LECTURE V. TEMPERATURE RADIATION. 34. The most common method of producing radiation is by impressing heat energy upon a body and thereby raising its tem- perature. Up to a short time ago this was the only method avail- able for the production of artificial light. The temperature is raised by heating a body by the transformation of chemical energy, that is, by combustion, and in later years by the trans- formation of electric energy, as in the arc and incandescent lamp. With increasing temperature of a body the radiation from the body increases. Thus, also, the power which is required to main- tain the body at constant temperature increases with increase of temperature. In a vacuum (as approximately in the incandes- cent lamp) , where heat conduction and heat convection from the radiating body is excluded, all the power input into the body is radiated from it, and in this case the power input measures the power of the radiation. The total power or rate at which energy is radiated by a heated body varies with the fourth power of its absolute temperature, that is : If A = surface area, Tl = absolute temperature of the radia- tor and T2 = absolute temperature of the surrounding objects on which the radiation impinges : the total power radiated by the body is (Stefan's Law) : Pr = kA (TV - ?V), (1) where for a black body, as the carbon filament with Pr given in watts per square cm. k is of the magnitude k = 5 X 1(T12; (2) !T2 is usually atmospheric temperature or about 300 degrees abs. If Tl does not differ much from Tv that is, when considering the radiation of a body raised slightly above the surround- 70 TEMPERATURE RADIATION. 71 ing temperature, as an electric machine, equation (1) can be written : Pr = kA (T, - T2) (TV + T*T2 + 7\7y + 7y); or, approximately, Pr = 4 kAT* (T, - T), (3) where T is the room temperature (Tl — T) the temperature rise of the radiator above room temperature; that is, for moderate temperature differences the radiation power is proportional to the temperature rise. This equation (3) gives the law generally used for calculating temperature rise in electric machinery and other cases where the temperature rise is moderate. Obviously, in air the power given off by the heated body, P, is greater than the power radiated, Pr, due to heat convection by air currents, etc., but as heat conduc- tion and convection also are approximately proportional to the temperature rise, as long as the latter is moderate, equation (3) can still be used, but with the numerical value of k increased to k^ so as to include the heat conduction and convection: in stationary air A^ reaches values as high as fct = 25 X 10~12 to 50 X 10~12. As soon, however, as the temperature rise (Tl — T) becomes comparable with the absolute temperature T, the equation (3) can no longer be used, but the complete equation (1) must be used, and when the temperature of the radiator, Tv is very much greater than the surrounding temperature T2, T24 becomes negli- gible compared with 7\4 and equation (1) can, for high tempera- tures, thus be approximated by: Pr = kATf; (4) That is, the radiation power, as function of the temperature, gradually changes from proportionality with the temperature rise, at low temperature rise, to proportionality with the fourth power of the temperature for high temperature rises. Inversely then, with increasing power input into the radiator and thus increasing radiation power, its temperature first rises proportional to the power input and then slower and ultimately approaches proportionality with the fourth root of the power output: 4/p- T =V — • ll V kA 72 RADIATION, LIGHT, AND ILLUMINATION. In Fig. 27 is shown the radiation curve, with the temperatures T as ordinates and the radiated power Pr as abscissas, the upper curve with 100 times the scale of abscissas. Thus, to double the temperature rise from 10 deg. cent, to 20 deg. cent, requires doubling the power input. To double, how- ever, the temperature rise from 1000 deg. cent, to 2000 deg. cent, requires an increase of the power input from 12734 to 22734, or more than ten fold. At high temperature the power input, there- fore, increase enormously with the increase of temperature. FIG. 27. With bodies in a vacuum, the radiation power is the power input and this above law can be used to calculate the tempera- ture of the radiator from the power input. In air, however, a large part of the energy is carried away by air currents, and this part of the power does not strictly follow the temperature law of radiation, equation (1). For radiators in stationary air (that is, not exposed to a forced blast, as the centrifugal blast of revolving machinery), the total power input for high tempera- ture (as expended by radiation and heat convection) varies with a high power of the temperature, so that the radiation law equa- tion (1) can still be used to get a rough approximation of the relative values of temperatures. It, therefore, is not permissible to assume the temperature rise as proportional to the power input as soon as the temperature TEMPERATURE RADIATION. 73 rise is considerable and even in electrical apparatus of fire-proof construction as some rheostats, etc., where a higher temperature rise is permitted, the calculation of this temperature rise must be approximated by the general law (1) and not the law of propor- tionality (3), as the latter would 'give entirely wrong results. For instance, assuming a temperature rise of 50 deg. cent, per watt per sq. in. a cast silicon rod, which — at bright incandes- cence — can dissipate 200 watts per sq. in. would give by (3), a temperature rise of 10,000 deg. cent. This obviously is impos- sible, as silicon melts at about 1400 deg. cent. 35. With increasing temperature of the radiator, the intensity of the radiation increases, and at the same time the average frequency of radiation also increases, that is, the higher frequen- cies increase more rapidly than the lower frequencies and higher and higher frequencies appear, until ultimately frequencies are reached where the radiation becomes visible to the eye, as light. When with increasing temperature the radiation just begins to be visible, it appears as a faint colorless grey, "gespenster grau" exhibiting the same weird and indistinct appearance as are seen at higher intensities in the monochrome blue and violet radia- tions ; that is, we see a faint grey light, but when we look at it, it has disappeared : the reason is that the sensitivity of the sensitive spot of the eye for very faint light is less than that of