A and W. As the refractive index of one medium W, then, is understood its re- fractive index against empty space or against air : sn a where S is the velocity of light in empty space = 3 X 1010, and Sl the velocity in the medium, of which ^ is called the refractive index. From equation (4) it follows, that, if ^_2 is the refractive index between medium 1 and medium 2, £2_3, the refractive index between medium 2 and medium 3, dl-3 = £2_3 -*- ^_2 = refractive index of medium 1 and medium 3; that is, the refractive index between any two media is derived as the ratio of their refractive indices against a third medium, as, for instance, against air. 24 RADIATION, LIGHT, AND ILLUMINATION. 11. Incidentally, it is interesting to consider the corresponding relations in electric waves. In an electric circuit, the speed of propagation of an electric wave is, when neglecting the energy losses in and by the con- ductor: S = -L= , (5) VLC where L is the inductance, C the capacity of the conductor per unit length (the length measured in the same measure as the speed S). The inductance L is proportional to the permeability /*, and the capacity C proportional to the dielectric constant, or specific capacity K of the medium surrounding the conductor, that is, the medium through which the electric wave propagates; that is, A V p* where A is a proportionality constant. The ratio of the speed of propagation of an electric wave in two media 1 and 2 thus is: <,, for empty space, fj. = 1 and « = 1; hence, (8) where Sl is the speed of propagation in the medium of constants /^ and jcr Comparing equation (8) with (4) it follows : Vl = d*-, (9) that is, the square of the refractive index d equals the product of permeability JJL and dielectric constant K. Since for most media the permeability /JL = 1, for all except e maneti mri the magnetic materials RELATION OF BODIES TO RADIATION. 25 This relation between the constant of the electric circuit K and the constant of optics d was one of the first evidences of the identity of the meclium in which the electric field exists with the medium which carries the light waves. It is, however, only approximately correct, as the refractive index d varies with the frequency and is derived for the extremely high frequencies of light radiation, while K refers to stationary conditions. A better agreement is thus reached when using as d the refractive index extrapolated for infinite wave lengths. 12. It is found that the different component frequencies of a beam of radiation are deflected differently when passing from one medium into another, and the higher frequencies are deflected FIG. 16. more than the lower frequencies, thus showing that the velocity of propagation decreases with an increase of frequency, that is, a decrease of wave length. This gives a means of resolving a mixed radiation into its com- ponent waves, that is, into a spectrum, by refraction. A narrow beam of light B (Fig. 16) is passed through a prism P of transparent material, and the component frequencies then appear on the screen A (or are seen by the eye) side by side, the red R to the left, the violet V to the right, in Fig. 16, and the green G in the middle. It is obvious that the material of the prism must be transparent to the radiation; thus, when studying ultra-violet radiation to which glass is opaque, glass prisms cannot be used, but some material transparent to ultra-violet light such as a quartz prism must be used. 26 RADIATION, LIGHT, AND ILLUMINATION. The beam of light also can be resolved into its components by a diffraction grating, in which case the lower frequencies are deflected more than the higher frequencies ; that is, the red more than the violet. These two forms, the refracting spectroscope and the diffract- ing spectroscope, now enable us to resolve a beam of mixed radia- tion into its components and thus study its spectrum. 13. I show you here a number of typical spectra: (1). The spectra of an incandescent lamp and an alcohol lamp with Welsbach mantel. These are continuous spectra, that is, show all the radiations from red over orange, yellow, green, blue, indigo to violet, uniformly shading into each other. (2a). The spectrum of the mercury lamp. This is a line spectrum, that is, shows only a finite number of bright lines on black background. It contains five bright lines ; greenish yellow, bright green, indigo and two violet, one faint dark green line, and 1 1 1 1 1 1 1 Ij RED ORANGE 1 YELLOW 1 GREEN BLUE INDIGO VIOLET FIG. 17. a number of very faint red and orange lines, of which three are indicated dotted in Fig. 17. (26). The spectrum of an arc between titanium carbide elec- trodes. This also is a line spectrum, but unlike the mercury spectrum, which has only six bright lines, the titanium spectrum contains many thousands of bright lines, so that with the low power of the spectroscope which you have, the lines blurr into each other and we see only the most prominent or brightest lines on a uniformly luminous background, which latter requires a more powerful spectroscope to resolve into lines. (3) . The band spectrum. This shows a number of bright bands, frequently gradually fading out at their edge and separated by dark spaces. It thus differs from the continuous spectrum (1) in being discontinuous, that is, missing certain ranges of frequency, and differs from the line spectrum (2) in that the band spectrum has a number or range of frequencies in each band, where the line RELATION OF BODIES TO RADIATION. 