Published by the McGraw-Hill Book. Company Successors to tKe Book Departments of tKe McGraw Publishing Company Hill Publishing" Company FVibliahers of Books for Elec trical Worl d TKe Engineering" and Mining" Journal TKe Engineering Record FV>wer and TKe Engineer Electric Railway Journal American Machinist frffffj>Tffir>TffffffffffffiT>TgffffiTffirirjffffffffffffTffffffff *.' 2 l ; W O 13 c r * ^~* .2 a 'c O g RADIATION, LIGHT AND ILLUMINATION A SERIES OF ENGINEERING LECTURES DELIVERED AT UNION COLLEGE BY CHARLES PROTEUS STEINMETZ, A.M., PH.D. >\ COMPILED AND EDITED BY JOSEPH LEKOY HAYDEN NEW YORK McGRAW-HILL BOOK COMPANY 239 WEST 39TH STREET 1909 \ \ COPYRIGHT, 1909, BT THE McGRAW-HILL BOOK COMPANY NEW YORK AUTHOR'S PREFACE. THE following lectures were given as a course of instruction to the senior students in electrical engineering at Union University. They are however intended not merely as a text-book of illuminating engineering, nor as a text-book on the physics of light and radiation, but rather as an exposition, to some extent, from the engineering point of view, of that knowledge of light and radiation which every educated man should possess, the engineer as well as the physician or the user of light. For this purpose they are given in such form as to require no special knowledge of mathematics or of engineering, but mathematical formalism has been avoided and the phenomena have been de- scribed in plain language, with the exception of Lectures X and XI, which by their nature are somewhat mathematical, and are intended more particularly for the illuminating engineer, but which the general reader may safely omit or merely peruse the text. The lectures have been revised to date before publication, and the important results of the work of the National Bureau of Standards, contained in its recent bulletins, fully utilized. CHARLES PROTEUS STEINMETZ. SCHENECTADY, September, 1909. iii COMPILER'S PREFACE. A SERIES of eight experimental lectures on " Light and Radia- tion" were delivered by Dr. Steinmetz in the winter of 1907-8 before the Brooklyn Polytechnic Institute. Unfortunately no stenographer was present and no manuscript prepared by the lecturer. A far more extended course of experimental lectures was however given by Dr. Steinmetz at Union University in the winter of 1908-9, on " Radiation, Light, Illumination and Illu- minating Engineering," and has been compiled and edited in the following. Two additional lectures have been added thereto by Dr. Stein- metz to make the treatment of the subject complete even from the theoretical side of illuminating engineering : Lecture X on "Light Flux and Distribution" and Lecture XI on "Light Intensity and Illumination." These two lectures give the elements of the mathematical theory of illuminating engineering. With the exception of the latter two lectures the following book contains practically no mathematics, but discusses the subjects in plain and generally understood language. The subject matter of Lecture XII on "Illumination and Illuminating Engineering" has been given in a paper before the Illuminating Engineering Society; the other lectures are new in their form and, as I believe, to a considerable extent also in their contents. In describing the experiments, numerical and dimensional data on the apparatus have been given, and the illustrations drawn to scale, as far as possible, so as to make the repetition of the experiments convenient for the reader or lecturer. Great thanks are due to the technical staff of the McGraw-Hill Book Company, which has spared no effort to produce the book in as perfect a manner as possible. JOSEPH L. R. HAYDEN. SCHENECTADY, September, 1909. CONTENTS. LECTURE I. NATURE AND DIFFERENT FORMS OF RADIATION. 1. Radiation as energy. j 2. Measurement of the velocity of light. 2 3. Nature of light. 4 4. Difference of wave length with differences of color. Meas- urement of wave length and of frequency. Iridescence. The ether. 6 5. Polarization proving light a transversal vibration. Double refraction. 7 6. The visible octave of radiation. Ultra-red and ultra-violet radiation. 9 7. The electric waves. 15 8. The spectrum of radiation covering 60 octaves. 16 LECTURE II. RELATION OF BODIES TO RADIATION. 9. Electric waves of single frequency, light waves of mixed frequency. 20 10. Resolving mixed waves into spectrum. Refraction. 21 11. Relation of refractive index to permeability and dielectric constant. 24 12. Spectrum. 25 13. Continuous spectrum. Line spectrum. Band spectrum. Combination spectra. 26 14. Reflection, absorption and transmission. 29 15. Conversion of absorbed radiation into heat and light. 30 16. Transmitted light. 31 17. Opaque colors and transparent colors. 32 18. Objective color and subjective color. 33 19. Effect of excess and of deficiency of certain wave length of the illuminant on the opaque and the transparent colors. vii viii CONTENTS. PAGE LECTURE III. PHYSIOLOGICAL EFFECTS OF RADIATION. Visibility. 20. The eye. 37 21. Dependence of sensitivity of the eye on the color. Mechan- ical equivalent of light. Comparison of intensities of different colors. 40 22. Sensitivity curves of eye for different intensities. 43 23. Change of shape of sensitivity curve with intensity. 45 24. Harmful effect of excessive radiation power. 48 25. Protective action of eye. 50 26. Specific high frequency effect beginning in blue. 51 27. Perception of ultra-violet light. Harmful effects of ultra- violet. 52 28. Arcs as producers of ultra-violet rays. 55 Pathological and Therapeutic Effects of Radiation. 29. Power effect and specific high frequency effect. 57 30. Light as germicide and disinfectant. 59 LECTURE IV. CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. Chemical Effects. 31. Indirect chemical action by energy of radiation. Direct chemical action. 63 32. Chemical action of red and yellow rays in supplying the energy of plant life. Destructive action of high frequency on plant life. 64 Physical Effects. 33. Fluorescence and phosphorescence. 66 LECTURE V. TEMPERATURE RADIATION. 34. Production of radiation by heat. 70 35. Increase of intensity and frequency with temperature. 73 36. Efficiency and temperature. 76 37. Carbon incandescent lamp. 78 38. Evaporation below boiling point. Allotropic modifications of carbon. 81 39. Normal temperature radiation. 84 40. Colored body radiation. 85 41. Measurement of temperatures by radiation. 89 42. Colored radiation and heat luminescence. 90 CONTENTS. i x PAGE LECTURE VI. LUMINESCENCE. Fluorescence and Phorphorescence. 43. Radioluminescence. Electroluminescence. Thermolumi- nescence. Physical phosphorescence. Chemical phos- phorescence. Biological phosphorescence. 94 44. Pyroluminescence. Chemical luminescence. 96 45. Electroluminescence of gases and vapors. 98 Disruptive Conduction. 46. Geissler tube and spark. Disruptive voltage. 101 47. Change from spark to Geissler glow. 105 Continuous Conduction. 48. Nature of continuous or arc conduction. 106 49. Distinction between arc and spark discharge. Ill 50. Continuity at negative. 113 51. Rectification of alternating voltages by arcs. 117 52. Efficiency and color. 122 53. Most efficient light producer. 123 54. Electro-conduction from negative, long life, non-consuming positive, limitation in the available materials. 125 55. Arc most efficient method of light production. 126 LECTURE VII. FLAMES AS ILLUMINANTS. 56. Hydrocarbon flames. 128 57. Effect of rapidity of combustion and of flame shape on smokiness. 130 58. Effect of oxygen atom in the hydrocarbon molecule on luminosity. 132 59. Mixture of hydrocarbon with air. 133 60. Chemical luminescence. 134 61. Flames with separate radiator. 135 LECTURE VIII. ARC LAMPS AND ARC LIGHTING. Volt- Ampere Characteristics of the Arc. 62. Arc length and voltage. 137 63. General equations of the arc. 140 Stability Curves of the Arc. 64. Instability on constant voltage.. 142 65. Equations of the vapor arc. 145 Arc Length and Efficiency. 66. Maximum efficiency length of carbon arc. 146 67. Maximum efficiency length of luminous arc. 148 X CONTENTS. PAGE LECTURE VIII. ARC LAMPS AND ARC LIGHTING (Continued). Arc Lamps. 68. The elements of the arc lamp. 151 69. Differential arc lamp. 153 70. Series arc lamp. 157 71. Luminous arc lamp. 160 Arc Circuits. 72. Constant potential and constant current. The mercury arc rectifier system. The arc machine. 160 73. The constant current transformer. The constant current reactance. 163 LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION. 74. Measurement of radiation as power. 166 75. Light a physiological quantity. 167 76. Physiological feature involved in all photometric methods. 169 77. Zero method photometers. 170 78. Comparison of lights. 172 79. Flicker photometer. 173 80. The luminometer. 175 81. Primary standards of light. 177 82. Proposed primary standards. 178 83. Illumination and total flux of light. Incandescent lamp photometry. 179 84. Arc lamp photometry. 182 85. Discussion. Mean spherical, horizontal, downwards, maxi- mum, hemispherical candle power. 184 LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. Light flux, light flux density, light intensity. 186 87. Symmetrical and approximately symmetrical distribution. 187 88. Calculation of light flux from meridian curve of symmetri- cal radiator. 188 Distribution Curves of Radiation. 89. Calculation of distribution curves. Point or sphere of uniform brilliancy. 190 90. Straight line or cylindrical radiator. 195 91. Circular line or cylinder. 197 92. Single loop filament incandescent lamp as illustration. 200 CONTENTS. xi PAGE LECTURE X. LIGHT FLUX AND DISTRIBUTION (Continued). Shadows. 93. Circular shade opposite and symmetrical to circular radia- tor. 202 94. Calculation of the meridian curves of a circular radiator, for different sizes of a symmetrical circular shade, and for different distances of it. 206 95. Circular shade concentric with end of linear radiator. 210 Reflection. 96. Irregular reflection. 212 97. Regular reflection. 215 98. Reflector with regular and irregular reflection. 218 Diffraction, Diffusion and Refraction. 99. Purpose of reducing the brilliancy of the illuminant. 221 100. Effect of the shape of the diffusing globe on the distribu- tion curve. 223 101. Prismatic refraction and reflection. 224 LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. Intensity Curves for Uniform Illumination. 102. Calculation of intensity distribution of illuminant for uniform total, horizontal and vertical illumination. 226 103. Uniform illumination of limited area. 229 Street Illumination by Arcs. 104. Discussion of problem. 234 105. Combined effect of successive lamps. Room Illumination by Incandescent Lamps. 106. Distribution curve of lamp. Calculation of resultant total intensity of direct light. 107. Reflection from walls and ceiling. 246 108. Total directed and diffused illumination. 251 Horizontal Table Illumination by Incandescent Lamps. 109. Location of lamps. 253 xii CONTENTS. PAGE LECTURE XII. ILLUMINATION AND ILLUMINATING ENGINEERING. 110. Physical and physiological considerations. 256 111. Light flux density. Illumination. Brilliancy. 259 112. Physical problems. Ceilings and walls. Reflectors, diffus- ing globes, diffracting shades, etc. 260 113. Objective illumination. Subjective illumination. Con- traction of pupil. Intrinsic brilliancy. Direct and in- direct lighting. 261 114. Fatigue. 263 115. Differences in intensity and in color. Control of color differences. Shadows and their control. Directed and diffused light. 265 116. Direction of shadows. 267 117. Color sensitivity in relation to required intensity of illu- mination. 269 118. Domestic lighting. 270 119. The twofold problem of domestic lighting: daylight and artificial light. 271 120. Street lighting. 272 121. Defects of present street lighting. 273 122. Tower lighting. 274 LECTURE XIII. PHYSIOLOGICAL PROBLEMS OF ILLUMINATING ENGINEERING. 123. Physical side of illuminating engineering. Physiological problems. 277 124. Physiological difference between diffused and directed light. 278 125. Indefmiteness of diffused light. Shadows cast by diffused daylight. Equivalent diffusion near light source of large extent. 279 126. Equivalent diffusion by using several light sources. 281 127. Unequal diffusion in different directions. Complex shadows. 282 128. Physiological light distribution. 283 129. Physiologically, light not a vector quantity. 284 130. Resultant effect of several light sources. 287 RADIATION, LIGHT, AND ILLUMINATION. LECTURE I. NATURE AND DIFFERENT FORMS OF RADIATION. 1. Radiation is a form of energy, and, as such, can be produced from other forms of energy and converted into other forms of energy. The most convenient form of energy for the production of rad- iation is heat energy, and radiation when destroyed by being intercepted by an opaque body, usuaDy is converted into heat. Thus in an incandescent lamp, the heat energy produced by the electric current in the resistance of the filament, is converted into radiation. If I hold my hand near the lamp, the radiation intercepted by the hand is destroyed, that is, converted into heat, and is felt as such. On the way from the lamp to the hand, how- ever, the energy is not heat but radiation, and a body which is transparent to the radiation may be interposed between the lamp and the hand and remains perfectly cold. The terms "heat radiation " and " radiant heat," which are occasionally used, therefore are wrong: the so-called radiant heat is not heat but radiation energy, and becomes heat only when, intercepted by an opaque body, it ceases to be radiation; the same, however, applies to any radiation. If we do not feel the radiation of a mercury lamp or that of the moon as heat, while we feel that of a coal fire, it is merely because the total energy of the latter is very much greater; a sufficiently sensitive heat-measuring instrument, as a bolometer, shows the heat produced by the interception of the rays of the mercury lamp or the rays of the moon. The most conspicuous form of radiation is light, and, therefore, it was in connection with this form that the laws of radiation were first studied. 1 2 RADIATION, LIGHT, AND ILLUMINATION. 2. The first calculations of the velocity of light were made by astronomers in the middle of the eighteenth century, from the observations of the eclipses of the moons of Jupiter. A number of moons revolve around the planet Jupiter, some of them so close that seen from the earth they pass behind Jupiter and so are eclipsed at every revolution. As the orbits of Jupiter's moons were calculated from their observations by the law of gravita- tion, the time at which the moon M should disappear from sight, FIG. 1. when seen from the earth E, by passing behind Jupiter, 7 (Fig. 1), could be exactly calculated. It was found, however, that some- times the moon disappeared earlier, sometimes later than cal- culated, and the difference between earliest and latest disappear- ance amounts to about 17 min. It was also found that the disappearance of the moon behind Jupiter occurred earlier when the earth was at the same side of the sun as Jupiter, at A, while the latest disappearance occurred when the earth was on the opposite side of the sun from Jupiter, at B. Now, in the latter case, the earth is further distant from Jupiter by the diameter ASB of the orbit of the earth around the sun S, or by about 195,000,000 miles and the delay of 17J min. thus must be due to the time taken by the light to traverse the additional distance of 195,000,000 miles. Seventeen and one-third min. are 1040 sec. and 195,000,000 miles in 1040 sec. thus gives a velocity of light of or 188,000 miles per sec. Later, the velocity of light was measured directly in a number of different ways. For instance, let, in Fig. 2, D be a disk per- forated with holes at its periphery. A lamp L sends its light through a hole H in the disk to a mirror M located at a con- siderable distance, for instance 5 miles; there the light is reflected NATURE AND DIFFERENT FORMS OF RADIATION. 3 and the mirror is adjusted so that the reflected beam of light passes through another hole H l of the disk into the telescope T. If the disk is turned half the pitch of the holes the light is blotted out as a tooth stands in front of both the lamp and the telescope. Again turning the disk half the pitch of the holes in the same 5_MOE_S FIG. 2. direction the light reappears. If the disk is slowly revolved, alter- nate light and darkness will be observed, but when the speed in- creases so that more than from 10 to 20 holes pass per second, the eye is no longer able to distinguish the individual flashes of light but sees a steady and uniform light; then increasing the speed still more the light grows fainter and finally entirely disappears. This means when a hole H is in front of the lamp, a beam of light passes through the hole. During the time taken by the light to travel the 10 miles to the mirror and back, the disk D has moved, and the hole H v which was in front of the telescope when the light from the lamp passed through the hole H Q , has moved away, and a tooth is now in front of the telescope and intercepts the light. Therefore, at the speed at which the light disappears, the time it takes the disk to move half the pitch of a hole is equal to the time it takes the light to travel 10 miles. Increasing still further the velocity of the disk D, the light appears again, and increases in brilliancy, reaching a maximum at twice the speed at which it had disappeared. Then the light reflected from the mirror M again passes through the center of a hole into the telescope, but not through the same hole H t through which it would have passed with the disk stationary, but through the next hole H 2 , that is, the disk has moved a distance equal to the pitch of one hole while the light traveled 10 miles. Assume, for instance, that the disk D has 200 holes and makes 4 RADIATION, LIGHT, AND ILLUMINATION. 94 rev. per sec. at the moment when the light has again reached full brilliancy* In this case, 200 X 94 = 18,800 holes pass the telescope per second, and the time of motion by the pitch of one hole is sec., and as this is the time required by the light 18,800 to travel 10 miles, this gives the velocity of light as 10 * > lo,oOU or 188,000 miles per sec. The velocity of light in air, or rather in empty space, thus is 188,000 miles or 3 X 10 10 cm. per sec. For electrical radiation, the velocity has been measured by Herz, and found to be the same as the velocity of light, and there is very good evidence that all radiations travel with the same velocity through space (except perhaps the rays of radioactive substances). 3. Regarding the nature of radiation, two theories have been proposed. Newton suggested that light rays consisted of extremely minute material particles thrown off by the light- giving bodies with enormous velocities, that is, a kind of bom- bardment. This theory has been revived in recent years to explain the radiations of radium, etc. Euler explained the light as a wave motion. Which of these explanations is correct can be experimentally decided in the following manner: Assum- ing light to be a bombardment of minute particles, if we com- bine two rays of light in the same path they must add to each other, that is, two equal beams of light together give a beam of twice the intensity. If, however, we assume light is a wave motion, then two equal beams of light add to one of twice the intensity only in case the waves are in phase, as A l and B^ in Fig. 3 add to C r If, however, the two beams A 2 and B 2 are not in phase, their resultant C 2 is less than their sum, and if the two beams A 3 and B 3 in Fig. 3 happen to be in opposition (180 degrees apart), that is, one-half wave length out of phase with each other, their resultant is zero, that is, they blot each other out. Assuming now we take a plain glass plate A (Fig. 4) and a slightly curved plate B, touching each other at (7, and illuminate them by a beam of uniform light as the yellow light given by coloring the flame of a bunsen burner with some sodium salt a part of the light b, is then reflected from the lower surface of NATURE AND DIFFERENT FORMS OF RADIATION. 5 the curved glass plate B, a part c, passes out of it, and is reflected from the upper surface of the plain glass plate A. A beam of FIG. 3. reflected light a, thus is a combination of a beam b and a beam c. The two beams of light which combine to a single one, a, differ from each other in phase by twice the distance between the two glass plates. At those points d v d v etc. at which the distance FIG. 4. between the two glass plates is J wave length, or j, J, etc., the two component beams of a would differ by \, f , |, etc. wave lengths, and thus would blot each other out, producing darkness, 6 RADIATION, LIGHT, AND ILLUMINATION. while at those points where the distance between the glass plates is J, 1, lj, etc. wave lengths, and the two component beams a thus differ in phase by a full wave or a multiple thereof, they would add. If, therefore, light is a wave motion, such a structure would show the contact point C of the plates surrounded by alternate dark rings, d, and bright rings, y. This is actually the case, and therefore this phenomenon, called " interference" proves light to be a wave motion, and has lead to the universal acceptance of the Eulerian theory. Measuring the curvature of the plate B, and the diameter of the dark rings d, the distance between the plates B and A at the dark rings d, can be calculated and as this distance is one- quarter wave length, or an odd multiple thereof, the wave length can be determined therefrom. The wave length of light can be measured with extremely high accuracy and has been proposed as the absolute standard of length, instead of the meter, which was intended to be 10~ 7 of the quadrant of the earth. 4. It is found, however, that the different colors of light have different wave lengths; red light has the greatest wave length, and then in the following order: red, orange, yellow, green, blue, indigo, violet, the wave length decreases, violet light having the shortest wave length. If in experiment (Fig. 4) instead of uniform light (monochro- matic light), ordinary white light is used, which is a mixture of all colors, the dark and bright rings of the different colors appear at different distances from each other, those of the violet near- est and those of the red the furthest apart, and so superimpose upon each other, and instead of alternately black and light rings, colored rings appear, so-called interference rings. Wherever a thin film of air or anything else of unequal thickness is inter- posed between two other materials, such interference colors thus appear. They show, for instance, between sheets of mica, etc. The colors of soap bubbles are thus produced. The production of such colors by the interference of rays of light differing from each other by a fractional wave length is called iridescence. Iridescent colors, for instance, are those of mother-of-pearl, of opal, of many butterflies, etc. Light, therefore, is a wave motion. NATURE AND DIFFERENT FORMS OF RADIATION. 1 The frequency of radiation follows from the velocity of light, and the wave length. The average wave length of visible radiation, or light, is about l w = 60 microcentimeters,* that is, 60 X 10~ 8 cm. (or about ^ field: 15 20,000 km. = 12,500 mi. 25 12.000 km. = 7, 500 mi. 3.15 60 5, 000 km. = 3, 100 mi. 133 2,250 km. = 1,400 mi. High frequency cur- \ rents, surges and oscillations, arcing V (9.57) 31.64 grounds, lightning phenomena, etc. J Wireless telegraph ( 10 5 3 km. = 10,000 ft. 9.63 ) A ~, waves : ( 10 7 30 m. = 100 ft. 16.25 \ 6 ' 62 Herzian waves: 10 7 10 9 30 m. = 100 ft. 30 cm. = 1 ft. 16.25 ) 22.90 I 12.3 Limit of electric waves : 6X10 10 0.6 cm. = 0.25 in. 28.55 ) ) First gap : [4.25] Ultra-red rays : 10' 2 4X10' 30,000x10-" =0.03 cm. 76xlO~ 8 cm. 3280 ) ftAQ 41.48 f b>ba Visible light rays : j 7.7X10' 76xlO- 6 cm. 39xlO~ e cm. 41.48 i ft Q7 42.45 ] U where A is a proportionality constant (depending on the physio- logical measure of L) and \ is the minimum perceptible value of illumination or the "threshold value," below which sensation ceases. The minimum value of change of intensity i, which is still just perceptible to the average human eye, is 1.6 per cent. This, then, is the sensitivity limit of the human eye for changes of illumination. Obviously, when approaching the threshold value i , the sensi- tivity of the eye for intensity changes decreases. The result of this law of sensation is that the physiological effect is not proportional to the physical effect, as exerted, for instance, on the photographic plate. The range of intensities permissible on the same photographic plate, therefore, is far more restricted. A variation of illumination within the field of vision of 1 to 1000, as between the ground and the sky, would not be seriously felt by the eye, that is, not give a very great difference in the sensation. On the photographic plate, the brighter portions would show 1000 times more effect than the darker portions and thus give bad halation while the latter are still under exposed. A photographic plate, therefore, requires much smaller variations of intensity in the field of vision than permissible to the eye. In the same man- ner the variations of intensity of the voice, used in speaking, are far beyond the range of impression which the phonograph cylin- der can record, and when speaking into the phonograph a more uniform intensity of the voice is required to produce the record, otherwise the lower portions of the speech are not recorded, while at the louder portions the recording point jumps and the voice breaks in the reproduction. 21. The sensitivity of the eye to radiation obviously changes with the frequency, as it is zero in the ultra-red, and in the ultra- violet where the radiation is not visible and thus gradually increases from zero at the red end of the spectrum to a maximum somewhere near the middle of the spectrum and then decreases again to zero at the violet end of the spectrum; that is, the physi- PHYSIOLOGICAL EFFECTS OF RADIATION. 41 ological effect produced by the same radiation power as one watt of radiating power is a maximum near the middle of the visible spectrum and decreases to zero at the two ends, about as illustrated by the curves in Fig. 21. Inversely, the mechanical equivalent of light, or the power required to produce the same physiological effect as one candle power of light is a maxi- mum near the middle of the spectrum and decreases from there to infinity at the end of the visible range, being infinite RED YELLOW GREEN BLUE VIOLET FIG. 21. in the ultra-red and ultra-violet, where no power of radiation can produce visibility. It thus varies about as indicated in Fig. 22. The mechanical power equivalent of light, thus, is not constant, as the mechanical energy equivalent of heat which is 426 kgm. or 4.25 kile-joule per calorie but is a function of the frequency, that is, of the color of radiation, with a maximum, probably not very far from 0.01 watt per candle power in the middle of the spectrum. When comparing, however, the physiological effects of different frequencies of radiation, that is, different colors of light, the diffi- culty arises that different colored lights cannot be compared photometrically, as all photometers are based on making the illu- mination produced by the two different sources of light equal, and when these sources of light are of different color they can never become equal. As long as the colors are not very different - two different shades of yellow or yellowish white and white the eye can still approximately estimate the equality of intensity and 42 RADIATION, LIGHT, AND ILLUMINATION. thus compare them, though not as accurately as when the two sources of light are of the same color. With very great color differences, as green light and orange light, this is no longer feasible. However, an accurate comparison can still be made on the basis of equal ease in distinguishing objects. As the pur- FIG. 22. pose for which light is used is to distinguish objects, the correct comparison of lights obviously is on the basis of equal distinctness of objects illuminated by them; that is, two lights, regardless whether of the same or of different colors, give the same candle power, that is, the same physiological effect, if they enable us to distinguish objects with the same ease at the same distance. Experience has shown that the sharpest distinction, that is, the greatest accuracy in comparing different lights in this manner, is reached by determining the distance from the source of light at PHYSIOLOGICAL EFFECTS OF RADIATION. 43 which print of moderate size just ceases to be readable. For this purpose the print must be a mixture of letters which do not form intelligible words and the point which can be determined most accurately is where large letters, as capitals, are still readable, while small letters are already unreadable (see p. 174) . Obviously, in comparing different colors of light the object must be colorless, that is, the print be black on white. This method of comparison of the physiological effect, by what has been called the "lumino- meter," is theoretically the most correct, as it is independent of the color of light. It is, however, not as accurate as the compari- son by photometer, and thus the average of a number of observa- tions must be used. The only error which this method leaves is that due to the difference in the sensitivity of different eyes, that is, due to the differences between the sensitivity curves (Fig. 21), and this in most cases seems to be very small. 22. It is found, however, that the sensitivity curve for different colors of radiation is a function of the intensity of radiation; that is, the maximum sensitivity point of the eye is not at a definite frequency or wave length, but varies with the intensity of illumi- nation and shifts more towards the red end of the spectrum for high, towards the violet end of the spectrum for low intensity of illumination, and for illumination of very high intensity the maxi- mum physiological effect takes place in the yellow light, while for very low intensity of illumination it occurs in the bluish green light; that is, at high intensity yellow light requires less power for the same physiological effect than any other color of light, while for low intensity, bluish green light requires less power for the same physiological effect than any other color of light. Thus, if an orange yellow light, as a flame carbon arc, and a bluish green light, as a mercury lamp, appear of the same intensity from the distance of 100 feet, by going nearer to the lamps the orange yellow appears to increase more rapidly in intensity than the bluish green, and from a very short distance the former appears glaring bright, while the latter is disappointing by not showing anywhere near the same apparent intensity. Inversely, when going further and further away from the two lamps the orange yellow light seems to fade out more rapidly than the bluish green, and has practically disappeared while the bluish green is still markedly visible. A mercury lamp, therefore, can be seen from distances from which a much brighter yellow flame arc is practi- 44 RADIATION, LIGHT, AND ILLUMINATION. cally invisible, but inversely, from a very short distance the yellow light appears dazzling, while a mercury lamp of higher candle power appears less bright. Fig. 23 illustrates the change of sensitivity with intensity, by approximate curves of the variation of the relative sensitivity of the average human eye with the intensity i of illumination in v FIG. 23. meter candles (or rather log i) as abscissas, for red light, wave length 65.0; orange yellow light, wave length 59; bluish green light, wave length 50.5; and violet light, wave length 45.0. As seen for red light as well as violet light the two ends of the visible spectrum the sensitivity is low, while for orange yellow as well as bluish green light near the middle of the visible range the sensitivity is high. For bluish green light, however, the sensitivity is high at low and moderate intensities but falls off for high intensities, while for orange yellow light the sensitivity is high at high intensities and falls off at medium and low intensities and ultimately vanishes, that is, becomes invisible at intensities many times higher than those at which green light is still well visible. Red light vanishes from visibility still earlier than orange yel- low light, while violet light remains visible even at very low intensities. The vanishing points of the different colors of light, that is, PHYSIOLOGICAL EFFECTS OF RADIATION. 45 the minimum intensities which can just be perceived are, approxi- mately, at: Color red orange yellow green blue violet Wave length l w = 67 60.5 57.5 50.5 47 . 43 x 10~ fl Meter-candles in- tensity .... i = 0.06 0.0056 0.0029 0.00017 0.00012 0.00012 Relative radiation power po = 10,000 1000 100 1 2 20 That is, the minimum visible amount of green light represents the least amount of power; the minimum visible amount of blue light requires twice as much power as green light; violet light 20 times as much, but yellow light 100 times and red light even 10,000 times as much power as green light at the threshold of visibility. While the intensity of radiation varies inversely proportional to the square of the distance, it follows herefrom that the physio- logical effect of radiation does not vary exactly with the square of the distance, but varies somewhat faster, that is, with a higher power of the distance for orange yellow or the long-wave end of the spectrum, and somewhat slower, that is, with a lesser power of the distance than the square, for bluish green or the short-wave end of the spectrum. This phenomenon is appreciable even when comparing the enclosed alternating carbon arc with the open direct current car- bon arc : by photometer, where a fairly high intensity of illumi- nation is used, the relative intensity of the two arcs is found somewhat different than by luminometer, that is, by reading distances nearer the lower limit of visibility. For low intensities, the alternating arc compares more favorably than for high intensities. It follows, therefore, that in the photometric comparison of illuminants, where appreciable color differences exist, the inten- sity of illumination at which the comparison is made must be given, as it influences the result, or the candle power and the distance of observation stated. 23. Not only the sensitivity maximum is different for low and for high intensity of illumination, but the shape of the sensi- tivity curve also is altered, and for low intensity is more peaked, that is, the sensitivity decreases more rapidly from a maximum towards the ends- of the spectrum than it does for high intensity 46 RADIATION, LIGHT, AND ILLUMINATION. of illumination as indicated by the curves in Fig. 24 which shows approximate sensitivity curves of the average human eye : (a) for every low illumination near the treshold value of visi- bility or 0.001 meter-candles; (b) for medium illumination, 4.6 meter-candles; (c) for very high illumination, 600 meter-candles. lu,*-. 1.65 I = 45.0 1.70 50.0 L t \ \ \ FIG. 24. (1 meter-candle is the illumination produced by 1 candle power of light intensity at 1 meter distance; N meter-candles, thus, the illumination produced by a light source of N candle power at 1 meter distance or of 1 candle power at -= meter distance, etc.). VN As seen, curve (a) ends at wave length /, = 61 X 10~ fl ; that is, for longer waves or orange and red light, 0.001 meter-candles is below the threshold value of visibility, hence is no longer visible. The maximum visibility, that is the sensitivity maximum of the human eye, lies at wave length. Z = 51.1, bluish green for very low intensity, curve (a). Z = 53.7, yellowish green for medium intensity, curve (b). 1 = 56.5, yellow for high intensity, curve (c). The sensitivity maximum varies with the intensity about as shown in Fig. 25; that is, it is constant in the bluish green for low intensities, changes at medium intensities in the range be- tween 0.5 and 50 meter-candles and again remains constant in the yellow for still higher intensities. PHYSIOLOGICAL EFFECTS OF RADIATION. 47 The sensitivity curves, as given in Fig. 24, have the general character of probability curves : where l wo is the wave length at maximum sensitivity and H Q is the sensitivity at this wave length, that is, the maximum sensi- tivity and k s is a constant which is approximately 120 for low, LOG t= - 3 I 2 - 1 * 1 + a 4 3 57 - 0. X)l 0. bi i 1 1 1 ^1 )0 100 ^x ME s ER-C, NDLE '/ ';\ V / / Sr, H=H< * (j*~ i) 2 ^s >c *~- , / [gg S FIG. 25. 