the surround- ing retina and the first glimmer of light thus disappears as soon as we focus it on the sensitive spot. With increasing tempera- ture, first the lowest of the visible frequencies appear and become visible as red light, and with still further increase of temperature gradually orange, yellow, green, blue, violet and ultra-violet rays appear and the color thus changes from red to orange, yellow, yellowish white and then white, the latter at that temperature where all the visible radiations are present in the same propor- tion as in daylight. With still further increase of temperature, the violet end of the spectrum would increase faster than the red end and the light thus shift to bluish white, blue and violet. The invisibility of the radiation of low temperature is not due to low intensity. I have here an incandescent lamp at normal brilliancy. If I decrease the power input and thereby the radi- ated power to T^ it becomes invisible, but if we move away from the lamp to 10 times the previous distance, we get only T^ the radiation reaching our eyes and still the light is very plainly 74 RADIATION, LIGHT, AND ILLUMINATION. visible. The invisibility in the former case, thus, is not due to low intensity, but to low frequency. The fraction of the total radiation, which is visible to the eye as light, thus increases with the increasing temperature, from zero at low temperature — where the radiator does not give sufficiently high frequencies to be visible — and very low values when it just begins to be visible in red light, to a maximum at that temperature where the average frequency of the radiation is in the visible range, and it would decrease again for still higher temperature by the average frequency of radiation shifting beyond the visible into the ultra-violet. The efficiency of light production by incandescence thus rises with increasing tempera- ture to a maximum, and then decreases again. As the total radiation varies with the fourth power of the temperature, it thus follows that the visible radiation first varies with a higher power of the temperature than the fourth, up to the maximum efficiency point, and beyond that increases with less than the fourth power of the temperature. The temperature at which the maximum efficiency of light production by incandescence occurs, that is, where the average frequency of temperature radiation is in the visible range, probably is between 5000 and 8000 deg. cent, and as the most refractory body, carbon, boils at 3750 deg. cent., this temperature thus is unattainable with any solid or liquid radiator. Practically all bodies give the same temperature radiation, that is, follow the temperature law (1), differing only by the numerical value of the constant fc; that is, with increase of temperature the radiation intensity increases and the average frequency of radiation increases in the same manner with most solid and liquid bodies, so that at the same temperature all the bodies of normal temperature radiation give the same radiation curve; that is, the same distribution of intensity as function of the frequency and thus the same fraction of visible to total radia- tion, that is, the same efficiency of light production. If T is the absolute temperature in deg. cent, and lw the wave length of radiation, the power radiated at wave length /„, and temperature T1 by normal temperature radiation is : b P (IJ = c,Alw % ^ , (Wien's law) ; or' r • i. * r1 P (U = c,Alw a\e V-l\ (Planck's law) ; TEMPERATURE RADIATION. 75 where a = 5 for normal temperature radiation or black body radiation; b = 1.42, and A = surface area of the radiator. Integrating the formula of Wien's law over lw from 0 to oo , gives the total radiation : P- f °°P (lw)dlw = Mr-1; «/o thus, for a = 5; or, Stephan's law, as discussed above. The maximum energy rate at temperature T occurs at the wave length lw = lm given by: dP (lw) ~Ji — = °> dlw which gives: lmT =- = 0.284; a or, 0.284 = 50 X 10~6 thus gives: T - = 5680 deg. With normal temperature radiation the efficiency of light pro- duction is thus merely a function of the temperature and does not depend upon the material of the radiating body, provided that the material is such as to withstand the temperature. As the efficiency maximum of normal temperature radiation is far beyond the attainable, within the range of temperature avail- able up to the boiling point of carbon, the efficiency of light pro- duction by incandescence continuously increases, but even then the octave of visible radiation is at the far upper end of the radia- tion curve, and thus the problem of efficient light production is to operate the radiator at the highest possible temperature. The efficiency of light production is rather low even at the maximum efficiency point and with the average frequency of radiation in the visible range, since this visible range is less than one octave; under these most favorable conditions the visible 76 RADIATION, LIGHT, AND ILLUMINATION. energy probably does not much exceed 20 per cent of the total radiation, the rest falls below and above the visible frequencies. 36. At the highest attainable temperature, the boiling point of carbon, the efficiency is much lower, probably below 10 per cent and this would be the highest efficiency attainable by normal temperature radiation. It is utilized for light production in the carbon arc lamp. The carbon arc flame gives practically no light, but all the light comes from the incandescent tips of the carbon electrodes, mainly the positive, which are at the boiling point of carbon and thus give the most efficient temperature radiation. Obviously, in the carbon arc lamp a very large part of the energy is wasted by heat conduction through the carbons, heat convection by air currents, etc., and the total efficiency of the carbon arc lamp, that is, the ratio of the power of the visible radiation to the total electric power input into the lamp, thus is much lower than the radiation efficiency, that is, the ratio of the power of the visible to the total radiation. Thus the efficiency of the carbon arc is considerably increased by reducing the loss by heat conduction, by the use of smaller carbons — the life of the carbons, however, is greatly reduced thereby, due to their more rapid combustion. The carbon arc lamp thus gives the most efficient incandescent light, as it operates at the highest temperature, the boiling point of carbon. But by doing so the radiator is continuously con- sumed and has to be fed into the arc. This requires an operating mechanism and becomes feasible only with large units of light. To attain the highest possible efficiency of light production by temperature radiation with a permanent radiator, thus requires the use of extremely refractory bodies, since the efficiency in- creases with the increase of the temperature, and is still very low at the melting point of platinum. To exclude all the losses of energy by heat conduction and heat convection, the radiator is enclosed in a vacuum, so that all the power input is converted into radiation. Even in this case the efficiency of light production is still relatively low. The vacuum used in the incandescent lamp, thus, is not only for the purpose of protecting the filament from combustion. Filling the globe with some gas which does not attack the carbon would do this and yet it would very greatly lower the efficiency, TEMPERATURE RADIATION. 