27 spectrum has only 'one single frequency in each line. Such band spectra are usually characteristic of luminescent compounds or of gases and vapors at high pressure, while elementary gases or vapors give line spectra. Absorption and fluorescence also give band spectra, and I thus show you a band spectrum by opera- ting a mercury lamp in a tube of uranium glass, behind a trans- parent screen colored by rhodamine (an aniline dye which fluoresces red). As you see, the spectrum shows a broad red band, due to the reddish screen, and a greenish yellow band due to the uranium glass, while the normal mercury lines are de- creased in intensity. (4). If you now look with the spectroscope at the Welsbach mantel through the mercury arc stream, you see the continuous spectrum of the mantel and superimposed upon it the line spec- trum of the mercury lamp. The light giving mercury vapor thus is transparent for the light of the Welsbach mantel back of it, and lets it pass through, with the exception of those particular fre- quencies which it gives itself; that is, a luminous gas absorbs those frequencies of radiation which it produces, but is trans- parent for all other frequencies. This is easily understood: an atom on which a vibration impinges will be set in motion by it and thus absorb the energy of the impinging vibration if it is able to vibrate with the frequency of the impinging vibration; that is, to resonate with it, but will not be affected by any other frequency to which it cannot respond, and thus is transparent to all frequen- cies of vibration, except to those to which it can respond; that is, which it produces when vibrating. When looking at a continuous spectrum through a luminous gas or vapor, two cases thus may occur: either the spectrum lines of the gas are brighter than the continuous spectrum, as in the present case, and then appear as bright lines on a bright back- ground, or the continuous spectrum is brighter than the lines of the gas spectrum in front of it and the lines of the gas spectrum appear less bright than the background, that is, appear as dark lines on a bright background. Such a spectrum is called a reversed spectrum, or absorption spectrum. It shows the lines of the gas or vapor spectrum, by contrast, dark on the brighter back- ground of the continuous spectrum. The sun and many fixed stars present such a reversed spectrum : the sun's spectrum shows the spectrum lines of all the elements 28 RADIATION, LIGHT, AND ILLUMINATION. which are in the sun's atmosphere as dark lines on the continuous spectrum given by the inner core of the sun. Whether the line spectrum of a gas or vapor is reversed by the continuous spectrum of a solid or liquid back of it or not depends upon the relative intensity, and thus, to some extent, on the rela- tive temperature. Some fixed stars show bright lines on a less luminous background, due possibly to a higher temperature and greater thickness of their atmosphere, and sometimes bright lines and dark lines occur simultaneously, or dark lines may change to bright lines at such places at which, by some activity, as a tem- perature rise, their brilliancy is greatly increased. FIG. 18. Combinations of the different types of spectra: continuous spectrum, line spectrum, band spectrum, reversed spectrum, frequently occur, as we have seen bands and lines together in the modified mercury spectrum, and in this case, by turning on an incandescent lamp, we can still add a continuous spectrum due to the light of the incandescent lamp reflected from the walls of the room. So also in the continuous spectrum of incandescent bodies, bright bands or dark bands occasionally appear, that is, regions in the spectrum of greater or lesser intensity, as will be discussed in the paragraphs on colored radiation and selective radiation. RELATION OF BODIES TO RADIATION. 29 14. When a beam of radiation impinges upon a body it is resolved into three parts : one part is reflected, that is, does not enter the body at all, but is thrown back. The second part is absorbed in the body, that is, converted into another form of energy (which other form of energy usually is heat, but may be chemical energy, some other frequency of radiation, etc.) and the third part is transmitted, that is, passes through the body, and out of it, if the body is not too thick. No body reflects, or absorbs, or transmits all the radiations, but even the most per- fectly reflecting body absorbs and transmits some radiation, the most transparent body reflects and absorbs some radiation, etc. Reflection may be either regular reflection, or irregular reflec- tion. In the former case (Fig. 18) the beam of light is reflected under the same angle under which it impinges upon the body, and the body thus acts as a mirror, that is, gives a virtual image FIG. 19. back of it as shown in dotted line in Fig. 18. In the latter case (Fig. 19) the light is reflected irregularly in all directions. A body which reflects all the frequencies of radiation uniformly, that is, in which the percentage of the impinging radiation, which is reflected, is the same for all frequencies of radiation, is called a colorless body, and a body which reflects a higher percentage of the radiation of some frequency than of other frequencies, is called a colored body, and its color is the color of radiation, that is, the frequency or frequencies which it reflects more than other frequencies. A colorless body which reflects all the radiation impinging upon it is called a white body. Most nearly white bodies are silver, magnesia, chalk, etc. A body which reflects none of the radiation impinging upon it, but absorbs