62 for high intensities and changes in approximately the same range of intensities in which l wo changes; k s is also plotted in Fig. 25. This effect of the intensity of illumination on the sensitivity of the eye is very important in illuminating engineering as it deter- mines the color shades which are most effective for the particular purpose. For instance, in sending the light to great distances, for signalling, etc., the bluish green of the mercury lamp is best suited, carries farthest, and the yellow flame arc the poorest; the white carbon arc superior to the yellow flame arc, even where the latter is of greater intensity. Inversely, where a big glare of light is desired, as for decorative purposes, for advertising, etc., the yellow flame carbon arc is best suited, the bluish green mer- cury lamp disappointing. Apparent exceptions may exist : for instance, the long waves of the orange yellow penetrate fog better than the short waves of bluish green, and for lighthouses, where the important problem is to reach the greatest possible distance in fog, yellow light, thus, may be superior. In general, however, the bluish green is superior 48 RADIATION, LIGHT, AND ILLUMINATION. in visibility to the orange yellow for long distances, and inversely, the orange yellow is superior for short distances. At the limits of visibility the eye is very many times more sensitive to green light and, in general, high-frequency light, than to orange yellow and, in general, low-frequency light. A necessary result of the higher sensitivity of the eye for green light is the preponderance of green in gas and vapor spectra. As no special reason exists why spectrum lines should appear more frequently at one wave length than at any other and as the radia- tion is most visible in the green, this explains, somewhat, the tendency of most highly efficient illuminants towards a greenish or yellow color (as, for instance, the Welsbach mantel, the Nernst lamp, etc.). Pathological and Other Effects on the Eye. 24. Radiation is a form of energy, and thus, when intercepted and absorbed, disappears as radiation by conversion into another form of energy, usually heat. Thus the light which enters the eye is converted into heat, and if its power is considerable it may be harmful or even destructive, causing inflammation or burns. This harmful effect of excessive radiation is not incident to any particular frequency, but inherent in radiation as a form of energy. It is, therefore, greatest for the same physiological effect, that is, the same amount of visibility, for those frequencies of light which have the lowest visibility or highest power equiva- lent, that is, for the red and the violet and least for the green and the yellow, which for the same amount of visibility represent least power. Hence, green and greenish yellow light are the most harmless, the least irritating to the eye, as they represent the least power. We feel this effect and express it by speaking of the green light as "cold light" and of the red and orange light as "hot" or "warm." The harmful effect of working very much under artificial illumination is largely due to this energy effect, incident to the large amount of orange, red, and especially ultra- red in the radiation of the incandescent bodies used for illumi- nants and thus does not exist with "cold light," as the light of the mercury lamp. Blue and violet light, however, are just as energetic, or "hot," as orange and red light, and the reason that they are usually not recognized as such is that we have no means to produce efficiently PHYSIOLOGICAL EFFECTS OF RADIATION. 49 powerful blue and violet light, and if we could produce it would not be able to use it for illumination, due to the specific effects of this light which will be described in the following. If, in Fig. 26, the curve A represents roughly the mechanical power equivalent of light for average intensity, that is, the power required to produce the same physiological effect or the same candle power, the distribution of power in an incandescent lamp YELLOW GREEN FIG. 26. carbon filament would be somewhat like C. That is, the physio- logical effect falls off somewhat towards the green, as C drops more than A, and almost vanishes in the blue and violet, as C rapidly decreases, while A, the power required to give the same physiological effect, rapidly increases. From the yellow towards the red the physiological effect again decreases somewhat, but 50 RADIATION, LIGHT, AND ILLUMINATION. the radiation still increases towards the ultra-red. Dividing C by A then gives the distribution of the physiological effect, curve C', that is, of visibility, in the incandescent lamp spectrum, show- ing that the color of the light is yellow. Hg gives the distribu- tion of power in the mercury spectrum. It is shown in dotted lines, as the distribution is not continuous, but the power massed at definite points, the spectrum lines of mercury. Hg' then gives the visibility curve by dividing Hg by A. As seen, the ratio of the area of Hg* to Hg, that is, the ratio of the physiological effect to the power, is much less than the ratio of the area of C' to C; that is, the former produces for the same amount of visibility far less heat and thus is safer. 25. Excessive intensity, such as produced at a short-circuiting arc, is harmful to the eye. The human organism has by evolu- tion, by natural selection, developed a protective mechanism against the entrance of radiation of excessive power into the eye : at high intensity of illumination the pupil of the eye contracts and thus reduces the amount of light admitted, and a sudden exposure to excessive radiation causes the eyelids to close. This protective mechanism is automatic; it is, however, responsive mainly to long waves of radiation, to the red and the yellow light, but not to the short waves of green, blue and violet light. The reason for this is apparently that all sources of excessive radia- tion which are found in nature, the sun and the fire, are rich in red and yellow rays, but frequently poor in rays of short wave length, and, therefore, a response to short wave lengths alone would not be sufficient for protection as they might be absent in many intense radiations, while a response to long waves would be sufficient since these are always plentiful in the intense radiations found in nature. It is only of late years that illuminants, as the mercury lamp, which are deficient in the long waves, have been produced, and for these the protective action of the eye, by contracting the pupil, fails. This absence or reduction of the contraction of the pupil of the eye in the light of the mercury lamp is noticed when passing from a room well illuminated by incandescent lamps, to one equally well illuminated by mercury lamps and inversely. When changing from the incandescent light to the mercury light, the illumination given by the latter at first appears dull and inferior as the pupil is still contracted, but gradually gains in intensity as the pupil PHYSIOLOGICAL EFFECTS OF RADIATION. 51 opens; and inversely, coming from the mercury light to the incan- descent light, the latter first appears as a big glare of light, the pupil still being open, but gradually dulls down by the contraction of the pupil. This absence of the automatic protective action of the eye against light deficient in long waves is very important, as it means that exposure to excessive intensity of illumination by mercury light may be harmful, due to the power of the light, against which the eye fails to protect, while the same or even greater power of radiation in yellow light would be harmless, as the eye will pro- tect itself against it. The mercury lamp, therefore, is the safest illuminant, when of that moderate intensity required for good illumination, but becomes harmful when of excessive intensity, as when closely looking at the lamp for considerable time, when operating at excessive current. The possibility of a harmful effect is noticed by the light appearing as glaring. This phe- nomenon explains the contradictory statements occasionally made regarding the physiological effect of such illuminants. 26. Up to and including the green light, no specific effects, that is, effects besides those due to the power of radiation, seem yet to exist. They begin, however, at the wave length of blue light. I show you here a fairly intense blue violet light, that is, light containing only blue and violet radiation. It is derived from a vertical mercury lamp, which is surrounded by two concentric glass cylinders welded together at the bottom. The space be- tween the cylinders is filled with a fairly concentrated solution of potassium permanganate (strong copper nitrate solution or a cupric-ammon salt solution, though not quite so good may also be used) which is opaque to all but the blue and violet radiations. As you see, the light has a very weird and uncanny effect, is extremely irritating: you can see by it as the intensity of illumi- nation is fairly high, but you cannot distinguish everything, and especially the lamp is indefinite and hazy : you see it, but when you look at it it disappears, and thus your eye is constantly try- ing to look at it and still never succeeds, which produces an irritating restlessness. It can well be believed that long exposure to such illumination would result in insanity. The cause of this weird effect which is difficult to describe is that the sensitive spot on the retina, that is, the point on which we focus the image 52 RADIATION, LIGHT, AND ILLUMINATION. of the object which we desire to see, or the fova F in Fig. 19, is blue blind, that is, does not see the blue or violet light. Thus we see the lamp and other objects indistinctly on the outer range of the retina, but what we try to see distinctly disappears when focused on the blue blind spot F. This spot, therefore, is often called the " yellow spot," as we see yellow on it due to the absence of the vision of blue at this particular place of the retina. To produce this effect requires the mercury lamp; most other illuminants do not have sufficient blue and violet rays to give considerable illumination of this color and even if they do, no screen which passes blue and violet is sufficiently opaque to the long waves not to pass enough of them to spoil the effect, if the illuminant is rich in such long waves. The mercury lamp, how- ever, is deficient in these, and thus it is necessary only to blind off the green and yellow rays in order to get the blue and violet light. I show you here a mercury lamp enclosed by a screen consist- ing of a solution of naphtol green (an aniline dye) which transmits only the green light. As you see, in the green the above-described effect does not exist, but the vision is clear, distinct and restful. 27. Beyond the violet the radiation is no longer visible to the eye as light. There is, however, a faint perception of ultra-violet light in the eye, not as distinct light, but rather as an indis- tinct, uncomfortable feeling, some form of dull pain, possibly resulting from fluorescence effects caused by the ultra-violet radiation inside of the eye. With some practice the presence of ultra-violet radiation thus can be noticed by the eye and such light avoided. In the ultra-violet, and possibly to a very slight extent in the violet and even in the blue, a specific harmful effect appears, which probably is of chemical nature, a destruction by chemical dissociation. This effect increases in severity the further we reach into the ultra-violet, and probably becomes a maximum in the range from one to two octaves beyond the violet. These very short ultra-violet rays are extremely destructive to the eye : exposure even to a moderate intensity of them for very few minutes produces a severe and painful inflammation, the after effects of which last for years, and long exposures would probably result in blindness. The chronic effects of this inflam- mation are similar to the effect observed in blue light : inability or difficulty in fixing objects on the sensitive spot F, so that with- out impairment of the vision on the rest of the retina clear dis- PHYSIOLOGICAL EFFECTS OF RADIATION. 53 tinction is impaired and reading becomes difficult or impossible, especially in artificial illumination. It appears as if the sensitive spot F, or the focusing mechanism of the eye, were over-irritated and when used, for instance in reading, becomes very rapidly fatigued and the vision begins to blur. If further irritation by ultra-violet light or by attempting to read, etc., is avoided, gradually the rapidity of fatigue decreases, the vision remains distinct for a longer and longer time before it begins to blur and ultimately becomes normal again. The inflammation of the eye produced by ultra-violet light appears to be different from that caused by exposure to high- power radiation of no specific effect, as the light of a short circuit of a high-power electric system, or an explosion, etc. The main differences are: 1. The effect of high-power radiation (power burn) appears immediately after exposure, while that of ultra-violet radiation (ultra-violet burn) appears from 6 to 18 hours after exposure. 2. The external symptoms of inflammation: redness of the eyes and the face, swelling, copious tears, etc., are pronounced in the power burn, but very moderate or even entirely absent in the ultra-violet burn. 3. Complete recovery from a power burn even in severe cases usually occurs within a few days, leaving no after effects, while recovery from an ultra-violet burn is extremely slow, taking months or years, and some after effects, as abnormal sensitivity to radiation of short wave lengths, may be practically permanent. The general phenomena of a severe power burn are : Temporary blindness immediately after exposure, severe pains in the eyes and the face, redness of eyes and face, swelling, copi- ous tears, etc. These effects increase for a few hours and then decrease, yielding readily to proper treatment: application of ice, cold boric acid solution, etc., and complete recovery occurs within a few days. In chronic cases, as excessive work under artificial illumination, the symptoms appear gradually, but recovery, if no structural changes in the eyes have occurred, is rapid and complete by proper treatment and discontinuance of work under artificial illumination. Most artificial light is given by temperature radiation (incan- descent lamp, gas and kerosene flame), and therefore its radiation 54 RADIATION, LIGHT, AND ILLUMINATION. consists of a very small percentage only of visible light (usually less than 1 per cent), while most of its energy is in the ultra-red and invisible, and for the same amount of visible radiation or light the total radiated power thus is many times greater than with daylight. Regarding chronic " power burn," artificial light, therefore, is much more harmful than daylight, that is, much more energy enters the eye under incandescent illumination than under much more powerful daylight illumination. In a severe ultra-violet burn no immediate symptoms are noticeable, except that the light may appear uncomfortable while looking at it. The onset of the symptoms is from 6 to 18 hours later, that is, usually during the night following the ex- posure, by severe deep-seated pains in the eyes; the external appearance of inflammation is moderate or absent, the vision is not impaired, but distinction made difficult by the inability to focus the eye on any object. The pains in the eyes and head- ache yield very slowly; for weeks and even months any attempt of the patient to use the eyes for reading, or otherwise sharply distinguishing objects, leads to blurring of the vision; the letters of the print seem to run around and the eye cannot hold on to them, and severe headache and deep-seated pains in the eyes follow such attempt. Gradually these effects become less; after some months reading for a moderate length of time during daylight is possible, but when continued too long, or in poor light, as in artificial illumination, leads to blurring of the vision and head or eye ache. Practically complete recovery occurs only after some years, and even then some care is necessary, as any very severe and extended strain on the eyes temporarily brings back the symptoms. Especially is this the case when looking at a light of short wave length, as the mercury arc; that is, there remains an abnormal sensitivity of the eye to light of short wave lengths, even such light which to the normal eye is perfectly harmless, as the mercury lamp. In chronic cases of ultra-violet burn, which may occur when working on unprotected arcs, and especially spark discharges (as in wireless telegraphy), the first symptoms are: occasional headaches, located back of the eyes, that is, pains which may be characterized either as headache or as deep-seated eye ache. These recur with increasing frequency and severity. At the same time the blurring of the vision begins to be noticeable PHYSIOLOGICAL EFFECTS OF RADIATION. 55 and the patient finds it more and more difficult to keep the eye focused for any length of time on objects, as the print when read- ing. These symptoms increase m severity until the patient is obliged to give up the occupation which exposed him to ultra- violet light, and then gradual recovery occurs, as described above, if the damage has not progressed too far. In mild cases recovery from power burns may occur in a few hours and complete recovery from mild ultra-violet burns in a few weeks. Both types of burn may occasionally occur simultaneously and their symptoms then successively. For instance, in a case of an exposure while working for about half an hour with a flame-carbon arc without enclosing glass globe (such an arc contains large amounts of high-power radia- tion, of yellow and orange color, but also a considerable amount of ultra-violet rays), the symptoms of the power burn increased in severity for a few hours, and then rapidly vanished by the application of cold water, and recovery was practically complete six hours after exposure; then some hours later, in the middle of the night, the patient was awakened by severe pains in the eyes, the symptoms of the ultra-violet burn, and had to seek medical attendance. Under proper treatment recovery occurred in a few days, but the blurring of the vision was appreciable for some days longer, and the sensitivity to high-frequency light for some weeks. 28. Arcs produce considerable amount of ultra-violet light,* and in former experiments we have used a high frequency iron arc for producing ultra-violet light and also have seen that even a very thin sheet of glass is opaque for these radiations. For very long ultra-violet rays, that is, the range close to the visible violet, glass is not quite opaque, but becomes perfectly opaque for about one-quarter to one-half octave beyond the violet, and in this first quarter of an octave the harmful effect of the ultra-violet radia- tion is still very small and becomes serious only when approach- ing a distance of about one octave from the visible end of the violet. Clear transparent glass thus offers a practically complete protection against the harmful effects of ultra-violet light, except when the latter is of excessive intensity, and thus arcs enclosed * An arc between silicon terminals emits especially powerful ultra-violet radiation accompanied by little visible light. 56 RADIATION, LIGHT, AND ILLUMINATION. by glass globes are harmless. It is, however, not safe to look into and work in the light of open metal arcs for too long a time. The carbon arc gives the least ultra-violet rays, so little that even without enclosure by glass it is fairly safe; metal arcs give more and the mercury arc gives the greatest amount and reaches to the farthest distance beyond the visible, and these very destruc- tive very short ultra-violet rays have so far only been observed in the radiation of a low temperature mercury arc in a quartz tube : quartz being transparent to these rays while glass is opaque. The high temperature mercury arc in a quartz tube, that is, arc operated near atmospheric pressure as it is used to some extent for illumination, especially abroad, seems to be much less dan- gerous than the low temperature or vacuum arc, but it also requires a protecting glass globe. In general, no metal arc, spark discharge, or glow discharge should ever be used industrially or otherwise without being en- closed by a glass globe, preferably of lead glass, if located so that it may be looked at. Those experimenting with arcs or other electric discharges should always protect their eyes by the inter- position of a glass plate. Thus the sparks of wireless telegraph stations, the discharges of ozonizers, the arcs of nitric acid generators, electric furnaces, etc., may be dangerous without glass enclosure. While artificial illuminants, and especially metal arcs, give an appreciable amount of ultra-violet light, these ultra-violet rays extend only to about one-quarter octave beyond the visible violet and if, as is always the case, the illuminant is enclosed by glass, the harmful effect of these long ultra-violet rays is negli- gible. The radiation of the sun also contains ultra-violet rays, and a larger percentage compared with the total radiation than any glass-enclosed artificial illuminant, and as the light of the sun, that is, daylight, is recognized as perfectly harmless, as far as this specific destructive action is concerned, the same applies to the artificial illuminants, as they contain less ultra-violet rays than the light of the sun. This specific destructive action on the eye of short ultra-violet radiation extends beyond the blank space in the spectrum of radiation (Fig. 14) and still exists, though possibly to a lesser extent, in the X-rays. PHYSIOLOGICAL EFFECTS OF RADIATION. 57 Pathological and Therapeutic Effects of Radiation. 29. Radiation impinging on the tissue of the human body or other living organisms exerts an influence depending on intensity, power and frequency. The effect on the eye has been discussed in the preceding paragraphs. The specific chemical effect in supplying the energy of plant life will be more fully discussed in the following under chemical effects. As is to be expected, the effect of radiation on the living protoplasm of the cells is stimulating if of moderate intensity, destructive if of excessive intensity; that is, by the energy of the radiation the motions of the parts of the protoplasm-molecule are in- creased, and, if the intensity of radiation is too high, the mole- cule thus is torn asunder, that is, destroyed, the living cell killed and inflammation and necrosis (mortification) result. If the intensity is moderate, merely an increase of the rapidity of the chemical changes in the protoplasm, which we call life, results; that is, the radiation exerts a stimulating effect, in- creasing the intensity of life, causing an increased renewal of worn-out tissue and reconstruction, and thus is beneficial or curative, especially where the metabolism is sluggish. Just as in the action on the eye, two different effects probably exist : a general effect due to the energy of the radiation which with sunlight is a maximum beyond the visible close to the red end of the spectrum, and with most artificial illuminants (those based on incandescence) reaches a maximum still further in the ultra-red and a specific effect depending on the frequency. The power effect is general and probably fairly uniform throughout the exposed tissue, appears simultaneous with or immediately after the exposure, and thus practically no danger of harmful results from destruction of tissue exists, as excessive intensity makes itself felt immediately, before far-going destruc- tion of tissue can occur, and, therefore, the only possible danger which could exist would be in the indirect effect of stimulation on other organs of the body, as the heart. Thus the use of in- candescent light as stimulant appears fairly harmless. Different is the specific action of high-frequency radiation. This occurs only some time after exposure, from a few hours to several weeks (with X-rays) . As these higher frequencies are not felt by the body as such and exert a powerful action even at such 58 RADIATION, LIGHT, AND ILLUMINATION. low intensities that their energy is not felt as heat, and, further- more, . the susceptibility of different people may be different, there is nothing to guard against excessive and thereby harmful exposure. Furthermore, the damage is far more severe and lasting than with the power effect, and fatal cases have occurred years after exposure. Possibly, as may be expected from selective action, only a few cells in the living tissue are killed by the radiation, and the disintegration products of these dead cells then gradually involve the surrounding living cells, causing their destruction or degeneration, so that the harm is far out of proportion with the immediate destructive effect of the radia- tion proper, especially with penetrating forms of radiation, as X-rays and radium rays, in which the lesions are correspondingly deep-seated. High-frequency radiation (violet, ultra-violet, X-ray) should therefore be used only under the direction of experts fully familiar with their physiological action and danger. The specific action of high-frequency radiation is still absent in the green, begins slightly in the blue and violet, increases into the ultra-violet and persists up to the highest frequencies of the X-rays. It is shared also by the radiation of the radio-active substances, as the alpha and beta rays of radium. While the maximum of this effect probably also lies in the ultra-violet, from one to two octaves beyond the visible spectrum, the effect is profoundly modified by the transparency or opacity of the tissue for different frequencies, and the character of the stimu- lating and pathological effects greatly depends on the depth to which the radiation penetrates the body. The largest part of the organism is water. Water is trans- parent for visible light, becomes more and more opaque in the ultra-red as well as in the ultra-violet, and is again fairly trans- parent for X-rays. Blood is fairly transparent for the long visible rays of red and yellow, but nearly opaque for the shorter violet and ultra-violet rays. Hence next to the X-rays which can pass through the body, the longest visible rays of red and yellow penetrate relatively deepest into the body, though even they are practically absorbed within a short distance from the surface. Thus while the energy maximum of the sunlight is in the ultra-red, the maximum physiological effect probably is that of the red and yellow rays : the same which are the active PHYSIOLOGICAL EFFECTS OF RADIATION. 59 rays in plant life. The violet and ultra-violet rays are absorbed close to the surface of the body by the blood, which is opaque for them. They can thus be made to penetrate deeper as is done in their therapeutic use by freeing the tissue of the body from blood by compression or other means. Even then, how- ever, probably only the longest ultra-violet rays penetrate, the very short ones being kept out by the opaque character of the water in the tissue. The penetration of the radiation of the sunlight into the human body is very greatly reduced by acclimatization, which leads to the formation of a protective layer or pigment, more or less opaque to the light. Such acclimatization may be permanent or temporary. Permanent acclimatization has been evolved during ages by those races which developed in tropical regions, as the negroes. They are protected by a black pigment under the skin, and thereby can stand intensities of solar radiation which would be fatal to white men. A temporary acclimatiza- tion results from intermittent exposure to sunlight for gradually increasing periods : tanning, and enables the protected to stand without harmful effects exposure to sunlight which would pro- duce severe sunburn in the unprotected. This acquired protec- tion mostly wears off in a few weeks, but some traces remain even after years. A slight protection by pigmentation also exists in white men, and its differences lead to the observed great differences in sensi- tivity to solar radiation: blondes, who usually have very light pigmentation, are more susceptible to sunburn and sunstroke than the more highly pigmented brunette people. In sunburn we probably have two separate effects super- imposed upon the other: that due to the energy of the solar radiation and the specific effect of the high frequencies, which to a small extent are contained in the sunlight. The two effects are probably somewhat different, and the high-frequency effect tends more to cause inflammation of the tissue, while the energy effect tends towards the production of pigmentation (tanning), and the symptoms of sunburn thus vary with the different pro- portions of energy radiation and of high-frequency radiation as depending on altitude, humidity of the air, the season, etc. 30. The action of radiation on living organisms is stimulating if of moderate intensity, destructive if of high intensity. Thus 60 RADIATION, LIGHT, AND ILLUMINATION. it is analogous with that of any other powerful agent or drug, as alcohol, caffeine, etc. The intensity of light which is destruc- tive to life largely depends on the amount of light to which the organism is accustomed. Those organisms which live in the dark may be killed by an amount of light which is necessary for the life of other organisms. Amongst the saprophytic bacilli, for instance (the germs of putrefaction), many species live in the light, and die, or at least do not multiply, if brought into the dark, while other putrefactive bacilli live in the dark and are killed by light. The latter also is the case with the pathogenic bacilli, that is, the disease germs, as the bacillus of tuberculosis, cholera, etc. As these live in the dark, the interior of the body, they are rapidly killed by light. Light, and radiation in general, therefore is one of the most powerful germicides and disinfect- ants. One of the most effective prophylactic measures, espe- cially against the diseases of civilization, as tuberculosis, etc., thus is to flood our homes with light, especially direct sunlight, while our habit of keeping the light out of our houses by curtains, shades, etc., closing our residences almost light-tight, when leaving them for some time, converts them into breeding places of disease germs, and then we wonder about mortality. Obviously excessive light intensity ultimately becomes harm- ful even to the human organism, and it is therefore advisable to protect ourselves against the light when it becomes annoying by its intensity. It has even been claimed that the impossibility of white men to become permanently acclimatized in the tropics and the change in the temperament of the population of our country within a few generations from their immigration: the increased nervousness, restlessness and "strenuousness," are the result of the greater intensity of the sunlight, especially its high-frequency radiation, compared with the more cloudy climate of our original European home. Whether this is the case remains to be further investigated. It is hard to believe, however, that such a profound effect should result from the exposure of a small part of the body, face and hands, to a more intense light, and the failure of acclimatization in the tropics could well be explained by the higher temperature and its damag- ing effect, while the change from Europe to America is not merely a change from a more cloudy to a more sunny climate, but from a maritime climate, that is, climate having fairly uniform PHYSIOLOGICAL EFFECTS OF RADIATION. 61 and slowly changing temperatures, to a continental climate, with its rapid changes of temperature and enormous temperature extremes, and the difference between continental and maritime climate may be suspected as the cause in the change of the tem- perament of the races. As men have lived for ages in the light, the cells of the human body are far more resisting to the light than the disease germs, which for ages have lived in the dark; and light, and more particularly the high-frequency violet and ultra-violet radiation and the X-rays, thus have found a useful therapeutic application in killing disease germs in the human body. Thus, by expos- ing the diseased tissue to high-frequency radiation, the disease germs are killed, or so far damaged that the body can destroy them, while the cells of the body are still unharmed, but stimu- lated to greater activity in combating the disease germs. As seen, for this purpose the radiation must be of sufficient intensity and duration to kill or damage the bacilli, but not so intense as to harm the cells of the body. Surface infections, as tubercu- losis of the skin (scrofulosis, lupus), thus are effectively and rapidly cured by high-frequency light. More difficult and less certain the effect is if the infection is deeper seated, as then the radiation must penetrate a greater thickness of tissue to reach the bacilli, and is thereby largely absorbed, and the danger thus exists that, before a sufficient intensity of radiation can be brought to the seat of the infection, the intensity at the surface of the tissue may become harmful to the cells of the body. In this case the more penetrating X-rays would be more applicable, as they can penetrate to any depth into the body. They are, however, so far distant in frequency from the light radiation, that the acclimatization of the body to the light radiation probably exists only to a lesser extent against the X-rays; that is, the difference in the destructive effect on the bacilli and on the cells of the body, on which the curative effect is based, prob- ably is less with the X-rays than with the long ultra-violet waves. Since Dr. Finsen introduced phototherapy and radiotherapy, about fifteen years ago, it thus has found a very extended and useful field, within its limitation. This greater destructive action of radiation on micro-organisms than on the cells of the human body, extends not merely to the pathogenic bacilli, but to all organisms living in the dark. 62 RADIATION, LIGHT, AND ILLUMINATION. Thus the spermatozoa which biologically are independent living organisms seem to be killed by X-rays before any damage is done to the body, and permanent sterility then results. Amongst the cells of the body differences seem to exist in their resistivity. It is claimed, for instance, that the sensory- nerves are first paralyzed by violet radiation and that intense violet light can thus be used to produce local anaesthesia, suf- ficient for minor operations. Occasionally the effect of light may be harmful in the relation of the human body to invading bacilli. In some eruptive in- fections, as smallpox, ulceration of the skin (leading to mark- ing) seems to be avoided if the patient is kept from the light, and the course of the disease mitigated. As red light, however, seems to have no effect, instead of perfect exclusion of light, which is not very feasible, the use of red light thus seems to offer an essential advantage. LECTURE IV. CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. Chemical Effects. 31. Where intense radiation is intercepted by a body chemical action may result by the heat energy into which the radiation is converted. This, however, is not a direct chemical effect of radiation but an indirect effect, resulting from the energy of the radiation. Direct chemical effects of radiation are frequent. It is such an effect on which photography is based : the dissociating action of radiation on silver salts, the chloride in ordinary photographic paper, the bromide and iodide in the negative plate and the quick printing papers. This chemical action is greatest in the violet and ultra-violet and decreases with increasing wave length, hence is less in the green, small in the yellow, and almost absent in the red and ultra-red, so that the short waves, blue, violet and ultra-violet, have sometimes been called " chemical rays." This, however, is a misnomer, just as the term "heat rays" sometimes applied to red and ultra-red rays. In so far as when intercepted they are converted into heat, all rays are heat rays, but neither the ultra-red nor any other radiation is heat, but it may become heat when it ceases to be radiation. Thus all radiations are chemical rays, that is, produce chemical action, if they strike a body which is responsive to them. The chemical action of radiation is specific to its frequency and seems to be some kind of a resonance effect. We may picture to ourselves that the frequency of vibration of a silver atom is that of violet or ultra-violet light, and therefore, when struck by a wave of this frequency, is set in vibration by resonance, just as a tuning fork is set in vibration by a sound wave of the frequency with which it can vibrate, and if the vibration of the silver atom, in response to the frequency of radiation, becomes sufficiently intense, it breaks away from the atom with which it is chemically 64 RADIATION, LIGHT, AND ILLUMINATION. combined in the compound, the silver bromide, etc., and this compound thus splits up, dissociates. The phenomenon, how- ever, must be more complex, as a simple resonance vibration would be especially pronounced at one definite frequency, the frequency of complete resonance, and rapidly decrease for higher and for lower frequencies. The chemical action of radiation on silver compounds, however, does not show such a response to any definite frequency, but, while strongest in the ultra-violet, ex- tends over the entire range from the frequency of green light beyond the ultra-violet and up to the highest frequencies of X-rays. That the chemical activity of radiation is some form of resonance, is, however, made very probable by the relation which exists between the active frequency range and the weight of the atom or molecule which responds to the radiation. Thus, while the fairly heavy silver atom (atomic weight 108) responds to rays near the violet end of the visible spectrum, the much lighter oxygen atom (atomic weight 16) responds only to much higher frequencies, to those of the physiologically most destructive rays, about one to two octaves beyond the visible spectrum. These very short radiations energetically produce ozone 3 ,from oxygen 2 , probably by dissociating oxygen molecules 2 ,into free atoms, and these free atoms then join existing molecules: + 2 = 3 , thus forming ozone. Possibly their destructive physiological action is due to this ability to cause resonance with the oxygen atom and thereby destroy molecular structures. 