77 as can be seen by admitting air into the lamp bulb, when the filament drops down to dull red heat, before it burns through. With a metal filament lamp this can be seen still plainer, as the filament lasts longer in air. A search, thus, has been made and is still being made, through- out the entire range of existing bodies, for very refractory mate- rials. Such materials may be chemical elements or compounds. However, the combination of a refractory element with one of very much lower melting point lowers its melting point, and very refractory compounds, thus, may be expected only amongst the combinations of very refractory elements with each other. The chemical elements, arranged in order of their atomic weight, exhibit a periodicity in their properties which permits FIG. 28. a systematic study of their properties. In diagram Fig. 28 the elements are arranged in order of their atomic weight in the "periodic system." The height of their melting point is indicated by the darkness of the background. That is, the most refractory elements, wolfram and carbon, are shown on black background. The ele- ments of somewhat lower, but still so very high melting point that they cannot be fused by any temperature attainable by combustion, but require the electric furnace, are shown on cross shaded background. Inversely, the elements of the lowest melt- ing point, mercury under the metals and helium under metal- 78 RADIATION, LIGHT, AND ILLUMINATION. loids, are shown on white background, and the easily fusible metals and gaseous metalloids on lightly shaded background. As seen, there are two peaks of refractoriness, one amongst the metalloids, in carbon, and one under the metals in wolfram (or tungsten), and around these two peaks all the refractory elements are grouped. Inversely, there are also two depressions, or points of minimum melting point, in helium under the metalloids, around which all the gaseous elements are grouped, and in mer- cury under the metals, around which all the easily fusible metals are grouped. It is interesting to note that the melting point rises towards wolfram from both sides, as diagrammatically illustrated at the top of Fig. 28, in such a manner that the maximum point should be expected in the space between wolfram and osmium and the unknown element, which belongs in this space of the periodic system, thus should be expected to have still a higher melting point than wolfram, and thus give a higher efficiency of light production. As metal alloys almost always have lower melting points than their most refractory element, very refractory compounds thus may be expected only in the compounds between the very refrac- tory elements, in which at least one is a metalloid, that is, amongst the carbides and borides and possibly silicides and titanides. 37. Some of the earliest work on incandescent lamps was carried out with metal filaments. Platinum and iridium, how- ever, were not sufficiently refractory to give good efficiencies, and the very refractory metals were not yet available in sufficient purity. A small percentage of impurities, however, very greatly lowers the melting point, especially with metals of very high atomic weight. For instance, wolfram carbide contains only 3 per cent of carbon and 97 per cent of wolfram and even 0.5 per cent of carbon in wolfram metal thus means that 16 per cent of the metal consists of the easily fusible carbide. Very soon, therefore, metal filaments were abandoned and car- bon used as lamp filament. While carbon is the most refractory body, remaining solid up to 3750 deg. cent., it was found that the carbon filament could not be operated much above 1800 deg. cent, without shortening the life of the lamp below economic limits by the evaporation of the carbon and the resulting blackening of the lamp globes. All bodies evaporate below their melting point. TEMPERATURE RADIATION. 79 Thus water evaporates considerably below the boiling point and even below the freezing point : ice and snow gradually disappear by evaporation even if the temperature never rises above the melting point. Considerable differences, however, exist between different bodies regarding their rate of evaporation. Thus water and benzine have practically the same boiling point, but at the same distance below the boiling point, benzine evaporates much faster than water; that is, has a much higher vapor tension. Carbon has a very high vapor tension, that is, shows a very rapid evaporation far below the boiling point, and since in the incan- descent lamp the carbon vapor condenses and is deposited on the globe and carbon is black, it blackens the globe and obstructs the light. Also, the decrease of the filament section by evaporation increases its resistance and thereby decreases the power consump- tion and so still "further lowers the efficiency. While, therefore, carbon remains solid up to 3750 deg. cent., at about 1800 deg. cent, its rate of evaporation is such as to lower the candle power of the lamp by 20 per cent in 500 hr. life, and at this tempera- ture it gives only an output of one candle power for 3.1 watts input. Operating the carbon filament at higher temperature would increase the efficiency and thus reduce the cost of energy for the same amount of light, but would decrease the useful life of the lamp and, therefore, increase the cost of lamp renewals, and the most economical operation, as determined by balancing the cost of lamp renewals against the cost of energy, is reached by operating at such temperatures that the candle power of the lamp decreases by 20 percent within 500 hr. life. The life of a lamp down to a decrease of candle power by 20 per cent, thus, is called the