l12 Absorption and emission

Ultra-red and-ultra violet

We return to the solar spectrum. We see a band of colour of finite length; it is red at one end, violet at the other end. However, the visible ends, unless the light has passed through a substance absorbing it - which will be excluded here - are not the spectrum's real ends. While we do not see its continuation beyond these visible ends, we can nevertheless detect them. A sensitive thermometer, placed into the individual sections of the spectrum, indicates that the temperature rises from the violet end towards the centre of the spectrum. Moreover, beyond the visible red end, in the ultra-red, it is higher than in the visible red. If you photograph the spectrum with certain precautionary measures, you obtain an image which continues far beyond the violet end into the ultra-violet. Hence the waves emanating from the source of light generate light, heat and chemical decomposition (actinic action). But the waves are the same, only the means by which they become visible differ. The same ultra-red, which on meeting the thermometer causes the mercury to rise, and the same ultra-violet, to which the photographic plate reacts with chemical decomposition, our eye would sense as light, if the retina could react to it.

Formation of pigment by absorption of light

However, already in the visible region of the spectrum we can note - that is, see - that the reaction to waves of different lengths can assume quite different forms depending on the nature of the reacting substance. Hitherto, we have always assumed that a substance when subjectws to light either lets it completely pass through or reflects it completely. If this assumption were strictly justified, all substances would be either completely transparent or completely opaque. Moreover, the opaque ones, when they reflect incident daylight in all directions uniformly, would appear to be completely white. However, transparent materials are neither totally transparent nor are all opaque ones white. Most of them have colour. The difference in their colouring is largely explained by the fact that they partially absorb, reflect and let pass incident light.

Daylight is a mixture of infinitely many mono-chromatic kinds of light; they manifest their differences by causing the impression of a different colour. However, this difference is only for the eye - physiological. Physically speaking, the kinds of light of various colour differ by the associated wave length. If white light encounters a substance, the body is met by a flood of waves of all possible lengths in between that of the red and that of the violet. The difference in the appearance of substances is now explained by their behaviour with respect to waves of different wave lengths. Surfaces, which reflect waves in all directions, do not prefer any of them nor prejudice them, appear to us to be white, those which absorb all of them black, those which during reflection or absorption prefer one or the other of them coloured (selective absorption). A substance of purely green appearance - we refer to a green of a specific wave length - is then such that it absorbs all other wave lengths and only reflects that which belongs to this green. If you illuminate it with blue light, it appears to be black, because no rays come to it which it can reflect. In other words, the colour, in which an opaque body appears to be to us in daylight, is that which the absorbed kinds of light complement to white. This also explains why coloured substances have in daylight another colour than by the light of a candle or an electric arc: In every source of light, the mixture of single coloured kinds of light differs; since the colours which a coloured substance cooresponds to definite waves, its appearance depends on whether and in what strength the source of light under consideration emits these waves.

The colours of transparent substances have a similar explanation. In this case, the eye senses the waves which have passed through. Pure blue glass appears to be blue, because it only lets pass those to which the eye reacts by blue-sensation. Hence, if you hold between the blue glass and the light source a piece of red glass, no light at all enters your eye, because the red glass only lets red rays pass which are absorbed by the blue glass. These two pieces of glass, each of which is transparent by itself, become opaque when placed on top of which other.

You call the cproperty of permeability and impermeability for waves of a substance its transparency and opacity, referred to the eye. However, the eye is only a means of testing waves, to which it reacts. Strictly speaking, we must ask whether a substance lets pass waves or not. It is a different question how one is to recognize transparency, whether by letting the transmitted waves act on the retina or on photographic plates or on a thermometer or whatever.

Like the refraction of light, its absorption also depends on whether a substance, into which it enters, is isotropic or not. Only in isotropic substances, it does not depend on the direction of the path of the light. Hence, coloured, isotropic substances, whatever is the direction in which you look through them, have the same colour. However, in mono-axial coloured crystals, the absorption along the axis differs from that at right angle to it (dichroitic, base colour and axis colour), in bi-axial ones, in all anisotropic directions (pleochroitic) and moreover for different colours in a different manner (Wilhelm Karl Haidinger 1795-1871, he also advanced the terminology dichroism and pleochroism).

Weakening of light by absorption (Beer's law)

Coloured transparent substances allow certain wave lengths to pass, but not others; those which they let pass determine their colour. However, the transparency for a colour is limited. The thicker is the layer, through which the waves pass, the more of their energy is converted underway into heat; if you make the layer thick enough, it becomes opaque. The absorption of light with the increasing thickness explains also why substances, which let pass light with different colours, have quite a different appearance depending on how thick is the layer through which you view: The thinner layer allows yet all colours to pass, which a thicker one absorbs. The law of absorption of Beer 1825-1863 states: The absorbed intensity of light is proportional to the incident one, and layers of equal thickness absorb equal fractions of incident light. If an incident, homogeneous intensity of light I₀ experiences in the thickness dx of a layer the loss dI₀, then -dI₀ = mI₀dx, where m is the absorption coefficient. The light intensity I_a , which remains after passage through the layer with thickness d is: I_a = I₀·e^-md, where e is the base of the natural logarithm. (This formula is approximate, because almost always dispersed radiation is superimposed on the emerging light) The colours, which a given substance extinguishes in the spectrum of white light sent through it, tell you which waves it absorbs. The spectrum of the emerging light is called its absorption spectrum. It is the characteristic spectrum of a body which does not glow. Absorption spectrum analysis is of great importance for certain physiological problems, because the materials to be investigated have according to their nature an absorption spectrum (for example, for chlorophyll- and blood-problems).

Anomalous dispersion

Anomalous dispersion is closely linked to absorption. You extinguish in the spectrum of white light the green and green-blue light and shift all, which lies to the left hand side of the gap, to the right end, all which lies on the right hand side, to the left end. You then have the sequence: Blue, violet, black (absorption bands), red, orange, yellow - this is approximately the spectrum of anilin-red, by means of which Christian Christiansen 1843-1917 1870 discovered (again) anomalous dispersion. F.P.Le Roux 1832-1907 1860 had discovered it in iodine vapour. It is of great significance in Astrophysics since 1900 through the solar theory of Julius and more recently through the explanation of the width of the Fraunhofer lines by Unsöld.

In order to survey the progress of anomalous dispersion, you use since Kundt 1871 the method of cross-prisms with the test sample as second prism. A simple refraction spectrum is not sufficient for this purpose, because in the case that several colours are refracted equally strongly - which could happen in view of the irregularity of this refraction - they appear one upon another. However, in a cross-spectrum, where every section of the spectrum is dispersed again at right angle to the length direction of the spectrum (by a second prism, the dispersion of which differs from that of the first one), colours which cover each other may be separated. The cross-spectrum is curved and disintegrated into two pieces, displaced with respect to each other, a typical form of which shows Fig. 796. Certain colours are completely absent (here yellow) and the neighbouring light on the red side (red, orange) is more strongly (!) diverted than that on the blue side(green, blue) - the characteristic feature of anomalous dispersion.