32. Response to the long waves of red and ultra-red light thus may be expected from atoms or groups of atoms which are very much heavier than the silver atom, and this indeed seems to be the case in the action of radiation on the life of the plants. There the response is not by atoms, but by the much heavier groups of atoms, radicals of carbon compounds, which separate and recom- bine in response to radiations and thus produce in vegetable organisms the metabolism which we call life. The action of radiation on plant life thus seems to be a chemi- cal action, and this would be the most important chemical action, as on it depends the life of the vegetation and thereby also the existence of animal life and, thus, our own. This action by which the vegetation converts the energy of radiation into chemical energy is related to the presence of chlorophyl, a green body which exhibits a red fluorescence. I show you here a solution CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. 65 thereof in alcohol. This use of the energy of radiation occurs only in those parts of the plant in which chlorophyl is present, usually shown by its green color, that is, in the leaves and young stems. In those plants in which the leaves have lost their chloro- phyl in taking up other functions as the function of protection against attack by conversion into spines in the cacti the stems and trunks have acquired the function of energy supply from radiation, and show the green color of chlorophyl. When the leaves die in the fall their chlorophyl disappears and they change to yellow or red color. Those parts of the plants which contain chlorophyl, mainly the leaves, take carbon dioxide (C0 2 ) from the air through breathing openings (stomata), absorb the radia- tion, and convert its energy into chemical energy, and use this energy in splitting up or dissociating the C0 2 , exhausting the oxygen 2 and using the carbon in producing the complex carbon compounds of their structure: fiber (cellulose), starch, proto- plasm, etc. The energy of plant life thus is derived from radia- tion and their work is constructive or synthetic, that is, they produce complex chemical compounds from simple ones: the carbon dioxide of the air, the nitrates and phosphates of the soil, etc. Inversely, the animal organism is analytic, it converts the chemical energy of complex compounds into mechanical and heat energy by splitting them into simpler compounds, burning them in the lungs or gills. For the supply of mechanical energy which maintains the life, the animal organism thus depends upon the synthetic work of the vegetation by consuming as food the complex compounds constructed by the plants from the energy of radiation, either directly (vegetarians), or indirectly, by eating other animals, which in their turn live on the vegetation. Thus, while the plants take in from the air carbon dioxide C0 2 , exhaust the oxygen 2 , and convert the C into complex compounds, the animal takes in oxygen 2 , by it burns up the complex carbon compounds derived from the plants, and exhausts C0 2 as product of combustion, but in its ultimate result, all life on the earth de- pends for its energy on radiation, which is made available in the plants by conversion to chemical energy and used as such by the animals. The radiations which supply the energy of plant life, probably are the long waves of yellow, red and ultra-red light, while the short waves of blue, violet and ultra-violet cannot be used by the 66 RADIATION, LIGHT, AND ILLUMINATION. plant, but are harmful, kill the vegetation. This can easily be understood : to the long waves of red and yellow light the atoms do not respond, but only the much heavier groups of atoms or car- bon radicals, and these thus separate and recombine and thereby constitute what we call life. To very short waves, that is, high frequencies, these heavy groups of atoms cannot respond, but single atoms would respond thereto and thus by their separation break up and destroy the atomic groups. That is, the resonant dissociation produced by low frequency of radiation extends only to the groups of atoms and thereby results in their separation and recombination to heavier molecules : life, while the resonant dis- sociation produced by high frequencies extends to the atom and thereby splits up and destroys the molecules of the living organ- ism, that is, death. Therefore the short waves of radiation, green, blue, etc., which are more or less harmful to plants, are not used but are reflected by the chlorophyl; hence the green color. To some extent violet radiation is absorbed by chloro- phyl, but it is questionable whether the energy of violet light directly contributes to the chemical action, and it is rather probable that the violet radiation is converted into red light by fluorescence chlorophyl fluoresces red and used as red light. Excessive violet radiation seems to be harmful. Physical Effects. 33. Some of the most interesting physical effects of radiation are those by which it is converted into another form of radiation : fluorescence and phosphorescence. Many substances have the property of converting some of the radiation which is absorbed by them into radiation of a different wave length, that is, act as frequency converter of radiation, fluorescence. Many bodies when exposed to radiation store some of the energy of radiation in such a manner as to give it out again afterwards and thus, after exposure to light, glow in the darkness with gradually decreasing intensity, phosphorescence. These phenomena probably belong to the least understood effects of radiation. They are very common, but phosphorescence usually lasts such a short time that it can be observed only by special apparatus, although a few bodies continue to phos- phoresce for hours and even days. Fluorescence also is usually CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. 67 so weak as to escape notice, although in a few bodies it is very strong. The change of frequency in fluorescence always seems to be a lowering of the frequency, that is, an increase of wave length, and in phosphorescence also the light given out seems always to be of lower frequency than the light absorbed and indeed, fluores- cence and phosphorescence seem to be essentially the same phenomenon, radiation is absorbed and its energy given out again as radiation of lower frequency and that part of the returned radiation which appears during the absorption we call fluores- cence, that part which appears later, phosphorescence. There is, however, frequently a change of the color of the light between fluorescence and phosphorescence and also between phosphores- cence immediately after exposure to light and some time after- wards. For instance, some calcite (calcium carbonate or lime- stone) fluoresces crimson, but phosphoresces dark red. The phosphorescence of calcium sulphide changes from blue in the beginning to nearly white some time after, etc. Due to the change of frequency to longer waves the longest visible rays, red, orange and yellow, produce no fluorescence or very little thereof, as their fluorescent and phosphorescent radia- tion would usually be beyond the red, in the invisible ultra-red. Blue, violet and ultra-violet light produce the most intense effects, as a lowering in frequency of these radiations brings them well within the visible range. Ultra-violet light is best suited for studying fluorescence as it is not visible, and thus only the fluorescent light is visible; white light, for instance, does not show the same marked effect, since the direct white light is superimposed upon the light of fluorescence. Most brilliant effects, however, are produced by using a source of light which is deficient in the frequencies given by fluorescence and then looking at the fluorescent body through a glass having the same color as that given by fluorescence. Thus the least traces of red fluorescence can be discovered by looking at the body through a red glass, in the illumination given by the mer- cury lamp. As the mercury lamp contains practically no red rays, seen through a red glass everything appears nearly black or invisible except red fluorescent bodies, which appear self-lumi- nous, glowing in a light of their own, and appear like red hot bodies. 68 RADIATION, LIGHT, AND ILLUMINATION. In the illumination given by the mercury lamp I here drop a few drops of a solution of rhodamine 6 G, rhodamine R and uranine (aniline dyes) into a large beaker of water. As you see, when sinking down and gradually spreading, they appear especially against a dark background as brilliant luminous clouds of orange, red and green, and seen through a red glass they appear like clouds of fire. I change to the illumination given by the incandescent lamp and all the brilliancy disappears, fluorescence ceases and we have a dull red colored solution. I show you here the sample card of a silk store of different colored silks. Looking at it through a red glass, in the mercury light all disappear except a few, which you can pick out by their lumi- nosity: they are different colors, pinks, reds, heliotrope, etc., but all containing the same red fluorescent aniline dye, rhodamine. A glass plate coated with a thick layer of transparent varnish, colored by rhodamine, appears like a sheet of red hot iron in the mercury light, especially through a red glass, while in the light of the incandescent lamp it loses all its brilliancy. This solution of rhodamine 6 G in alcohol, fluoresces a glaring orange in the mercury light, in the light of a carbon arc lamp (or in daylight) it fluoresces green and less brilliant. Thus you see that the color of the fluorescent light is not always the same, but depends to some extent on the frequency of radiation which causes the fluorescence. Here I have a sheet of paper covered with calcium sulphide and a lump of willemite (zinc silicate) and some pieces of calcite. As you see, none of them show any appreciable fluorescence in the mercury light. But if I turn off the mercury light, the calcium sulphide phosphoresces brightly in a blue glow, the others do not. Now I show you all three under the ultra-violet rays of the condenser discharge between iron terminals, or ultra-violet lamp (Fig. 11) and you see all three fluoresce brilliantly, in blue, green and red. Turning off the light all three continue to glow with about the same color, that is, phosphoresce, but the red fluorescence of the calcite very rapidly decreases, the green glow of the willemite a little slower, but the blue glow of the calcium sulphide screen persists, decreasing very little. I now hold my hand back of it and close to it and you see the picture of the hand appear on the screen by an increase of the luminosity where by contact with the hand the temperature of the screen was slightly CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. 69 raised, thus showing the effect of the temperature rise in increas- ing phosphorescence. These substances which I show you, calcium sulphide, cal- cium carbonate (calcite), zinc silicate (willemite), are not fluo- rescent or phosphorescent themselves, but their luminescence is due to a small percentage of some impurities contained in them. Chemically pure substances and concentrated solutions of the aniline dyes, or these dyes in their solid form, do not show the luminescence, but only when in very diluted solutions; that is, luminescence as fluorescence and phosphorescence seems to be the property of very diluted solutions of some substances in others. Thus a sheet of paper or cardboard colored red by rhodamine does not fluoresce, but if a small quantity of rhoda- mine is added to some transparent varnish and the paper colored red by a heavy layer of this varnish it fluoresces brightly red. To show you the fluorescent spectrum, I have here a mercury lamp surrounded by a very diluted solution of rhodamine 6 G, and some rhodamine R, contained between two concentric glass cylinders. As you see, through the spectroscope a broad band appears in the red and the green light has faded considerably. You also notice that the light of this lamp, while still different from white light, does not give anything like the ghastly effect of human faces, as the plain mercury lamp, but contains considerable red rays, though not yet enough. I also show you a mercury lamp surrounded by a screen of a very dilute solution of uranine: you see, its light is bright greenish yellow, but much less ghastly than the plain mercury light and the spectroscope shows the mercury lines on a fluorescent spectrum, which extends as a con- tinuous luminous band from the green to and beyond the red. You also see that with this uranine screen the mercury lamp gives more light than without it : considerable of its ultra-violet and violet light is converted to yellow and thereby made visible or more effective. 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, T l = absolute temperature of the radia- tor and T 2 = absolute temperature of the surrounding objects on which the radiation impinges : the total power radiated by the body is (Stefan's Law) : P r = kA (TV - ?V), (1) where for a black body, as the carbon filament with P r given in watts per square cm. k is of the magnitude k = 5 X 1(T 12 ; (2) !T 2 is usually atmospheric temperature or about 300 degrees abs. If T l does not differ much from T v 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 : P r = kA (T, - T 2 ) (TV + T*T 2 + 7\7y + 7y); or, approximately, P r = 4 kAT* (T, - T), (3) where T is the room temperature (T l 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, P r , 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 fc t = 25 X 10~ 12 to 50 X 10~ 12 . As soon, however, as the temperature rise (T l 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, T v is very much greater than the surrounding temperature T 2 , T 2 4 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 P r 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 1273 4 to 2273 4 , 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 l w the wave length of radiation, the power radiated at wave length /, and temperature T 1 by normal temperature radiation is : b P (IJ = c,Al w % ^ , (Wien's law) ; or ' r i. * r 1 P (U = c,Al w 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 l w from to oo , gives the total radiation : P- f P (lw)dl w = 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 l w = lm given by: dP (l w ) ~Ji = > dl w which gives: l m T =- = 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 k Q of black body radiations : k = bk Q . 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 = bk = (1 - a) fc c , 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 A l receives as much radiation from element A 2 as ele- ment A 2 receives from A r Of the radiation received by a surface element A l by the radia- tion law, that part which exists in the radiation produced by A 1 is absorbed, that part which does not exist in the temperature radiation of A v is reflected, and the total radiation issuing from A x , 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 M l and M 2 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 S 2 below S l with a single opening, we can by it cut out a single green color, and by moving the shutter S 2 bring this to coincidence in shade with the resultant color of shutter S v and the position of the shutter S 2 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. LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, represented by the conversion of the radiation absorbed by a body into radiation of a different wave length. Usually luminescence at ordinary temperature, or at moderate temperatures, that is, temperatures below incandescence, is called fluorescence or phosphorescence. Fluorescence and Phosphorescence. Fluorescence is the production of radiation from the energy supplied to and absorbed by the fluorescent body, while phos- phorescence is the production of radiation from the energy stored in the phosphorescent body. This energy may be derived from internal changes in the body, as slow combustion, or may have been received by the body at some previous time as by exposure to light a calcium sulphide screen absorbs the energy of incident radiation, stores it in some form, and afterwards radiates it. Fluorescence and phosphorescence usually occur simulta- neously : the energy supplied to such a luminescent body brings about certain changes in the body as vibrations of the atoms, or whatever it may be which cause the body to send out radia- tion. As long as this energy is supplied, the radiation of the body continues, that is, it fluoresces. The changes in the body which make it luminesce, represent energy storage the kinetic energy of the luminescent vibration, etc. and when the energy supply to the body ceases, the radiation issuing from the body does not instantly cease, but continues, with gradually decreasing intensity, until the stored energy is dissipated : the body phos- 94 LUMINESCENCE. 95 phoresces. Inversely, fluorescent radiation probably does not appear instantly at full intensity, as energy has first to be stored. The persistence of the luminescence after the power supply has stopped, as phosphorescence, is very short, except with a few substances, where it lasts for days. Where the energy of phos- phorescent radiation is supplied by the energy of chemical change in the body as with yellow phosphorus obviously the phosphorescence persists as long as these chemical changes can occur. The different forms of luminescence may be distinguished by the character of the energy which is converted into radiation. The conversion of radiation energy into radiation of different wave length, either immediately, or after storage in the body, thus may be called radio-fluorescence and radio-phosphorescence. It was discussed in Lecture II. The same bodies, exposed to an electric discharge in a vacuum (Geissler tube or Crooke tube) show electro-luminescence, fluores- cence as well as phosphorescence, and usually with the same color as in radio-luminescence. Thermo-luminescence is exhibited by some materials, as the violet colored crystals of fluorite (CaFl 2 ), which, when slightly warmed, luminesce it is this which gave the name "fluores- cence" to the phenomenon. Some solutions, when crystallizing, show light during the formation of crystals, and thus may be said to exhibit a physical phosphorescence. Chemical phosphorescence is exhibited by yellow phosphorus and its solutions, which in the air glow by slow combustion, at ordinary atmospheric temperature. As the ignition point of phosphorus, that is, the temperature where it spontaneously ignites, is little above atmospheric temperature, the chemical phos- phorescence of phosphorus occurs at temperatures a few degrees below ignition; it ceases, however, at very low temperature. The chemical luminescence, as shown by phosphorus, is not an exceptional phenomenon, but many substances exhibit chemi- cal phosphorescence at temperatures a few degrees below their ignition temperature, as the result of slow combustion. With those substances which have an ignition point above incandes- cence, this cannot be observed, but it is observed, for instance, in carbon bisulphide, CS 2 , which ignites spontaneously at about 96 RADIATION, LIGHT, AND ILLUMINATION. 180 deg. cent., and a few degrees below this temperature phos- phoresces in air, by slow combustion. A biological phosphorescence is shown by many forms of life: some bacilli of putrefaction phosphoresce, and are the cause of the faint glow occasionally observed in decaying food, especi- ally fishes. Amongst insects, numerous sea animals of dif- ferent classes, especially deep-sea animals, phosphorescence is frequently met, but its origin, that is, the mechanism of light production by the firefly, etc., is still unknown. When splitting a sheet of mica, or shaking a well-exhausted tube containing mercury, flashes of light are seen in the darkness. This, however, is not real phosphorescence but due to electrostatic flashes of frictional electricity. The light given by fluorescence and phosphorescence of solids or liquids, gives a continuous spectrum, that is, is a mixture of all frequencies, just as is the case with temperature radiation; it differs, however, from temperature radiation by the distribu- tion of the energy in the spectrum, which is more or less charac- teristic of the luminescent body, and to some extent, also, of the method of exciting the luminescence. Thus crystalline calcium tungstate, W0 4 Ca, fluoresces white in the X-ray, light blue with ultra-violet light; the aniline dye, rhodamine, 6 G, in alcoholic solution fluoresces green in daylight, crimson in the light of the mercury lamp; willemite (calcium silicate) shows a maximum fluorescent radiation in the green, some chalcites in the red, etc. So far, fluorescence and phosphorescence nave not yet found any extended industrial application. 44. Some of the characteristic forms of luminescence at higher temperatures are pyro-luminescence, chemical-luminescence, and electro-luminescence. As pyro-luminescence or heat-luminescence, must be considered all radiation, produced by heat, which exceeds at some wave length the intensity of the black body radiation at the same temperature. Whether real pyro-luminescence exists, is uncertain, but by an extension of the definition any colored temperature radiation may be considered as heat luminescence of a grey body of an albedo which as normal temperature radiation would give the same total radiation at the same temperature as the colored radiator. Heat luminescence has been discussed already under colored radiation. LUMINESCENCE. 1 97 Chemical Luminescence. Whenever intense chemical changes take place at higher tem- perature, luminescence frequently occurs. I have here an ordi- nary, non-luminous bunsen flame. I dip a platinum wire into a solution of lithium chloride, LiCl, and then hold it into the lower edge of the flame: the flame colors a bright red, and through the spectroscope you see a bright deep red line and a less bright orange line, the spectrum of Li. After a little while, the color- ing disappears by the LiCl evaporating from the wire, and the flame again becomes non-luminous. I repeat the same experi- ment, but dip the platinum wire into sodium chloride, NaCl, solution, and you see the flame colored brightly yellow, and the spectroscope shows one yellow line, the sodium line D. Dipping the platinum wire into thallium chloride, T1C1, I color the flame a bright deep green, the characteristic Tl spectrum, which has one bright green line. As you see, the green coloring disappears more rapidly than the yellow did, and the flame turns yellow; the Tl salt is more volatile than the sodium salt, evaporates more rapidly, and as it contains some Na as impurity, the latter be- comes visible as yellow flame coloring after the Tl has evap- orated. In the bunsen flame these salts are evaporated, split up into their elements by the flame gases, and recombine, and by these chemical changes the atoms of Li, Na or Tl are set in vibration, and as vapors, being free to vibrate without mutual interference, they vibrate with their characteristic frequency, that is, give a definite frequency and thus color of the light, independent of the temperature; if we introduce the same salts into the carbon arc we get the same color and the same spectrum lines, only much brighter, as at the much higher temperature of the arc flame the vibration is far more intense; but it is of the same frequency, and in this respect essentially differs from temperature radiation which varies in frequency with the temperature. In the same manner by introducing Sr, Ba or Ca salts in the bunsen flame, the flame is colored with other character- istic colors; bright red, green, orange The spectroscope shows in every case a spectrum having a number of definite lines which are brightest and most numerous in the red for Sr, in the green for Ba, and in the orange yellow for Ca. In general, 98 RADIATION, LIGHT, AND ILLUMINATION. metal spectra show a number, frequently very many lines in the visible range. As Sr, Ba, Ca, are much less volatile than Li, Na, Tl, to get good effects in the bunsen flame, instead of the chlorides, the nitrates, or preferably the chlorates or perchlorates are used, which are more unstable, and thus easier split up and carried into the flame. At the much higher temperature of the carbon arc, the chlorides, or even the still more refractory oxides are used. Chemical luminescence is used industrially in fireworks and colored signal lights; salts of these metals with acids which con- tain a large amount of easily split off oxygen, as nitrates, or more commonly chlorates and perchlorates, are mixed with some com- bustible material, as charcoal, sugar, sulphur, antimony sulphide, etc. When ignited, the combustible burns with the oxygen given off by the nitrates or chlorates, and in the focus of this intense chemical action, intense luminescence of the metal is produced. Thus Sr gives a bright red, Ba a green, Ca an orange yellow, copper ammon a blue coloring. Electro-luminescence of Gases and Vapors. 45. Industrially this is the most important form of lumines- cence. Solids and liquids can be made to luminesce only indi- rectly by exposure to electric discharges, as electrical fluorescence. Gases, however and under gases here and in the following we include vapors as, for instance, the carbon vapor, which is the conductor in the carbon arc become electro-luminescent by being used as conductors of the electric current. It is a charac- teristic of electric conduction of the gases that this conduction is accompanied by the production of radiation, and in the electric conduction of gases we thus find the means of a more direct conversion of electric energy into radiation, and thus into light. It is, therefore, in this direction that a radical advance in the efficiency of light production would be possible, and the subject of electric conduction of gases (including vapors) thus is of the highest importance. Two forms of electric conduction in gases exist: disruptive conduction, as represented by the Geissler discharge or the elec- trostatic spark, and continuous conduction, as represented by the electric arc. LUMINESCENCE. 99 Disruptive Conduction. In disruptive conduction the conductor is the gas which fills the space between the terminals, and in carrying the current is made luminous. The color of the light and its spectrum is that of the gas which fills the space, and the electrode material has no effect on the phenomenon, is immaterial (in the Geissler tube, or the spark gap, any material may be used as terminal, if it otherwise is suitable, that is, is not destroyed by whatever heat is produced at the terminals, or by the chemical action of the gas in the space, etc.) usually, however, the electrodes gradually dis- integrate in disruptive conduction. Disruptive conduction is discontinuous; that is, no current exists below a certain definite voltage, while above this voltage there is current. The voltage at which conduction begins is called the disruptive voltage. It is the minimum supply voltage at which current exists : if the supply voltage rises above this value there is current; if it drops below the disruptive voltage the current ceases, but begins again spontaneously as soon as, the voltage rises above the disruptive value. Disruptive conduction thus occurs equally well with unidirectional, with alternating, or with oscillating currents. It is best studied with alternating or oscillating voltage supply, as with a steady unidirectional voltage, the disruptive conduction, that is, conduction by the gas filling the space between the electrodes, tends to change to continuous conduction, by vapors forming at the negative elec- trode and gradually bridging the space between the electrodes, and thereby replacing the gas which fills the space, by the elec- trode vapor as conductor. This is usually expressed by saying: the electrostatic spark between two terminals starts, or tends to start, an arc. Disruptive conduction, thus, does not follow Ohm's law; it is zero below the disruptive voltage, while with a supply voltage exceeding the disruptive voltage of the gas between the terminals, current exists, but the terminal voltage is apparently indepen- dent of the current, that is, if the other conditions as temperature, gas pressure, etc., remain the same, the terminal voltage of the Geissler tube or the spark gap remains the same and independent of the current, and the current is determined by the impedance between the. Geissler tube or spark gap and the source of 100 RADIATION, LIGHT, AND ILLUMINATION. e.m.f., or by the available power of the supply source. A Geissler tube, thus, cannot be operated directly on a constant potential supply of unlimited power, but requires a current limiting im- pedance in series with it, or a source of limited power, that is, a source in which the voltage drops with increase of cur- rent, as a constant current transformer or an electrostatic machine, etc. The disruptive voltage essentially depends on the gas pressure in the space between the electrodes, and also on the chemical nature, and on the temperature of the gas. It is over a wide range, directly proportional to the gas pressure. Thus, at n atmospheres pressure the voltage required to jump a spark between two terminals is n times as great as at one atmosphere. This law seems to hold from the highest pressures which have been investigated down to pressures of a few mm. mercury, that is, down to about T ^ atmosphere. When coming to still lower pressures, however, the disruptive voltage decreases less, ulti- mately reaches a minimum usually somewhere between 1 mm. and 0.1 mm. mercury pressure and then increases again and at extremely high vacua becomes much higher than at atmos- pheric pressure, so that it seems that it is infinite in a perfect vacuum, that is, no voltage can start conduction through a perfect vacuum. As the gas filling the space is the conductor in disruptive conduction, it is easily understood that in a per- fectly inert space, or an absolute vacuum, no disruptive con- duction would exist. The visible phenomena of disruptive conduction very greatly change with the change of gas pressure; from the electrostatic spark at atmospheric pressures to the Geissler tube glow in the vacuum; but the change is gradual, thus showing the identity of the two phenomena. At atmospheric pressure, disruptive conduction occurs by a sharply denned, relatively thin and noisy spark of very high brilliancy, which traverses the space between the electrodes in an erratic zigzag path, not unlike in appearance to the mechanical fracture of a solid material; and, indeed, the spark is an electrostatic rupture of the gas. If the electrostatic field is fairly uniform, as between parallel plates, or between spheres of a diameter 1.5 or more times their distance, with gradual rising voltage, the spark occurs when the disruptive voltage is reached, without being preceded, at lower voltage, by LUMINESCENCE. 101 any other phenomenon. If, however, the electrostatic field is not uniform, as, for instance, between needle points or small spheres or wires, with increasing voltage the disruptive strength of the gas is exceeded at those places where the field intensity is highest, as at the needle points, before the disruptive voltage of the spark gap is reached, and then a partial break down occurs at the points of maximum field intensity, as at the needle points, or at the surface of high potential conductors, etc. A blue glow, then, appears at the needle points followed by violet streamers (in air, the color being the nitrogen spectrum; in other gases other colors appear), and gradually increases in extent with increasing voltage, the so-called " brush discharge," or " corona." Between needle points the brush discharges increase in extent, and approach each other until they bridge nearly 60 per cent of the gap, and then the static spark occurs. At higher gas pressures the spark increases in brilliancy, in noisiness, but gets thinner. If, however, we gradually decrease the gas pressure, the spark gets thicker, less brilliant, and less noisy, its edges are less sharply defined, that is, get more diffused, and ultimately it passes between the terminals as a moderately bright, thick and noiseless stream, gradually fading at its outside, and at still higher vacua it fills the entire space of the vacuum tube. At the same time the required voltage is decreased with decreasing gas pressure, as discussed above. 46. I show you here (Fig. 31) the gradual change from the static spark to the Geissler tube glow: in a closed glass tube G, I have two needle-shaped terminals, 5 cm. distant from each other, and supply them with energy from a small 33, 000- volt trans- former. You see the oscillating static spark at atmospheric pressure. By now exhausting the tube, while the voltage is maintained at the terminals, you can watch the gradual change from the static spark to the Geissler tube glow. In this experi- ment, a small condenser, a Leyden jar, is shunted across the high- potential terminals of the transformer, to guard against the disruptive conduction changing to continuous conduction, that is, to an arc, and a reactance inserted into the low-tension pri- mary of the step-up transformer, to limit the discharge current, as shown diagrammatically in Fig. 31. If the Geissler tube has a considerable diameter, 3 to 5 cm., the Geissler discharge with alternating current is striated; that 102 RADIATION, LIGHT, AND ILLUMINATION. is, disk-shaped bright spots with diffused outlines alternate with less luminous spaces, about as shown in Fig. 32. The distance between the luminous disks increases with decrease of the gas pressure. Two sets of such disks exist, one issuing from the one, the other from the other terminal. They are stationary FIG. 31. only if the gas pressure is perfectly constant, but separate and contract with the slightest change of pressure, hence are almost never at rest, but constantly moving through each other. The two sets of disks, by passing through each other during their motion, give rise to a number of different appearances. Some of the successive shapes are shown in Fig. 32. The voltage distribution in the space between the terminals, in disruptive conduction, also: changes with the pressure- at LUMINESCENCE. 103 atmospheric pressure, practically all the voltage is consumed in the space between the terminals, and between needle points for distances of 10 cm. and over very closely 4000 volts effective alternating per cm. (10,000 volts per inch) are required (a 2-cm. gap between needle points, however, requires 10,000 volts). With II II II FIG. 32. decreasing gas pressure the voltage consumed in the space be- tween the terminals decreases,but the voltage consumed at the terminals increases, and in a good Geissler tube vacuum with nitrogen gas filling the space between the terminals, from 1000 to 3000 volts may be consumed at the terminals, while the voltage consumed in the space between the terminals may drop as low as 2 volts per cm. The voltage consumed at the terminals seems to decrease v ith increase of their size. The voltage consumed in the space be- 104 RADIATION, LIGHT, AND ILLUMINATION. tween the terminals, that is, in the luminous stream of the Geiss- ler tube, seems to be practically independent, not only of the current, but also of the size of the tube, as should be expected with a disruptive discharge. It varies, however, with the tem- perature, and is different with different gases, that is, different gases have different disruptive strength. The light given by the Geissler tube shows the spectrum of the gas, and thus is very bright and fairly efficient with a gas as nitro- gen, which gives a large number of spectrum lines in the visible range, and less efficient with a gas as carbon dioxide or hydrogen, in which the lines in the visible range represent only a small part of the radiated energy. The industrial use of the electro-luminescence of discontinuous conduction, that is, Geissler tube lighting, is still very limited (Moore tube). So far only nitrogen gives a fairly good efficiency, reaches apparently values between the tungsten lamp and the tantalum lamp ; or, a specific consumption of two watts per mean spherical candle power. The color of the nitrogen spectrum is a golden yellow. As the range of gas pressure in which the voltage is near the minimum is very narrow, and the gas pres- sure changes during operation, by absorption at the electrodes, etc., means have to be provided to maintain constant gas pressure by automatically feeding gas into the tube whenever the pres- sure drops below the minimum voltage or maximum efficiency point. The greatest disadvantage of Geissler tube lighting, however, is the high voltage required at the terminals. To get fair efficiency the tube must be so long that the voltage con- sumed in the stream which represents the power converted into light is much larger than the voltage consumed at the terminals which represents wasted power. With a terminal drop of 2000 volts, and two volts per cm. in the conducting gas stream, to use half of the supply voltage for light production, thus 2000 requires a tube length of - = 1000 cm. = 10 m. or 33 feet, 2 and to use 80 per cent of the supply voltage for light production, that is, waste only 20 per cent of the supplied power in heating onrvrj the terminals, requires a tube length of = 40 m. or 133 feet. of the mercury spectrum. The terminals are quiet, as they do not participate in the conduction. I now connect terminals 1 and 2 through a resistance, to 'a direct current supply, and tilt the tube momentarily to let some mercury run over from 2 to 1, and by thus momentarily connecting these terminals, establish the current and so start the arc, and you see the mercury arc pass between terminals 1 and 2, and see at one terminal the negative one a rapidly moving bright spot, which marks the point from which the vapor stream issues which carries the cur- rent. We have here in one and the same vacuum tube, and with the same material thus, the same color and spectrum of light, both types of conduction the continuous high current and low voltage conduction of the mercury arc, and the striated high voltage low current disruptive conduction of the Geissler dis- charge through mercury vapor. The conducting vapor stream which carries the current in the arc, at least in all arcs which so far have been investigated, issues 108 RADIATION, LIGHT, AND ILLUMINATION. from the negative terminal or cathode, and is in rapid motion from the negative towards the positive. The character of the arc, therefore, is determined by the material of the negative terminal, the temperature of the arc stream in general probably is the temperature of the boiling point of the negative terminal, 3J=10 OHMS FIG. 34. and the spectrum of the arc is the spectrum of the negative ter- minal. An exception herefrom, occurs only in those cases in which the positive terminal contains material which boils below the temperature of the arc stream (flame carbons) and the posi- tive terminal is made so small that its tip is raised to the temperature of the arc stream, and at this temperature heat evaporation of the material of the positive occurs. These vapors enter the arc stream, and there become luminous, possibly by chemical luminescence, and add their spectrum to that of the arc conductor, that is, the negative material. In this case the arc spectrum shows the negative as well as the positive material, or at least the more volatile components of the positive material. LUMINESCENCE. 