useful life, and when comparing the efficiencies of incandescent lamps it is essential to compare them on the basis of the same length of useful life: 500 hours with the carbon filament, since obviously by shortening the life higher efficiencies could be reached in any incandescent lamp. The operating temperature of the carbon filament lamp, thus, was limited by the vapor ten- sion of carbon and not by its boiling point. This limitation of carbon lead to the revival of the metal fila- ment lamps in recent years. First arrived the osmium lamp, with 1.5 watts per candle power. The melting point of osmium is very high, but still very much below that of carbon, but the vapor tension of osmium is very low even close to its melting point, so 80 RADIATION, LIGHT, AND ILLUMINATION. that osmium could be operated at temperatures far closer to its melting point without appreciable evaporation; that is, without blackening and falling off of candle power, or, in other words, could be run at a temperature from which carbon was excluded by its too rapid evaporation. Osmium, however, is a very rare metal of the platinum group, and found only in very limited quantities in very few places and is one of those substances of which no search could very greatly increase the supply, and while one pound of osmium is sufficient for some 30,000 filaments, the total amount of osmium which has ever been found on earth would not be sufficient for one year's supply of incandescent lamps. Osmium, therefore, was excluded from general use by its limited supply. The metal tantalum does not have quite as high a melting point as osmium, hence can be operated only at 2 watts per candle power. Tantalum also is a very rare metal, but, unlike osmium, it is found in very many places, though in small quantities, but it is one of those substances, like the rare earth metals used in the Welsbach mantel, of which it seems that the supply could be infinitely increased when required by the industries and the prices thus would go down with the demand, just as has been the case with the rare earths of the Welsbach mantel. Last of all, however, was made available the most refractory of all metals, wolfram or tungsten, and as lamp filament permitted to lower the specific consumption to 1 to 1.25 watts per candle power, that is, higher than any other incandescent radia- tor. Wolfram melts far lower than carbon, probably at about 3200 deg. cent., but far above the temperature to which the car- bon filament is limited by evaporation, and having practically no vapor tension below its melting point, it can be operated far above the temperature of the carbon filament, and thus gives a much higher efficiency. Tungsten (or rather wolfram, as the metal is called, tungsten is the name of its ore) is a fairly common metal, its salts are industrially used to a very large extent for fire-proofing fabrics and its supply practically unlimited. These metal filaments thus differ from the carbon filament in that their temperature is limited by their melting point and not by evaporation, as is the case with the carbon filament, and thus their useful life is usually ended by the destruction of the filament by melting through at some weak spot, but not by blackening. TEMPERATURE RADIATION. 81 These filament lamps do not blacken the globe, except when the vacuum is defective or becomes defective, and by the residual gases in the lamp globe volatile compounds are formed, as tungs- ten oxide, which then deposits on the globe and terminates the life of the lamp. Even then their blackening is characteristically different from that of the carbon filament, in that it occurs very rapidly, and the lamp, after running possibly for hundreds or thousands of hours without blackening, suddenly blackens within a few days and thereby becomes inoperative, while with the carbon filament the blackening is gradual throughout the life. 38. By the use of these refractory metals the efficiency of light production by temperature radiation has been greatly increased, by permitting the use of higher temperatures in the radiator than were permissible with the carbon filament due to its evaporation. However, regarding the rate of evaporation, different modifications of carbon show very different characteris- tics. The carbon filaments first used in incandescent lamps were made by carbonizing vegetable fiber, as bamboo, or by squirting a solution of cellulose through a small hole into a hardening solu- tion and carbonizing this structureless horn-like fiber. These filaments had a very high vapor tension, thus could not be run as hot as the modern carbon filament and so gave a lower effi- ciency. They are now used only as base filaments, that is, as core on which a more stable form of carbon is deposited. Such a form of carbon was found in carbon deposited on the filament by heating it in the vapor of gasolene or other hydrocarbons. This carbon deposit is of much lower electric resistance than the base on which it was deposited, its negative temperature coeffi- cient of electric resistance is lower and its vapor tension so much lower as to make it possible to operate the lamp at a specific con- sumption of 3.1 watts per candle power. Of late years a still more stable form of carbon has been found in the so-called "me- tallic carbon," produced from the gasolene deposited carbon shell of the filament, by exposing it for several minutes to a tempera- ture at the boiling point of carbon; that is, the highest attainable temperature in an electric carbon tube furnace. Hereby the gasolene deposited carbon of the filament shell — the inner base does not appreciably change its characteristics — acquires metal- lic characteristics: a low electric resistance, a positive tempera- 82 RADIATION, LIGHT, AND ILLUMINATION. ture coefficient of electric resistance, metallic luster and elasticity and very low vapor tension, so that it can be run at higher tem- perature corresponding to a specific consumption of 2.5 to 2.6 watts per candle power, with very little blackening. These metal- lized carbon filament lamps exhibit characteristics similar to the metal filament lamps; their life is largely limited by breakage and not by blackening. Whether hereby the possibilities of carbon are exhausted or still more stable forms of carbon will be found, which permit raising the filament temperature as near to the boiling point of carbon as the temperature of the wolfram filament is to its melt- ing point * and thereby reach an efficiency superior to that of the tungsten lamp, remains to