In this or a similar manner disperse all substances which are strongly coloured (have surface colour) and display in the spectrum sharp absorption bands - such as anilin colours, chlorophyll, also the metals. The anomaly always occurs near an absorption band: Coming from the red side of the normal spectrum, the refractive index n increases at first normally with decreasing wave length, however, very strongly shortly before the absorption regime, and at the band n jumps from an exceptionally large value to an exceptionally small value. It starts again with this value beyond the band, in order to then increase with dropping wave length very quickly and then again normally. (This process is repeated in every absorption band.)

The sharper the absorption band and the closer to it you can observe dispersion, the more distorted appears this section of the cross-spectrum. If a substance has several of them (carmine has two, permanganate potash five), there corresponds to every band a gap in the dispersion curve. The most strongly absorbing substances are the metals, the glowing gases have the sharpest absorption bands - for both of them, dispersion of light uncovers unusual relationships.

Even Metals are transparent in sufficiently thin layers. By means of prisms (manufactured electrolytically) with a refraction angle of the order of seconds, Kundt has determined refraction indices of metals. Silver, gold and copper have refraction indices which are smaller than unity; light spreads in them (in silver four times) faster than in vacuum*; in contrast, dispersion in gold and copper is normal, in platinum, bismuth, iron and nickel anomalous. - You can also - by a trick - give glowing gases the form of prisms and expand them in a cross-spectrum; their anomalous dispersion was discovered by Kundt in 1880.

* This does not at all contradict what was said above with regard to the velocity of light in vacuum as limiting velocity. We have there imagined the entire space to be a vacuum, that is, the only medium - in a homogeneous medium, refraction of light is not possible, while here the space contains several substances. In every homogeneous substance, which fills the entire space, the velocity of propagation of light is the limiting velocity. If the entire space is filled with air, the limiting velocity is the velocity of light in air; if the entire space is filled with silver, it is the velocity of light in silver, etc.

Kundt perceived dispersion by absorbing substances as the normal case and that by transparent ones as a special case - in other words: Anomalous dispersion is the rule, normal dispersion is an exception. (This singular case yields an uninterrupted curve as cross-spectrum, the next, less special case, two separate curved sections, the most general case, many separate curved segments.) All new dispersion theories allow for an interrelationship between refraction and absorption; they assume the presence of interaction between the ether and the molecules of the absorbing substance (the electrons charging them, respectively), that is, an influence of the molecules on the ether's motion, and, especially for anomalous dispersion, a relationship between absorption and friction between the parts of every absorbing molecule. The dispersion formula of Sellmaier-Ketteler-Helmholtz also applies to anomalous dispersion.

Phosphorescence and fluorescence

Absorption of rays of light is frequently accompanied by fluorescence and phosphorescence. There exist substances which, as they are illuminated, glow on their own, and in the process emit light of colours other than those of the agitating light. Fluorescence - named after fluorspar which glows in this way - ceases when the stimulating light stops. Phosphorescence (this term is linked to the glowing of phosphor in darkness) continues also subsequently, for some substances for many hours. Fluorescence is know to everyone from the blue glitter of petroleum in daylight, phosphorescence from the subsequent glow of luminous paint. Both phenomena are only a consequence of the light, absorbed at the surface, whence they are clearest in reflected light. For example, fluorescent substances are petroleum, fluorspar, sulphorous quinine and the escilin of horse chestnut, all of which glow blue, and barium-platino-cyanide, which glows green-yellow (on the fluorescence screns of X-ray techniques).

Especially noteworthy is that a fluorescent substance converts light in a certain sense before it reradiates it. For example, if the incident light is yellow, it irradiates - in the case that the passing light has no colour, weakly yellowish or brownish light, that is, only light-weak colours from the violet end of the spectrum and absorbs the ultraviolet rays - only such light, which lies in the spectrum from yellow towards red, for example, orange coloured light. If it is violet, it can emit every colour according to its nature, which lies from violet towards red. In other words: It converts - in general, but there are also deviations from this rule of Stokes - light into light of larger wave length.

If you compare a substance, caused to fluoresce, with a source of sound, caused to sound by resonance, this means: It sends out a tone which is lower than the exciting tone. Even ultra-violet light, which is not seen (because the light wave is too short to be able to stimulate you eye), becomes demonstrable in that a fluorescent substance can convert it into violet or blue light. (Analogously, a tone, which is too high to be heard, can be lowered by retardation of its period into an audible tone.) Hence fluorescence is an auxiliary tool for the examination of ultra-violet light. According to the Quantum Theory, fluorescence is linked to a process in the atom, which only occurs when the atom under consideration takes in a definite quantity of energy. If the emitted fluorescent light has the frequency n_a= c/l_a (c = velocity of light), this energy must be at least be hn_a (h Planck's active quantum). If the light irradiated has the wave length l_a, it can only introduce the energy hn_e into the individual atom, since this is the magnitude of the quanta, out of which the energy of the light of that frequency is composed. Hence, in agreement with experiments, fluorescence can only occur, when hn_e > hn_a or when n_e > n_a and l_e < l_a.

Fluorescence and phosphorescence are also of interest, because they make the bodies concerned into sources of light by themselves (the subsequent glowing of luminous paint). Different from ordinary sources of light is a photo-lumiescent source which glows at relatively low temperatures: It emits without a temperature increase light (chemi-luminescence). Other luminescence phenomena are the light of glow worms, the light caused by electrical discharges in rarefied gases (the tubes of Heinrich Johann Wilhelm Geissler 1815-1879), the light which arises during heating of certain crystals (fluorspar), the light which appears during fracture of certain crystals, for example, of sugar and of ZnS-crystals during scintillation (Latin = spark, tribo-luminescence), etc. The waves they emit are exclusively waves of light in the real sense, whence sources of luminescent light are very economical.

Radiation of artificial sources of light

If we could make luminescence strong enough, it would become the most economical source of light. However, we do not know of any other way than that via matter; in order to generate light, we must heat the substance which is to become a source of light. The variety of the waves, which it then emits - variety in the length of the waves - increases with its heating up, and there grows simultaneously the amplitude of every individual wave. If you heat up a platinum wire by an electric current, which you gradually strengthen, it emits to start with only quite long waves, which only generate heat. As the temperature rises, shorter waves join in; eventually, it begins to glow, at first ashen (only observable in darkness), gradually red, then orange, yellow and eventually white, while the brightness of every individual colour grows on its own. Finally, those waves join in, which are too short for stimulating the eye and which only act chemically (actinic). In other words, the source of light - the glowing wire - emits eventually waves of all possible lengths. All of them generate heat, but very little light.

A comparison demonstrates how extravagant this kind of light is: Let a musical organ have an arbitrary number of pipes of all possible lengths, including those too long and too short, which vibrate while stimulated, but do not sound. If you blow into these pipes one after the other, at first into the longest ones, finally into into the shortest ones, there arises a sea of air waves of all possible lengths - however, only a small section of them act on your ear. In other words, you spend an enormous amount of energy, in order to generate all vibrations to obtain just a few useful tones. This energy wasting organ is like the artificial sources of light.