all, is called a block body. The 30 RADIATION, LIGHT, AND ILLUMINATION. most nearly black bodies are lampblack, charcoal, etc. A body which reflects a constant part of the impinging radiation, that is, the same part or percentage for all frequencies, is called a grey body, and the ratio of the reflected light to the total impinging light is called its whiteness or albedo. A perfectly white body thus has albedo 1, a perfectly black body albedo 0, and a body which reflects one-quarter and absorbs the other three-quarters of the radiation of any wave length impinging upon it, would be said to have albedo 0.25. Black, white and grey thus are not considered as colors in physics. As examples of colorless bodies I show you here : Regular reflection: polished silver, white; polished iron, grey. Irregular reflection: powdered magnesia, white; lampblack, black; powdered zinc, barium sulphide, grey. As example of colored bodies I show you : Regular reflection: polished copper, red; polished gold or brass, yellow. Irregular reflection: mercury sulphide (cinnabar), red; potas- sium bichromate, orange; magnesium chromate, yellow; copper acetate-arsenite (paris green), green; copper oxide hydrate precipitated by ammonia, blue; ultra-marine, indigo ; magnesium permanganate mixed with magnesia, violet. 15. Of the radiation which enters a body, that part which is absorbed is usually converted into heat. Thus a black body, when exposed to radiation, becomes hotter than a white body, which reflects, or a transparent body, which transmits, most of the radiation. Thus the globe of a colored incandescent lamp, which absorbs more of the radiation than a transparent globe, becomes hotter than a clear glass globe. When scattering dirt on the snow it can be made to melt down far more rapidly in the spring, under the rays of the sun, than when remaining clean, etc. Some bodies convert the absorbed radiation into chemical energy, into other frequencies of radiation, etc. Bodies which convert the absorbed radiation, or rather a part thereof, into radiation of different, as far as known always lower, frequencies, are called fluorescent bodies. Thus the solu- tion of rhodamine in alcohol, which I show you here, fluoresces red. It transmits red light, but absorbs green, blue and violet light, and converts a part thereof into red light. This is best RELATION OF BODIES TO RADIATION. 31 illustrated by exhibiting it in a source of light which contains no red rays, as the mercury lamp. You see in the rays of the mer- cury lamp the rhodamine solution looks bright red, the red light seems to come from the inside of it, and especially through a red glass the solution looks like a red hot incandescent body. Here then, as no red light reaches the solution, the red light given by it must be produced by frequency conversion from other radiation. The spectroscope shows especially the bright green mercury line weakened. The phenomena of conversion of absorbed light into other forms of energy will be more fully discussed in the following paragraphs. 16. By the transmitted light, that is, the radiation which passes through them, bodies are again divided into colorless bodies; that is, such bodies which transmit the same percentage of radiation for every wave length or frequency, and colored bodies; that is, bodies which transmit a larger percentage of radiation of some frequencies than of others, and as the trans- parent color of a body, then, is understood the color, that is, the frequency, of that radiation of which the greatest percentage is transmitted. Thus a red glass is one which transmits a higher percentage of red radiation than of any other radiation. A body, then, is called transparent, if it transmits all the radia- tion, and opaque, if it transmits no radiation, but absorbs or reflects all. If only a part of the radiation is transmitted, but in such manner that it is the same part for all frequencies, the body is called grey; or imperfectly transparent, if the part which is not transmitted is absorbed in the body ; and translucent, if the part which is not transmitted is irregularly reflected inside of the body. The most perfectly transparent bodies, for visible light, are glass, water, quartz, etc. ; the most opaque are the metals, and perfectly, or almost perfectly opaque are the magnetic metals, perhaps due to the very low speed of propagation in these metals, which would result from the high value of the permeability /* by equation (8) paragraph 11. As example of colorless bodies I show you here a glass tube filled with water, transparent; a tube filled with nigrosine solu- tion in alcohol, opaque and black; a very diluted solution of nigrosine with traces of other aniline dye for color correction, in 32 RADIATION, LIGHT, AND ILLUMINATION. alcohol, as grey, and a tube filled with an emulsion of water with a solution of chloroform in white paraffin oil, which latter solu- tion has the same specific gravity as water, translucent. Samples of transparent colored bodies are: carmine solution, red; potassium bichromate solution, orange; potassium chromate solution, yellow; nickel sulphate solution, green; copper nitrate solution, blue; diluted potassium permanganate solution, or diluted solution of iodine in chloroform, violet. As seen, the terms " colorless" and " colored" have two dif- ferent meanings when applied to the reflected radiation and when applied to the transmitted radiation, and the color of a body in reflected light may be different, and frequently is differ- ent, from its color in transmitted light, and some