be seen, but does not appear entirely impossible. Carbon exists in a number of "allotropic" modifi- cations of very different characteristics (similar to phosphorus in "yellow phosphorus," "red phosphorus" and " metallic phos- phorus") to a greater extent than any other element, probably due to the tendency of the carbon atom to join with other carbon atoms into chains and rings, which tendency is the case of the infinite number of carbon compounds. These form two main groups : the chain carbon derivates (methane-derivates) and the ring carbon derivates (benzol derivates). The latter are far more stable at high temperatures, since the breakage of the mole- cule by temperature vibration is less liable in a ring structure than a chain : a single break splits the molecule in a chain forma- tion, while with a ring formation it still holds together until the break closes again. Chain hydrocarbons at higher temperatures usually convert to ring hydrocarbons. It is, therefore, reasonable to assume that the carbon skeleton left by the carbonization of the hydrocarbons also may exist in either of the two characteris- tic atomic groupings : as chain carbon and as ring carbon, and that the latter exhibits a much greater stability at high tempera- ture than the former, that is, a lower vapor tension. Cellulose is a chain hydrocarbon, and as in carbonization it never passes through a fluid state, the molecular structure of its carbon atom probably remains essentially unchanged. Thus the base fila- * As carbon boils, at atmospheric pressure, below its melting point, and the limiting temperature is that at which the filament ceases to be solid, with carbon the limit is the boiling point temperature, while with tungsten it is the melting point. TEMPERATURE RADIATION. 83 ment would be a chain carbon, and its low stability and high vapor tension, that is, the ease of breaking up of the molecules by evaporation, thus would be accounted for. A carbon compound, however, which passes through the vapor state in carbonization, as the gasolene vapor in treating the car- bon filament, would as vapor at high temperature largely convert into ring structures, that is, benzol derivates, and thus give a car- bon deposit consisting largely of molecules in which the carbon atoms are grouped in rings. These molecules, therefore, are more stable at high temperatures, and thus exhibit the lower vapor tension shown by the gasolene deposited coating of the base filament. This deposited carbon, however, must be expected to have numerous side chains attached to the ring nuclei of the molecules, and the side chains are relatively easily split off at high temperatures, as is well known of the benzol derivates. As a result thereof, this form of carbon, which I may call " interme- diate carbon," still shows a considerable vapor tension, due to the side chains of the ring structure. Exposure to extremely high temperatures splits off these side chains, which then re- arrange into the only form of carbon stable at these very high temperatures; that is, ring structure and the "metallic" form of carbon produced from the gasolene deposited carbon by the elec- tric furnace, thus would be the ring structure of the carbon molecule, that is, the condensation of numerous rings, similar to that found in anthracene, etc. It, therefore, would have a very high stability at high temperature; that is, be difficult to split up and thus show the low vapor tension characteristic of the me- tallic carbon. In other words, the high vapor tension of most forms of carbon would be the result of the dissociation of com- plex carbon molecules of chain structures, or of side chains of ring structures, and a carbon atom of complete ring structure thus would only show the vapor tension corresponding to the molecular weight, which is very high, due to the large number of atoms in the molecule. Thus two characteristic allotropic modifications of carbon may exist besides the transparent carbon or diamond : (a)^ Chain carbon: high resistance, negative temperature co- efficient of electric resistance, non-metallic character, high vapor tension at moderate temperature. (6). Ring carbon: low resistance (within the range of 84 RADIATION, LIGHT, AND ILLUMINATION. metallic resistivities), positive temperature coefficient of re- sistance, metallic character, low vapor tension at high tem- peratures. The latter one, obviously, is best suited as an incandescent radiator. It may be possible to introduce into the ring structure of the carbon molecule other atoms of very refractory nature, as boron, titanium, silicon, and by their chemical affinity still further in- crease the stability of the molecule, so that it does not appear outside of the possibility to find a form of carbon which as radia- tor would be superior to any metal filament. 39. Most bodies show the same characteristic in their tempera- ture radiation; that is, the total radiation varies in the same man- ner with the temperature as the fourth power of the absolute temperature. Thus the distribution of the frequencies in the radiation is the same for the same temperature, varies in the same manner with the temperature, so that the distribution of the radiation power between the different frequencies is a charac- teristic of the temperature, independent of the material of the body, and can be used for determining the temperature of the radiator. Such bodies, therefore, are said to give normal temperature radiation. Many bodies of normal temperature radiation give the same intensity, or power of radiation, at the same temperature, that is, have the same radiation constant k in equation (1) ; these bodies are called " black bodies," and their radiation " black body radia- tion." Their radiation is the maximum temperature radiation given by a body. Other bodies of normal radiation give a lower intensity or radiation, but so that their radiation is at any tem- perature and for any frequency the same fraction of the radiation of a black body. Their radiation, then, is called "grey body radiation," and they also would follow the radiation law equa- tion (1), but with a constant k, which is a fraction of the constant kQ of black body radiations : k = bkQ. For temperature radiation the following law applies : "The temperature radiation of a body is at any temperature and at any frequency the same percentage of black body radiation TEMPERATURE RADIATION. 