109 With the exception of this case of heat evaporation from the positive terminal, the material of the positive terminal does not participate in the phenomena occurring in the arc. Thus the positive can be made of any conducting and refractory material, and if made sufficiently large not to get too hot, does not con- sume; only the negative terminal of the arc consumes in feeding the arc flame, that is, supplying the vapor conductor, but the positive is inherently non-consuming, and may be made a perma- nent part of the arc-lamp mechanism. On the contrary, if the positive is made so large that its temperature remains very much below the arc temperature, condensation of the arc vapor occurs at it, and it builds up, that is, increases in size. Consumption of the positive terminal is thus due merely to the heat produced at it by combustion or heat evaporation. While the arc conductor issues from the negative terminal, in general more heat is produced at the positive terminal. Thus with both terminals of the same size and material, as usual in the carbon arc, the positive gets hotter, and therefore in open air burns off faster, which has led to the erroneous assumption that the positive feeds the arc. While carbon is the material most commonly used as termi- nals, the carbon arc is not a typical arc, but is an exceptional arc. (1) Because carbon is one of the very few substances which change directly from the solid to the vapor state, that is, do not melt at atmospheric pressure, but boil below the melting point. (2) Carbon is the most refractory substance and the tempera- ture of the carbon arc higher than the boiling point of any other substance. Any material existing in the terminals of a carbon arc thus evaporates, and by entering the arc stream shows its spectrum, so that luminescent material can be fed into the carbon arc from either terminal. (3) At the temperature of the carbon arc all gases and vapors have become good conductors, and a carbon arc thus can operate equally well on alternating current as on direct current; that is, the voltage required to maintain the carbon arc is. sufficient, after the reversal of current, to restart it through the hot carbon vapor. A typical arc is shown in Fig. 35 as the magnetite arc, with a lower negative terminal M consisting of magnetite, the non-consuming upper terminal C of copper, and of such 110 RADIATION, LIGHT, AND ILLUMINATION. size that it does not get so hot as to oxidize or evaporate, but sufficiently hot to avoid condensation of magnetite vapor on it. The arc flame consists of an inner cylindrical core A, of bluish white color and high brilliancy, slightly tapering at both ends, which is surrounded by a less luminous shell B, of more yellowish color, narrowest at the negative end, and increasing in diameter towards the positive, surrounding the latter. The inner core A is the arc conductor, or con- ducting vapor stream, while the outer shell B is non-conducting luminous vapor, possibly containing particles of solid material floating in it as incan- descent bodies. The arc conductor A issues from a depression S in a melted pool P formed on the surface of the terminal M. This depression S is in a rapid and erratic motion, and thereby causes a constant and rapid flickering of the arc. It is this flickering, inherent to all arcs in which the negative terminal is fusible (which therefore does not exist in the carbon arc), which has retarded the industrial development of the more efficient metal arcs until late years. Its cause is the reaction exerted by the velocity of the vapor blast from the negative, which presses the surface of the liquid pool down at the point from which the current issues. The starting point of the current con- tinuously climbs up the side of this depression, in shortening the arc, but, in doing so, depresses its new starting point, that is, the depression S, and thereby the negative end of the arc stream moves over the surface the faster the more fluid the surface is. In the mercury arc, this phenomenon of the running spot at the negative terminal is also very marked, but not so objectionable, as the arc stream is so long that the flicker at the negative terminal has no effect on the total light. This flickering disappears in the magnetite arc if we destroy the fluidity of the melted magnetite by mixing with it some much more refractory material, as chromite. The chromite remains solid and holds the melted magnetite like a sponge. The reaction of the vapor blast, then, cannot depress its starting point, and no tendency exists of shifting the starting point, and the arc becomes FIG. 35. LUMINESCENCE. Ill steady. In this manner such arcs have now been made steady and thereby suitable for industrial use. 49. Since the arc conduction issues as a rapidly moving vapor stream from the negative terminal or cathode, it must be con- tinuous at the cathode; if interrupted even for a very short time at the cathode, a break exists in the continuity of the conductor and conduction ceases, that is, the arc extinguishes. At any other point of the arc stream, however, a break in the continuity of the stream may exist, provided that current continues from the negative, since such a break in the continuity of the con- ducting vapor stream is bridged again, and conduction re-estab- lished by the vapor stream coming from the negative. Thus the FIG. 36. arc can be started by merely starting a conducting vapor stream from the negative, as by an auxiliary arc. As soon as this con- ducting vapor reaches the positive terminal, it closes the circuit and establishes conduction. An arc can be shifted or jumped from one positive terminal to another one, but cannot be shifted from negative to negative; the negative terminal, as the source of the conducting vapor stream, must be continuous. To illustrate this, I have here (Fig. 36) in a hand lamp two copper rods A and B of about 5 mm. diameter, as arc terminals, separated by 2.5 cm., and connected into a 220- volt direct-cur- rent circuit, with sufficient resistances in series to limit the current to about 4 amperes. A third copper rod of the same size, C, is connected by a flexible lea.J to the upper terminal B. I close the reversing switch S so as to make A negative, and B and O , . '.. i \. , : ; ,- ,. . - 112 RADIATION, LIGHT, AND ILLUMINATION. positive, and start an arc between A and C by touching C to A. I draw this arc to about 4 cm. length, and without touching C with B, as soon as the conducting vapor stream of the arc AC (the inner core A of Fig. 35) touches B, as shown in Fig. 36, the arc leaves C and goes to B, that is, by the arc AC I have started arc AB. If I had separate resistances in series with the terminals B and (7, the arc AC would also continue to exist after it started arc AB- otherwise, as two arcs cannot run in parallel, the longer arc, AC, goes out as soon as the shorter arc AB starts. I now reverse the circuit by throwing switch S, and make A positive, and B and C negative, again start AC by contact, and draw it out until the arc flame wraps itself all around terminal FIG. 37. B } but the arc does not transfer. I even insert 10 ohms resist- ance r l in series with C (Fig. 37), so that the voltage AB is about 40 volts higher than AC, that is, B by 40 volts more negative than C, and still the arc does not transfer. I now touch C with B and separate it again; if during contact the negative spot during its motion happens to run over to terminal B, the arc con- tinues between B and A; if, however, the negative spot has remained on C, when separating again, the arc remains at C as negative, although B is more negative by 40 volts. An arc therefore can be started at its normal starting voltage by an auxiliary arc having the same negative, but not by an auxiliary arc with the same positive, and an arc can be shifted from one positive to another, but not from one negative to LUMINESCENCE. 113 another. The cause is, as explained above, the necessity of the continuity at the negative terminal as the source of the conduct- ing vapor stream. Still more startling is the following demonstration : I shift the resistance r l from C to B, and start the arc from A to B, with B as negative, by bringing these terminals into contact with each other, and then separating them. The auxiliary terminal C (Fig. 38) now is by 40 volts more negative than the negative terminal B of the arc. I now cut slowly through the arc stream by moving C across it between A and B, as shown in Fig. 38: the arc AB remains, but no current goes to C, although more r =20 OHMS ws FIG. 38. negative, that is, at a higher potential difference and a shorter distance against A than B is. I even hold C for some time in the conducting core of the arc AB, and still the current does not shift from the negative B to the still more negative terminal C. This experiment is interesting in demonstrating that a conductor immersed into the arc flame does not assume the potential of the arc flame, but may differ therefrom by considerable voltage, and that it therefore is not feasible to determine the potential dis- tribution in an arc by means of exploring electrodes, as has frequently been attempted. Obviously, if I now reverse the circuit, and make B and C positive, A negative, the current leaves B and goes to C as soon as C touches the conducting core of the arc AB. 50. The electric arc, therefore, is a unidirectional conductor, that is, the vapor stream is conducting between its negative 114 RADIATION, LIGHT, AND ILLUMINATION. terminal A in Fig. 36, that is, the starting point of the arc stream, and any point reached by it which is positive to A, but is non-conducting for any point which is negative with respect to A. If, now, in Fig. 38, with the terminal C immersed in the arc stream, I connect A and C to a source of alternating voltage, as shown in Fig. 39, while a direct-current arc flows from A to B, with A as negative, then during that half-wave of the alternating voltage, for which C is positive to A, there is current between A and (7, while for the reverse half-wave, in which C is negative to A, there is no current. The arc thus rectifies the alternating voltage, and the rectification is complete, that is, there is T= 30 OHMS MAA FIG. 39. current during one half-wave only, but no current at all dur- ing .the other. I show you this experimentally, using 50 volts alternating between A and (7. With this arrangement, to maintain the rectification continuously, obviously the ter- minal C would have to be cooled. Alternating voltage thus can be rectified by means .of the unidirectional character of the arc : if a continuous vapor stream is maintained from one terminal, either by direct-current ex- citation or by overlapping several waves of alternating cur- rent, current is in that direction only in which this exciter terminal is negative, but not in the opposite direction. . Such arc rectifiers of which the mercury arc rectifier is the most commonly used have been developed and extensively introduced in the industry, of la.te years, for operating, low-volt- LUMINESCENCE. 115 age constant direct potential and high-voltage constant direct- current circuits from a source of alternating voltage. Regarding the electrical phenomena occurring in arc rectification, see " Theory and Calculation of Transient Electric Phenomena and Oscillations/' Section II, Chapter IV. The inability of an alternating voltage to maintain an arc, I show you here on the same apparatus by connecting the two terminals (Fig. 40) A and B to the 1000-volt terminals of a transformer with sufficient resistance in series to limit the current. While 220 volts direct current easily maintained a steady 2-cm. arc between these terminals, with 1000 volts alternating between the terminals, if I try to produce an alternating arc by gradually separating the terminals, the circuit opens before the terminals have separated 1 mm.; that is, 1000 volts alter- nating cannot maintain an arc of 1 mm. between these copper Fh i = iu unM5 v W 110 VJOLTS 60 CYCLES FIG. 40. terminals. The cause is obvious: to maintain an arc between two terminals, a voltage is required sufficiently high to restart the arc at every half-wave by jumping an electrostatic spark between the terminals through the hot residual vapor of the preceding half-wave. The voltage required by an electro- static spark, that is, by disruptive conduction, decreases with increase of temperature: for a 13-mm. (0.5-in.) gap, it is about 10,000 volts at atmospheric temperature, 7000 volts at the boiling point of mercury (360 deg. cent.), 2500 volts at the boiling point of zinc (1000 deg. cent.), 500 volts at the boiling point of magnetite (2000 deg. cent.), 100 volts at the boiling point of titanium carbide (3000 deg. cent.), 40 volts at the boiling point of carbon (3500 deg. cent.). The voltage re- quired to maintain a 13-mm. alternating arc must therefore be 116 RADIATION, LIGHT, AND ILLUMINATION. Sit least as high as given by a curve somewhat like curve I in Fig. 41 * (to bring the values of voltage within the scale of the figure, the logarithm of voltage, as ordinate, is plotted against the temperature as abscissa). The voltage required to maintain an arc, that is, the direct- current arc voltage, increases with increasing arc temperature, and thereby increasing radiation, etc. For a 13-mm. (0.5-in.) FIG. 41. arc it is approximately shown as Curve II in Fig. 41 : 20 volts for the mercury arc, 40 volts for the zinc arc, 60 volts for the * As the disruptive voltage also depends on the chemical nature of the vapor, that is, some gases and vapors have a higher disruptive strength than others, as discussed above, the arrangement of the different materials regard- ing their alternating arc voltages is not entirely determined by their boiling points, but modified by individual characteristics. It further depends on the current: at higher currents and thus larger amounts of residual vapor, the voltage is lower. It further depends on the frequency: the lower the fre- quency and the greater, therefore, the cooling effect during the reversal of current the higher is the required voltage. LUMINESCENCE. 117 magnetite arc, 75 volts for the titanium carbide arc, 80 volts for the carbon arc.* As seen from Fig. 41, the curves I and II intersect at some very high temperature, near the boiling point of carbon, and materials which have a boiling point above the temperature of intersection of these curves require a lower voltage for restart- ing the arc than for maintaining it, and a voltage sufficient to maintain the arc restarts it at every half-wave of alternating current, that is, such materials can maintain a steady alternat- ing arc at the same voltage as a direct-current arc. Even materials like titanium carbide, in which the starting voltage is not much above the running voltage, maintain a steady alter- nating arc, as in starting, the voltage consumed during running in the steadying resistance or reactance is available. Alternating arcs thus can be maintained at moderate volt- ages only by a few materials of extremely high boiling points, as carbon and carbides, but by far the largest number of materials cannot be used as terminals of an alternating-current arc. In Fig. 41 the range between the curves I and II is the " rectify ing range," as in this range unidirectional current is produced from an alternating source of voltage through the arc, if the arc conductor is maintained by excitation of its negative terminal. The voltage range of rectification thus is highest in the mercury arc, which has the lowest temperature, and vanishes in very high-temperature arcs. The carbon arc thus cannot give complete rectification, while the mercury arc, or zinc arc, etc., can do so. The mercury arc, having the greatest recti- fication range, thus is practically always used for this purpose. Below curve II of Fig. 41 no conduction occurs, between curves I and II, unidirectional conduction takes place, and above curve I, disruptive conduction and alternating current can exist. 51. The light, and in general the radiation given by the arc proper, that is, by the vapor conductor which carries the cur- rent between the terminals, is due to luminescence, that is, to a more or less direct transformation of electric energy into * This voltage also is not merely a function of the arc temperature, but modified somewhat by the chemical individuality of the material. It is a function of the current and decreases with increase of current, so that above values are approximate only, corresponding to about 4 amperes. 118 RADIATION, LIGHT, AND ILLUMINATION. radiation, without heat as intermediary form of energy. The quality or color of the light, or its spectrum, that is, the fre- quency or frequencies of radiation given by the arc stream, thus are not a function of the temperature, as in the radiation produced by heat energy, but the frequencies are those at which the luminescent body is capable of vibrating, that is, are determined by the chemical nature of the luminescent body or vapor conductor. The efficiency of light production thus does not directly depend upon the temperature, does not in- crease with increase of temperature, as in temperature radia- tion, but to some extent rather the reverse. We have the same relation as in other energy transformations: when converting heat into other forms of energy, the more intense the heat, that is, the higher the temperature, the higher efficiency we may expect. When transforming, however, some form of energy differing from heat, into another form of energy, as mechanical into electrical energy, the heat produced repre- sents a waste of energy, and the lower the temperature, the higher in general, other things being equal, would be the effi- ciency. The efficiency of light production by the arc thus is not a function of the temperature, but the lowest temperature arc, the mercury arc, is one of the most efficient. The light given by the arc contains only a finite number of definite wave lengths, that is, gives a line spectrum: very few lines in the ordinary mercury arc, many thousands in the tita- nium arc. The color of the light is essentially characteristic of the nature of the luminescent body. For instance, it is white in the titanium arc, as the lines of the titanium spectrum are fairly uniformly distributed over the entire visible range. The light of the calcium arc is orange yellow, as the spectrum lines of calcium are more frequent and more intense in the orange- yellow range of radiation, etc. Frequently a change of the color of the luminescent light of the arc occurs with the temperature, but it does not follow a definite law, as in temperature radiation, but is a char- acteristic particularity of the luminescent body: some of the spectrum lines increase more rapidly in intensity, with increas- ing temperature, than others, and the resultant color of the light changes thereby. For instance, the ordinary iron arc, as produced by 4 amperes direct current across a gap of 2 cm. LUMINESCENCE. 119 between iron or magnetite terminals, and requiring about 75 volts, is white and very brilliant, that is, has a spectrum with many lines about uniformly distributed over the visible range. We can greatly increase the temperature of the arc by using a high-frequency condenser discharge: in this case very large currents of very short duration exist as oscillations between the terminals, with periods of rest between the oscillations, very long compared with the duration of the current. In this case the duration of the current is too short to feed a large volume of electrode vapor into the arc stream, and as the current is very large during the short moment of the discharge, the vapor between the terminals is very greatly overheated. Oscil- lating condenser discharges thus offer a means of increasing the temperature of the arc stream very greatly beyond the boiling point of the material. When using a condenser discharge be- tween iron terminals, we thus get an iron arc of very much higher temperature, and this arc gives very little visible light, but a very large amount of ultra-violet radiation. It is this arrangement which we have used in the preceding to produce ultra-violet light by the so-called " ultra-violet iron arc." In the iron arc the average wave length of the radiation thus shifts with increasing temperature to shorter wave lengths, or higher frequencies, similar as in temperature radiation. The reverse is the case with the mercury arc: the ordinary mercury arc in an evacuated glass tube, with ample condensing chamber, gives practically no red light; only a very powerful spectroscope can discover some very faint red lines. If now the condensation of the mercury vapor is made insufficient, by obstructing ventilation, or greatly raising the current, or omitting the condensing chamber in the construction of the lamp, and the mercury vapor pressure and thereby the tem- perature increased, at least three red lines located about as shown in Fig. 42 become visible in the mercury spectrum even in a low-power spectroscope, Ill Oi i\J W IJ\J W Cl Ok-'CLiLlWO^V^lJC, and increase in intensity with _J [ I m v. ^ ,/ YELLOW <^^-^_ ^ BLUE VlO increasing vapor pressure. To show you this I use a U-shaped FlG - 42 - mercury lamp constructed as shown half size in Fig. 43. I con- nect the lamp into a 220-volt direct-current circuit, with an inductive resistance in series thereto, to limit the current, and 120 RADIATION, LIGHT, AND ILLUMINATION. start the arc by pouring some mercury over from one side to the other. Immediately after starting the lamp you see no red lines in the low-power spectroscope which I have here. As with the large current which I use 3 amperes the mercury vapor cannot freely condense, the mercury vapor pressure rises and FIG. 43. presses the mercury level down in the center tubes, up in the outside tubes, as indicated at b in Fig. 43, and thereby enables us to measure the mercury pressure. Gradually you see the three red lines appear, and increase in intensity, and when the vapor pressure has risen to about 5 cm., the three red lines are fairly bright, and numerous other red and orange mercury lines have appeared. At this pressure we are so close to the softening point of the glass that we cannot go further, but by operating the mercury arc in a quartz tube, vapor pres- sures of several atmospheres can be produced, and then the red lines are very much more intense, many more lines have be- come visible in the mercury spectrum, and the light is far less greenish than the low-temperature mercury arc, more nearly white. Still much higher temperatures can be reached in the mercury arc in an ordinary glass tube by using the condenser discharge. I have here, in Fig. 44, a mercury-arc tube with four LUMINESCENCE. 121 terminals the same which I used in Fig. 34 for showing simultaneously the mercury arc and the Geissler discharge. I connect terminals 3 and 4 to the high potential terminals of a step-up transformer, but shunt a small condenser C across 3 and 4; you see, in the moment where I connect the condenser, the previously existing green and striated Geissler discharge changes r=so OHMS 3 r % \ \ -f- JL2JUL&L J>UP00Q 0000 r oooo T III 1-^-40 1-7-40 1 r=.io OHMS 110 VOLTS 60 CYCLES 2 = 10 OHM 110 VOLTS 60 CYCLES *m FIG. 44. to a bright pinkish-red arc, and the spectroscope shows that the spectrum lines in the red and orange have greatly increased in number, and have increased in intensity beyond that of the lines in the green and blue, and the color of the light therefore has changed from green, to pinkish red. We have here in the same mercury tube shown diagram- matically in Fig. 44 all three forms of luminescence of mercury vapor: the high-current low-voltage, low-temperature arc of 122 RADIATION, LIGHT, AND ILLUMINATION. uniform green color, from 1 to 2; the green high-voltage low- current striated Geissler discharge, from 2 to 3, and the red high- voltage mercury arc, from 3 to 4. In the mercury arc, as result of the more rapid increase of intensity of the red lines, the color of the light thus changes with increase of temperature from bluish green at low tempera- ture to white to red at very high temperature, that is, the aver- age frequency decreases with increase of temperature, just the reverse from what is the case with temperature radiation. The change in the distribution of the power of radiation between the different spectrum lines, with change of tempera- ture, may increase the efficiency of light production if the lines in the visible range increase faster than in the ultra-red and ultra-violet or may decrease if the visible lines in- crease slower or may increase in some temperature range, decrease in some other temperature range, but all these changes are characteristic of the luminescent material, and do not obey a general law. Thus in the mercury arc the efficiency of light production, with increase of temperature, rises to a maximum at about 150 deg. cent., then decreases to a minimum, and at still higher temperature increases to a second maximum, higher than the first one, possibly between 600 and 800 deg. cent., and then decreases again. 52. Essentially, however, the efficiency of light production by the arc is a characteristic of the material of the arc stream, and thus substances which give a large part of their radiation as spectrum lines in the visible range as calcium give a very efficient arc, while those substances which radiate most of their energy as lines in the invisible, ultra-violet or ultra-red - as carbon give a very inefficient arc. The problem of efficient light production by the arc therefore consists in selecting such materials which give most of their radiation in the visible range. Carbon, which is most generally used for arc terminals, is one of the most inefficient materials : the carbon arc gives very little light, and that of a disagreeable violet color; it is practi- cally non-luminous, and the light given by the carbon arc lamp is essentially incandescent light, temperature radiation of the incandescent tip of the positive carbon. The fairly high effi- ciency of the carbon arc lamp is due to the very high tempera- ture of the black body radiator, which gives the light. LUMINESCENCE. 123 The materials which give the highest efficiencies of light production by their spectrum in the arc stream arcs mercury, calcium and titanium. As mercury vapor is very poisonous, the mercury arc has to be enclosed air-tight, and has been developed as a vacuum arc, enclosed by a glass or quartz tube. Its color is bluish green. Calcium gives an orange-yellow light of very high efficiency, and is used in most of the so-called "flame-carbon arcs," or "flame arcs." Titanium gives a white light of extremely high efficiency. It is used in the so-called "luminous arc," as the magnetite arc in direct-current circuits, the titanium-carbide arc in alternating- current circuits. 53. Two methods exist of feeding the light-giving material into the arc stream : (1) By electro-conduction, that is, using the material as the vapor conductor which carries the current. In this case, it must be used as negative, as the vapor conductor is supplied from the negative; such arcs are called "luminous arcs." (2) By heat evaporation; in this case, a very hot arc must be used, and thus usually a carbon arc is employed. As the posi- tive terminal is the hottest, the material is mixed with the car- bon of the positive terminal, and as negative terminal either a plain carbon, or also an impregnated carbon used; such arcs are called "flame arcs." The method of heat evaporation is always used witri calcium, since no stable conducting calcium compound is known which may be used as negative arc terminal. With titanium, usually electro-conduction is employed, that is, a titanium oxide-mag- netite mixture, or titanium carbide, used as negative terminal, and any other terminal, as copper or carbon, as positive ter- minal. Titanium can also be introduced by heat evaporation by using a titanium-carbon mixture as positive terminal or as both terminals of the flame-carbon arc. Both methods of feeding electro-conduction and heat evapo- ration have advantages and disadvantages. Electro-conduction has the great advantage that the tem- perature of the terminals is immaterial, as heat plays no part in feeding the luminescent material into the arc flame. The posi- tive terminal of the arc can be made sufficiently large and of 124 RADIATION, LIGHT, AND ILLUMINATION. such material as not to consume at all, and the trimming of the lamp thus reduced to the replacing of one electrode only the negative. The negative electrode also can be made so large as to remain fairly cold, and therefore consumes only at the very slow rate required to supply the arc vapor, but does not con- sume by combustion or heat evaporation. Thus its rate of con- sumption can be reduced to 1 mm. or less per hour (while the open carbon arc of old consumes about 5 cm. of electrodes per hour), and thereby even with a moderate size of electrode a life of electrodes of 100 to 200 hr. or even much more secured. This method of feeding thus lends itself very well to long-burning arcs, as they are almost exclusively used for American street lighting. By electro-conduction higher efficiencies can be reached than by heat evaporation, as the arc vapor stream when produced by electro-conduction can be made to consist entirely of the vapor of the luminescent material, as when using metallic titanium as negative terminal. A disadvantage of the method of feeding the arc by electro- conduction is the much greater limitation in the choice of materials: the material must be an electric conductor, which is stable in the air, and reasonably incombustible. In the method of feeding by heat evaporation any material can be used, as it is mixed with carbon, and the conductivity is given by the carbon. Thus, in the titanium arc, either metallic titanium or titanium carbide or sub oxide must be used, but the most com- mon titanium compound, Ti0 2 , or rutile, is not directly suitable, since it is a non-conductor. In the direct-current titanium arc, the so-called magnetite arc, a solution of Ti0 2 , or rutile, in mag- netite, Fe 3 4 , which is conducting, is used, that is, a mixture of rutile with a considerable weight of magnetite. While mag- netite also gives a luminous arc, the white iron spectrum, the efficiency of the iron arc is lower than that of the titanium arc, and the efficiency of the magnetite arc thus lower than that of the pure titanium arc, though much higher than that of the carbon arc. Calcium cannot be used at all by electro-conduction: the only more common conducting calcium compound is calcium carbide. As negative terminal calcium carbide gives an arc of an efficiency far superior to that of the flame-carbon arc, but, as calcium carbide disintegrates in the air, it cannot be used. LUMINESCENCE. 125 Still greater is the limitation for alternating current; in this case the material, in addition to its other qualifications, must have such a high boiling point as to maintain a steady alternat- ing arc, as discussed above. Of the titanium compounds only titanium carbide seems to fulfill this requirement; of the iron compounds, apparently none. 54. The most serious disadvantage of the use of electro- conduction for feeding the arc, however, has been the inherently greater unsteadiness of metal arcs compared with the carbon arc. It is this feature which has retarded the development of true luminous arcs until recent years, that is, until means were found to produce steadiness by eliminating the nickering of the negative spot by the admixture of a more refractory material, chromite in the magnetite arc, and eliminating the unsteadiness due to the occasional momentary fading out of the luminous inner core of the arc by the admixture of a very small amount of some more volatile material. The great advantage of the method of feeding the luminescent material into the arc flame by heat evaporation, mainly from the positive, is the possibility of using carbon as arc conductor, which gives the inherent steadiness of the carbon arc, and thus has led to the development of this type of high efficiency arc, the flame arc, before the development of true luminous arcs. A further advantage is the possibility of using alternating current equally well and with the same electrodes as used with direct current, as the arc is a carbon arc and thus operative on alternating current Another advantage is the great choice of materials available, since practically any stable compound, whether conducting or not, can be used in the flame carbon. Thus in the yellow-flame arc, calcium fluoride, oxide and borates are used; in the tita- nium arc, the oxide (rutile) or the carbide may be used. The most serious disadvantage of the method of feeding by heat evaporation, which has so far excluded the flame arc from general use for American street illumination, is the rapid con- sumption of the electrodes and their consequent short life. Since the luminescent material is fed into the arc by heat evap- oration, the electrodes must be so small that their ends are raised to arc temperature, and thus rapidly consume by the combus- tion of the carbon. The combustion cannot be reduced by 126 RADIATION, LIGHT, AND ILLUMINATION. excluding the air by enclosing the arc with an almost air-tight globe, as in the enclosed carbon arc, since the luminescent material leaves the arc as smoke, and by depositing on the globe rapidly obstructs the light. The rate of consumption of the electrodes thus is the same as in the open carbon arc, 3 to 5 cm. (1 to 2 in.) per hour, and the flame-carbon arc even with very great length of carbon thus lasts only one night, that is, requires daily trimming. To some extent this difficulty may be reduced by using the same air again, after passing it through a smoke-depositing chamber in a so-called " circulating" or "regenerative" flame lamp. The mercury arc, being enclosed in a glass tube, necessarily must always be fed by electro-conduction from the negative. The calcium arc is always fed by heat evaporation from the carbon positive, with a carbon negative, or from positive and negative, by using flame carbons for both electrodes. The titanium arc is usually fed by electro-conduction from the neg- ative, but also by heat evaporation from the positive by using a titanium-flame carbon. 