bodies may be colorless in reflected light, but colored in transmitted light, and inversely. In materials of low absorption, the transmitted and the reflected colors must be approximately complimentary ; thus the transmitted color of the atmosphere is orange, the reflected color blue. 17. Colors are, therefore, distinguished into opaque colors and transparent colors. The opaque colors are those shown by the light reflected from the body, the transparent colors those shown by the light transmitted through the body. In reflected light, the transparent colors, therefore, show only when covering a white, that is, reflecting surface, and then, due to the light reflected from the white background of the transparent coloring body traversing this body twice, before and after reflection, and, therefore, depend in their brilliancy on the background. The difference between opaque and transparent colors, the former reflecting from the surface, the latter reflecting from back of the colored substance, is seen by comparing the appearance of the two classes of colors shown in 14 and in 16. In its general use, the terms colorless, white, black, transparent, opaque, refer only to the visible radiation, that is, to the frequen- cies within that octave which the eye perceives as light. More broadly, however, these terms may in physics be applied to the total range of radiation, and then many substances which are colorless for visible light, would be considered as strongly colored, that is, show for different frequencies great differences in the per- centage of radiation which they reflect or transmit. Thus we have seen that glass, which is transparent for visible light, is RELATION OF BODIES TO RADIATION. 33 entirely opaque for some ultra-violet light and also opaque for ultra-red light of low frequency, so in this broader sense would have to be called colored* the color of clear glass, however, is that of the visible spectrum; or, for instance, iodine solution, which is opaque for visible light, is transparent for ultra-red light, that is, its color is ultra-red, etc. In this broader sense, referring to the total range and not merely to the visible range, glass, water, mica, etc., are not color- less transparent but colored, and quartz is probably the most transparent and colorless body. 18. The color of the body, thus, is represented by that fre- quency or those frequencies. of radiation of which a higher per- centage are reflected or transmitted than of the other frequencies of radiation. This color, therefore, is a characteristic property of the body and independent of the character of the light and of its physiological effect on the eye, and can thus be called the actual or objective color of the body. If we consider diffused daylight as white, then the body appears to the eye in its objective or actual color when compared with a white body, that is, a body uniformly reflecting all radiation in the diffused daylight. Under other conditions, as, for instance, in artificial illumination, bodies do not always appear to the eye in their objective colors, but may show a very different color depending on the character of the source of light. For instance, I have here a plate of colored glass : looking through it at the mercury lamp you see the glass has an olive green color; but when I turn on an incandescent lamp you see that it is ordinary red glass. Its objective color is red, its subjective color in the mercury light is green. Looking through this glass in daylight it appears red as it transmits more red light than other colors of light, and the transmitted light thus contains a higher per- centage of red rays than diffused daylight. The rays of the mercury lamp, however, contain very little red light and very much green light, and while by this red glass a much higher percentage of the red light from the mercury lamp is trans- mitted than of its green light, this higher percentage of trans- mitted red light is very much less than the lower percentage of the transmitted green light, and, therefore, in the transmitted light, green still preponderates more than in the diffused day- light, that is, the glass appears green. For instance, if in the 34 RADIATION, LIGHT, AND ILLUMINATION. mercury lamp the ratio of red light to green light is only one hundredth of what it is in daylight, and the red glass transmits ten times as high a percentage of red as of green light, then in the light of the mercury lamp transmitted through this red glass the ratio of red light to green light is still only one-tenth of what it is in daylight, and the glass thus appears green. We have to distinguish between the actual or objective color of a body, which is a constant of the body, and its apparent or sub- jective color, which depends upon the light in which we view the body, and therefore may be very different for different illumi- nants, and bodies which have the same colors in one illuminant may have entirely different colors in another illuminant and inversely. It is, however, the subjective color of the body cor- responding to the particular illuminant used which we see, and which is, therefore, of importance in illuminating engineering, and the study of the subjective colors, therefore, is of foremost importance, and the success or failure of an illumination depends on the production of the desired subjective colors. 