85 as the absorbed radiation of the body is of the total impinging radiation." (KirchhofTs law.) This law relates the behavior of a body towards radiation impinging upon it from other bodies, with its behavior as radiator. A body which absorbs all the impinging radiation, that is, a black body, gives a maximum temperature radiation, and this radiation, thus, has been called the black body radiation. An opaque grey body of albedo a, that is, a body which reflects the same fraction a of the impinging radiation and thus absorbs the part (1 — a) of the impinging radiation, thus gives as radiator the part (1 - a) of black body radiation. That is, its radiation constant is k = bk0 = (1 - a) fcc, and the radiation constant of any opaque body, thus, is the radia- tion constant of the black body multiplied by 1 minus its albedo a. For a perfectly white or perfectly transparent body, the radia- tion constant, thus, would be zero; that is, this body would give no temperature radiation, would not become incandescent at high temperatures. 40. A colored body was defined as a body which reflects or transmits different fractions of the impinging radiation for dif- ferent frequencies. Such a colored body usually absorbs different parts of the impinging radiation for different frequencies and as radiator, then, would for different frequencies give different frac- tions of black body radiation; that is, its radiation for some frequencies would be a greater part of black body radiation. The radiation of such a body is called "colored body radiation." In colored body radiation the distribution of intensities throughout the spectrum, that is, for different frequencies, thus differs from that of the black or grey body at the same temperature, that is, colored radiation is not normal radiation and thus also does not follow the temperature law equation (1). For instance, if in Fig. 29, 1 is the curve of distribution of the intensity of radiation as function of the frequency, at a certain temperature, as the melting point of tungsten, for a black body; grey body radiation would be represented by curve II or III, in which the ordinates are a constant fraction of those of curve I. Curve II, for albedo a = 0.3, has the height 1 - a = 0.7 times that of black body radiation I, that is, radiates 70 per cent as 86 RADIATION, LIGHT, AND ILLUMINATION. much energy, at any temperature and of any frequency, as a black body. Curve III corresponds to albedo a = 0.6, or a radiation constant 1 - a = 0.4 times that of the black body. Colored body radiation, then, would be represented by curves IV and V. Representing the gctave of visible radiation by L, the area of the curve within the limits of L to the total area of the radiation curve, gives the ratio of power visible to total radiation, or the " radiation efficiency." As seen, this radiation efficiency is the same for black and grey bodies, I, II, III, and the only difference between the black and the grey body is that with the grey body the amount of light per unit radiating surface is less, but the 7 \ \ \ \\ FIG. 29. power required to maintain the temperature is correspondingly less, hence the efficiency is the same and merely a larger radiator surface required to produce the same amount of light ; the larger the surface, the higher the albedo of the radiator. For colored radiators, however, the radiation efficiency may be different and frequently is. In the colored body IV, in which the radiation in the visible range is a greater part of the black body radiation I than in the invisible range, the radiation efficiency is greater than that of colorless or normal radiation at the same temperature ; that is, such a colored body gives a higher efficiency of light production than corresponds to normal radiation at the same temperature. Such, for instance, is the case with the material of TEMPERATURE RADIATION. 87 the Welsbach mantel. Inversely, the colored body V, in which the radiation in the visible range is a lower percentage of black body radiation than in the invisible range, gives a lower efficiency of light production. Such, for instance, is the case with glass, which, therefore, would be an abnormally inefficient incandescent light producer. To illustrate the difference in the radiation of black and grey bodies, I show you here a piece of graphite rod, around which a strip of platinum foil is wrapped in an open spiral and then it is enclosed in a transparent quartz tube. Heating it in the bunsen flame, you see the graphite becomes bright red, while the platinum foil surrounding it is far less luminous and the quartz tube is not luminous at all, though all three have practically the same temper- ature, or if anything, the outer quartz tube is the hottest, the interior graphite rod the coolest. Still, the graphite gives the greatest amount of light : graphite is a black body and thus gives maximum radiation; the platinum as a grey body gives less radia- tion at the same temperature and the quartz as a transparent body which absorbs almost no radiation, thus, also, gives out almost no radiation, that is, does not become luminous at a temperature at which the graphite is bright red. I now drop a small platinum spiral into a mixture of the nitrates of thoria and ceria (the rare earths of the Welsbach mantel), and then immerse it in the bunsen flame. The nitrates convert to oxides, which fluff out into a very light and porous mass, which you see glow in a very intense, slightly greenish light, far brighter than the platinum wire immersed in the same flame. The dis- tribution of intensity of this radiation differs from that corre- sponding to any temperature, and the percentage of visible radiation, especially from the center of the visible spectrum (greenish yellow) , is abnormally large. This, therefore, is a colored radiator, giving a higher radiation efficiency than the normal temperature radiation. A radiation which does not follow the temperature law of normal radiation as regard to the distribution of intensity with the frequency, is called " selective radiation." Colored body radiation, thus, is selective radiation. In regard to their reaction on light impinging on them, in reflect- ing or transmitting it, most bodies are more or less colored and colorless bodies: black, grey, white, transparent, the exception. 