Solar radiation also contains all not-light waves; however, the sun has not only the task of giving light. If an artificial source of light is to give only light, it will be the more economical the more of its radiation energy acts on the eye. However, this is terrifyingly little; even for the economically best (Nernst-lamps, tantalum-lamps, wolfram-lamps), the efficiency is only a few percent. Nevertheless, generation of light by generation of very high temperatures is today (1935!) the only possible approach. In the case of sources of light of the same kind, the economy is larger, the higher the temperature. - The lower bound, at which solids begin to radiate light, differs for the various substances; it is for iron 405º, for platinum 408º, for gold 423º. It lies the higher, the more strongly the substance reflects.

Heat radiation

Substances, which are made into sources of light by heating, differ greatly by the variety of the wave lengths (colours) they emit. However, for all sources, Kirchhoff's law applies, which relates the emitted waves to those, which the substances also can absorb. This law is a special case of a more general one, due to Pierre Prevost 1751-1839, which applies to heat radiation. Radiation of light must be viewed as a special case of radiation of heat, whence the more general law applies in both situations. We will start our presentation with heat radiation and thereby complement simultaneously the earlier discussion.

Waves of light and heat differ purely physically - without reference to our sensation nerves - by their lengths. Both are the electro-magnetic waves of Maxwell's theory of light - ether waves -, however, those which we only sense as heat, are much longer than those which we also sense as light. Otherwise, they differ as little from each other as a water wave, generated by a dropping stone, from that, generated by an ocean liner. - However, when the differently long waves encounter our body and excite our sensing nerves, we sense them differently: If they stimulate the nerves in our skin, all of them generate heat sensation, if they stimulate our optical nerves, the longer ones do not generate any sensation (dark heat rays), however, the shorter ones cause sensation of light (their lengths lie between 0.4 and 0.8 m). In other words: The sensations differ, with which the nerves in the skin and the optical nerves react to waves of different lengths, but the waves are of the same kind. Just as light spreads throughout space by waves, so does radiated heat. There exist rays of heat and rays of light; the laws of reflection and refraction for waves of light also apply to waves of heat. The dark heat waves yield the same diffraction phenomena as the rays of light; they too can be double-refracted as well as polarized. Interference phenomena allow to measure the lengths of heat waves just as those of waves of light.

Following Karl Wilhelm Scheele 1742-1786 1777, heat transmitted by radiation is usually called radiating heat - which is not quite accurate, because during radiation there is no reference to a heat effect. Only when the radiation encounters a substance, which stops it, heat can be shown to exist. In contrast, a substance, which lets it pass as it lets rays of light pass, becomes as little warm as it glows. If on a day in winter, when water freezes, the sun's rays meet your skin, you feel it as heat, because the skin stops it. However, the air does not become warm, because it lets it pass. A thermometer, exposed to rays, behaves like your skin; it indicates therefore a temperature higher than that of the air. In order to measure the true temperature outside, you must protect the thermometer against radiation.

Experiments tell us: Substances exhibit a different behaviour towards heat rays - as different as that towards rays of light: They reflect it, let is pass or absorb it more or less. Lampblack and platinum black absorb almost all incident rays independently of their wave lengths; polished silver reflects almost all of them, rock salt and fluorspar let almost all pass. Hence: As there exist for light transparent (diaphanous) and opaque substances, there exist correspondingly also for heat diathermanal and athermal substances.

Whether a material lets light and heat pass depends on the lengths of the waves it lets pass. Colourless glass lets only very little of very long waves pass, that is, very little of dark heat rays (whence oven shields are made out of glass plates); it passes waves of medium length - waves of light, almost all of them - and none of the very short waves - the ultra-violet (chemically effective, actinic) waves. Hence you cannot employ for the formation of the extreme ultra-red and ultra-violet part of the spectruma glass prisms, you must use for the first a fluorspar or sylvite prism, for the second a quartz prism.

As waves of heat leave a source of heat A and encounter a substance B, depending on its nature, they are reflected or absorbed or allowed to pass. However, the substance itself is a natural source of heat, because every one of them is that and indeed at every temperature, because at every temperature its molecules are in motion, which we know as heat. The substance B, met by waves of heat from A, radiates itself waves of heat to A. This is even true for ice: If you replace in the concave mirror set-up in Fig. 307 A by the sphere of a mercury thermometer and B by a piece of ice, the mercury will drop immediately.

Exchange of heat radiation (Law of Prévost 1809)

The mutual behaviour of substances which radiate heat to each other is governed by a fundamental law. All substances in a closed space (Fig. 797), the walls of which neither allow heat to enter nor to leave, have, according to experience, eventually the same temperature. In fact, they mutually radiate heat, so that the initially colder substances warm up and the warmer substances cool down. However, this must not be understood in the sense that the warmer substances only radiate and the colder ones only take in heat; but, since every substance radiates at every temperature, so does also the colder one, but it receives more heat from the warmer one than the warmer one receives from it. In the end, when all the substances have the same temperature, they nevertheless do not cease to radiate, except that everyone absorbs as much heat as it loses, since its temperature remains constant: "It behaves like a lake, into which rain falls while simultaneously the same amount of water evaporates," whence follows the law of Pierre Prévost 1751-1839 1809: A substance radiates at a given temperature exactly as much as it absorbs at the same temperature. "The equilibrium radiation of neighbouring substances at equal temperature is one of the best stated facts" (Mach).

Hence a substance which absorbs much (little), radiates at the same temperature also much (little). Lamp-black and platinum black, which absorb very much, radiate therefore very much, polished silver, which absorbs hardly at all, very little. In other words: At equal temperature, lamp-black radiates much more than silver.

Let there be in a room with walls, which do not allow heat to pass, lamp-black R and polished silver S, and let both have the same temperature. The lamp-black radiates all the time very much; in order to maintain its temperature, it must therefore receive much radiation. However, the silver radiates very little, because it absorbs very little; however, it reflects alsmost all heat which comes to it. Hence constant temperature is maintained by the lamp-black receiving back its radiated heat (reflected by the silver) and absorbing it.

Remember for what follows: A substance which absorbs at equal temperature more (less) than another one, radiates at the same temperature also more (less) than the other one. As long as only heat waves are radiated, you can, of course, control this statement with heat measuring instruments (thermo-columns, bolometer). However, if its temperature is so high that is also radiates waves, which stimulate the retina (waves of light) - waves for which l < 0.8 m - you can see the difference in the radiation: If you hold a polished piece of platinum foil, blackened in one place (by means of soot or ink) into a Bunsen flame, the blackened section glows much more brightly than the not black one. Moreover, when you heat to red a heat-resistant plate (porcelain, stone-ware) with a black-white pattern (Fig. 798) and then view it in darkness, the black spots are brighter than the white ones - it becomes almost like a negative of the cold plate (Fig. 799), a visible proof of the fact that at the same temperature the blackened part radiates more strongly than the other part.

However, Prévost's law does not only apply to a substance's total radiation, but applies also to every single kind of wave contained in it: A substance, which absorbs waves of a definite length (colour) apportioned to it, when heated up radiates waves of this length (colour). A colourless glass, that is, glass which absorbs nothing at all, when heated to a certain temperature at which every opaque body glows red, hardly glows in darkness, that is, it also radiates as much as nothing. A coloured glass is different. If you heat a piece of yellow glass sufficiently, say one which absorbs blue rays, it glows in darkness clearly blue. - Hence, at the same temperature, metal glows more strongly than glass, and glass more than a gas. A substance, which remains quite transparent at the highest temperatures, will also not glow at such temperatures.