19. Broadly, an illumination discriminates for the color in which it is deficient and the color in which it is rich. The color in which the illuminant is deficient — as red in the mercury lamp, blue and violet in the incandescent lamp — appears black; the color in which the illuminant is abnormally rich — as yellow in the incandescent lamp, green in the mercury lamp — appears as white ; that is, both colors disappear, more or less ; as colors, be- come colorless. Thus in the yellow incandescent lamp, opaque yellow appears the same as white, opaque blue and violet appear more or less as black; transparent yellow appears colorless, trans- parent blue and violet appear colorless and from light transparent grey to opaque black. In the green mercury lamp, opaque green and white appear the same, opaque red appears as black; trans- parent green appears colorless, and transparent red appears colorless, from clear transparent to grey, to opaque black, de- pending upon its intensity. It is interesting to see the difference between opaque and transparent colors in this respect: as opaque colors the deficient color turns black, the excess color white; but as transparent colors both become colorless and more or less transparent. Thus, in the mercury lamp, red and green as transparent colors both vanish, or rather, very greatly decrease in their prominence. RELATION OF BODIES TO RADIATION. 35 As the eye perceives only the resultant of radiation, very dif- ferent combinations of radiation may give the same impression to the eye, but when blotting out certain radiations, as red and green, in the mercury lamp, these different combinations of radia- tion may not give the same resultant any more, that is, become of different colors, and inversely, different colors, which differ only by such component radiations as are blotted out by an illuminant, become equal in this illuminant. For instance, a mixture of red and blue, as a diluted potassium permanganate solution, appears violet in daylight. In the mercury light it appears blue, as the red is blotted out, and in the light of the incandescent lamp it appears red, as the blue is blotted out. I show you here, in the light of an incandescent lamp, two pieces of black velvet. I turn off the incandescent lamp and turn on the mercury lamp, and you see the one piece is blue, and the other black. Now I show you two pieces of brownish black cloth in the mercury light. Changing to the incandescent lamp you see that the one is a bright crimson, and the other still practi- cally black. In both cases the color deficient in the illuminant appeared as black. This tube of copper chloride crystals appears bright green in the incandescent lamp. In the mercury light it is a dirty white. The excess color, green, is blotted out. These crystals of didymium nitrate, which are a faint light pink in daylight, are dark pink in the incandescent light. In the mercury light they are blue : the color is a mixture of red and blue, and the one is blotted out in the mercury light and the other in the incandescent light. These two tubes, one containing a concentrated solution of manganese chloride, the other a solution of didymium nitrate, are both a dark pink in the incandescent light. In the mercury light the first becomes a very faint pink, the second becomes grass green. These tubes, one containing a solution of didymium nitrate, the other a diluted solution of nickel sulphate, appear both light green in the mercury light. In the incandescent lamp the former is dark pink, the latter dark green. [Didymium, which formerly was considered as an element, has been resolved into two ele- ments, praseodymium, which gives green salts, and neodymium, which gives pink salts. It is interesting to see that this separa- 36 RADIATION, LIGHT, AND ILLUMINATION. tion is carried out photometrically by the light: the mercury lamp showing only the green color of the praseodymium, the incandescent lamp the pink color of neodymium]. I have here a number of tubes, which seen in the light of the incandescent lamp contain red solutions of nearly the same shade. Changing to the mercury lamp you see that they exhibit almost any color. As the red disappeared in the mercury lamp the other component colors, which did not show in the incandes- cent lamp as they were very much less in intensity than the red, now predominate : potassium permanganate solution turns blue, carmine blue ; potassium bichromate, greenish brown ; coralline, (an aniline dye), olive green, etc., etc. Again, a number of tubes, which in the mercury light appear of the same or nearly the same blue color, turn to very different colors when seen in the incandescent lamp, due to the appearance of red and green, which were not seen with the mercury light. A solution of rhodamine, however, which looks a dull red in the light of the incandescent lamp, turns a glowing crimson in the mercury lamp, due to its red fluorescence. This diluted solution of rhodamine and methyl green (aniline dyes), which is grey in the light of the incandescent lamp, turns brownish red in the mercury lamp, the green is blotted out, while the rhodamine shows its red fluorescence. Thus, you see, the already very difficult prob- lem of judging the subjective colors of bodies under different illu- minants is still greatly increased by phenomena as fluorescence. To conclude then : we have to distinguish between colorless and colored bodies, between opaque colors and transparent colors, between color, as referred to the visible range of radiation only, or to the total range, including ultra-red and ultra-violet, and especially we have to realize the distinction between objective or actual color, and between subjective or apparent color, when dealing with problems of illuminating engineering.