88 RADIATION, LIGHT, AND ILLUMINATION. Regarding the temperature radiation produced by the body as radiator, most bodies are colorless, black or grey bodies, that is, give normal radiation or nearly so, and colored or selective radia- tion of appreciable intensity is the exception. Obviously, no perfectly black, or even perfectly colorless radia- tor exists, but even carbon shows a slight selectivity, a slightly greater intensity of radiation at the red end of the spectrum than corresponds to the temperature. Perfectly black body radiation, "however, is the radiation at the inside of a hollow body of uniform temperature, and the laws of black body radiation, thus, are studied on the radiation in the interior of a closed shell with opaque walls of uniform temperature. In the interior of such a hollow body of uniform temperature every surface element radiates to every other element and receives radiation from every other surface element, that is, the surface element Al receives as much radiation from element A2 as ele- ment A2 receives from Ar Of the radiation received by a surface element Al by the radia- tion law, that part which exists in the radiation produced by A1 is absorbed, that part which does not exist in the temperature radiation of Av is reflected, and the total radiation issuing from Ax, the radiation produced by it plus that reflected by it, together, thus, make up complete black body radiation. If, then, the hol- low radiator is a black body, it absorbs all the impinging radia- tion, reflects none, and the radiation issuing from it thus is the black body radiation produced by it. If the radiator is not a black body, buj a grey or a colored body, of any frequency of radiation, for which it has the albedo a, only the part (1 — a) is produced by it, but the part a of the impinging radiation of this frequency is reflected, and the total radiation of this fre- quency, thus, still is unity, that is, back body radiation. Obviously, the body cannot be perfectly closed, but must contain an opening, through which the interior radiation is observed, but if this opening is sufficiently small it introduces no appreciable error. The production of black body radiation from the interior of a hollow body obviously requires that the walls of the body be opaque; that is, that all the radiation produced inside of it is either absorbed or reflected, and also depends on the condition TEMPERATURE RADIATION. 89 that all the frequencies of black body radiation are present, since evidently, no frequency which is entirely absent in the radiation of the body could be produced by reflection. Furthermore, all the radiation must be temperature radiation, that is, no lumines- cence exist in the interior of the body. These requirements are easily fulfilled, except at extremely high temperatures. 41. The radiation laws offer a means of measuring tempera- ture, and the only means for those very high temperatures where the gas thermometer (that is, the measurement of temperature by the expansion of a gas) and the thermo-electric couple or the resistance pyrometer cannot longer be used, as no material exists which remains solid at temperatures such as those of electric furnaces, etc. As the total intensity of the radiation varies with the fre- quency, and the ratio of the intensity of radiation of any definite frequency to the total radiation, or the ratio of intensities at two different frequencies of radiation, is a function of the tem- perature, either can be used for measuring the temperature. For instance, measuring the intensity of the total radiation — which in vacuum enclosed radiators as incandescent lamp fila- ments is done by measuring the power input — gives the tem- perature if the body is a black body and its radiating surface measured. If one temperature is known, as, for instance, by the melting point of some substance, by comparing the total radia- tion power with that at the known temperature, other tempera- tures can be measured. Determining the ratio of the power of the visible radiation, and that of the total radiation — that is, the radiation efficiency — thus gives the temperature for black bodies as well as grey body radiators. By comparing the intensity of any two radiations we get the temperature. This can be done very easily by using two wave lengths of radiation in the visible range. For instance, the ratio of the intensity of the yellow and the blue radiation gives the temperature. Resolving, then, the radiation by a prism P in Fig. 30, into a spectrum, and by a shutter $t cutting out a definite width of yellow and of blue light, and combining these again by the mirror Ml and M2 we get a resultant green color which is intermediate between yellow and blue, and the nearer to the blue, the higher the temperature. Arranging, then, the mov- 90 RADIATION, LIGHT, AND ILLUMINATION. able shutter S2 below Sl with a single opening, we can by it cut out a single green color, and by moving the shutter S2 bring this to coincidence in shade with the resultant color of shutter Sv and the position of the shutter S2 then measures the temperature. The scale of such a direct vision pyrometer may either be calcu- lated from the radiation laws, or it may be calibrated by some known temperatures, as the melting points of gold, platinum, boiling point of carbon, etc. A number of types of such visual pyrometers have been devel- oped, and are very convenient. Their limitation, obviously, is that they apply only when the radiation is normal temperature radiation, but give wrong results where colored radiation or luminescence is present. Thus the FIG. 30. radiation given by the interior of a closed body of uniform tem- perature ceases to be black body radiation if the interior is filled with luminous vapors, as is frequently the case in the interior of electric furnaces. For instance, using such a visual pyrometer for the interior of the carbon tube furnace used for metallizing carbon filaments gives, frequently, quite impossible results, tem- peratures above those of the sun, due to the error caused by the luminescent silicon vapor filling the tube. The errors of temperature measurements by radiation are the greater the nearer together the radiation frequencies are which are used for the measurement, hence are greatest with the visual pyrometers, least in the methods based on the total radiation power. 42. In the temperature radiation of a colored body the ratio of the intensity of the radiation to that of a black body of the TEMPERATURE RADIATION. 