Conversely: A substance, which radiates waves of a certain length (colour), also absorbs waves of this colour. This is illustrated beautifully by flames which only emit a single colour. We are mainly interested in the consequence that a flame which, for example, only emits yellow rays, also absorbs them when they are sent to it. If it radiates only yellow rays of the visible spectrum, it glows them only as long as it emits yellow rays. If they are absorbed on the way to the eye, no visible rays whatever come from this flame to the eye and the flame seems to be dark.

Let us place two such flames A and B, one behind the other (Fig. 800), and look through A at B. Each of them emits yellow light, that is, they can also absorb such light, and therefore also the light of the other flame. The radiation of that part of B, which A covers up, must pass on its way to your eye through A. In the process it is absorbed by A, whence you receive in this direction only light from A. If A is equally hot as B, it emits to you just as much as the location of B, not accessible to your eye, had emitted, whence A appears to be just as bright as its environment and therefore does not contrast with B as background. However, if A is hotter than B (say, A is a Bunsen flame, B a spirit flame), it radiates more than the area of B missing in the field of view, whence A appears bright and B as a dark background. In contrast, if A is colder than B, it radiates less than the part of B, lacking in the field of vision, whence A appears to be dark on B as brighter lit background: The impression of darkness is called forth, as before that of brightness, by contrast with the environment. (This last case explains the origin of the Fraunhofer lines).

Link of emission to absorption (Kirchhoff 1860). Black body

Prévost's law states that a body which emits much also absorbs much, however, it does not state how much. This is the function of the laws of Kirchhoff and Stefan-Boltzmann. Assuming always that the wave length and the temperature are the same, Kirchhoff's law says firstly: The emission power E₁ of a body is proportional to its absorption power A₁ for the same wave length and temperature, that is, E₁ = C·A or E₁/A₁=C a constant. Secondly: The constant C is the same for all substances. If E₁, E₂, E₃ ··· and A₁, A₂, A₃ ··· are the emission powers and absorption powers of the substances 1, 2, 3, ···, then E₁/A₁ = E₂/A₂ = E₃/A₃ = ··· = C. Denoting by E_l,q and A_l,q the emission and absorption powers of any substance at the temperature q for the wave length l, the law becomes E_l,q / A_l,q = C or E_l,q = C·A_l,q . Thirdly: The law says something very important about the constant C. Kirchhoff introduced the perfectly dark body - the body which at an infinitely small thickness absorbs completely all rays which meet it. Its absorption power - the ratio of the intensity of the absorbed rays to that of the incident rays - is always = 1, because the intensity of the absorbed rays for it always equal that of the incident ray. Applied to the black body, for which A_l,q = 1, one has E_l,q = C. If we denote the black body by S and its emission power by S_l,q (for the wave length l at the temperature q), the law says: E_l,q/A_l,q=S_l,q , that is, the constant C is equal to the emission power of the back body. (Actually, it should be: E_l,q/A_l,q = S_l,q /1, that is, the emission power of any body is related to its absorption power as the emission power of the black body to its absorption power, which is, of course, = 1.) Hence the law says: The ratio of the emission power of a body to its absorption power equals the emission power of the black body - it is assumed all along that the wave length and the temperature are the same. - Thus, the emission power and the absorption power of all bodies have been related to that of one definite body - the black body.

Fundamental law of black rays. Planck's radiation formula (1900)

The number, which states the ratio of the emission and absorption powers of a body for a given wave length, is only a constant for a fixed temperature. If the temperature increases, this number also increases, because the emission power of the black body grows with the temperature. Hence, if you want to know for every temperature this number, you must know how the emission power of the black body increases with the temperature.The law S = s ·T⁴, derived empirically by Joseph Stefan 1835-1893 in 1879 and from thermodynamics by Boltzmann in 1884, tells: The emission power increases proportional to the fourth power of the absolute temperature of the black body. For example, if the temperature T is doubled, the radiation S rises to 16 times that value. The constant s is equal to 1.38·10^-12, when the per second and cm² radiated quantity of heat is measured in gram calories, or 5.75·10^-12, when it is measured in Watt/cm².

The equation S = s ·T⁴ yields the total radiation of the black body. However, in order to know its radiation power accurately, you would have to know how its radiation power varies with the temperature T for every individual wave length l. Experiments show that the energy content of the very long and very short waves of the spectrum is very low and the largest amount of the radiation energy is distributed over certain medium wave lengths. The wave length l_m with the largest amount of energy is called the wave length of maximum energy. As a substance is being heated, the intensity of the shorter waves it emits increases faster than that of the longer ones, whence the wave length of maximum energy shifts with the temperature T towards the shorter waves. Both are interrelated by the equation l_m·T = A (displacement law of Wien 1893), where A is a constant. The maximal energy E_m is linked to T by the equation E_m = B·T⁵ with B a constant. However, all of this does not state how large is in the spectrum of the black body the energy E for the wave length l at the temperature T . This is only done on the basis of the quantum theory by Planck's equation

E = C·l^-5/(e^c/lT - 1),

where C and c are constants. For the visible spectrum, this equation can be written in the form, given by Paschen and Planck

E = C·l^-5/e^c/lT.

Realization of the black body

There does not exist in Nature a perfectly black body. Nevertheless, you can create an almost ideal black body (Fig. 801): The internal wall S of a closed hollow body A is a black body, for example, a hollow sphere which has somewhere a small opening. Even when the inside of the hollow sphere is highly polished, you see the opening as a black spot (approximately for the same reason for which an eye's pupil, into which you look, seems to be black). Even at a uniformly reflecting surface, the light entering through the opening O is subject to an infinity of reflections; hence it is completely absorbed by the internal wall before it reaches again the opening. If the opening is very small and you heat up the hollow sphere so that it has everywhere the same temperature, then black radiation corresponding to this temperature comes out of the opening; you measure it, for example, with the bolometer. Lummer and Pringsheim have confirmed in this manner the validity of the Stefan-Boltzmann law up to 2300º as well as of Wien's displacement law and of the law of maximum energy up to 1650º, and have determined the value of the constant A = 2940, for clean platinum A = 2630. Measurements of Warburg and Müller 1913 yielded for the constant in Planck's law c=1.43cm·degree.

Fig. 802 displays the change of the energy of black radiation at a given temperature with the wave length (Lummer and Pringsheim 1899). At every temperature, the black body radiates more than every other body at the same temperature, so that its energy curves envelop those of all other rays, whence follows the important rule: You can with no source of light, which depends on pure temperature radiation, achieve greater brightness than with the black body. - The black body itself is the most uneconomical source of light, because it radiates at technically accessible temperatures the maximum energy in the spectrum's invisible part. The illumination industry is especially interested in the question concerning the dependence of brightness of the radiator cell on its temperature, and indeed the brightness of a definite colour. It rises rapidly with the temperature, much faster than the total radiation, which rises with the 4th power and the maximal energy which rises with the 5th power of the temperature. For example, the brightness of yellow doubles when the temperature of the black body only increases from 1800º abs. to 1875º abs., that is, it rises by about 4%; the brightness rises even faster at the violet end and more slowly at the red end of the spectrum. Also the total energy, sensed as light, increases in the case of platinum and the black body much faster than the maximum energy; it increases in the neighbourhood of red heat with the 30th power and at high white heat with the 14th power of the absolute temperature. The very exact determination of the temperature in the optical pyrometer (Holborn and Kurlbaum, Wanner) depends on brightness, for example, that inside an oven by a comparison with a small lamp inside the instrument.