55. As, by electro-luminescence, electric energy is converted more directly into radiation, without heat as intermediary form of energy, no theoretical limit can be seen to the possible effi- ciency of light production by the arc, and in the mercury, cal- cium and titanium arcs, efficiencies have been reached far beyond those possible with temperature radiation. Thus, specific con- sumptions of 0.25 watt per mean spherical candle power are quite common with powerful titanium or calcium arcs, and even much better values have been observed. It is therefore in this direction that a radical advance in the efficiency of light pro- duction appears most probable. At present, the main disad- vantage of light production by the arc is the necessity of an operating mechanism, an arc lamp, which requires some atten- tion, and thereby makes the arc a less convenient illuminant than, for instance, the incandescent lamp, and especially the limitation in the unit of light: the efficiency of the arc decreases with decrease of power consumption, and, while the arc is very efficient in units of hundreds or thousands of candle power, its efficiency is much lower in smaller units, and very small units cannot be produced at all. Thus, for instance, while a 500- watt flame arc may give 10 times as much light as a 500-watt LUMINESCENCE. 127 carbon arc, to produce by a flame arc the same amount of light as given by a 500-watt carbon arc requires very much more than one-tenth the power. So far no way can be seen of maintaining the efficiency of the arc down to such small units of light as represented by the 16- or 20-eandle power incandescent lamp. LECTURE VII. FLAMES AS ILLUMINANTS. 56. Two main classes of illuminants exist: those producing radiation by the conversion of the chemical energy of com- bustion the flames and those deriving the energy of radia- tion from electric energy the incandescent lamp and the arc lamp, and other less frequently used electric illuminants. Flames. To produce light from the chemical energy of combustion, almost exclusively hydrocarbon flames are used, as the gas flame, the candle, the oil lamp, the gasolene and kerosene lamp, etc.; that is, compounds of hydrogen and carbon or of hydrogen, carbon and some oxygen are burned. The hydrogen, H, com- bines with the oxygen, 0, of the air to water vapor, H 2 0, and the carbon, C, with the oxygen of the air, to carbon dioxide, C0 2 ; or, if the air supply is insufficient, to carbon monoxide, CO, a very poisonous, combustible, odorless gas (coal gas), which thus appears in all incomplete combustions and is present, also, as intermediary stage, in complete combustion. The mechanism of the light production by the hydrocarbon flame I illustrate here on the luminous gas flame : where the gas issues from the burner into the air, it burns at the surface of the gas jet. By the heat of combustion the gas is raised to a high temperature. Most hydrocarbons, however, cannot stand high temperatures, but split up, dissociate into simpler hydro- carbons very rich in hydrogen : methane, CH 4 , and in free carbon. The carbon particles formed by this dissociation of hydrocar- bon gas float in the burning gases, that is, in the flame, and are raised to a high temperature by the heat of combustion of the gases, thereby made incandescent, and radiate light by tem- perature radiation; until ultimately, at the outer edge of the flame, they are burned by the oxygen of the air, and thus destroyed. We can see these carbon particles, which, floating 128 FLAMES AS ILLUMINANTS. 129 in the flame in anjncandescent state, give the light if, by passing a cold porcelain or glass plate through the luminous flame, we suddenly chill it and thereby preserve the carbon particles from combustion; they appear then on the plate as a carbon deposit, soot or lampblack. The light given by the luminous hydrocarbon flame thus is due to black-body radiation, and the flame makes its own radiator, and afterwards destroys it by combustion. To give a luminous flame, the hydrocarbon must be suffi- ciently rich in carbon to split off carbon at high temperatures. Thus methane, CH 4 , does not give a luminous flame, since it con- tains the smallest amount of carbon which can combine with hydrogen, and therefore does not deposit carbon at high tem- peratures. Ethylene, however, C 2 H 4 , which is the foremost light giving constituent of illuminating gas, dissociates in the flame into CH 4 and C, and thus gives a luminous flame, as half of its carbon is set free and gives the incandescent radiator. If, however, the hydrocarbon is very rich in carbon, the amount of deposited carbon becomes so large that the energy of combustion of the remaining hydrocarbon is not sufficient to raise the carbon to very high temperatures, the luminosity therefore again decreases, the flame becomes reddish yellow, and a large amount of carbon escapes from the flame uncon- sumed, as smoke or soot, that is, the flame becomes smoky. To show you this, I pour some gasolene and some benzol in small glass dishes. The gasolene, having 2J hydrogen atoms per carbon atom, burns with a luminous flame and very little smoke. The benzol, having only one hydrogen atom per carbon atom, burns with a reddish-yellow flame, pouring out masses of black smoke. The proportion between the hydrogen and carbon required to give a luminous non-smoky flame, therefore can be varied only within narrow limits: too little carbon gives a less lumi- nous or non-luminous flame, too much carbon a smoky reddish flame. Hydrocarbons exist having almost any proportion between hydrogen and carbon, from a maximum of four hydrogen atoms to one carbon in methane, CH 4 , to practically pure carbon in anthracite coal. Some of them are shown in the following table, with the number of hydrogen atoms per carbon atom 130 RADIATION, LIGHT, AND ILLUMINATION. added in column a, and the percentage of carbon which is de- posited by dissociation, in column b ;* a thus may be called the luminosity index of the hydrocarbon. HYDROCARBONS. Name. State. Formula. Lumi- nosity Index (a). Car- bon Index (ft). Paraffines: Methane Gas. do.. CH 4 C 2 H 6 C 3 H 8 r 4 H 10 ^5 n !2 CH 14 C 10 H 22 ^14^30 C 20 H 42 U 24 1 50 C 2 H 4 C 2 H 2 C.H 6 C 10 H 8 C 14H 10 approx. 4.0 3.0 2.67 2.5 2.4 2.33 2.2 2.14 2.1 2.08 2 1 1 0.8 0.71 0.25 0.333 0.375 0.40 0.417 0.45 0.464 0.475 0.479 0.50 0.75 0.75 0.80 0.821 Ethane Propane . do... Butane . . do... Pentane . ... Liquid. ..do.. . . .do.... Gasolene Kerosene Mineral oil Vaseline .. .do.... Solid, do Paraffine Olefines: Ethylene Gas. Gas. Liquid. Solid, do.. Acetylenes: Acetylene Benzols: Benzol Naphthalene Anthracene 57. The proportion between carbon and hydrogen required to give a luminous non-smoky flame somewhat depends on the size of the flame, and, with a larger size, a higher proportion of hydrogen is required to avoid smoke than with a smaller flame, as in the latter, due to the larger surface compared with the volume, the combustion is more rapid. I show you this on the, gas flame : admitting a little gas, I get a small flame, which does not smoke, but if I open the stop-cock wide I get a large and smoky flame. With a moderate-sized flame without artificial ventilation, from 30 to 40 per cent of the carbon must be deposited to give good luminosity without smoke. This corresponds to a value a * Every four hydrogen atoms retain one carbon atom, while the rest of the carbon is set free. FLAMES AS ILLUMINANTS. 131 between 2.4 and somewhat less than three hydrogen atoms per carbon atom. Ethane, C 2 H 6 , with a = 3, still gives a luminous flame, but of somewhat lower luminosity, and, on the other side, the gasolene flame, a = 2.33, is slightly smoky. However, in very small flames in which the surface is larger compared with the volume, and the combustion thus very rapid, higher percentages of carbon can be used without smoke. Thus the flame of the parafnne candle a = 2.08 is still smokeless but begins to smoke if it gets large, and in extremely small flames, J in. or less diameter, even acetylene, a = 1, gives smokeless combustion. Increase of the rapidity of combustion by increasing the sur- face of the flame by using a flat or hollow cylindrical burner, and increasing the air supply by artificial draft, as by a chimney, gives smokeless flames even up to b = 50, or one carbon atom to two hydrocarbon atoms, a = 2. Thus kerosene, which, due to its high carbon content a = 2.14, smokes badly, except in very small flames, is burned smoke- lessly in lamps with chimneys and flat or hollow round burners, and then gives a high light intensity : with the rapid air supply and the large surface of the thin flame, the combustion is very rapid, a part of the free carbon is immediately consumed, the temperature is high, and thus the free carbon heated sufficiently to give considerable light, and to consume completely when leaving the flame. With a hydrocarbon still richer in carbon, as acetylene or benzol a = 1, artificial draft and large flame surface are no longer sufficient to give smokelessness, and the total range of hydrocarbons which can be burned with lumi- nous flames and without smoke thus is between from three to two hydrogen atoms per carbon atom. Hydrocarbons which are too rich in carbon to be burned smokelessly, as acetylene or benzol, obviously can be burned with a smokeless luminous flame by mixing them in the proper proportions with hydrocarbons deficient in carbon, which latter by themselves would give a non-luminous or nearly non-lumi- nous flame. Thus a mixture of one volume of acetylene, C 2 H 2 , with three volumes of methane, 3 CH 4 , (the number of mole- cules of gases are proportional to their volumes), gives a non- smoky luminous flame: 5 C to 14 H, or a = 2.8. Such hydrocarbons as acetylene, benzol, etc., which are rich 132 RADIATION, LIGHT, AND ILLUMINATION. in carbon, are used for enriching poor gas, that is, making it more luminous : gas which gives little free carbon, as water-gas (which is rich in H and CO both giving non-luminous flames), and which therefore would give a non-luminous or only slightly luminous flame, thus is improved in its light-giving quality by admixture of acetylene, etc. 58. If the hydrocarbon contains oxygen, as alcohol, C 2 H 6 0, etc., the presence of oxygen atoms reduces the luminosity or the tendency to smoke, by taking care of a corresponding num- ber of carbon atoms: the most stable compound is CO, and water vapor, H 2 0, as well as carbon dioxide, C0 2 , are reduced by carbon at high temperature with the formation of carbon monoxide, CO. During the dissociation of the hydrocarbon in the flame, each oxygen atom takes up one carbon atom, form- ing CO, which burns with a non-luminous flame. In approxi- mately estimating the luminosity or the tendency to smoke of a hydrocarbon containing oxygen, for each oxygen atom one car- bon atom is to be subtracted. To illustrate this I pour some aldehyde, C 2 H 4 0, and some amyl acetate, C 7 H 14 2 , in small glass dishes and ignite them. In both the ratio of hydrogen to car- bon atom is a = 2, corresponding to a luminous but smoky flame. You see, however, that the aldehyde burns with a per- fectly non-luminous flame : we have to put out the light to see it; while the amyl acetate burns with a luminous, non-smoky flame. Applying above reasoning, the oxygen accounts for one carbon atom in the aldehyde : C 2 H 4 = CO + CH 4 , and in CH 4 : a = 4, corresponding to a non-luminous flame, as observed. In amyl acetate, the two oxygen atoms take up two carbon atoms : C 7 H 14 2 = 2 CO + C 5 H 14 , and the ratio of hydrogen to carbon atoms is a = 2.8, or b = 30, corresponding to a luminous non- smoky flame, as observed. The same effect as given by oxygen contained in the hydro- carbon molecule obviously is obtained by mixing oxygen or air with the hydrocarbon. I illustrate this on the bunsen flame : closing the air supply, I have an ordinary luminous and somewhat smoky gas flame. I now gradually admit air, and you see first the smoke disappear, and then the luminosity decreases, and first the lower part, and then the entire flame, becomes non-luminous. When the luminosity has just disappeared, the amount of air mixed with the gas is just sufficient to take up FLAMES AS ILLUMINANTS. 133 all the carbon as CO, which would deposit otherwise and give the incandescent radiator, but it is far below the amount required for complete combustion, and, by still further increasing the air supply, you see the rapidity of combustion still further increase, as shown by the decreasing size of the flame. With increasing air supply, the size of the flame very greatly decreases, and, as the same total heat is produced by the combustion, this means that the heat is concentrated. in a smaller volume, that is, the temperature of the flame is increased, in other words, the non- luminous bunsen flame is of higher temperature than the lumi- nous gas flame. Hydrocarbons which are too rich in carbon to burn without smoke, as acetylene, can be burned with a smokeless flame by mixing them with oxygen or with air. Acetylene is always burned in this manner, and all acetylene-gas burners are con- structed so as to take in air with the acetylene gas before com- bustion, that is, are small bunsen burners or similar thereto. Since the temperature of the bunsen flame, due to the more rapid combustion resulting from the mixture with air, is higher than that of the ordinary gas flame, and in the acetylene flame in the acetylene air mixture a large part of the carbon is also immediately burned, the temperature of the acetylene flame is very high, and the deposited carbon therefore raised to a very high temperature, much higher than in the ordinary gas flame, and, as the result of the higher temperature, the black-body radiation of the free carbon in the acetylene flame is far more efficient, and of much whiter color than in the ordinary gas flame. Thus the hydrocarbons which are very rich in carbon, as acetylene, benzol, naphthalene, etc., if burned smokelessly by mixture with air, give whiter and more efficient flames, due to their higher temperature. Especially is this the case with acetylene, as the energy of combustion of acetylene is higher than that of other hydrocarbons of the same relative propor- tions of hydrogen and carbon: acetylene being endothermic, that is, requiring energy for its formation from the elements. 59. Since, as discussed in Lecture VI, chemical luminescence usually occurs where intense chemical reactions take place at high temperatures, and this is the case in the flame, chemical luminescence of the flame gases must be expected in the hydro- carbon flame. It does occur, but does not contribute anything 134 RADIATION, LIGHT, AND ILLUMINATION. to the light production, since the spectra of hydrogen and of carbon (or CO and CH 4 ) are practically non-luminous. The luminescence of the hydrocarbon flame therefore can be observed only with those hydrocarbons which are sufficiently poor in car- bon as not to deposit free carbon, as methane, alcohol, etc., or in which, by the admixture of air, the deposition of free carbon and thereby the formation of an incandescent radiator, is avoided, as in the bunsen flame. In this case, the blue color of the chemical luminescence of carbon-flame gases is seen: all non-luminous hydrocarbon flames are blue. 60. While light, and radiation in general, can also be pro- duced by the combustion of other materials besides hydro- carbons, industrially other materials are very little used. Burning magnesium gives a luminous flame of extremely high brilliancy and whiteness. Its light is largely due to tem- perature radiation, and the flame makes its own incandescent radiator; but unlike the hydrocarbon flame, in which the radiator is again destroyed by combustion, the incandescent radiator of the magnesium flame is the product of combustion, magnesia, MgO, and escapes from the flame as white smoke. While, how- ever, in the hydrocarbon flame the incandescent radiator is a black body, carbon, giving the normal temperature radiation, the radiator of the magnesium flame, magnesia, is a colored radiator, and its radiation is deficient in intensity in the ultra- red, and very high in the visible range, and thereby of a much higher efficiency than given by black-body radiation. The magnesium flame therefore is far more efficient than the hydro- carbon flame, and its light whiter. So also burning aluminum, zinc, phosphorus, etc., give lu- minous flames containing incandescent radiators produced by the combustion: alumina, zinc oxide, etc. Superimposed upon the temperature radiation of the incan- descent radiator of those flames is the radiation of chemical luminescence. Since, however, magnesium, zinc, aluminum, give fairly luminous spectra, in these flames the chemical lumi- nescence contributes a considerable part of the light, and where the luminescent light, that is, the metal spectrum, is of a marked color as green with zinc the flame of the burning metal also is colored. Hence burning zinc gives a greenish-yellow flame, burning calcium an orange -yellow flame, etc. FLAMES AS ILLUMINANTS. 135 Obviously, where during the combustion no solid body is formed, the light given by the flame is entirely chemical lumi- nescence. Thus burning sulphur gives a blue flame, and, if the temperature of combustion is increased by burning the sulphur in oxygen, it gives a fairly intense light, of violet color, and a radiation which is very intense in the ultra-violet. Thus before development of the ultra-violet electric arcs, as the iron arc, for the production of ultra-violet radiation lamps were used, burning carbon bisulphide, CS 2 , in oxygen. Carbon bisulphide, has the advantage over sulphur that, as liquid, it can easier be handled in a lamp, and especially the combustion of carbon (without adding much to the light, due to the non-luminous character of the carbon spectrum) greatly increases the flame temperature, and thereby the intensity of the radiation. Flames with Separate Radiator. 61. The hydrocarbons are the only sources of chemical energy which by their cheapness are available for general use in light production. Carbon, however, is a black-body radiator, and its efficiency of light production therefore very low, es- pecially at the relatively low temperature of the luminous hydrocarbon flame, and such flames are, therefore, low in efficiency of light production, with the exception of the acety- lene flame and other similar flames. Separating the conversion into light from the heat production; that is, using the hydrocarbon flame merely for producing heat, and using a separate radiator for converting the heat into light, offers the great advantage (1) That a colored body can be used as radiator, and thereby a higher efficiency of light production, at the same temperature, secured, by selecting a body deficient in invisible and thereby useless radiation. (2) That the rapidity of combustion can be greatly increased by mixing the hydrocarbon with air in a bunsen burner, and thereby the temperature of the flame increased, which results in a further increase of the efficiency of light production. Thus, by the use of suitable external radiators, in a non- luminous hydrocarbon flame, far higher efficiencies of light production are reached than by the use of the luminous hydro- carbon flame. 136 RADIATION, LIGHT, AND ILLUMINATION. The first use of external radiators probably was the use of a lime cylinder in a hydro-oxygen flame, in the so-called "lime light/' for producing very large units of light. in the days before the electric arc was generally available. In the last quarter of a century the external radiator has come into extended use in the Welsbach mantle; the hydro- carbon is burned in a bunsen burner, that is, mixed with air, so as to get a non-luminous flame of the highest temperature, and in this flame is immersed a cone-shaped web of a highly effi- cient colored radiator: thoria with a small percentage of ceria, etc., the so-called "mantle." The higher temperature, com- bined with the deficiency of radiation in the invisible range, ex- hibited by this colored radiator, results in an efficiency of light production several times as high as that of the luminous gas flame. The distribution of intensity in the spectrum of the Welsbach mantle obviously is not that of black-body radiation, but differs therefrom slightly, and the radiation is somewhat more intense in the greenish yellow, that is, the light has a slightly greenish-yellow hue. The Welsbach mantle is very interesting as representing the only, very extensive industrial application of colored radiation. LECTURE VIII. ARC LAMPS AND ARC LIGHTING. Volt- Ampere Characteristics of the Arc. 62. The voltage consumed by an arc, at constant current, increases with increase of arc length, and very closely propor- tional thereto. Plotting the arc voltage, e, as function of the 190 180 170 160 150 140 130 120 110 100 00 80 70 60 50 '40 30 20 10 I.fi6 0[5 25 1 FIG. 45. arc length, I, we get tor every value of current, i, a practically straight line, as shown for the magnetite arc in Fig. 45, for values of current of 1, 2, 4 and 8 amperes. These lines are steeper 137 138 RADIATION, LIGHT, AND ILLUMINATION. for smaller currents, that is, low-current arcs consume a higher voltage for the same length than high-current arcs, the in- crease being greater the longer the arc. These lines in Fig. 45 intersect in a point which lies at I = 0.125 cm. = 0.05 in. and e = 30 volts; that is, the voltage consumed by the arc consists of a part, e = 30 (for the magnetite arc), which is con- F;G. 46. stant, that is, independent of the arc length and of the cur- rent in the arc, but different for different materials, and a part, e v which is proportional to the arc length, Z, or rather to the arc length plus a small quantity, 1 L = 0.125 (for the magne- tite arc): e^ = \(l + 0.125), and depends upon the current, being the larger the smaller the current. Plotting the arc voltage, e, as function of the current, i, we get curves which increase with decrease of current, the increase being greater the longer the arc, as shown in Fig. 46, for the ARC LAMPS AND ARC LIGHTING. 139 magnetite arc, for I = 0.3, 1.25, 2.5, 3.75 cm. = 0.125, 0.5, 1 and 1.5 in. Subtracting from the voltage, 6, in Fig. 46, the con- stant part, e = 30 volts, which apparently represents the terminal drop of voltage, that is, the voltage which supplies the energy used in producing the conducting vapor stream at the negative, and the heat at the positive terminal, leaves the voltage, e l = e e QJ as the voltage consumed in the arc stream. The curves of arc-stream voltage, e v as function of the cur- rent, ij in Fig. 46, can with approximation be expressed by k cubic hyperbolas: e^i = k z 2 ; or, e l = j and since we find for Vi constant value of current: e l = k^ (I + 0.12), as function of arc length and current, i, the voltage of the arc stream is ex- pressed by : k (I + I) e i = TT 1 -' (1 and the total arc voltage by : , *(*+*,: (2) where e , k and Z t are constants of the terminal material (k, how- ever, varies with the gas pressure in the space in which the arc exists). This equation (2) represents the arc characteristics with good approximation, except for long low-current arcs, which usually require a higher voltage than calculated, as might be expected from the unsteady nature of such long thin arcs. The equation (2) can be derived from theoretical reasoning as follows: Assuming the amount of arc vapor, that is, the volume of the conducting vapor stream, as proportional to the current, and the heat produced at the positive terminal also as proportional to the current, the power p required to produce the vapor stream and the heating of the positive terminal is proportional to the current, i\ and, as the power is p = e Q i, it follows that the voltage, e , consumed at the arc terminals is constant. The power consumed in the arc stream : p l = ej,, is given off, by heat conduction, convection, and by radiation, from the sur- 140 RADIATION, LIGHT, AND ILLUMINATION. face of the arc stream, and thus, as the temperature of the arc stream is constant, and is that of the boiling point of the arc vapor, the power p l consumed in the arc stream is proportional to its surface, that is, to the product of arc diameter l d and arc length I, or rather the arc length I increases by a small quantity l v which allows for the heat carried away to the electrodes. As the diameter l d is proportional to the square root of the section of the arc stream, and the section of the arc stream, or the volume of the arc vapor, was assumed as proportional to the current, i, the arc diameter is proportional to the square root of the current, and the power p t consumed in the arc stream thus is proportional to the square root of the current, i, and to (I + IJ ; thatis ' p^kVid + lJ; and since p l = ej, which is equation (1), and herefrom, since e = e + e ir follows equation (2). 63. Since e represents the power consumed in producing the vapor stream and the heating of the positive terminal, and k the power dissipated from the arc stream, e and k are different for different materials, and in general higher for materials of higher boiling point and thus higher arc temperatures. It is, approximately, e = 13 volts for mercury, = 16 volts for zinc and cadmium, = 30 volts for magnetite, = 36 volts for carbon, k = 31 for magnetite (123 in inch measure), = 35 for carbon (130 in inch measure). The magnetite arc, of which the characteristics are shown in Figs. 45 and 46, thus can be represented by: ' (3) The least agreement with the theoretical curve (2) is shown by the carbon arc. This may be expected from the exceptional character of the carbon arc, as discussed in Lecture VI. Plot- ARC LAMPS AND ARC LIGHTING. 141 ting, in Fig. 47, the voltage, e, consumed by a carbon arc, at constant values of current i, as function of the arc length Z, as done for the magnetite arc in Fig. 45, when using only the observation for arc length of 0.25 in. and over, we get fairly satisfactory straight lines, which intersect at the point, giving e = 36 volts, but I, = - 0.8 cm. = - 0.33 in.; that is, a value much greater than for any other arc. For short arc VOLTS 150- 100 2 LE -20- 25 3 "5 cn 1J5 IN. FIG. 47. lengths, however, the observed values of voltage drop below the straight line, as shown in Fig. 47, and converge towards a point, at zero arc length, or e ' = 28 volts. This looks as if, of the potential drop of e = 36 volts of the carbon arc, only a part, e ' = 28 volts, occurs at the surface of the terminals, and the remaining part, e" = 8 volts, occurs in the space within a short distance from the terminal surface. If then the arc length is decreased to less than the distance within which the terminal drop e" occurs, the arc meets only a part of this ter- minal drop e", and, for very short arc length, only the terminal drop e ' occurs. Possibly the voltage e ' = 28 is consumed at the negative terminal in producing the conducting vapor stream, 142 RADIATION, LIGHT, AND ILLUMINATION. while the voltage e" = 8 is consumed by the moving vapor stream in penetrating a layer of dead carbon vapor formed by heat evaporation from the positive terminal, and surrounding this terminal. Stability Curves of the Arc. 64. From the volt-ampere characteristic of the arc, as rep- resented by equation (2) and reproduced in Fig. 48 as Curve I, for a magnetite arc of 1.8 cm. (about 0.75 in.) length, it follows that the arc is unstable on constant potential supply, as the, voltage consumed by the arc decreases with increase of current and, inversely, a momentary increase of current decreases the consumed voltage, and, on constant voltage supply, thereby increases the current, still further decreases the arc voltage and increases the current, and the arc thus short circuits; or a momentary decrease of current increases the required voltage and, at constant supply voltage, continues to decrease the cur- rent and thus increase still further the required voltage, that is, the arc goes out. On constant voltage supply only such apparatus can operate under stable conditions in which an increase of current requires an increase, and a decrease of current a decrease of voltage, and thus checks itself. Inserting in series with the arc, curve I, in Fig. 48, a constant resistance of 10 ohms, the voltage consumed by this resistance, e = ir, is proportional to the current, and given by the straight line II. Adding this voltage to the arc voltage curve I, gives the total voltage consumed by the arc and its series resistance, as curve III. In curve III, the voltage decreases with increase of current, for values of current below i = 2.9 amperes, and the arc thus is unstable for these low currents, while for values of current larger than i = 2.9 amperes, the voltage increases with increase of current. The point i = 2.9 amperes thus separates the unstable lower part of the curve III from the stable upper part. With a series resistance of r = 10 ohms, a 1.8-cm. mag- netite arc thus requires at least e = 117 volts supply voltage, and i = 2.9 amperes for steady operation. With a larger series resistance, as r = 20 ohms, represented by curve II' and III', a larger supply voltage is required, but smaller currents can be operated ; with a lower series resistance, r = 5 ohms, curves ARC LAMPS AND ARC LIGHTING. 143 II" and III", larger currents are required for stable operation, but a lower supply voltage is sufficient. When attempting to operate an arc close to the stability limit, i , where a small variation of voltage causes a large variation of current, the operation of the arc is unsatisfactory, that is, the FIG. current drifts; small variations of the resistance of the arc stream, and thereby of the voltage consumed by the arc, cause excessive fluctuations of the current. These pulsations of cur- rent can be essentially reduced by using a large inductance in series with the arc, and an arc can be operated very much closer to its stability limit if its series resistance is constructed highly inductive, that is, wound on an iron core. Obviously, 144 RADIATION, LIGHT, AND ILLUMINATION. no series inductance can extend stable operation beyond the stability point %. At the stability limit i QJ the resultant characteristic III in Fig. 48 is horizontal, that is, the slope of the resistance curve e f II, r = - i is equal but opposite to the slope of the arc char- de acteristic I, ; that is, at the stability limit, ii +r =-> ; <*> and, substituting equation (2) in (4), gives and the total voltage consumed by the arc of current i and length I and the series resistance r required to just reach sta- bility is E = e + ir, , fe (* + Z.) , * (Z + Z.) . e o ~r - ; r - 7: , \/i 2 Vt that is, /. VTV or, E^e+ti. ( 6) This curve is called the stability curve of the arc. It is shown as IV in Fig. 48. It is of the same form as the arc characteristic I, and derived therefrom by adding 50 per cent of the voltage consumed in the arc stream. Thus, in an arc requiring 80 volts, of which e = 30 volts are consumed at the terminals, ^ = 50 volts in the arc stream, for stable operation, a supply voltage of more than E = e + -^ = 80 + 25 = 105 volts is required. ARC LAMPS AND ARC LIGHTING. 145 The stability limit, on constant potential, thus lies at an ex- cess of the supply voltage over the arc voltage by 50 per cent of the voltage, e v consumed in the arc stream. In general, to get reasonable steadiness of the current, and absence of drifting, a supply voltage is used which exceeds the arc voltage by from 75 per cent to 100 per cent or more of the voltage, e v of the arc stream. 65. The preceding consideration applies only to those arcs in which the gas pressure in the space surrounding the arc, and thereby the arc vapor pressure and temperature, are constant and independent of the current, as is the case with arcs in air (even " enclosed" arcs, as the enclosure cannot be absolutely air- tight), as it is based on the assumption that the section of the vapor stream is proportional to the current. With arcs in which the vapor pressure and temperature vary with the current, as with vacuum arcs, as the mercury arc, the reasoning has to be correspondingly modified. Thus in the mercury arc in a glass tube, if the current is sufficiently large to fill the entire tube, and not so large that condensation of the mercury vapor cannot freely occur in the condensing chamber, the power p l dissi- pated by radiation, etc., may be assumed as proportional to the length Z of the tube, and to the current i: p i = 6l i = kli, (7) thus gives e 1 = kl f or independent of the current; and e = e + e v = e + A*; (8) that is, the voltage consumed by a mercury arc, within a cer- tain range of current, is constant and independent of the cur- rent, and consists of a constant part, the terminal drop e , and a part which is proportional to the length and to the diameter of the tube. Approximately it is for the mercury arc in a vacuum: 1.4 e = 13 volts ; k = -y- Id hence, , Calculating approximately the increase of vapor pressure and thereby of arc-stream resistance at high currents, and the 146 RADIATION, LIGHT, AND ILLUMINATION. increase of resistance at low current, due to the arc stream not completely rilling the vapor tube, gives for the vacuum arc the approximate equation: I e = e + df> 7 7 d al d -01 r- ^ where l d = diameter of arc tube, cm., I = length of arc, cm., i = current. For the mercury arc, it is : e = 13 volts, a = 1.68, 6 = 0.29 for mercury anode, = 0.167 for graphite or metal anode, c = 0.52. Arc Length and Efficiency. 66. The arc most frequently employed for illumination is the plain carbon arc. In this the arc flame of the vapor stream gives no useful light, but the light is given by the black-body radiation of the incandescent carbon terminal, mainly the positive terminal, which is hottest, and is given at high efficiency due to the very high temperature of the radiator. The light of the carbon arc thus is incandescent light, and not lumines- cence. In the alternating carbon arc, alternately, the two ter- minals are positive and negative, and, as relatively little heat is produced at the negative terminal, the average temperature of the carbon terminals of an alternating arc is lower, and the efficiency of light production therefore less. Thus, while direct- current carbon arcs reach efficiencies corresponding to specific consumptions of from 1 to 1.5 watts per mean spherical candle power, alternating carbon arcs show only from 2.5 to 3 watts per candle power, or even still higher specific consumption. Thus, the only excuse for the use of the alternating carbon arc is the much greater simplicity and convenience of the electric generating apparatus, the stationary transformer, compared to the arc machine with the direct-current arc, and with the de- velopment of the constant-current mercury-arc rectifier; this ARC LAMPS AND ARC LIGHTING. 147 difference in the simplicity of generation of the arc current has largely disappeared. In the direct-current carbon arc, the light comes mainly from the positive terminal; in the alternating carbon arc equally from both terminals, and the distribution curve of the light thus is different. Since in the carbon arc no useful light comes from the arc flame, the voltage and therefore the power consumed in the arc flame is wasted, and in general, therefore, the efficiency of light production of the carbon arc is the higher the shorter the arc. Thus comparing in Fig. 49 a 1-in. carbon arc A with a FIG. 49. 0.5-in. carbon arc B, the former requires, at 5 amperes, 112 volts and 560 watts, the latter only 84 volts and 420 watts, but radiates the same amount of light from the incandescent tip of the positive carbon. As the 1-in. arc requires 33 per cent more power, and only produces the same amount of light, it is less efficient than the latter. Thus, the shorter we make the arc and the less power we therefore consume in it the more efficient seems the light production, as we produce the same amount of light radiation from the positive terminal in either case. When we come to short arc lengths, however, while the same amount of light is produced at the positive terminal, we do not get the same amount of light from the lamp, as an increasing part of the light is intercepted by the negative ter- minal. Thus with the 1-in. arc, A, in Fig. 49, the light escapes 148 RADIATION, LIGHT, AND ILLUMINATION. freely from the incandescent positive only in the space above the lines m, while at m the shadow of the negative terminal begins to obstruct the light more and more, and does so com- pletely vertically below the arc. In the 0.5-in. arc B the area covered by the shadow of the negative terminals is somewhat increased, but in both arcs A and B the obstruction of the light by the shadow of the negative is still so small that the saving in power far more than makes up for it. In the 0.125-in. arc, however, C in Fig. 49, the shadow of the negative ter- minal m has crept up greatly, and thus, when decreasing the arc length, a point is reached where the increasing shadow of the negative terminal reduces the light more than the de- creasing arc length reduces the power supply. Maximum efficiency of light production thus is reached in the carbon arc at a certain definite arc length (which depends on the size of the electrodes and on the current), at which the change of power consumption just balances the change of radiated light, which results from a change of arc length and thereby of shadow of negative terminal. With the high-current (9 to 10 amperes) open arcs, the maxi- mum efficiency point is at about J-in. arc length, giving a voltage consumption of about 45 to 50 volts. Such arcs require daily trimming, and therefore are no longer used in American cities, except in a few places. The open or short-burning arc has been practically entirely superseded by the enclosed or long-burning arc lamp, in which the arc is enclosed by an almost air-tight globe, the combustion of carbon is greatly decreased, and the life of the carbons thus increased about tenfold. In the open arc of large current, the carbon terminals burn off into a rounded shape, but in the enclosed arc, the current being less and combustion greatly reduced, the carbon terminals burn off to more flat shape, and thus obstruct the light more; and, furthermore, since at the lower current the size of the incandescent spot of the positive terminal is less, the maximum efficiency of light production in the enclosed arc lamp is reached at a much greater arc length, about f in. As the result thereof, the enclosed arc lamp, with 5, 6.5 or 7.5 amperes in the arc, consumes from 70 to 75 volts. 