91 same temperature is different for different frequencies of radia- tion, and the average wave length of radiation and the total intensity of radiation of a colored body thus do not vary with the temperature in the same manner as is the case with the black and the grey body, that is, the normal radiation. The intensity of colored body radiation at any frequency cannot exceed the inten- sity of radiation of a black body at the same temperature and frequency, since the radiation of the black body is the maximum temperature radiation at any temperature and frequency. A body which gives at any frequency a greater intensity of radiation than a black body of the same temperature is called luminescent, that is, said to possess "heat luminescence." Char- acteristic of heat luminescence, thus, is an excess of the intensity of radiation over that of a black body of the same temperature for some frequency or range of frequencies, and the color of lumin- escence is that of the radiation frequencies by which the lumin- escent body exceeds the black body. It is not certain whether such heat luminescence exists. The high efficiency of light production of the Welsbach man- tel, of the lime light, the magnesium flame, the Nernst lamp, etc., are frequently attributed to heat luminescence. The rare oxides of the Welsbach mantel, immersed in the bunsen flame, give an intensity of visible radiation higher than that of a black body, as a graphite rod, immersed in the same flame, and if we assume that these oxides are at the same tempera- ture as the flame in which they are immersed, their light must be heat luminescence and not colored radiation, as the latter can- not exceed that of a black body. It is possible, however, that these oxides are at a higher temperature than the flame surround- ing them, and as the radiation intensity of a black body rapidly rises with the temperature, the light radiation of the rare oxides, while greater than that of a black body of the flame temperature, may still be less than that of a black body of the same tempera- ture which the oxides have, and their radiation, thus, colored temperature radiation and not luminescence. Very porous materials, as platinum sponge, absorb considerable quantities of gases, and by bringing them in close contact with each other in their interior cause chemical reaction between them, where such can occur, and thus heat and a temperature rise above surround- ing space. Thus platinum sponge, or fine platinum wire, immersed 92 RADIATION, LIGHT, AND ILLUMINATION. in a mixture of air and alcohol vapor at ordinary temperature, becomes incandescent by absorbing alcohol vapor and air and causing them to combine. The oxides of the Welsbach mantel, as produced by the deflagration of their nitrates, are in a very porous state, and thus it is quite likely that in the bunsen flame they absorb gas and air and cause them to combine at a far more rapid rate than in the flame, and thereby rise above the flame temperature. An argument in favor of this hypothesis is, that these oxides, when immersed in the bunsen flame in close contact with a good heat conductor, as platinum, and thereby kept from rising above the flame temperature, do not show this high lumi- nosity. I have here a small, fairly closely wound platinum spiral filled with these oxides. Immersing it in the bunsen flame you see the oxides and the platinum wire surrounding them glow with the same yellow light, but see none of the greenish luminosity exhibited by the oxide when free in the flame, except at a few points at which the oxide projects beyond and is not cooled by the platinum spiral. The absence of a high selective luminosity of these oxides, when heated electrically in a vacuum or in an inactive gas, also points this way. The gradual decay of the luminosity shown by such radiators may be due to their becoming less porous, by sintering — this would account for the very rapid decay of the light of the lime cylinder in the hydro-oxygen flame, and the very small decay of the more refractory oxides in the Welsbach mantel — but it also may be the general characteristic of luminescence, as we have found in the discussion of fluorescence and phosphorescence. In favor of heat luminescence as the cause of the very high effi- ciency of these radiators is, however, the similarity of the con- ditions under which it occurs, with those we find in fluorescence and phosphorescence. Just as neither calcium sulphide nor zinc silicate nor calcium carbonate are fluorescent or phosphorescent, when chemically pure, but the fluorescence and phosphorescence are due to the presence of a very small quantity of impurities, as manganese, so the pure oxides, thoria, erbia, ceria,donot give very high luminosity in the bunsen flame, but the high luminosity is shown by thoria when containing a very small percentage of other oxides. While the existence of heat luminescence in these rare oxides is not certain, no theoretical reason exists against it, as at ordi- TEMPERATURE RADIATION. 93 nary temperature we have in phosphorescence the same phenome- non of the production of a radiation exceeding in intensity that of a black body of the same temperature: the black body radia- tion at ordinary temperature contains no visible rays, while that of a phosphorescent body does. Heat-luminescence, thus, may be considered as fluorescence at high temperature. However, to some extent, the question of the existence of heat luminescence depends upon the definition of luminescence, and any colored radiation may be considered as heat luminescence of a grey body. For instance, the radiation represented by curves IV and V of Fig. 29, may be considered as colored temperature radiation, as they are below black body radiation, curve I. But as they exceed at some frequencies the curves of grey body radiation II and III, they may also be considered as heat lumi- nescence of a grey body. If, then, we compare such curves of selective radiation, IV and V, with normal temperature radiation of the same total intensity — that is, with a grey body radiation of the same power at the same temperature — all such selective radiation can be considered as heat luminescence. While the term " luminescence" is usually applied only to abnormally high radiation in the visible range, in its general physical meaning it applies to abnormal radiation of any fre- quency range, and curve V in Fig. 29, for instance, would be the curve of a grey body, which luminesces in the ultra-red, while curve IV would be that of a grey body, in which the heat lumi- nescence is in the visible range. In general, however, it is preferable to consider as luminescence only such radiation as exceeds the black body radiation of the same temperature, and this will be done in the following, while radiations which differ in their frequency distribution from the black body, without exceeding it in intensity, are considered as colored body radiations.