In the spectrum of the Sun, l_m = 0.433m. Should the radiation properties of the sun be in agreement with those of the black body, the true temperature of the Sun is 6790º abs. - The solar constant and the Stefan-Boltzmann law yield the effective temperature of 6033º abs. at the surface of the Sun, whence in 1935 this temperature was assumed to be between 6000º and 6800º. The solar constant is the amount of heat in cal, which per minute would meet the surface of the earth from the sun at the median distance during perpendicular irradiation, if the earth did not have an atmosphere. Its most probable value was in 1935 1.939 cal/min·cm² (Abbot, Fowle, Aldrich).

The spectrum of the light of radiating substances

At sufficiently high temperatures, the radiations of solid and fluid (molten) substances appear to the eye to be almost equal. (To the eye! The thermo-electric pile indicates differences as well in the total value of radiated energy as in the different sections of the spectrum.) Hence, the spectrum of a white-hot solid or a fluid body never divulges the composition of the body. This is quite different in the case of gases and vapours. They do not yield a continuous spectrum like fluid and solid substances, but (Fig. 807) a spectrum consisting of sharp individual lines of light, separated by gaps without light. For example, glowing sodium vapour (cooking salt in the Bunsen burner) yields a spectrum of two characteristic, strongly yellow,close to each other lines of light; hydrogen in a Geissler tube, caused to glow by an electric discharge, has a spectrum in the visible range of three characteristic strong lines (red, green-blue and blue-violet). Every glowing gas has its characteristic line spectrum; under certain conditions, this is so definite, that it can yield an identification of a gas. These conditions demand that the layer of the glowing gas be thin and its density there small. The thicker the layer and the denser the gas, the wider become the lines (bands). In the case of a substantial increase in pressure, the spectrum can even become continuous.

Due to their property of emitting strongly individual colours (selective emission), glowing gases can be used as sources of mono-chromatic light - a sodium salt yields yellow light in the Bunsen burner, a potassium salt violet light, a lithium salt red light. In chemical analysis, you draw conclusions regarding the chemical constitution of a substance from the colours obtained in Bunsen burners; thus, yellow colouring suggests a presence of sodium, violet of potassium, etc.

Apart from the continuous spectra of solid and fluid glowing substances and the line spectra ofgases (emission spectra with bright and absorption spectra with dark lines), there are still the band spectra, which arise under special conditions and consist of glowing bands, but split in the presence of stronger dispersion into groups of very many lines. According to many experimental results, the theory of Bohr allots to the line spectra the atom as carrier, to the band spectra the poly-atomic molecule. - Emission spectra are only radiated by atoms or molecules when they are stimulated, for example, by an electric discharge or by very high temperatures. The absorption line spectrum always appears, when atoms or molecules, which are not stimulated, are irradiated by light with a continuous composition. We will consider emission spectra below.

Arc spectrum. Spark spectrum

In order to vapourize an element and cause it to glow, you employ according to needs the Bunsen flame, an oxy-hydrogen blowpipe, an electric arc or an electric spark. The spectrum of an element depends on the method by which it has been produced. The spark and arc spectra of the same element have quite a different appearance and this difference corresponds to a fundamental cause; the arc spectrum belongs to the neutral atom, the spark spectrum to the ionized one (and this is again different for the simply and multiply ionized atom, depending on whether the stimulation deprived the neutral atom of one or several electrons). Hence, if the spark spectrum of an element appears anywhere, for example, in the spectrum of a star, it is a sign that the element is present there in an ionized state. However, the spark spectra of many elements are not known and also many of the lines cannot be observed, because they lie in the extreme ultra-violet, which is absorbed by Earth's atmosphere. Hence these elements, when they occur in an ionized state, cannot be recognized. This explains why we observe - or better recognize - on the Sun and also on fixed stars only 57 of the 92 elements of the periodic system. Thermodynamics shows us how to compute the ionization degree of a gas as a function of pressure and temperature. The experimental result agrees with the theoretical prediction (Saha 1920).

Width of spectral lines. Satellites

A spectral line is not a geometrical line, but has a certain width, that is, it does not correspond to a single wave length, defined by a number, but a range of them. Not all of these different wave lengths are represented with the same brightness, that is, there is a certain brightness distribution in a spectral line. You can measure them micro-photographically (J.F.Hartmann and Koch). Raising the pressure in the glowing vapour widens the line, often asymmetrically, for example, more towards the larger wave lengths (Doppler effect). - A bright spectral line is frequently accompanied by "satellites", a number of more or less bright ones, very closeby secondary lines; sometimes they include bright ones so that in the set none of them can be viewed to be the principal line.

Cd-lines have only few satellites; especially, you cannot detect a satellite at the bright red one with l 6439. This the reason why the Union Internationale pour les Recherches Solaires has selected it as wave length normal for spectroscopic measurements, in which you determine spetrograms in wave lengths relative to that of known lines. You relate now all measurements of such wave lengths to this red Cd-line. It has been measured with an accuracy of 1 : 10⁷ (René Benoit 1844-1922, Charles Fabry 1867-1945, Alfred Perot 1863-1925 1906).

Spectral analysis

Bunsen and Kirchhoff discovered in 1859 that every gas has a characteristic spectrum. On this fact rests spectral analysis, which determines from the spectrum of a source of light its chemical constitution. In order to be able to examine solid and fluid substances spectral-analytically, you must convert them into a gas or vapour. You examine gases in glass tubes of the form shown in Fig. 803. You cause them to glow by sending the discharge of a spark inductor through them. The capillary yields then a bright line of light - a source of light.

You observe the spectrum with a spectroscopic apparatus (Fig. 804). The light of the flame B to be tested passes through a slit in the collimator tube C, goes refracted by the prism through the telescope S into your eye. In order for the slit to appear as sharp as possible in the telescope S - its image is not only brought about by the lenses - the light must also pass through the prism - you give the prism the minimum position. In order to be able to register the location of the lines, seen in the spectrum, and compare it with the location of the lines of known spectra, you employ a scale, which you see in the telescope next to the spectrum. You create it with the tube R. You place into the focal plane of the lens a reduced millimetre scale s, photographed on to a glass plate. You project it on to the face of the prism facing the telescope and reflect it through the telescope, so that you see it simultaneously with the spectrum. Thus, you can characterize the positions of the lines by numbers which you see next to them. In order to compare the spectrum to be examined with another one, that is, to evaluate it in terms of wave lengths relative to the wave lengths of known lines, an arrangement is made by which you can generate two superimposed spectra.