67. Entirely different are the conditions in the luminous ARC LAMPS AND ARC LIGHTING. 149 arc, as the magnetite arc. In this, the light is given by the vapor stream, and not by the terminals, and the voltage e and power consumed by the terminal drop thus is wasted, and the voltage e l and power p t consumed by the arc stream is useful for light production. The greater, therefore, the voltage e l of the arc stream is, compared with the terminal drop e , or in other words the longer the arc, the higher is the efficiency of light production. Thus a 4-amp. magnetite arc of 0.125-in. length requires 41 volts, while a 0.5-in. 4-amp. arc requires 64 volts ; that is, only 56 per cent more voltage and thus power, but gives about four times the light. A 1-in. arc requires 95 volts or 48 per cent more power than the 0.5-in. arc, and gives twice the light. The greater, thus, the arc length of the luminous arc, with the same current, the higher is the efficiency. How- ever, at the same current, the longer the arc, the greater is the power consumption. In the design of the arc lamp the power consumption is given, and the problem is to select the most efficient arc length for a given and constant power consumption. As an increase of arc length increases the arc voltage for the same power consumption, the current has to be decreased, and the efficiency of the arc conductor decreases with decrease of current. Thus, with increasing arc length at constant power consumption in the luminous arc, a point is reached where the decrease of current required by the increase of arc length and thus arc voltage decreases the efficiency more than the increase of arc length increases it. Thus with the luminous arc, for a given power consumption, a definite arc length exists, which gives maximum efficiency. Assuming the light given by the arc to be proportional to the arc length and the current in the arc, L = k'li, (9) if the power p shall be consumed in the arc, ei = p] (10) however, by (2), e=e + ^ (11) Vi (neglecting the small quantity l v as the calculation can obviously be approximate only). 150 RADIATION, LIGHT, AND ILLUMINATION. From (10) and (11) follows: ~ (12) fe and, substituting this in (9), gives: k L = - (pVi - ejVi), (13) and the maximum amount of light produced by power p is given by: dL This gives (14) 3e hence, by (13): z , (15) and herefrom, by (12) and (11), the values of the arc length Z and the arc voltage e. Assuming p = 300 watts, and the constants of the magnetite arc: e Q = 30, k = 31, gives: i = 3.33 amperes, e = 90 volts, I = 2.21 cm. = 0.885 in. Near the maximum efficiency, where the efficiency curve is horizontal, the efficiency does not vary much for moderate changes of current and of arc length. Thus, in above instance, practically the same efficiency is reached for currents from 3 amperes to 4 amperes. Larger currents and shorter arc lengths, however, are pref- erable in an arc lamp. (1) Because the shorter and thicker arc is less affected by minor air currents, etc., than the thin long arc, hence, is steadier. (2) The shorter arc gives lower voltage, and this, in constant- current arc lighting, permits with the same total circuit voltage the use of more arc lamps in series. Thus in the magnetite arc lamp a current of 4 amp. has been chosen. i = 4: e = 75 volts, and I + l^ = 0.73 in., or about f-in. arc length. ARC LAMPS AND ARC LIGHTING. 151 In general, obviously the maximum efficiency points of lumi- nous arcs occur at much greater arc lengths than in the plain carbon arc. Since the lower efficiency of the alternating carbon arc is due to the lower temperature of the terminals, which are heated during one half-wave only, and in the luminous arc the tem- perature of the terminals does not determine the light pro- duction, but the light is produced by the vapor stream, no essential difference exists in the efficiency of a luminous arc, and practically no difference in the efficiency of the flame- carbon arc, whether operated on alternating or on direct current; that is, the alternating luminous or flame-carbon arc, with the same luminescent material, has the same efficiency as the direct- current luminous or flame-carbon arc, but the alternating plain carbon arc is much less efficient than the direct-current carbon arc. Arc Lamps. 68. The apparatus designed for the industrial production of light by arc conduction, or the arc lamp, in general comprises four elements : (1) The current-limiting or steadying device. (2) The starting device. (3) The feeding device. (4) The shunt protective device. (1) From the volt-ampere characteristic of the arc as given by equation (2) and curves, Fig. 46, it follows that an arc can- not be operated directly on constant voltage supply, but in series thereto a steadying device must be inserted; that is, a device in which the voltage increases with the current so that the total voltage consumed by the arc and the steadying device increases with increase of current, and pulsations of current thus limit themselves. All arc lamps for use on constant voltage supply thus contain a sufficiently high steadying resistance, or, in alternating-current circuits, a steadying reactance. Arc lamps for use on constant-current circuits, that is, cir- cuits in which the current is kept constant by the source of power supply, as the constant-current transformer or the arc machine, require no steadying resistance or reactance. 152 RADIATION, LIGHT, AND ILLUMINATION. Where several lamps are operated in series on constant poten- tial mains, as two flame-carbon arcs in series in a 110-volt cir- cuit, or five enclosed arc lamps in a 550-volt railway circuit, either each lamp may have its own steadying resistance, or a single steadying resistance or reactance of sufficient size may be used for all lamps which are in series on the constant poten- tial mains. (2) Since the arc does not start itself, but has to be started by forming the conducting vapor bridge between the terminals, all arc lamps must have a starting device. This consists of a mechanism which brings the terminals into contact with each other and then separates them, and hereby forms the vapor conductor, that is, starts the arc. (3) As the arc terminals consume very rapidly in some arcs, as the open carbon arc, and very slowly in others, as the enclosed carbon arcs or the luminous arcs, some mechanism must be provided which moves the terminals towards each other at the rate at which they are consumed, and thereby main- tains constant arc length and thus constant voltage and power consumption. With arcs in which the electrodes consume very slowly, as the magnetite arc, the feeding may occur only at long intervals, every quarter or half hour, or even less frequently, while in arcs with rapidly consuming electrodes, as the flame arcs, practically continuous feeding is required. (4) The circuit between the arc electrodes may accidentally open, as by a breakage of one electrode, or by the consumption of the electrodes if the lamp-trimmer has forgotten to replace them, or one of the electrodes may stick and fail to feed, and the arc thus indefinitely lengthen. In such cases, either the entire circuit would open, and thus all the lamps in series in this circuit go out, or, if the circuit voltage is sufficiently high, as in a constant-current series system, the arc lamp would be consumed and the circuit damaged by a destructive arc. Thus a device is necessary which closes a shunt circuit between the lamp terminals in case the lamp voltage becomes excessive by a failure of proper operation of the lamp. Where only one lamp is operated, on constant potential low- voltage supply, no such protective device is needed. If with two or more lamps in series on constant potential supply, no ARC LAMPS AND ARC LIGHTING. 153 objection exists, in case of the failure of one lamp, to have the others go out also, the shunt protective device may also be omitted, except if the circuit voltage is so high that it may damage the inoperative lamp, as is the case with 550 volts. When operating a number of lamps in series on constant potential supply, as two flame lamps on 110 volts, the shunt circuit, which is closed in case of the failure of one lamp to operate, must have such a resistance, or reactance with alter- nating currents, that the remaining lamp still receives its proper voltage, even if the other lamp fails and its shunt circuit closes. With alternating-current lamps, this does not require a reactance of such size that the potential difference across the reactance equals that across the lamp, which it replaces, but the reactance must be larger; that is, give a higher potential difference at its terminals, than the lamp which it replaces, to leave the normal operating voltage for the remaining lamp, since the voltage consumed by the reactance is out of phase with the voltage consumed by the lamp. 69. For illustration, the operating mechanism of a constant direct-current arc lamp is shown diagrammatically in Fig. 50 : The lower electrode A is held in fixed position. The upper electrode B slides loose in a holder C, and thus, if there is no current through the lamp, drops down into contact with the lower carbon, as shown in Fig. 50. When there is a current through the arc circuit, its path is from terminal 1 through electromagnet S, holder C, upper electrode B, lower electrode A to terminal 2. The electromagnet S is designed so as to give a long stroke. When energized by the current, it pulls up its armature, the lever DD', which is pivoted at E. Through the rod F, the lever D pulls up the clutch G. This clutch and its operation are shown in larger scale in Fig. 51, A and B', it con- sists of a metal piece G, which has a hole somewhat larger than the upper electrode B. This electrode slides freely through the hole, if the clutch G is in horizontal position, as shown in Fig. 51a. When the rod F pulls the clutch G up, and thereby inclines the piece G, as shown in Fig. 516, the edges p and q of the hole in the piece G catch the electrode B, and, in the further upward motion of D and F, raise the other electrode, B, from contact with the lower carbon, A, and thereby start the arc. An elec- tromagnet of many turns of fine wire, and of high resistance, P, 154 RADIATION, LIGHT, AND ILLUMINATION. FIG. 50. FIG. 51a. FIG. 51b. connected in shunt between the lamp terminals 1 and 2, acts upon the side D' of the lever DD', opposite from the side D, on which the series magnet S acts. With the carbons in contact with each other, and practically no voltage between the lamp terminals 1 and 2, the coil P receives no current, and exerts no pull. When by the action of the series magnet S the lever D pulls up, and the arc starts and lengthens, its voltage increases, ARC LAMPS AND ARC LIGHTING. 155 a branch current is established through the shunt magnet P, and this shunt magnet thus opposes the series magnet S. With increasing arc length and thus arc voltage, a point is reached, where the shunt magnet P counterbalances the pull of the series magnet S, and the lever D and thereby the electrodes B come to rest; the arc has reached its full length, that is, the starting operation is over. As soon as, by the combustion of the electrodes, the arc length and thereby the arc voltage be- gins to rise, the current in the shunt magnet P, and thus its pull, increases, while that of the series magnet S, being ener- gized by the constant main current, remains constant; the lever D' thus pulls up, and lowers D, and thereby, through rod F and clutch G, the upper electrode B, and thus maintains con- stant arc length. During the combustion of the electrodes, by the operation of the shunt magnet P the clutch G and thereby the upper electrode B are gradually lowered, and the arc length thus maintained constant. Ultimately, however, the clutch G hereby approaches the horizontal position, shown in Fig. 51 A, so far, that the edges of the hole, p and q, cease to engage, and the electrode B is free and drops down on the lower carbon A. While dropping, however, the arc shortens, the arc voltage, and thereby the current in the shunt magnet P, decreases, the pull of this magnet decreases correspondingly, and the series magnet S pulls the clutch G up again, thereby catches the electrode B -usually before it has dropped quite down into contact with the lower carbon A and again increases the arc to its proper length, and the same cycle of operation repeats: a gradual feeding down of the upper electrode B by the shunt magnet until it slips, and is pulled up again by the series magnet S. From the same lever D is supported, by rod L, a contact- maker K. If then the upper electrode B should stick, and thus does not slip, when by the shunt magnet P the clutch G has been brought into horizontal position, or, if B has been entirely con- sumed, etc., the arc continues to lengthen and the pull of the shunt magnet P to rise, and D thereby goes still further down until contact-maker K closes the contacts MN, and thereby closes a shunt circuit from terminal 1 over resistance R, con- tacts MKN to terminal 2. In the same manner, if, by the breaking of one electrode or any other cause, the arc should be interrupted, for a moment the full current passes through shunt 156 RADIATION, LIGHT, AND ILLUMINATION. magnet P, it pulls up its armature D' to its full extent, and thereby closes the shunt circuit around the lamp. When the current is taken off the circuit, armature D drops down, and thereby K closes the shunt circuit, and clutch G releases the electrode B, and it drops down into contact with carbon A. In starting the lamp, two paths thus are available: over series magnet S, and electrodes B and A, or over resistance R and contacts MN. While the resistance of the former path is very low, it is not entirely negligible. Therefore a sufficient resistance R must be inserted in the by-path MN, so that in starting practically all the current passes over S and the elec- trodes, as otherwise the lamp would not start. During the pulling up of the armature D by the series magnet S, in start- ing, the contact K opens, before the clutch G has caught the electrode B', that is, while the electrodes are still in contact with each other, and the opening of contact K therefore breaks no appreciable voltage or current, hence is sparkless. In this lamp, no steadying resistance is used, as it is intended for operation on a constant-current circuit. If used on con- stant-potential circuit, as, for instance, a number in series on 550 volts, a steadying resistance R would be inserted, as indi- cated at R in Fig. 50. The starting of the arc is accomplished by series magnet S and clutch G; the feeding by shunt magnet P; the protective device is the contact MKN. Such an arc lamp is called a differential lamp, as it is con- trolled by the differential action of a shunt and a series magnet. It contains a floating system of control; that is, the upper electrode is suspended by the balance of two forces, exerted by the series and the shunt magnet; that is, by the current and the voltage; the upper carbon therefore is almost continuously moving slightly in following the pulsation of the arc resistance which occurs during operation. Since, with the plain carbon arc, the arc flame gives no light, this pulsation of the arc length is not objectionable; and, since the lamp regulates very closely and rapidly for constant terminal voltage, it is very easy on the circuit, that is, does not tend to produce surging of current and voltage in the circuit. The floating system of control is, there- fore, used in all carbon arc lamps. ARC LAMPS AND ARC LIGHTING. 157 Where a single lamp is operated on a constant-potential circuit, the mechanism can be simplified by omitting the pro- tective shunt circuit RMN, and omitting the shunt magnet P, as, with a change of arc length, the main current and thereby the pull of the series magnet S varies, and the control thus can be done by the series magnet. Such a lamp then is called a series lamp. An alternating-current series lamp is shown diagrammatically in Fig. 52. In starting, the series magnet S pulls up the electrode B by the clutch G, in the same manner as in Fig. 50. With increasing arc length and thus increasing voltage consumed by the arc, the current in the arc and thus in the series magnet S decreases, and thereby the pull of this magnet, until it just counterbalances the weight of the armature, and the motion stop. With the consumption of the carbons, the armature D, clutch G and elec- trode B gradually move down, until the clutch lets the carbon slip, the arc shortens, the current rises, and the magnet S pulls up again, the same as in Fig. 50. A reactance x in series with the lamp, as steadying device, limits the current. This reactance usually is arranged with different terminals, so that more or less reactance can be connected into circuit, and the lamp thereby operated, with the same arc voltage, on supply circuits of different voltage, usually from 110 to 125 volts. Obviously, such a series lamp can be used only as single lamp on constant potential supply, as it regulates by the varia- tion of current, and, with several lamps in series, the current would vary in the same manner in all lamps. One lamp would then take all the voltage, draw an arc of destructive length, while the other lamps would drop their electrodes together and go out. 70. With the luminous arc, in which the light is proportional FIG. 52. 158 RADIATION, LIGHT, AND ILLUMINATION. to the arc length, pulsations of the arc length, if appreciable, give pulsations of the light, and the floating system of control, which maintains constant voltage by varying the arc length in correspondence with the pulsation of arc resistance, thus is undesirable, and a mechanism maintaining fixed arc length is required. Such a mechanism, that of the magnetite arc lamp, is diagrammatically illustrated in Fig. 53. As, during operation, a melted pool forms on the sur- face of the electrode, the elec- trodes are left separated from each other when taking the power off the circuit, since when letting them drop to- gether when taking off the power as in the carbon arc they may weld together and the lamp thus fail to start again. A represents the lower or negative magnetite terminal which is movable, B, the non- consuming upper positive elec- trode, consisting of a piece of copper, with heat-radiating wings, W, which is a station- ary and fixed part of the lamp. C is the chimney required to FlG - 53 - carry off the smoke. When starting, the circuit, beginning at terminal 1, passes contacts MN, through a powerful electromagnet or solenoid and resistance R, to terminal 2. The solenoid pulls up its core D, and by the clutch G raises the lower electrode A into contact with the upper electrode, B, and thereby closes the circuit from 1 over series coil S, electrodes B and A, to terminal 2. The series coil S pulls up the core, and thereby opens the contact MN, thus cuts out the shunt circuit OR. The solen- oid thus loses its excitation, and drops the clutch G, and the lower terminal A drops away from the upper terminal B by a ARC LAMPS AND ARC LIGHTING. 159 distance which is fixed by an adjustable clutch, Q, and thus starts an arc of definite length. When during the consumption of this electrode A the arc length and thereby the arc voltage rises, the shunt magnet P increases in strength, and ultimately pulls the core F away from the series magnet S, closes the contact MN of the shunt circuit OR, and thereby energizes the solenoid 0. This again raises, by the clutch G, the lower electrode A into contact with the upper electrode B, and so repeats the cycle of operation. If the arc between A and B opens, the solenoid S loses its excitation, the coil F drops and closes the contact MN of the shunt circuit OR. If the arc resistance were perfectly constant, such a mechan- ism would not operate satisfactorily, as the arc would have to lengthen considerably to have the shunt coil P overpower the series coil S sufficiently to pull the core F down, close the con- tact MN, and thereby feed. The resistance of an arc, and thereby, at constant length, its voltage, pulsates, however, continuously, about as shown diagrammatically in Fig. 54, that is, peaks of voltage of vari- isol 110 1005 \r FIG. 54. ous height follow each other. Thus with an average arc volt- age of 75, momentary peaks of 85 volts will probably be reached every few seconds, peaks of 100 volts every few minutes, of 110 volts every half hour. Adjusting the shunt magnet P so as to operate at 105 volts, a voltage peak above 105, which causes the lamp to feed, would be reached about every 20 minutes. During 20 minutes, however, the arc length does not appre- 160 RADIATION, LIGHT, AND ILLUMINATION. ciably increase by the consumption of the electrode. Due to the character of the arc as a pulsating resistance, such a con- trolling mechanism thus maintains constant arc length by a potential magnet set for a voltage considerably above the aver- age arc voltage. Such a mechanism, controlling for constant arc length, does not operate for constant voltage at the lamp terminals, but allows the pulsation of the arc resistance to appear as pulsation of the terminal voltage. In a constant-current circuit, with many lamps in series, these voltage pulsations of the individual arcs overlap and have no effect on the circuit. When operating, however, a lamp of such a mechanism on a low-voltage constant potential circuit, a highly inductive steadying resistance is de- sirable, to take care of the pulsations of arc voltage. 71. The open or short-burning carbon arcs of former times which have survived only in a few cities were operated on constant direct-current circuits of 9.6 and 6.6 amp. with 40 to 45 volts per lamp. The present enclosed or long-burning carbon arcs are oper- ated on constant-current circuits of 5 amp. and 6.6 amp. direct current, or of 6.5 and 7.5 amp. alternating current, with about 72 volts at the lamp terminals. They are operated as single lamps, of 5 to 9 amp. on direct- or alternating-current constant potential circuits of 110 to 125 volts, or two lamps in series on circuits of 220 to 250 volts. The flame-carbon arcs, as short-burning open arcs, are usually operated two in series on constant-potential circuits of 110 to 125 volts, or four in series on circuits of 220 to 250 volts, with 10 to 15 amp. in the arc. The luminous arcs are operated on 4- and 6.6-amp. constant direct-current circuits (magnetite lamp), with 75 volts per lamp, and on 3- and 4.5-amp. constant alternating-current cir- cuits (titanium-carbide arc), with 80 volts per lamp. Arc Circuits. 72. Arc lamps are built for, and operated on, constant-poten- tial supply, and on constant-current supply. In general, the constant-potential arc lamp is less efficient, as voltage and thereby power is consumed in the steadying resistance which is required to limit the current, that is, to give an approximate ARC LAMPS AND ARC LIGHTING. 161 constant-current effect, as discussed above. In alternating- current circuits, reactance may, and usually is, employed in- stead of the steadying resistance, and the waste of power thereby greatly decreased. Voltage, however, is still consumed and the power factor lowered. An additional waste of energy generally occurs in constant- potential arc-lamp circuits, due to the standard distribution voltages of low-potential circuits being higher than necessary for the operation of a single lamp, but too low for the operation of two lamps in series. Thus with an enclosed 5-amp. carbon arc lamp, with about 70 volts at the arc, a supply voltage of 95 to 100 volts would be sufficiently high above the stability curve of the arc (Fig. 46) to give steady operation. Distri- bution voltages, however, vary between 110 to 130 volts, and the difference thus must be consumed in resistance, giving an additional waste. (Except in those rare cases, where as steady- ing resistance some useful devices, as incandescent lamps, can be employed.) With an enclosed arc lamp on a 125- volt cir- cuit, only 36 volts, or 29 per cent, are usefully employed in heating the carbon terminals and thereby producing the light, while the remaining 71 per cent is wasted in the resistance and in the non-luminous arc flame. Somewhat better are the conditions when operating two high-current open arcs, as two flame lamps, in series on such a circuit. However, at the lower distribution voltage, as 110 volts, the supply voltage may be already so close to the stability limit of the arc that the arcs are not as steady as desirable. The low-current, long luminous arcs of electro-conduction, as the magnetite arc, can in general be operated only with diffi- culty on circuits of 110 to 125 volts, and therefore are, for constant-potential service, frequently designed for operation as single lamps on 220 to 250 volts supply, with extra great arc length. For indoor illumination, constant-potential arc lamps must obviously be used, as safety does not permit the introduction of the high-voltage series arc circuits into houses. For out- door illumination, as street lighting, in the United States the constant-current arc lamp is, with the exception of the interior of a few very large cities, as New York, used exclusively, due to its greater efficiency, and the greater distance to which the cur- 162 RADIATION, LIGHT, AND ILLUMINATION. rent can be sent at the high voltage of the constant-current circuit. In American towns and cities, where arc lamps are used for street lighting, practically always the entire city up to the farthest suburbs is lighted by arc lamps, and frequently arc lamps installed even beyond the reach of the high-potential primary alternating-current supply. To reach such distances with low-voltage constant-potential supply, is impossible, and thus the constant-current series system becomes necessary. In European cities, where a prejudice exists against high-voltage constant-current circuits, and people are satisfied to have arc lamps only in the interior of the city, and leave the lighting of the suburbs to gas lamps, constant-potential street lighting is generally employed, and is eminently satisfactory within the limitations with which European cities are satisfied, but would be impossible in the average American city. Where plain carbon arcs are used in American cities the enclosed arc lamp is exclusively installed, and open arc lamps have survived only in a few exceptional cases, mainly where political reasons have not yet permitted their replacement by modern lamps. The lesser attention required by the enclosed arc lamp weekly trimming instead of daily with the open arc lamp has been found to make it more economical than the open arc lamp of old. In Europe, where labor is cheaper, and the daily attention not considered objectionable, the open or short-burning arc lamp has maintained its hold, and the en- closed arc lamp has never been used to any great extent. With the development of the flame carbon, the flame arc, therefore, has found a rapid introduction in Europe, while in the United States it has been excluded from use in street lighting, due to its short-burning feature, which requires daily trimming, and is used only for decorative purposes, for advertising, etc., and for low-grade interior lighting, as foundries, etc. In spite of the lower efficiency of the alternating carbon arc, the constant-current circuits used for arc lighting are generally alternating, due to the greater convenience of generation of alternating current, and constant direct-current arc circuits used only where the city or the electric light company lays stress on the efficiency of light production. While the development of the constant-current mercury arc rectifier has made the generation of constant direct current ARC LAMPS AND ARC LIGHTING. 163 almost as simple and convenient as that of alternating current, this has very little increased the use of the direct-current en- closed arc lamp, but when changing to direct current sup- ply, usually the arc lamp is also changed to the luminous arc, the magnetite lamp, which gives more light and consumes less power. In constant-current arc circuits, usually from 50 to 100 lamps are operated in series on one circuit, with circuit volt- ages of 4000 to 8000 volts. Seventy-five-lamp circuits, of 6000 volts, probably are the most common. 73. Constant direct current was produced by so-called "arc machines" or "constant-current generators." Of these only the Brush machine has survived, and is now also beginning to disappear before the mercury arc rectifier, which changes the alternating current of the constant-current transformer to direct current without requiring moving machinery. The Brush machine in its principle essentially is a quarter- phase constant-current alternator with rectifying commutator. An alternator of low armature reaction and strong magnetic field regulates for constant potential: the change of armature reaction, resulting from a change of load, has little effect on the field and thereby on the terminal voltage, if the armature reaction is low. An alternator of very high armature reaction and weak field, however, regulates for constant current: if the m.m.f., that is, the ampere-turns required in the field coil to produce the magnetic flux, are small compared with the field ampere-turns required to take care of the armature reaction, and the resultant or magnetism-producing field ampere-turns thus the small difference between total field excitation and armature reaction, a moderate increase of armature current and thereby of armature reaction makes it equal to the field excitation, and leaves no ampere-turns for producing the mag- netism; that is, the magnetic flux and thereby the machine voltage disappear. Thus, in such a machine, the current out- put at constant field excitation rises very little, from full volt- age down to short circuit, or, in other words, the machine regulates for approximately constant current. Perfect constant- current regulation is produced by a resistance shunted across the field, which is varied by an electromagnet in the machine circuit, and lowered that is, more current shunted through it, and 164 RADIATION, LIGHT, AND ILLUMINATION. thereby the field excitation decreased if the machine cur- rent tends to rise by a decrease of the required circuit voltage, and inversely. The constant-current regulation of the arc machine thus is not produced by its so-called " regulator/' but approximate constant-current regulation is inherent in the machine design, and the regulator merely makes the regulation perfect. A more explicit discussion of the phenomena in the arc machine, and especially its rectification, is given in Chapter III of Section II of "Theory and Calculation of Transient Electric Phenomena and Oscillations." In alternating-current circuits, approximate constant-current regulation is produced by a large reactance, that is, by self- induction, in the circuit. In transformers, the self-induction is the stray field, or the leakage flux between primary coil and secondary coil. In the constant-current transformer, which is most generally used for constant alternating-current supply from constant alternating voltage, the primary turns and the secondary turns are massed together so as to give a high mag- netic stray flux between the coils. Such a transformer of high internal self-induction, or high stray flux, regulates approxi- mately for constant current. Perfect constant-current regula- tion is produced by arranging the secondary and the primary coils movable with regard to each other, so that, when low cir- cuit voltage is required, the coils move apart, and the stray flux, that is, the reactance, increases, and inversely. The motion of the coils is made automatic by balancing the magnetic repulsion between the coils by a counter- weight. A discussion of the constant-current transformer and its mode of operation is given in "Theory and Calculation of Alternating Current Phenomena," Fourth Edition, page 85. In the so-called "constant-current reactance," the two coils of the constant-current transformer are wound for the same current, and connected in opposition with each other, and in series to the arc circuit into the constant-potential mains. With the coils close to each other, the reactance is a minimum, and it is a maximum with the coils their maximum distance apart. The constant-current reactance has the advantage of greater cheapness, but also has the serious disadvantage that it connects ARC LAMPS AND ARC LIGHTING. 165 all the arc circuits electrically with the constant-potential alter- nating-current system, and any ground in an arc circuit is a ground on the constant-potential supply system. As grounds are more liable to occur in arc circuits, the constant-current reactance is therefore very little used, and generally the con- stant-current transformer preferred, as safer. In the constant direct-current mercury-arc rectifier system, the constant-potential alternating-current supply is changed to constant alternating current by a constant-current transformer, and the constant alternating current then changed to constant direct current by the mercury-arc rectifier. An explicit dis- cussion of the phenomena of the constant-current mercury arc rectifier is given in Chapter IV of Section II of " Theory and Calculation of Transient Electric Phenomena and Oscillations." If the constant-current arc circuit accidentally opens, with a Brush machine as source of supply, the voltage practically vanishes, as the machine has series field excitation, and thus loses its field on open circuit. The constant-current trans- former, however, maintains its voltage, and gives maximum voltage on open circuit. The mercury arc rectifier, when sep- arately excited by a small exciting transformer, also maintains its voltage on open circuit. If, however, after starting, the excitation is taken off, that is, the exciting circuit opened, as is permissible in a steady arc circuit, the voltage in the arc circuit disappears if the arc circuit is opened. Inversely, when connecting an arc circuit to a Brush arc machine, an appre- ciable time elapses while the voltage of the machine builds up, while with the constant-current transformer and thus also with the constant-current mercury arc rectifier system, full volt- age exists even before the circuit is closed. LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION. 74. Since radiation is energy, it can be measured as such by converting the energy of radiation into some other form of energy, as, for instance, into heat, and measuring the latter. Thus a beam of radiation may be measured by having it impinge on one contact of a thermo-couple, of which the other contact is maintained at constant temperature. A galvanom- eter in the circuit of this thermo-couple thus measures the voltage produced by the difference of temperature of the two contacts of the thermo-couple, and in this manner the temper- ature rise produced by the energy of the incident beam of radia- tion is observed. Probably the most sensitive method of measuring even very small amounts of radiation is the bolometer. The beam of the radiation (or after dissolving the beam into a spectrum, the wave length of which the power is to be measured) impinges upon a narrow and thin strip of metal, as platinum, and thereby raises its temperature by conversion of the radiation energy into heat. A rise of temperature, however, produces a rise of electric resistance, and the latter is measured by enclosing the platinum strip in a sensitive Wheatstone bridge. The rise of temperature of the platinum strip by the small power of radia- tion obviously is so small that it could not be observed by any thermometer. Electric resistance measurements, however, can be made with extreme accuracy, and especially extremely small changes of resistance can be measured. Thus a change of resistance of 1 in a million and, with very sensitive measure- ments, even many times smaller changes can be observed. As 1 deg. cent, produces a resistance change of about 0.4 per cent, a change of one millionth corresponds to a temperature rise f ?tfW deg. cent. Thus, by the bolometer, extremely small amounts of radiation can be measured, as, for instance, the power of the moon's radiation, etc. 166 MEASUREMENT OF LIGHT AND RADIATION. 