In order to be able to examine the entire spectrum in a telescope and thus without great effort to bring the prism always into the minimum position, you form the prism as shown in Fig. 664, place the slit tube C and the telescope S permanently perpendicularly to each other and rotate the prism. In order to achieve the greatest possible dispersion, you let the light pass consecutively through several prisms (Fig. 805); everyone of them contributes to the extension of the band of light. In order to be able to observe a source of light, which moves (lightning, meteors, etc.) or with respect to which the point of observation moves, as sometimes in astronomical spectroscopes, the spectroscopes in which the slit tube and the telescope are inclined to each other, are inconvenient. For these purposes, you employ a spectroscope with a direct view. Fig. 806 displays a pocket spectroscope and its most important part, the prism with a straight view comprising 3 crown and 2 flint glass prisms, which together avoid a definite colour deviation of the refracted light, but let the colour dispersion remain. (Compare the achromatic prisms, which remove colour dispersion, but leave the deviation unchanged.) Instead of a prism, you frequently employ a grating. The deviation of the individual colours is then proportional to the corresponding wave lengths.

Doppler principle

The location of a certain spectral line is specified by a number on a conventionally defined scale (cf. above). However, the location does not only depend on the chemical constitution of the source of light, but also on its velocity with respect to the spectroscope, that is, to the observer. We know that the height of a tone, the analogue to colour, differs according to the relative velocity of the source of sound and the listener. If you replace the ear by the eye and the source of sound by that of light and take into consideration that the colour (that is, the refractibility) of the light depends on the number of light waves, which the eye receives each second, like the height of the tone depends on the number of sound waves, you will understand that a source of light, which at rest appears to be yellow, should tend towards red (corresponding to a deepening of the tone), if it moves fast enough away and otherwise towards violet (corresponding to a rise in the tone), if it approaches fast enough. The mere eye is not sensitive enough for the actually occurring changes. But the spectroscope displays already a minimal change in colour - it is a change in refraction - by displaying the spectral lines of the source of light in question at another scale line location as usually, displaced towards red if the source of light moves away from you, towards violet, if it approaches you. You can compute from the size and the direction of the distance of a line from its normal location the velocity of the source of light, its approach and its moving away in the direction of viewing. This is also true for the dark lines, since their bright environment also is displaced. - In the neighbourhood of the D-line, a displacement of 1 Å-E. signifies already a velocity of 50 km/sec; with the best spectroscope, you can detect still 50 m/sec.

The velocity at which, far example, Sirius moves away from us has been computed by Sir William Huggins 1824-1910 to be67 km/sec. For such astronomical processes, it is assumed that the Doppler principle also applies to waves of light; this has been proved by Belopolski 1901 by means of terrestrial sources of light and using distances, which are available in laboratories. Using a number of mirrors, which move very fast with respect to each other and between which the light passes to and fro, he has generated on a photographic plate two spectra of Fraunhofer lines, from the relative displacement of which the measurement and theoretical computation are in complete agreement*. The Doppler principle has also assisted with the determination of the rate of rotation of the sun (K.H.Vogel 1872). As the Sun rotates about its axis, it brings its eastern rim closer to us and moves away its western rim, at the Equator at about 2 km.sec. Hence you see in a spectroscope of large dispersion the Fraunhofer line of the eastern rim moved towards violet, that of the western rim towards red from their normal locations, because the absorbing layer of gas moves towards us at the eastern rim, that at the western rim moves away from us. The velocities of the rims can be computed from the magnitude of the displacements of the locations from which the lines originate.

*Experimental generation of the Doppler effect for light - 350 m/sec - is due to Zeeman and Risco 1929.

This displacement decides also another question: Certain Fraunhofer lines only arise from absorption by Earth's atmosphere, not already from that of the sun; how can the tellurous lines be distinguished from the solar ones? Answer: The Sun's atmosphere moves relative to the observer, but not to Earth's atmosphere, whence the tellurous lines are those, which do not move in the spectrum irrespectively of whether the sSun's light comes from the eastern or western rim, the solar ones those which move in the process (Cornu 1889). - The periodic change of brightness of certain stars is explained by the presence of a double star system, of which the one part is not visible: For example, the periodic reduction in the brightness of Algol is due to its periodic, partial obscurance by one almost equally large, and indeed dark star, which circles around it and enforces motion about a common centre of gravity. The motion of the bright star towards Earth and away from it is betrayed by the shift of the lines in the spectroscope and is in agreement with the period of the change of brightness.

In the case of terrestrial sources of light, the Doppler effect in canal ray particles is known (Johannes Stark 1874-1957 1905). Their velocity can reach 10⁵ km/sec, that is, it induces very much stronger displacements than fixed stars. The spectrum of the glowing atoms and molecules of the canal rays displays (at a prescribed method of observation) beside the undisplaced line of the resting gas one line, displaced towards violet in the Doppler effect, when the rays are directed to the slit of the spectral equipment, towards red when they are directed away from it. The magnitude of Dl of the displacement is determined by Dl/l = v/c. Since there arise different v, the displaced line is not sharp and has several maxima. For example, the Doppler effect has been observed in canal rays in the case of hydrogen, helium, nitrogen, oxygen, argon, chlorine, potassium, sodium.

Moreover, the general motion of the heat of molecules causes a Doppler effect. In every gas, heated to glowing, the light of which enters the spectral apparatus, appears the effect of the widening of the spectral lines (first discovered by Lippich 1838-1913 1870). The width of the spectral lines is a problem on its own, none is strictly mono-chromatic, everyone embraces a perceptible interval of wave lengths. However, so many causes superimpose during the widening of the lines that a unique reply to the associated questions has hitherto (in 1935) not become possible.

Spectral series (Balmer 1885). Combination principle (Ritz1908)

Among the most important results of spectral analysis is the discovery of the series of spectral lines - to start with, in the hydrogen spectrum, Johann Jakob Balmer 1825-1898 discovered: If you multiply the number 3545.6 by 3²/(3² - 4), 4²/(4² - 4), 5²/(5² - 4), 6²/(6² - 4), you obtain the wave lengths of the first four hydrogen lines H_a, ···, H_d in Ångström units (Å.-E.). Balmer's general formula for the wave length is: l = h·m²/(m² - 4) Å.-E., where h = 3645.6 and m is an integer which, however, cannot be smaller than 3, since l = for m = 2 and becomes even negative for m = 1, which has no physical meaning. The deviation of the thus computed wave lengths from the ones measured by Ångström is not even 1/40,000 of the wave length. The lines which are united by such a formula form a series. The one above ends with the line for m = 6. But if you set m = 7, 8, 9, ···, you can continue it computationally to m = , to which corresponds l = 3645.6, that is, a finite wave length, since l=h/(1-4/m²) becomes l = h for m = . However, do there actually correspond to the computed wave lengths existing spectra lines? All lines, the wave lengths of which satisfy that formula up to m = 31, have been observed. The larger m, the closer they approach each other (Fig. 807) until eventually they cannot be separated by known dispersion equipment, that is, they form a continuum. Also this has been observed (Evershed): In fact, its start coincides with the smallest computed line (m = ). You now employ that formula for practical purposes in the form 1/l = = R(1/2² - 1/m²), where is the wave number (number of wave length in 1 cm), R = 109,678 cm^-1 (the Rydberg constant of hydrogen) and m = 3, 4, 5, ···. It arises from the first formula by setting h = 4/R. The generalized Balmer formula = R(1/n² - 1/m²) raises the question, whether lines also correspond to n = 3 or n = 1 (Fig. 829)?. Paschen has demonstrated the first (Paschen series) in ultra-red. Chester Smith Lyman has discovered the others in the ultra-violet (Lyman series). Other lines than those computed with integral n do not occur with hydrogen. Accordingly, you can write the wave numbers of all lines of the hydrogen spectrum in the form = R(1/n² - 1/m²), that is, as differences of two terms of the form R/n². One of the greatest achievements of Bohr's atomic theory is the complete agreement between the value of the theoretically determined Rydberg constant R of hydrogen and its experimentally determined value.

The formula for is a special case of a general, spectroscopic, empirical law - Ritz's combination principle (1908): Arbitrary combinations of the frequencies of known spectral lines of a chemical element (by addition or subtraction) yield the frequencies of further spectral lines of the same element. Bohr's frequency condition is equivalent to this principle.

According to the theory, the order of the lines in a series is a property of all spectra; however, it is known empirically only for one part, for example, for the alkalis Li, Na. K, Rb, Cs and the alkaline earths Mg, Ca, Sr, Ba (Kayser and Runge, Paschen, Rydberg). However, you cannot manage here only with a single formula, you require for the compilation several mutually similar ones. Those which belong to one formula form a series. Hence you distinguish between the principal series, two auxiliary series and the Bergmann-series, whereas the series of the alkalis contain only double lines (like the typical two yellow sodium lines), those of the alkaline earths contain only mono-plet and triplet lines. Most important is the discovery of the quantitative relations between the wave numbers of the different lines of a spectrum. For example, in the sodium spectrum - its structure is typical for the alkali group, the first group of the periodic system of elements - the wave numbers belonging to the two D-lines differ by 17.2 cm^-1: The same difference occurs also between the lines of every pair of the first auxiliary series, and also of the second auxiliary series. Also, in the group of the alkaline earths, there occur wave number differences for the auxiliary series. These differences are the larger, the larger is the atomic weight of the element under consideration. - The presentation of the wave numbers as differences of two terms is possible for all spectra. You can coordinate with the lines of a spectrum the system of electron terms for all spectra; in general, this is simpler and clearer than that of the lines.

Solar spectrum. Origin of Fraunhofer lines

Spectrum analysis offers two advantages over chemical analysis: It displays the presence of trace elements (often only 10^-5 mg, which easily or always escape ordinary analysis) and also the composition of bodies, which we only see glow and cannot subject to routine analysis. The first of these advantages yielded the discovery of new substances, for example, cesium, rubidium and thallium, the second even a chemical analysis of stars.

We are especially interested in the solar spectrum. Strictly speaking, it is not continuous; it displays fine dark lines - the Fraunhofer lines - of which more than 62,00 are known. Kirchhoff has explained their origin using the laws of absorption and emission. Recall what we have said about two flames which radiate towards each other only light of one colour and one of which is hotter than the other. Let the sodium flame A, as has been assumed there, emit only yellow light. The spectroscpe then displays for A alone two close together lines of yellow light. However, let now B be a source of white light, say, a white glowing lime cylinder. Since it emits all wave lengths between red and violet, is also emits that wave length, which also comes from A and which is not at all visible to A. We are only interested in these waves. You can imagine the source of white light (recall the analogue of the organ) to be replaced by the mono-chromatic flames, the radiation of all of which replaces the radiation of the glowing lime cylinder. One flame among them emits exactly the same rays as A. Now place A and B, one behind the other, in front of the spetroscope. If A is colder than the flame corresponding to it, it absorbs the yellow waves more strongly than it emits them, that is, it extinguishes from the white light exactly those yellow rays, which correspond to its own, but allows all the others to pass through it. However, when just those waves of the white light are absorbed, which in the spectrum yield those two sharp yellow lines, then the colours of the absorbed waves are absent and there arise at the corresponding location two gaps. A itself radiates yellow light, but much less intensely than B; at the location of missing yellow in the field of view of B appears now a much weaker yellow line: This much weaker yellow seems to be dark in contrast to its bright environment and gives the impression of the black gaps. (Inversion of spectra lines). From red to violet, you see then all colours, but in yellow two dark lines. If you remove the white light B, the yellow lines in the spectrum of A are again quite bright (because they are surrounded by almost complete darkness). Hence the black lines have arisen in that out of the white flame just those colours, which belong there in the spectrum, have been absorbed by the colder flame A.

Next consider an application of this fact. There are in the solar spectrum close together two dark lines, at the same location where arise the two dark lines in the spectrum of the lime, white glowing cylinder as you bring the sodium flame between the lime cylinder and the slit of the spectroscope. Hence, Kirchhoff concluded: The Sun is a white glowing body (corresponding to B) and emits a continuos spectrum; however, it is surrounded by a glowing gaseous atmosphere (corresponding to A). The rays of heat and light tit emits must pass through this atmosphere, in order to reach us. This atmosphere is colder than the Sun's body, but radiates itself light and heat. But since it is colder, it absorbs - and this is the point! - from the light of the white glowing solar body one part (just as the colder flame A). The gaps in the solar spectrum, which of course corresponds to certain wave lengths, identify the absorbed wave lengths. Since the position of the two characteristic lines, which one can generate by sodium vapour, correspond exactly to the gap of the Fraunhofer D-line in the solar spectrum, you conclude that sodium is present in the body of the Sun and its surrounding atmosphere. The other Fraunhofer lines have been explained in the same manner by the presence of other chemical elements. Kirchhof drew the general conclusion: "The dark lines in the solar spectrum arise through those substances in the Sun's atmosphere, which, as they vapourize in a flame, have bright lines at the corresponding location of their own spectrum". In this manner. it has been shown that the Sun's atmosphere contains most of the metals known to us.

Kirchhoff's concept of the structure of the sSun was confirmed brilliantly by the flash spectrum: At the instant of the start (end) of a total solar eclipse, when the sun's glowing surface (photosphere) is covered for us by the Moon and the last (first) rays of light seem to glow like lightening, you observe a spectrum in which the Fraunhofer lines - in the normal solar spectrum dark against a bright background (absorption spectrum) - appear bright against a dark background (emission spectrum). This has the interpretation: The Fraunhofer lines do not arise in the entire ( in the case of a total eclipse visible as corona) solar atmosphere, but essentially only in its innermost layer, touching the Sun like a shell, called the inverting layer and chromosphere. From the duration of the visibility of its spectrum, the height of the inverting layer is estimated at 600 km, the height of the chromosphere at 10,000 km.

Anomalous dispersion of gases

Also in glowing gases, the absorption of light is linked to anomalous dispersion, whence every Fraunhofer line and every inverted spectral line is an absorption band, that is, makes it possible. Indeed, Kundt discovered it in 1880 by means of the earlier described set-up while observing the inversion of the sodium line. Just this observation has proved the reliability of the method of crossed prisms: Cross-dispersion deforms the spectrum in a striking manner and it was especially the form of the spectrum which drew Kundt's attention, while he was not at all thinking of crossing, to an actually present crossing and furthermore to its cause - dispersion anomaly. He explained the curvature which he observed, similar to the one shown in Fig. 808, by the anomalous dispersion of sodium vapour, which had to rise in a prismatic layer from the Bunsen burner. Fig. 809 (Becquerel 1898, Julius 1900) shows clearly what strange forms the cross spectrum of sodium vapour can assume at a suitable production of prismatically formed flames. The spectrum displays, corresponding to two absorption bands - that is what they are - , two gaps, that is, it is subdivided into three parts. The centre piece of Fig. 809 represents the spectral domain between the D-lines, the gaps between it and the side pieces the D-lines themselves - all strongly dispersed and enlarged. The sharper the absorption bands and the closer to them you can measure the refraction, the more distorted is the spectral image of the observed region. Fig. 809 displays one in which the bands were approached within 0.1Å-E.. - Sodium vapour disperses already anomalously at temperatures at which it still does not glow (Wood).