167 The total radiation energy of a body for a given time can be measured by absorbing it and measuring the heat produced by it, as ; for instance, the amount of ice melted in a calorimeter. Any particular range of the total radiation, as, for instance, the total visible radiation, can be measured in the same manner by passing the radiation first through a body which absorbs that part which is not desired, for instance, a body transparent to visible, but opaque to invisible radiation. As no body is perfectly transparent to one, perfectly opaque to another radi- ation, the separation of the radiation by absorption is nec- essarily incomplete, and correction must therefore be made in the result. This makes this method rather inconvenient and inaccurate. Even when measuring the total radiation by absorption in a calorimeter, it is practically impossible to collect the total radiation without either losing some, or including energy, which is not radiation, but heat conduc- tion or convection. Obviously, by enclosing the radiator in the calorimeter, the latter would measure not only the radi- ation, but also the power lost by heat conduction, convec- tion, etc. Sometimes the power of radiation can be measured by meas- uring input and losses. Thus, in an incandescent lamp, the electric-power input is measured, and the power lost by heat conduction and convection estimated if not entirely negligible. In those cases in which all or most of the energy supplied is converted into radiation, as in an incandescent lamp, this method is the most exact. However, it can directly measure only the total radiation power. To measure the different parts of the radiation so as to determine separately the power in the visible, the ultra-red, and the ultra-violet range, the method of input and losses can be used to give the total radiation power, and, by bolometer or other means, the relative powers of the component radiations measured in a beam of light. From the total radiation and the ratio of its components, then, follows the values of radiation power of the components. 75. Light, however, cannot be measured by any of the pre- ceding methods, since light, in the sense in which it is con- sidered photometrically, is not power, but is the physiological effect of certain wave lengths of radiation, and therefore can- not be measured, physically, as power, but only physiologically, 168 RADIATION, LIGHT, AND ILLUMINATION. by comparison with other physiological effects of the same nature. The power of visible radiation obviously can be measured, and thus we can express the power of the visible radiation of a mercury lamp or an incandescent lamp in watts. But the power of visible radiation is not proportional to the physiologi- cal effect, and thus not a measure thereof. One watt of green radiation gives many times as great a physiological effect, that is, more light, as does one watt of red or violet radiation, and, besides, gives a different kind of physiological effect: a differ- ent color. The unit in which illuminating value of light, or its intensity, is expressed as the "candle-power," is, therefore, a physiological and not a physical quantity, and hence it has no direct or con- stant relation to the unit .of power, or the watt. The unit of light intensity has been chosen by convention: as the physio- logical effect exerted on the human eye by 5 sq. mm. of melting platinum, or by a flame burning a definite chemical compound as amyl acetate or pentane at a definite rate and under definite conditions, etc. Broadly, therefore, the conception of a chemical equivalent of light, that is, a relation between candle power and watt, is irrational, just as, broadly, a relation between time and distance is irrational; that is, just as distance cannot be expressed by the unit of time, so candle power cannot be expressed by a unit of power, as the watt. A relation between two such inherently different quantities can be established only by an additional conventional assumption, and varies with a change of this extraneous assumption. Thus stellar distances are measured in " light years," that is, by the distance traveled by the light in one year, as unit. So also the physiological effect of one definite color of light, as that of the green mercury line, or the yellow sodium line, or the red lithium line, can be related to the unit of power, or the watt, and we may speak of a me- chanical equivalent of green light, or of yellow light, or of red light. When doing so, however, we give to the term " mechan- ical equivalent" a different meaning from what it has in physics, for instance, as "mechanical equivalent of heat." The latter is the constant relation between two different forms of the same physical quantity, while, for instance, the "mechanical MEASUREMENT OF LIGHT AND RADIATION. 169 equivalent of green light " is the relation between a physiolog- ical effect and the physical quantity required to produce the effect, and thus is not necessarily constant, but may, and does, vary with the intensity of the effect, the individuality of the observer, etc. It appears, however, that at higher intensities the relation is very nearly constant and the same with differ- ent observers, so that it is possible to express the physiological effect of a definite wave length of radiation, within the accuracy of physiological measurements, by the power consumed in pro- ducing this wave length of radiation; but it becomes entirely impossible to compare physiological effects of widely different wave lengths by comparing the power required to produce them. When speaking of mechanical equivalent of light, it thus must be understood in the extended meaning of the word, as discussed above. 76. In photometry, and in general in illuminating engineer- ing, it is of essential importance to keep in mind this difference in the character of light, as physiological effect, and radiation, as physical quantity of power. This is the reason why all attempts to reduce photometry to a strictly physical measure- ment, and thereby bring photometric determinations up to the high grade of exactness feasible in physical observations, have failed and must necessarily fail; we cannot physically compare an effect as light, which is not a physical quantity, but somewhere in all photometric methods the physiological feature, that is, the judgment of the human eye, must always enter. Photometric tests therefore can never have the accuracy of strictly physical determinations. All attempts to eliminate the judgment of the human eye from photometry, by replac- ing it by the selenium cell, or the photographic plate, or Crookes' radiometer, etc., necessarily are wrong in principle and in results: some of those instruments, as the bolometer, the radiometer, etc., compare the power of the radiation, others, as the selenium cell or the photographic plate, the power of certain changes of radiation, but their results are comparisons of power, and not of physiological effects, and thus they can- not be of value in measurement of illuminating power. Measurements of light thus are made by comparison with an arbitrarily chosen conventional unit, a primary standard 170 RADIATION, LIGHT, AND ILLUMINATION. of light, as " standard candle," or a duplicate or multiplicate thereof. Obviously, in measurements of light, usually not the primary standard of light is used, but a more conveniently arranged secondary standard of light, that is, a standard which has been calibrated by comparison, directly or indirectly, with a primary standard. 77. The most accurate method of comparing lights is the zero method, as represented by the different types of photom- eters. The illumination produced by the two different sources of light the one to be tested and the standard are made equal by changing the relative distances of the sources. At equal illumination their intensities are proportional to the square of their distances. Thus, for instance, in the bunsen photometer, as shown diagrammatically in its simplest form in Fig. 55, the FIG. 55. two white screens A and B are illuminated, the one, A, by the light, L, which is to be tested, the other, B, by the standard S, as a calibrated or standardized 16-cp. incandescent lamp, and then either L or S or both are moved until, seen from (7, the two sides A and B of the screen become equal, that is, the divid- ing line C between them disappears. When this is the case, L -T- S = x 2 -T- 7/ 2 , where x and y are the two distances of the sources from the screen. Different modifications of the bunsen photometer are most commonly used. As the sensitivity of the eye to differences of illumination is not very great, usually a number of readings are taken on the photometer, and then averaged. For testing incandescent lamps, L, as standard S, a calibrated incandescent lamp is used, operated on the same voltage supply, so that fluctuations of light caused by minor fluctuations of sup- ply voltage eliminate by appearing in both sources L and S. MEASUREMENT OF LIGHT AND RADIATION. 171 For similar reasons, when testing gas lamps or other flames, L, as S, a flame standard, as the pentane lamp, is used, so that the effect of barometric pressure, humidity of the air, etc., appears in both lamps and thereby does not appreciably affect the comparison of their light. A quick and approximate method of comparison of sources of light is given by the shadow photometer by moving an object between the two lamps until the two shadows of the object give the same darkness. When this is the case, the illumination at the object is the same, and the intensities of the two sources are then proportional to the square of their dis- tances from the object. Street lamps can, in this manner, be rapidly compared, with fair accuracy, by pacing the distance from the one to the other, and noting when the two shadows of the observer are equal in dark- ness. If then at x steps from the one lamp, L lt the shadows are equal, and y further steps are required to reach the second lamp, L , it is : A very convenient form of photometer, which gives good results even where the two lights are of some- what different color, is the FlG 56 paraffine photometer. A block of paraffine is cast, as shown in Fig. 56, divided by a sheet of tinfoil in the center C, and covered with tinfoil except at the top and on the sides A and B. It is advantageous to have the center sheet of tinfoil C perforated by a hole D. The block of paraffine then is held so that the side A is illu- minated by the one lamp, L, the side B by the other lamp, S, as shown in Fig. 57. As paraffine is translucent, the entire block then appears luminous, and a beam of light is seen traversing 172 RADIATION, LIGHT, AND ILLUMINATION. the block from the hole D, on the side which receives less light. By moving the paraffine block between the lamps L and S, until both sides of it are of the same luminosity, that is, the dividing line C and the beam cast by hole D disappear, equality of the two illuminations can be located rapidly and with great accuracy. FIG. 57. 78. When comparing lamps giving light of the same color, as incandescent lamps of the same filament temperature, that is, the same efficiency, exact comparisons can be made within the limits of sensitivity of the eye for intensity differences by the photometer by making the two sides A and B of the Bunsen photometer screen, or the two halves of the paraffine block, identical, that is, making the dividing line C disappear. If, however, the color of the two lights is not the same, as, for instance, when comparing a tungsten lamp and an ordinary incandescent lamp, no position of the photometer can be found where the dividing line C between A and B (Figs. 55, 57) dis- appears, but a color difference always remains. To make a comparison, it is therefore necessary for the eye to judge when the two sides A and B are of the same intensity while of different colors. If the color difference is small, as between two different types of incandescent lamps, this can be done with fair accuracy, though obviously not as accurately as the com- parison of lights of identical colors. If, however, the color difference is great, as between the mercury arc and the orange- yellow carbon filament lamp, the uncertainty of equality of the intensity of illumination becomes very great, and constant errors appear, due to the difference of the physiological effect of different colors, and differences also appear between differ- ent observers, so that the photometric comparison of light sources of greatly different colors is quite unreliable, and that not merely by inaccuracy, but by unknown and individual con- stant errors. In such cases, frequently lights of intermediary color are used to reduce the differences in each observation. Thus the carbon filament lamp is compared with the tungsten lamp, the MEASUREMENT OF LIGHT AND RADIATION. 173 tungsten lamp with the carbon arc lamp, and the latter with the mercury arc lamp. Hereby the uncertainty of each obser- vation is reduced by the reduced color difference. In the final result, however, the comparison of the carbon incandescent- lamp standard and the mercury arc lamp no advantage is gained, because the errors of the successive measurements add. Especially is this the case with the constant errors, that is, errors due to the specific color effect, and in consequence thereof the inaccuracy of the final result is not much better than it would be by single and direct comparison. A photometer which is sometimes used for comparing lights of different color, and is based on a different principle from either of the above discussed instruments, is the flicker pho- tometer. In its simplest form it consists of a stationary disk, illuminated by the one lamp, and a rotating half disk or sector in front of it, which is illuminated by the other lamp. At slow rotation a flicker shows, which disappears if the speed be- comes sufficiently high. It is obvious that the more nearly equal the effect on the eye of the two illuminations that of the stationary disk and that of the revolving sector the lower is the speed at which the flicker disappears, and, by adjusting the distances of the two lamps so as to cause the flicker to dis- appear at the minimum speed, the instrument indicates equality of the effect of the two successive illuminations on the eye. This is frequently considered as representing equality of the illumination, and the instrument in this manner used to com- pare illuminations. There is, however, no reason why this should be the case, but, on the contrary, it is improbable. As the persistence of vision, and in general the physiological effects of different colors, are different, the flicker photometer must be expected to have a constant error which increases with color difference; that is, it does not compare lights of different color by their illuminating values, but by some other feature not directly related thereto. 79. The photometer thus cannot satisfactorily compare lights of different colors. After all, this is obvious: the photom- eter compares by identity, but lights of different colors can- not be identical, and thus two such lights cannot be more broadly compared than any other two quantities of different character; that is, a green light can no more be equal to a red 174 RADIATION, LIGHT, AND ILLUMINATION. light than a piece of stone can be equal to a piece of ice. A comparison of quantities of different nature is possible only regarding particular features of the quantities which they have in common. Thus a piece of stone and a piece of ice can be compared regarding their weight, or their density, etc. In the same manner, two different colors of light, or in general two different frequencies of radiation, can be compared by any feature which they have in common. Thus, for instance, the photographic plate compares them in their chemical activity, the bolometer by their physical energy. Light is used for seeing things by, that is, distinguishing objects and differences between objects. Regarding this feature, the distinction of objects given by them, different colored lights can be compared, and a green light can be made equal to a red light in illuminating value. It thus means that any two lights, regardless of their color, have the same intensity if, at the same distance from them, objects can be seen with the same distinctiveness, as, for in- stance, print read with equal ease. The only method, therefore, which permits comparing and measuring lights of widely differ- ent color is the method of " reading distances," as used in the so-called luminometer. It after all is the theoretically correct method of comparison, as it compares the lights by that prop- erty for which they are used. Curiously enough, the lumi- nometer, although it has the reputation of being crude and unscientific, thus is the only correct light-measuring instrument, and the photometer correct only in so far as it agrees with the luminometer, but, where luminometer and photometer disagree, the photometer is wrong, as it gives a comparison which is different from the one shown by the lights in actual use for illumination. The relation between luminometer and photometer for meas- uring light intensity, therefore, is in a way similar to the relation between spark gap and voltmeter when testing the disruptive strength of electrical apparatus: while the voltmeter is fre- quently used, the exact measure of the disruptive strength is the spark gap and not the voltmeter, and, where the spark gap and voltmeter disagree, the voltmeter must be corrected by the spark gap. In the same manner the luminometer measures the quality desired the illuminating value of the light but MEASUREMENT OF LIGHT AND RADIATION. 175 FIG. 58. the photometer may be used as far as it agrees with the lumi- nometer. 80. The luminometer can hardly be called an instrument, but it is merely a black box, as shown in Fig. 58, to screen off all extraneous light, and allow only the light of the source which is to be ob- served, to fall on the print. The print obviously must be black on white, that is, complete absorption and complete reflection, so as not to discriminate in favor of particular colors. No great accuracy could be reached by merely com- paring the ease of reading the same kind of print with different sources of light. A high accuracy, however, is reached by using a print which does not give definite words in which letters which are not clearly seen cannot be guessed from the sense of the word or sentence but a jumble of letters, capitals and small letters, arranged in meaningless words. Such a luminometer chart is given below: Amhof dirito amritu, Lisno ladse pemrane odo Ulay Foresca 1598720 woleb noitaidar. Ybod ergy may Pewos ex Idetnera, bsor poge Morf Tenscerophop War- dog; Omsk whykow efforau tespo ygnew col Brispo Monas albo darmosphor? Cottef vol Demno myo 36802 Erbtomy, quot Hiaworu pio Nio cuguab Qaphla- qua H 530 K b n q; 267 Lloysir baraka nunc, cinq Viamara W x 4 zoliaq kama nambosi erianoscum. Zaraz didym fore ik yiquia Fumne. With such a printed chart in the luminometer, the observer moves towards the light or away from it or the light is moved, with the observer stationary until a point is found at which the large letters, as the capitals, can be clearly dis- tinguished, but the small letters are indistinguishable. This point can be found with great sharpness, and the accuracy of 176 RADIATION, LIGHT, AND ILLUMINATION. observation by the luminometer when used in this manner is nearly as great as that of the ordinary photometer, but, unlike the photometer, the luminometer gives consistent and reliable readings even with widely different colors of light. The comparisons made by the luminometer of widely differ- ent colored lights by different observers agree remarkably well, showing that the distribution of color sensitivity is prac- tically the same in different human eyes. Only occasionally a person is found with abnormally low sensitivity for some par- ticular color this obviously is not a fault of the instrument, but in the nature of the measured object, which is a physiologi- cal effect, and as such may be different in different persons. The luminometer can be still further improved by illuminat- ing one half of the printed chart from the one, the other half from the other, source of light, and then moving the two sources to such distances that the small letters on both sides of the chart become indistinguishable, while the capitals are distinguishable. As well known, the luminometer is largely used for measuring street illumination, as it is very simple and requires no special technical training. Such observations, where the distances are measured by pacing, are crude, and, to get exact results by the luminometer, the same care is required as when using the pho- tometer. The limitation of the luminometer, as generally used, is that it compares lights at constant and relatively low intensity of illumination. The relative intensity of light sources of differ- ent colors changes however over a wide range with the inten- sity of illumination at which they are compared, as discussed in Lecture III. A complete comparison of different colored lights therefore requires measurements at different intensities of illumination. With a photometer, the intensity of illumination can usually be varied over a wide range by bringing the light sources nearer to the screen or removing them farther. In the lumi- nometer, only a moderate change of the intensity of illumina- tion, at which the comparison is made, can be produced by using different sizes of print, and the interpretation of such tests is difficult. A wide and definite range of intensities of illumination, at which comparison of the light sources is made by the lumi- MEASUREMENT OF LIGHT AND RADIATION. 177 nometer, can be secured by using gray print on white back- ground, and lights of different colors thereby compared over a wide range of illuminations. With a luminometer chart of gray letters, of albedo a, on white background, the illumination or light flux density, at which the luminometer readings are made as described above, is: where i is the illumination or light flux density when using black print on white background. 81. Since light is a physiological effect, the measurement of this effect requires a physiological unit, which is more or less arbi- trarily chosen. Such a unit may be a unit of light, that is, of light intensity or light flux, as a flame, or it may be a unit of light-flux density or illumination, that is, of light flux per unit area. Thus, a fairly rational unit of light-flux density or illumination would be the illumination required at the limits of distinguish- ability of black print of a specified type, on white back- ground, that is, the light flux per unit area by which, with such black print on white background, the capitals and large letters can still be distinguished, while the small letters are indistin- guishable. Usually so-called " primary standards " have been chosen as units of light intensity. Violle recommended as standard the light at right angles from 1 sq. cm. of melting platinum. (Ap- proximately 20 cp.) This unit has never been introduced, partly due to the difficulty of producing it, partly due to the unsuitability of platinum for this purpose: platinum gives gray-body radiation, therefore any impurity, as a trace of car- bonized dust, may increase the light. Candles have been largely used for standards, as the name of the unit implies, made and burned under definite specifications. As individual candles vary widely in their light, the use of the candle as standard necessarily is very crude and inaccurate, and thus unsatisfactory. The only primary standard which has found extensive and international use is the amyl-acetate lamp of Hefner. This is a lamp burning arnyl acetate at a definite rate, with a definite 178 RADIATION, LIGHT, AND ILLUMINATION. height of flame and definite conditions regarding air pressure and humidity. This Hefner lamp, or German candle, equals about 90 per cent of the British candle and equals 90 per cent of the international candle. Amyl acetate has been chosen, as it can easily be produced in chemical purity, and gives a good luminous flame. The flame, however, is somewhat reddish, thus markedly different from the color of the carbon incandescent lamp, and departs still much more from that of the tungsten lamp. Instead of amyl acetate, pentane has been used and is still used. It gives a somewhat whiter flame, but the pentane lamp is not as constant. However, the Hefner lamp, while universally used as pri- mary standard, is altogether too inconvenient for general pho- tometric use, and, for this purpose, usually incandescent lamps are employed which have been compared with, and standard- ized by, the Hefner lamp. In reality, from these standard incandescent lamps, by comparison, other incandescent lamps have been standardized, and so on, until of late years the Hefner lamp has been finally abandoned as primary standard of light, and we have no primary standard; but the standard of light is maintained by comparison with incandescent lamps kept for this purpose; that is, it is maintained by duplication of samples, and by international agreement an incandescent lamp unit has been adopted as the standard or " international candle." 82. A number of primary standards have lately been pro- posed, but none has yet been much developed. Some work was done on the acetylene flame, burning in oxygen. It has a very suitable white color, but its intensity is very sensitive to slight impurities of the acetylene, and such impurities, as hydrogen, are difficult to avoid. A suitable unit appears to be the normal temperature radiation at specified temperature, and the temperature could be defined by the ratio of the radiation power of definite wave lengths. Thus, such a unit would be an incandescent lamp, radiating x watts at such temperature that the power radiated between wave lengths 45 and 55 bears to the power radiated between wave lengths 60 to 70 the ratio y. The radiated power x could prob- ably be determined from electric power input and losses. Such a unit would probably be replaceable with considerable exact- ness, but would still be arbitrary. MEASUREMENT OF LIGHT AND RADIATION. 179 A further possible unit would be the light given by one watt visible radiation, by normal temperature radiation at a definite temperature the latter specified and measured by the ratio of radiation power of two different ranges of wave length. Such definition would base the physiological effect, under speci- fied conditions of temperature, on the unit of power, or the watt, as unit of light. Its disadvantage is the difficulty of measuring the power of the total visible radiation, since at the ends of the visible spectrum the power is high and the physio- logical effect low, and a small error in the limits of the spectrum would make a considerable error in the result. More satisfactory, therefore, appears the derivation of a primary standard of light by combining three primary colors of light in definite power proportions. Thus, choosing three lines of the mercury spectrum in the mercury arc in a vacuum, perfect steadiness and high intensity can easily be produced in the red, green and blue, about equidistant from each other, these three radiations would be combined in definite propor- tions chosen so as to give the desired color of the light, probably a yellowish white and in such qualities as to give one watt total radiation, or, if as unit the illumination is used, to give one microwatt per sq. cm.; that is, the standard of illumination would be the illumination produced by one microwatt of radiation power, composed of the three wave lengths of the three chosen mercury lines, in definite proportions. Such a standard, derived by combination of definite wave lengths, which are easily reproducible, appears the most satis- factory in regard to permanence. It would incidentally give a numerical expression to color values, as any color then would be represented by the numerical ratio of the power of the three standard spectrum radiations, which, mixed together, give the color.* 83. Light is produced for the purpose of illumination. The raw material used in illumination is the flux of light issuing from the illuminant. The important characteristic of the illu- minant, by which it is judged, thus is the total flux of light issuing from it, and its measurement one of the main objects of photometry. * Proc. A. I. E. E., (1908). 180 RADIATION, LIGHT, AND ILLUMINATION. The photometer or luminometer, however, gives the light intensity in one direction only. Thus, to measure the total flux of light, the light intensity in all directions in space must be determined, and added, or averaged, to get the average intensity of light, usually called the "mean spherical intensity." If the light intensity were the same in all directions, one single photometric observation would give it, and therefrom, by multiplying with 4 TT, the total flux of light would be obtained. This, probably, is never the case. Many illuminants, however, give a symmetrical distribution of light around an axis, so that the distribution curve is the same in all meridians. This is practically the case with the or- dinary incandescent lamp with oval filament, and also with the tantalum and the tungsten lamp. Thus if the curve, shown in Fig. 59, is the distribution curve in one meridian, it is the same FIG. 59. in every other meridian, and for photometric test of the illumi- nant it is sufficient to measure the light intensities in one merid- ian only, for instance, from 10 to 10 degrees. To get herefrom the mean or average intensity, it would obviously be wrong to merely average all the intensities under equal angles, since the equatorial intensity covers a far greater area a zone of 10 de- grees width and 2 x circumference than the intensity of lati- tude j that is, under angle from the horizontal: the latter covers a zone of 10 degrees width and 2 it cos $ circumference, and the polar intensity covers only a point. To get the total flux of light, the intensity under each angle < MEASUREMENT OF LIGHT AND RADIATION. 181 thus is to be multiplied with the area of the zone which it covers, 2 nd cos , where d is the angular width of the zone (10 deg., for instance), and then added. The average or mean spherical intensity then is derived herefrom by dividing with the surface of the sphere, or by 4 re. Thus, to get the mean spherical intensity from the distribu- tion curve, the instantaneous values of intensity, taken under equal angles d, are multiplied each by cos <, then added, and ft the sum multiplied by -, where d, the angular distance under 2 which observations are taken, is given in radians, that is, 10 deg. gives d = - TT. This usually is done graphically. 180 Occasionally, as in incandescent lamps with single-loop fila- ment, the light intensity is not the same in all meridians, but a maximum in two opposite meridians: at right angles to the lamp, and a minimum in the two meridians at right angles to the former, giving a horizontal or equatorial distribution of FIG. 60. light intensity about as shown in Fig. 60. In this case the horizontal distribution curve may also be determined photo- metrically, averaged so as to give the mean horizontal intensity 182 RADIATION, LIGHT, AND ILLUMINATION. and the ratio of the mean horizontal intensity to the maximum horizontal intensity (or any other definite horizontal inten- sity); and the mean spherical intensity, as derived from the meridian of maximum horizontal intensity (or any other definite horizontal intensity), is multiplied with this ratio to get the real mean spherical intensity. Usually in this case measure- ments are taken only in one meridian, but during the test the lamp rotated around its vertical axis with sufficient speed, so that each observation in the meridian, under angle <, in reality is the mean intensity in the direction . Thus, in incandes- cent lamp tests, usually the lamp is revolved, so as to average between the different meridians. As the distribution of intensity in the meridian is the same, within the error of photometric test, for all incandescent lamps of the same type of filament, usually the distribution curve of one meridian is measured once for all, therefrom the ratio of horizontal to mean spherical candle power, the so-called spherical reduction factor, determined, and then in further photometric tests of lamps of this type only the horizontal intensity meas- ured, and from this, dividing by the spherical reduction factor, the mean spherical intensity is derived. Thus, while with the incandescent lamp the intensity varies in each meridian, and is different in the different meridians, the mean spherical intensity nevertheless is derived by a single photometric observation of the horizontal intensity with rotating lamp: the rotation aver- ages between the different meridians, and the spherical reduction factor translates from horizontal to mean spherical intensity. Reduction factors of incandescent lamps usually are between 0.75 and 0.80. 84. Far more difficult is the matter with arc lamps : in the ordi- nary carbon arc lamp, the intensity also varies in the meridian, and is different in the different meridians, but not with the same regularity as in the incandescent lamp, and, further- more, the intensity distribution between the different meridi- ans, as well as, to a lesser extent, the total light flux of the lamp, varies with the time. The arc is not steady and con- stant in position, as the incandescent filament, but wanders, and the light intensities on the side of the lamp, where the arc happens to be, thus are greater than on the side away from the arc. The meridians of maximum and of minimum intensity, MEASUREMENT OF LIGHT AND RADIATION. 183 however, do not remain constant in position, but continuously change with the wandering of the arc. Therefore, by measure- ments in a single meridian, the distribution curve of maximum and that of minimum intensity can be determined by waiting during the observation for the arc to come around to the side of the observer maximum and go to the opposite side minimum intensity. Such curves are shown in Fig. 61. FIG. 61. This, however, carried out for every angle in the meridian, makes arc-light photometry rather laborious, especially as the total intensity pulsates with the time, and therefore a considerable number of readings have to be taken in every position. Therefore, for arc light photometry, integrating photometers are especially desirable, that is, photometers which, by a single observation, determine more or less accurately the mean spherical intensity; that is, the average intensity, in all directions. With such an integrating photometer, by taking a number of successive readings and averaging, so as to eliminate the varia- tion of total intensity with the time, the mean spherical inten- sity, and thus the total flux of light, can be derived more rapidly. Such an integrating photometer is the Matthews photometer. It consists of a circle of inclined mirrors, which surround the lamp and reflect the light in all or, rather, a certain number of different angles into the photometer, and there the differ- ent reflected beams are by absorption reduced in the proportion 184 RADIATION, LIGHT, AND ILLUMINATION. of cos (f> and combined on the photometer screen. Obviously, the Matthews photometer does not average the intensity in all directions, but only in two meridians opposite to each other; however, by averaging a number of successive readings, very accurate results can be derived. A method of averaging in all directions is based on a similar principle as that by which the radiation from the interior of a closed sphere of constant temperature was found to be black- body radiation: if the lamp is located in the center of a closed sphere (perforated only at the place where the photometer enters) of perfectly white reflecting surface, then the light in- tensity throughout the entire inner surface of the sphere is uniform, and is the mean spherical intensity of illumination at the distance of the radius of the sphere. The reason is : every element of the interior of the sphere receives light directly from the lamp, and also light reflected from all the other elements of the sphere, so that the total light received at every element of the sphere is the same, hence is the average illumination. By enclosing the test lamp in the center of such a photometric sphere of sufficient size, its mean spherical intensity thus can be determined by a single reading. Such an arrangement has the further advantage that it allows a direct measurement of mean spherical intensity or light flux of such illuminants as the mercury lamp, in which the radiator is of such extent that it cannot be considered as a point without going to excessive distances. 85. Photometrically, and in illuminating engineering, only the mean spherical intensity which represents the total flux of light and the distribution curve which represents the distribution of this light in space are of importance. The "horizontal intensity 7 ' has been used as a conventional rating of incandescent lamps, but is merely fictitious, as it does not mean an actual average horizontal intensity, but the horizontal intensity which the light flux of the lamp would give with the standard mean spherical reduction factor, if the filament had the standard shape. Downward candle power and maximum candle power obvi- ously have no meaning regarding the light flux of the lamp, but merely represent a particular feature of the distribution curve. MEASUREMENT OF LIGHT AND RADIATION. 