Spectrograph. Spectro-heliograph (Hale 1892)

You can photograph spectra; for this purpose, you replace the eye piece of the spectroscope telescope by a camera, the plate of which is placed in the objective's focal plane (spectrograph). In the mono-chromator, you place instead of the eye piece a second slit, in order to isolate a definite wave length (colour). Specially prepared plates allows you to photograph deeply into the ultra red, lenses and prisms made out of quartz deeply into the ultra-violet. (Vaccumgraph for the extreme ultra-violet waves which the air absorbs.)

The weakening of the sun's light in the Fraunhofer lines (only the contrast to their neighbourhood lets them appear dark) makes them into ideal, line-like, mono-chromatic sources of light: Astrophysics employs them in order to photograph the Sun's disk in mono-chromatic light. This apparatus is called a spectro-heliograph (Fig. 810). The collimator tube C and the camera tube K (F is the photographic plate) have parallel lenses of equal focal length. The plane of the collimator slit S₁ lies in the focal plane of a telescope objective, directed at the Sun, whence the slit cuts a strip out of the image of its disk. The light, passing parallel through S₁ from the collimator tube meets the mirror G and through the prisms P₁, P₂ reaches the camera tube K. A sidewards movable slit in front of F isolates from the spectrum, coming from P₂, the Fraunhofer line which is to serve as source of light. It is isolated by rotation of the prisms P with respect to each other. You employ a clockwork to shift the entire equipment sidewards. The slit S₁ then passes over the image of the sun's disk and the slit S₂ shifts simultaneously in front of the photographic plate, so that the individual, slit-formed cuts of the image of the Sun's disk throw their images one next to the other on the plate (Fig. 811). Speaking fundamentally, you can convert the heliograph into a helioscope by replacing the photographic plate by your retina and observing with a magnifying glass, focussed at S₂ (Edward Everett Hale 1868-1938 1929).

Special classes of stars *

The sun is only one member of one of the classes into which the stars are subdivided. Most brighter stars appear to be purely white to blueish, many of them yellow to white-yellow, others orange to red. This fact suggests immediately that their spectra, as well as their temperature and their physical constitution differ. Hence you subdivide the stars according to their spectra in to classes (Angelo Secchi 1818-1878, Edward Charles Pickering 1846-1949) - today you use the classes formed and named by Miss A.J.Canon (Harvard College Observatory): P, O, B, A, F, G, K, M, R, N, Q.

* Source of this section is: Newcomb-Engelmann's "Popular Astronomy", 6th edition 1921.

O. White to yellow. Main class of stars with bright lines or bands (stars of the Wolf-Rayet-Type, z Puppis).
B. White. Helium stars. Hydrogen lines not yet as strong as in the class A, beside helium lines characteristic feature (stars in Orion. in the Pleiads, in Perseus, etc.)
A. White. Sirius stars. Hydrogen series in very strong, washed-out lines dominant. Helium lines not present, solar lines, especially H and K still very weak (Sirius, Vega).
F. Yellowish. Hydrogen series retires, calcium lines H and K most noticeable indication (a Aquilae, a Argus).
G. Yellow. Sun stars. Lines mentioned hitherto are joined by numerous metal lines, Fraunhofer lines G, H, K especially noticeable (Sun, Capella).
K. Deep yellow. Lines G, H and K still stronger than in the class G, hydrogen lines weak, the violet end of the spectrum remarkably weak in light (Arkturus, b Gemini).
M. Yellow red. The characteristics of the class K especially strong, besides absorption bands of titanium oxide especially strong (Beteigeuze, Antares)
N. Yellow red. (19 Piscium)
P. contains the planetary nebulae, R several related to N and K, but spectra which could not be placed there, Q abnormal and composite spectra, which do not fit any other class. There also exist transitions between the classes: For example, B1A (abbreviated B1) is a spectrum, which deviates only a little from the class B, but displays already, while weakly, the characteristics of the class A. The converse is true for the class B9A. 0 beside the letters of the classes indicates a spectrum which belongs exactly to one of the classes, for example, A0.

This subdivision arose for formal reasons, but eventually proved to be physically justified: Starting from the white stars of the class B, the colouring behaves gradually to the reddish and red stars of the classes M and N like with a white glowing body, which on being cooled becomes more and more red until it ceases to glow. (There do not occur with the stars other colours than these cooling colours.) Wien's displacement law suggests that the temperature drops from the B-stars towards the M-stars. If you study photometrically the individual spectral regimes, you can by means of Planck's radiation formula (as in the case of the sun) compute their effective temperatures.

The differences in the spectral types reflects therefore mainly those of the temperatures, their sequence almost becoming a temperature scale. Hence you can draw conclusions regarding the physical constitutions of the stars. Astrophysics applies the cosmogonic concept to the world of fixed stars and arrives at the conclusion: The different spectral classes correspond to the different stages in the development of a star; every star passes over billions of years through a number of these classes.

This concept starts out from the following idea. A fixed star is essentially a sphere of gas, to start with of extremely low density. The heat which the sphere loses by radiation is replaced by that heat which arises as a result of its (during the outward heat radiation arising) contraction. However, this source of energy is not sufficient; there must still exist an atomic source of energy. If the contraction outweighs, the temperature of the gas sphere rises above the earlier one, there arises more heat than can be radiated outwards, the gass sphere expands again and cools down correspondingly and removes the cause of the contraction, etc. The development hypothesis of Henry Norris Russell 1877 rests on the concepts of Lane, Johann Wilhelm Ritter 1776-1810 and Robert Emden 1862-1940: Beside the temperature, the density has an essential role. The star starts at a low temperature and density, and hence has a very large surface - the absolute brightness is therefore inspite of the low temperature very large (the absolutely very bright coloured stars). As the density rises (according to the Lane-Ritter law), the temperature of the star - its absolute brightness - remains more or less the same, because its reduction of surface (during the contraction) is compensated by a rise of its temperature. Hence the star passes through the series M K G F A with almost equal, very large absolute brightness until it reaches its temperature maximum (class B) at a certain density. From then on, the temperature drops all the time, the star passes through the series A F G K M, reduces due to its contraction its surface, whence its absolute brightness drops quickly from the class B onwards. Hence the life of a star follows the following scheme:

At the beginning are the bright reddish stars with large surfaces - the giants -, at the end the weak reddish stars with small surfaces - the dwarfs -, both belonging to the class M. Every star travels along the row twice, once in the direction M-B, the second time in the direction B-M. According to the views in 1935, this is the life of every fixed star. It introduces into the otherwise hardly surveyable abundance of spectra, brightnesses and temperatures of the fixed stars an intelligible context, whence it has found general acceptance.

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