185 Hemispherical candle power is used to some extent, especially abroad. It is a mixture between light flux and distribution curve, and as it gives no information on the total light flux, nor on the actual distribution curve, and may mislead to attribute to the lamp a greater light flux than it possesses by mistaking it with mean spherical candle power it has no excuse for exist- ence, and should not be used. LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout space is not uniform, but the light-flux density is different in different directions from an illuminant. Unit light-flux density is the light-flux density which gives the physiological effect of one candle at unit distance. The unit of light flux, or the lumen, is the light flux passing through unit surface at unit light-flux density. The unit of light inten- sity, or one candle, thus gives, if the light-flux distribution is uniform in all directions, unit flux density at unit distance from the radiator, and thus gives a total flux of light of 4 it units, or 4 it lumens (since the area at unit distance from a point is the surface of a sphere, or 4 it). The unit of light intensity, or the candle power thus given, with a radiator of uniform light-flux distribution, 4 x lumens of light flux, and inversely, a radiator which gives 4 it lumens of light flux, gives an intensity of one candle, if the intensity is uniform in all directions, and, if the distribution of the intensity is not uniform, the average or mean spherical intensity of the radiator is one candle. Thus one mean spherical candle rep- resents 4 it lumens of light flux, and very frequently the mean spherical candle is used as representing the light flux: the light flux is 4 TT times the mean spherical intensity, and the mean spherical intensity is the total light flux divided by 4 it, regard- less whether the light flux is uniformly distributed or not. The total light flux of an illuminant is derived by the sum- mation or integration of the intensities, that is, the flux den- sities at unit distance, in all directions from the radiator. 186 LIGHT FLUX AND DISTRIBUTION. 187 The distribution of light flux or of intensity is never uniform, and the investigation of intensity distribution of the light flux thus necessary. The distribution of the light intensity of an illuminant de- pends upon the shape of the radiator and upon the objects surrounding it; that is, the distribution of the light flux issuing from the radiator depends on the shape of the radiator, but is more or less modified by shadows cast by surrounding objects, by refraction, diffraction, diffusion in surrounding objects, etc. The most common forms of radiators are the circular plane, the straight line, that is, the cylinder, the circular line or circular cylinder and combinations thereof. 87. Very frequently the intensity distribution of an illumi- nant is symmetrical, or approximately symmetrical, around an axis. This, for instance, is the case with the arc lamp, the incandescent lamp, most flames, etc. If the distribution is perfectly symmetrical around an axis, the distribution in space is characterized by that in one meridian, that is, one plane pass- ing through the axis. If the distribution is not symmetrical around the axis, usually the space distribution is characterized by the distribution curves in two meridians at right angles to each other, the meridian of maximum and that of minimum intensity, and the distribution in the equatorial plane, that is, the plane at right angles to the axis. Distribution curves are best represented in polar coordinates, and the angle counted from the axis towards the equator (that is, complementary to the " latitude" in geography). As most illuminants are used with their symmetry axis in vertical direction, and the downward light is usually of greater importance, it is convenient in plotting distribution curves to choose the symmetry axis as vertical, and count the angle $ from the downward vertical towards the horizontal; that is, the downward beam would be given by (f> = 0, the horizontal beam by ^ = 90 deg., and the upward beam by = 180 deg. The usual representation of the light-flux distribution in po- lar coordinates does not give a fair representation of the total light flux, or the mean spherical intensity of the light source, but on the contrary frequently is very misleading. When com- paring different polar curves of intensity distribution, it is 188 RADIATION, LIGHT, AND ILLUMINATION. impossible to avoid the impression of the area of the curve as representative of the light flux. The area of the polar curve, however, has no direct relation whatever to the total light flux, that is, to the output of the illuminant, since the area depends upon the square of the radii, and the light flux directly upon the radii of the curve. Thus an illuminant of twice the inten- sity, but the same flux distribution, gives a polar curve of four times the area, and the latter gives the impression of a source of light far more than twice as great as the former. The meridian curves of intensity distribution are still more misleading: the different angles of the curve correspond to very different amounts of light flux: the horizontal intensity (< = 90 deg.) covers a zone of 2 rn circumference, while the intensity in any other direction (f> covers a zone of 2 rn sin circumference; that is, an area which is the smaller, the nearer (f> is to or 180 deg. ; the terminal intensity, upward or down- ward, finally covers a point only, that is, gives no light flux. As the result hereof, an illuminant giving maximum intensity in the downward direction, and low intensity in the horizontal, gives a much larger area of the polar curve than an illuminant of the same or even a greater total light flux which has its maximum intensity in the horizontal. Comparing, therefore, illuminants of different distribution curves, it is practically impossible not to be misled by the area of the polar curve, and thus to overestimate the illuminant having maximum downward intensity, and underestimate the illuminant having maximum horizontal intensity. The misleading nature of the polar curves of intensity dis- tribution in the meridian is illustrated by the curves in Figs. 64 and 99: the three curves of Fig. 64 give the same total light flux; that is, the same useful output; but 2 looks vastly greater than 1 or 3, and 3 especially looks very small. Curves 0, 1, 2, 3, 4 in Fig. 99 give the same total light flux, and curve 5 gives only one tenth the light flux. To the eye, however, the curve 4 gives the impression of a far more powerful illuminant than the curve 1, and curve 5 appears practically equal, if not larger than 1, while in reality it represents only one tenth the light output of 1. 88. In an illuminant in which the distribution of intensity is symmetrical around an axis, and thus can be represented LIGHT FLUX AND DISTRIBUTION 189 by one meridian curve, the total light flux is calculated thus: Let / = intensity at angle (counting the angle from one pole over the equator to the other pole). This intensity covers a zone of the sphere of unit radius of width d(j> and angle <,that is, a zone of radius (Fig. 62) r = sin<; thus surface dA = 2 n sin and the light flux in this zone therefore is: FIG. 62. = 27r/sind(/>. Jo CD (2) The light flux in the space from the downward direction = to the angle < = fa against the vertical or symmetry axis, then is fc 1 = 2 TT / sin dfa (3) */0 and the light flux in a zone between the angles (j) 1 and fa is (4) I. DISTRIBUTION CURVES OF RADIATION. (1) Point, or Sphere, of Uniform Brilliancy. In this case, the intensity distribution is uniform, and thus, if / = intensity of light, in candles, <= 4 nl = light flux, in lumens; (5) or, inversely: / = -. (6) The brilliancy of a radiator is the light-flux density at its sur- face. Thus, with a luminous point of intensity /, the brilliancy 190 RADIATION, LIGHT, AND ILLUMINATION. would be infinite; with a luminous sphere of uniform intensity distribution, and of radius r, the brilliancy is * 7 ' (7) B = ,2 ' hence, inversely proportional to the square of the radius of the spherical radiator. (2) Circular Plane of Uniform Brilliancy. 89. Such radiators are, approximately, the incandescent tip of the carbons in the (non-luminous) electric carbon arc, or the luminous spot in the lime cylinder of the lime light (hydro-oxygen flame), etc. Choosing the circular luminous plane as horizontal direction, the intensity distribution is symmetrical around the vertical, the vertical direction thus can be chosen as axis, and the angle < counted from the vertical upward. ' The intensity is a maximum 7 , ver- FlG - 63 - tically downward, for < == 0. In any other direction, under angle (f> against the vertical (Fig. 63), the intensity is / = / cos <, (8) and is zero for < = 90 deg. The light flux issuing from the radiator below angle is, by (3): hence, by (8) : rsin (j) cos (f)d -I. /cos 2* & I I -/{! -cos 24,}, (9) LIGHT FLUX AND DISTRIBUTION. 191 and the total light flux, from (f> = to = 90 deg. = , thus is : ft or The brilliancy of the source of light is the total light flux divided by the luminous area; or, * and, if r = radius of the luminous circle, A = ;rr 2 , and -?'' 02) or, 7 = r 2 ; (13) that is, the same as in class (1). Comparing (11) with (5), it thus follows that the total light flux of such a radiator, for the same maximum intensity, is only one quarter that of a radiator giving uniform intensity distribution throughout space, or inversely, with such a downward distribution of light, the maximum intensity is four times as great as it would be with the same total light flux uniformly distributed through space. The flux distribution is a circle having its diameter from the source of light downward. It is shown as 2 in Fig. 64, and the concentric circle giving uniform intensity distribution of the same total light flux is shown as 1. (3) Hollow Circular Surface. Such a radiator, for instance, is approximately the crater of the positive carbon of the arc lamp. As with such a radiator, as shown in section in Fig. 65, the projection of the luminous area in any direction is the same 192 RADIATION, LIGHT, AND ILLUMINATION. FIG. 64. FIG. 65. FIG. 66. LIGHT FLUX AND DISTRIBUTION. 193 as with the plane circular radiator (2), the same equations apply. (4) Rounded Circular Surface. Such, for instance, is approximately the incandescent carbon tip of the arc-lamp electrodes, when using carbons of sufficiently small size, so that the entire tip becomes heated. Assuming, in Fig. 66, the radiator as a segment of a sphere, and let 2 aj = the angle subtending this segment, r l the radius of this sphere. For all directions <, up to the angle co below the horizontal : 0< <-w ; the projection of the spherical segment in Fig. 66 is the same as that of a plane circle, and thus the intensity is given in class (1), as: i = 7 cos (/>. In the direction, -- - co <<<-, however, the intensity is A 2i greater, by the amount of light radiated by the projection Dyx, and, in the horizontal direction, the intensity does not vanish, but corresponds to the horizontal projection of the luminous segment. Above the horizontal, light still issues in the direction, from the segment Buv, and only for - + co < does the light Zi cease. If r 2 = radius of carbon, the radius of the luminous segment is sin co' the height of the segment is h = r l (1 cos co) r 2 (1 cos co) sin co 194 RADIATION, LIGHT, AND ILLUMINATION, hence the surface of the segment, or the luminous area, is A 2 = 2 rjin 2 r 2 2 7r (1 cos w) 2r 2 2 7r X 2 sin 2 2 2 4 sin 2 - cos - Z 2 COS 2 (14) Thus, if the luminous area is the same as in the plane circle class (2), it must be: TV 2 7T r 2 = rcos~; (15) and, if the brilliancy B is the same, the maximum intensity for = Ois cos 2 ; (16) that is, the rounding off of the circular radiator, at constant bril- liancy and constant luminous surface, decreases the maximum intensity 7 by the factor cos 2 -, but increases the intensity within the angle from co below to a> above the horizontal direc- tion. In Fig. 67 are plotted the distribution curves, for the same brilliancy and the same area of the radiator, for a plane circular radiator, as 1 ; a rounded circular radiator of angle co = 30 deg. as 2, and a rounded circular radiator of angle a> = 60 deg., LIGHT FLUX AND DISTRIBUTION. 195 as 3. As seen, with increasing rounding, gradually more and more light flux is shifted from the vertical into the horizontal direction. FIG. 67. Straight Line or Cylindrical Radiator. 90. Such radiators are represented approximately by the lum- inous arcs with vertical electrodes, by the mercury-arc tube, by straight sections of incandescent-lamp fila- ments, etc. The intensity distribu- tion is symmetrical with the radiator as axis. The intensity is a max- imum 7 at right angles 1,1 T i FIG. 68. to the radiator, or in horizontal direction, = 90 deg., when choosing the radiator as vertical axis. At angle <, the intensity is, Fig. 68, I = /o sin 0, (17) and is zero for = and (f> = 180 deg., or in the vertical. 196 RADIATION, LIGHT, AND ILLUMINATION. The light flux within angle from the vertical is, by (4), = 7r/ f (l-co ^o hence, , A _ / . sin 2 and the total light flux for (f> = K is * = v.; (19) or, inversely: ^_ ^ ? : (2Q) and the radiating surface is A = ^ (21) where Z is the length; w the diameter of radiator. The bril- liancy, therefore, is ^ (22) may be called the linear maximum intensity, or, maximum inten- sity per unit length. Most of the light 'of a linear vertical radiator issues near the horizontal, very little in downward and upward direction. Put- ting = J $, gives the angle , which bisects the light flux : sin 2 (f> n * =4' and herefrom, by approximation, $ = 66 deg.; that is, half the light flux issues within the narrow zone from 24 deg. below to LIGHT FLUX AND DISTRIBUTION. 197 24 deg. above the horizontal, or in the space between a and a' in Fig. 68. It is interesting to compare the three radiators, (1), (2), and (5), on the basis of equal maximum intensity, and on the basis of equal light flux, thus : Light flux <, at equal maximun intensity / Maximum intensity 7 , at equal light flux $ Uniform. 47T/ 4 4^ 1 Circle. Cylinder. 7T= 3.14 1=1.27 7T As seen, at the same maximum intensity, the cylinder gives nearly as much light flux as given by uniform distribution, that is, its deficiency in intensity in the polar regions represents very little light flux. The circular plane, however, gives only one quarter as much light flux as uniform distribution. With the same horizontal intensity of a cylindrical radiator, as the vertical intensity of a circular plane, the former gives TT = 3J4 times the flux of light. In Fig. 64 the three distribution curves are shown for the same total flux of light: curve 1 for uniform intensity, 2 for a plane circle, and 3 for a straight cylinder as radiator. (6) Circular Line or Cylinder. In the spirals, loops or ovals of in- candescent-lamp filaments, circular radiators, or sections thereof, are met. Let r = radius of the circular radi- ator, w = diameter of the radiator cylinder, shown in section in Fig. 69. The intensity is a maximum in the direction at right angle to the plane of the circle. The projection of the radiator in this direction of maximum intensity, $ = 0, has the length: 2 TIT; and if, by (24) : wB 69 - maximum linear intensity, 198 RADIATION, LIGHT, AND ILLUMINATION. where B = brilliancy, it is, I Q =27rrI Q '=2rwB. (25) This is in the direction in which the projection of the radiator is a circle of radius r, and thus circumference 2 TTT. In any other direction , the projection of the radiator is an ellipse, with r and r cos (f> as half axes, as seen from Fig. 69. If I = the circumference of this ellipse, the intensity in the direction bears to the maximum intensity 7 the same ratio as the circumference of the ellipse to that of the circle; that is, I-I t ^Ifl. (26) 2 nr The circumference of an ellipse with the half axes a and c is I = (a + c) n (1 + q), I/a - c\ 2 1 /a - c\ 4 1 /a - c\ 8 W 4 \a + c) + 64 Va + c) + 256\a + c) + ' ' where The ratio of the circumference of the ellipse to its maximum diameter, y = , is given in Table I, and plotted in Fig. 70, w T with the ratio of the half axes, that is, cos as abscissas. TABLE I. CIRCUMFERENCE OF ELLIPSE. c - COS d>. a V = Tr- f V= ir- 1.0 1.571- s 1.571 = 5 2 2 0.9 .495 10 1.560 0.8 .418 20 1.525 0.7 .345 30 1.470 0.6 .278 40 1.390 0.5 .210 45 1.350 0.4 .150 50 1.305 0.3 .110 60 1.220 0.2 .055 70 1.120 0.1 .025 80 1.045 .000 90 1.000 LIGHT FLUX AND DISTRIBUTION. 199 \ y - 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 \ X N X X. X ^ \ ^ C( minimum p, mayimu/Ti imet erof Ellii sis I ,i. 4 0*5 6 7 8 9 -^v 1.5 1.4 1.3 1.2 1.1 1.0 0.0 0.8 0.7 0.6 0.5 0.4 0.3 0.2 '0.1 ^ \ \ \ ^ x ^ V, 1 2 Angle^Deglrees 3.0 40 1?0 6 *i tt f > FIG. 70. FIG. 71. In Fig. 72 is plotted the intensity distribution in the meridian of such a circular radiator. This shows a maximum 7 in the vertical, and a minimum ^= 7 7T in the horizontal. Theoretically, exactly in the horizontal, = 90 deg., the in- tensity should be ~, as one half ft of the circle shades the other half. In most cases of such circular radiators, sections of incandescent- lamp filaments, w is so small com- pared with r, that it is practically impossible to have the radiator perfectly in one plane, as would be required for one half to shade the other half. (7) Single-Loop Filament. FIG. 72. 200 RADIATION, LIGHT, AND ILLUMINATION. 92. As an illustration of the use of the distribution curves of different typical forms of radiators, the distribution curves of a single-loop incandescent-lamp filament may be calcu- lated. Such a filament consists of two straight sides, joined by a half circle, as shown in Fig. 73. The distribution of in- tensity is not symmetrical around any axis, but ap- proximately so around the axis Z in Fig. 73. The meridian of maxi- mum intensity is the plane YZ, at right angles to the plane of the filament ; the meridian of minimum in- tensity is the plane of the filament, XZ, and the least variation of intensity occurs in the equatorial plane XY. The distribu- tion curves in all three of .these planes are required. Assuming the straight sides as of a length equal to twice the diameter of the loop, or of length 4 r, where r = radius of the half circle. As it is impossible to produce and maintain such a filament perfectly in one plane, we assume, as average deviation of the two straight sides A and B of Fig. 73 from the vertical, an angle of 10 deg. The intensity distribution of the straight sides A and B in any meridian plane thus is that of a straight radiator, (5), at an angle of 10 deg. against the vertical. Let // = maximum intensity per unit length. Then the meridianal distribution of the sides A + B is : FIG. 73. 7 = 4 r/ sn + 10) + sin (0 - 10) } (28) Hereto in the meridian of maximum intensity is added the light LIGHT FLUX AND DISTRIBUTION. 201 intensity produced by a half circle of radius r, (6); that is, ' 2 = -' (29) where I is the circumference of the ellipse which projects the circle of radius r, under angle <, and is given by Table I and Figs. 70 and 71. FIG. 74. In the meridian of minimum intensity, the light intensity 7 3 produced by the projection of the half circle in its own plane, under angle (f>, is added to the intensity 7 t . This projection is, by Fig. 73, c = r (1 + cos <), (30) and thus 7 3 = c7 ' = rI Q ' (1 + cos 0). (31) In the equatorial plane, the intensity, due to the straight sides A + B, is constant, and is that of a straight radiator under angle 10 deg. from the direction of maximum intensity; hence is 7 = 8 rI ' cos 10. (32) To this is added the intensity produced by the half circle of radius r, that is, 7 2 ; hence, in the meridian of maximum intensity, 7 = 7j + 7 2 , Curve 1 of Fig. 74; in the meridian of minimum 202 RADIATION, LIGHT, AND ILLUMINATION. intensity, / = 7 X 4- 7 3 , Curve 2 of Fig. 74 ; and in the equator, 7 = 7 + 7 2 , Curve 3 of Fig. 74. (8) In Table II are recorded the intensity distribution of the different radiators discussed in the preceding paragraphs. TABLE II. Circular surface. Single-loop filament. * Rounded by Circular Meridian of Plane. 30 deg. 60 deg. Max. intensity. Min. intensity. Equator. 7.00 6.50 5.25 3.14 1.70 1.70 5.51 10 6.88 6.40 5.18 3.12 1.73 1.68 5.50 20 6.57 6.12 4.94 3.05 2.47 2.35 5.46 30 6.05 5.63 4.56 2.94 3.19 2.97 5.41 40 5.35 4.98 4.07 2.78 3.84 3.53 5.33 50 4.50 4.19 3.55 2.61 4.41 4.02 5.24 60 3.50 3.25 3.01 2.44 4.88 4.41 5.16 70 2.39 2.31 2.44 2.24 5.23 4.70 5.06 80 1.21 1.47 1.90 2.09 5.44 4.88 4.98 90 0.75 1.37 2.00 5.51 4.94 4.94 100 0.39 1.00 110 09 07 120 0.04 130 02 140 005 150 77. SHADOWS. 93. The radiator of an illuminant can rarely be arranged so that no opaque bodies exist in its field of light flux and obstruct some light, that is, cast shadows. As the result of shadows, the distribution of intensity of the illuminant differs more or less from that of its radiator, and the total light flux is less. The most common form of shadow is the round shadow sym- metrical with the axis of the radiator, that is, the shadow of a circular plane concentric with and at right angles to the sym- metry axis of the illuminant. Such for instance are, approxi- mately, the shadows cast by the base of the incandescent lamp, by the top of the arc lamp, etc. Such also are the shadows of LIGHT FLUX AND DISTRIBUTION. 203 the electrodes in the arc lamp in that most common case where the electrodes are in line with each other. As an example may be considered the effect of a symmetrical circular shadow on the light flux and its distribution with a circular plane and with a straight line as radiator. (1) Circular Plane Opposite to Circular Plane of Radiator. Shadow of negative carbon in front of the positive carbon of the carbon arc. In Fig. 75, let 2 r be the diameter of a circular plane radiator (positive carbon) ; 2 r l the diameter of the plane, which casts a shadow (negative car- bon of the arc lamp); and I the distance be- tween the two. Assume 7 as the maximum intensity of the light flux issuing from the radiator AOB (which is in downward direction, hence com- pletely or partly intercepted by the circle Afl^BJ. Then, the intensity of the light flux from the radiator, in any direction $, is, according to reasoning under heading I, class (2) , 7 = / cos0. (1) In this direction , the circle A l B l projects on the plane AB as a circle A 2 B 2) with radius r v and the center 2 of this circle has from the center of the radiator the distance FIG. 75. a = 00 tan (2) If now the projected circle 2 overlaps with the radiator circle O v the area S of overlap, shown shaded in Fig. 76, is cut out from the radiator by the shadow, and the light flux in the direction thus reduced from that of the complete radiator surface, Trr 2 , to that of the radiator surface minus the shaded part S, that is, xr 2 -S, or in the proportion 2 * -S s r'x (3) 204 RADIATION, LIGHT, AND ILLUMINATION. and the intensity of the remaining light flux, in the direction , thus is I = I q cos <. (4) If the distance, a, between the circles and 2 is greater than the sum of radii, I tan (j> > r + r 17 the circles and 2 do not overlap, and in that direction no shadow is cast. The light intensity thus is reduced by the shadow of the lower carbon only for those angles which are smaller than the angle i given by r + r ~--A (5) In the direction in which < is smaller than the angle, r. r tan ^ 2 = ~ > (6) and the shadow 2 thus covers the entire radiator 0, no light issues, but the radiator is completely shaded. This can occur only if r t >r, and if this is the case, a circular area below the radiator receives no light. If fj= r, the intensity becomes zero only in the direction = 0; and if 7\ < r, the light in the downward direction is merely reduced, but nowhere completely extinguished. The shaded area of the radiator consists of two segments, of the respective radii r and r 1 : S = D + D r Let 2 co = angle subtending segment D and 2 co^ = angle subtending segment D v and denoting the width of the segments thus w = AC, and the total width of the shaded area is p = AB 2 = w + w,. (7) From Fig. 76, a = 00 2 = OA + J~0 2 - AB 2 = r + r, - p; or, p = r + r t - a; hence, by (2), p = r + TI - tan 0. (8) LIGHT FLUX AND DISTRIBUTION. In A 2 EO, 205 sin < sin sin ( r . - sm aj, and hence, Furthermore, S = D + D, and, by (3), (9) (10) (ID (12) (13) (14) (15) (16) For different values of w the values of to w t p D D, S q are calculated from equations (10) (11) (12) (13) (14) (15) (16) and then q plotted as function of p in Fig. 78. 206 RADIATION, LIGHT, AND ILLUMINATION. From equation (8) then follows, for every value of <, the cor- responding value of p, herefrom the value of q and by (4) the value of /. fl 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 *> N ^ N ^ \ ^ \ > \\ s ^V in \ \ \I v I\ \ \ V \n P = 5 o 1 2 3 t 5 6 7 8 ^ FIG. 78. 94. In Table III are given the values of p and q for the ratio of radii : ^- = 2.0; 1.0; 0.7, corresponding to a shadow sec- tion equal to 4 times, 1 times, and 0.5 times the section of the radiator. These are plotted as curves I, II, III, in Fig. 78. TABLE III. P' r -l=2. r 3-1. r TI r = 0.7. I. II. III. IV. 1.000 1.000 1.000 96 0.1 0.962 0.964 0.968 0.2 0.885 0.895 0.910 0.3 0.785 0.810 0.835 0.4 0.675 0.715 0.748 0.5 0.6 65 0.560 0.435 0.615 0.500 0.660 0.575 532 0.660 0.569 520 0.7 71 0.308 0.380 0.502 500 0.477 0.8 0.85 0.183 0.255 0.500 0.386 340 0.9 0.070 127 500 0.95 0.028 063 1.0 500 t If < 1, the curve III represents the effective light-living area only up to the values of p, where w l = r v but beyond this value, at least in the application to the shadow cast by the LIGHT FLUX AND DISTRIBUTION. 207 negative carbon of the arc lamp, the shaded area is not merely the circle O/, but also the area shown shaded in Fig. 77, which is shaded by the shadow cast by the sides of the lower electrodes. From the value p, which corresponds to w l = r v the area S then increases by 2^ (p-p)', hence, if S'= shaded area for p = p'j for any value of p>p v and q = l ;- ^j^. (17) XT nr 2 This is shown in Table III and in Fig. 78 as curve IV. Such curves of intensity of a plane circular radiator of radius r, shaded by a concentric circular shade of radius r l at distance I [corresponding to a diameter of positive carbon 2 r, of negative carbon 2 r i; and an arc length Z], are given in Figs. 79 to 82, and the numerical values given in Table IV. r I Fig. 79 gives the curves for - = 2, and the arc lengths, = 0.25; 0.5; 1.0; 2.0, as curves I, II, III, IV. Fig. 80 gives the r 2r curves for - = 1, and the arc lengths, = 0.25; 0.5; 1.0; 2.0, r I r as curves I, II, III, IV. Fig. 81 gives the curves for - = 0.7, I r and the arc lengths, - = 0.25; 0.5; 1.0; 2.0, as curves I, II, III, IV. In Fig. 82 are shown, for comparison, the intensity curves for i-2; 2 - r = 2 ' asL 5-1; 1-1, as II. ^ = 0.7; ~=0.5, as III. T T As seen from Fig. 82, a larger shade at greater distance, I, gives approximately the same light flux and a similar distribu- tion, but gives a much sharper edge of the shadow, while a smaller 208 RADIATION, LIGHT, AND ILLUMINATION. V////A W/\ v////\ FIG. 81. FIG. 82. LIGHT FLUX AND DISTRIBUTION. 209 j co i b- t^. o i^ o co o 10 10 o co o o o o o -i o o o o eo r^. oo oo oi o> o> d 11 S 3 II ! !! t^.^t"o cooo iooo oooo O-. cococo o^co i-io>t^ eoooo . I . '. o i-i . od o o> d I C ~l IO -oOOSO 8 10 CO !! l!i ! 03COOOOOOOO . . . . . . CO IO Tj< CO CM O o o . o o CM * co oo o T-H o t^OlO O5O5i I t^Ct^ t^CO>O O^CO M i I O O t>I d t^^H-^ cOOSi-H CO-^iO i-^CO*O o I CO O^ft^ OCMrfrl Ot^QO a II CO OC^-* COt>-00 OOOOt^ t^-COO >OTt- if* CO IO O t^ CO -* O CO CO OS *< t>- O--H CN(M(M OCO-iO 2 3 a II *TI v. o d COOO -^COOO t^OO OO- 00 OOi-< -iCS|0 1^ CO 10 00 (N Tt< t>-t^t>. 10^.00 J3 3 o OOO O-l<-l r-i-iCN COCMCO COCOCO CO^-iOO i CO ^H -** CO OS t^ >-irt- b, t^ CO >O U5 T*I CO CO ^i O O* 1 V- IN O O O 00 O OS CO o CO ** CO t- OS 11 O- O OT-ICO Tt*^iO lO-^CO CO-OO c4 11 Tl t- . . . . . . . . - o CO i-i co co t^ o O ... ... ... OOO i-i ,-H O O s 88JS8Q e- o 10 o o o o o m o to o o o 10 o 10 o o o ri t-HCOCO COCO-* ^IOO COcOt^ t^OOOOOS 210 RADIATION, LIGHT, AND ILLUMINATION. shade at shorter distance, III, gives a far broader half shadow, which extends even to the vertical direction. This is illustrated by the distribution of the open arc and the enclosed arc in clear globes that is, without means of diffrac- tion or diffusion. In the enclosed arc the distance between the electrodes, I, is made larger, since the ratio of radii is greater, as due to the smaller current the diameter of the radiator, 2 r, is smaller than in the open arc. The enclosed arc has a much sharper edge of the shadow, that is, narrower half shadow, than the open arc, thus requiring means of diffusion of the light even more than the open arc. Where the shade which casts the shadow is rounded, the dis- tribution curve is somewhat modified by similar considerations, as have been discussed under headings I, class (4). This is fre- quently the case where the shadow is cast by the electrodes of an arc, and especially so in the carbon arc, in which the negative electrode which casts the shadow is more or less rounded by combustion. (2) Circular Plane Concentric with the End of Linear Radiator. 95. This condition is approximately realized by the shadows of the electrodes of a luminous arc with vertical electrodes. Let, in Fig. 83, 2 r 1 = diameter of the lower electrode, I = length of the linear- radiator, and 2 w the diameter of the radiator. Neglecting first the diameter 2 w of the radi- ator, the part of the radiator which, in the direction <, is shaded, is s = r, cot <, (18) and the reduction factor of the light, or the ratio, by which the intensity of light flux of the radiator proper (heading I, class (5)), / = 7 sin 0, has to be multiplied, is = 1 - COt <, (20) LIGHT FLUX AND DISTRIBUTION. 211 and the light intensity in the direction < thus is /= qI Q sin J sin ^ r / r i = / (sin $ j cos For values of less than fa, where. tan T - 1 , (21) (22) the light flux is zero, that is, complete shadow would exist if there were no diffusion, etc. If we now consider the diameter, 2 w, of the radiator, we get the same distribution of intensity, except in the angle where fa' and fa' is given by tan fa' = -*- w and tan fa" = - 1 L In this narrow angle the light flux fades from the value which it has at fa" and which is the same as given by equation (21) to at fa', while, when neglecting 2w, the intensity would become zero at fa by equations (22) and (21). As illustrations are plotted in Fig. 84 and recorded in Table IV, FIG. 84. 212 RADIATION, LIGHT, AND ILLUMINATION. the distribution of light flux for =0.25; 0.5; 1; 2, as curves I, ^ r i II, III, IV, corresponding to an arc length equal to J, J, 1 and 2 times the electrode diameter. 777. REFLECTION. 96. As rarely the distribution of intensity and the brilliancy of the radiator are such as desired, reflection, diffraction, and diffusion are used to a considerable extent to modify the distribu- tion curve and the brilliancy of the radiator. Reflection may be irregular or regular reflection. In irregular reflection, the light impinging on the reflector is thrown back irregularly in all directions, while in regular reflection the light is reflected under the same angle under which it impinges on the reflector. The former is illustrated by a piece of chalk or other dull white body, the latter by the mirror. A. Irregular Reflection. Irregular reflection is used in indirect lighting to secure dif- fusion and low intrinsic brilliancy of the light source by throw- ing the direct light against the ceiling and illuminating by the light reflected from white or light colored ceilings. In some luminous arcs, the so-called flame carbon arc lamps, irregular reflection is used to direct most of the light downward by using a small circular reflector usually hollow immediately above the arc, the so-called " economizer." In this case the smoke produced by the arc largely deposits on the reflector and thereby maintains it of dull white color, the deposit of most flame carbons being calcium fluoride and oxide and thus white. In irregular reflection, the reflector is a secondary radiator; that is, if <$! = that part of the flux of light of the main radiator which is intercepted by the reflector, and a = albedo of the reflector (that is, the ratio of reflected light to impinging light, or the "ef- ficiency of the reflector"), the radiator is a generator of the light flux a$ r As an example may be discussed the intensity distribution of a vertical FlG - 85 - luminous arc L having a circular (irregular) reflector R immediately above the arc, as shown in Fig. 85. Let 2 aj = angle subtended by the reflector R from LIGHT FLUX AND DISTRIBUTION. 213 the base of the arc, I the (vertical) length of the arc. The radius of the reflector then is r l = I tan co, and the light flux intercepted by the reflector is calculated in the manner as dis- cussed under heading II, Class (2) ; that is, if 7 is the maximum or horizontal intensity of the arc L, the intensity in the direc- tion (180 deg. - <) will be 7 = 7 sin <. (1) The reflector then intercepts the entire light flux issuing from the radiator L between 180 deg. and 180 co, and the part q of the light flux issuing between 180 co and 90 deg., which is given by r, cot (180 - ) . A q = - - - = tan co cot <; (2) i hence, the light flux intensity which is intercepted by the reflec- tor is A = ?/o sin * = 7 tan co cos <, (3) and the light intensity issuing into space from the main radiator in this angle, - < << (180 - co), is % sn = 7 (sin $ tan co cos (/>). (4) Therefore the light flux intercepted by the reflector within the angle (f> = to ^> = co (or rather, = 180 deg. to = 180 co) is within the angle < = &> to = - is $/' = 2 ^7 / g sin 2 (j>d(j> = 2 nI tan o> / cos ^ sin I + cos 2 7 sin 2 co (5) 214 RADIATION, LIGHT, AND ILLUMINATION. and therefore the total light flux intercepted by the reflector is *1 * */ + ^l" = <"> and the reflected light flux, or light flux issuing from the reflector as secondary radiator, is 4> 2 = a^ 1 = xI Q aco, (6) where a = albedo. As the reflector is a plane circular radiator, its maximum intensity is in the downward direction, and is given under head- ing I, class (2), as ^ V = - = /o", (7) 71 and herefrom follows the intensity of radiation of the secondary radiator in any direction <, r - / " cos < = 7 aw cos 0. (8) The total intensity of radiation of main radiator and reflector or secondary radiator combined, in the lower hemisphere, or for < (j> < -j is Zi / = /' + /" = / o (gin + aaj cos <); (9) and in the upper hemisphere light flux issues only under the angle - < $ < K tu, and is Zi I = I' = 7 (sin ^ - tan w cos 0). (10) FIG. 86. For to = 75 deg. = and a = 0.7, the intensity distribution 12 is plotted in Fig. 86 and given in Table V. The distribution LIGHT FLUX AND DISTRIBUTION. 215 curve is of the type characteristic of most flame carbon arc lamps. Substituting the numerical values in (9) gives and in (10) gives 7 = 7 (sin $ + 0.92 cos 7 = 7 (sin $ - 3.73 cos TABLE V. Regular: a = 0.6. . Irregular reflection. a = 0.7. > 7T - 0) r All the light flux issuing from the main radiator between the upper vertical and the angle w t (0 < < < 6^) 1' = 7 sin (15) is wasted by passing through the central hole in the reflector. LIGHT FLUX AND DISTRIBUTION. 217 Of the light flux issuing between angle ^ and - from the upper 2i vertical, the part f = I Q tan a) 2 cos (j>, for*> 2 <(<^ (20) 2i is received by the reflector, with the exception of that part which passes through the hole in the reflector. The total light flux intensity reflected by the reflector, or the useful light flux of the virtual or secondary radiator, thus is, if a = albedo of the reflector, Within the angle ->< > aj 2 from the upper vertical, 2 7"= a (I 2 7 X ) = aI Q (tan co 2 tan ajj cos <; (21) within the angle a) 2 >(f> >a> l from the upper vertical, I'" = a (P - 7J = 7 (sin < - tan ^ cos <) ; (22) and for ^ > < > 0, /"" = a (/' - 7') = 0; (23) . 218 RADIATION, LIGHT, AND ILLUMINATION, hence, the light intensity of the illuminant, consisting of vertical radiator and ring-shaped mirror reflector, for < < Wj is 7=7 sin<; (24) for Wj< < ^ 2 is /= /'+ i"' = / o { (1 + a) sin - a tan ^ cos <) } ; (25 for I = P + I" = 7 { sin + a (tan w 2 tan w^ cos < } ; (26) for and for 7 -= 7/ = 7 (sin tan a> 2 cos <), 7 = 0. 17 n (27) For ^= 60 = , ^ 2 = 85= , and albedo a= 0.7, the in- O OU tensity distribution is plotted in Fig. 88 and recorded in Table V. FIG. 88. Substituting the numerical values in the foregoing, we have: (24) 7 = 7 sin<, (25) 7 = 7 (1.7 sin $ - 1.21 cos <), (26) 7 = 7 (sin < + 6.79 cos 0), (27) 7 = 7 (sin - 11.43 cos <). 98. As it is difficult to produce and maintain completely regular reflection, usually some irregular reflection is superim- posed upon the regular reflection. For the irregular reflection, the reflector is a horizontal plane radiator. LIGHT FLUX AND DISTRIBUTION. 219 The light flux reflected by a plane circular reflector subtending angles co 1 to co 2 , by (6), is $.,= */ a' K L "i), (28) where a' is the albedo of irregular reflection. This light flux gives in the lower hemisphere the maximum intensity for = as 7." - 7 a' (o, 2 - a,,), (29) and thus the intensity of the irregularly reflected light in the direction < is 7 2 = / " cos - wj cos (, (30) and this intensity thus adds to that given by equations (24) to (27) in the preceding. If some light is obstructed by the shadow of the lower elec- trode, then the light intensity of the main radiator, /', in the lower hemisphere within the angle fa < (/> < - > is reduced to 2 (31) and becomes zero for <,, where tan < t == y as discussed I/ under heading II, class (2), equations (21), (22), where r { is the radius of the lower electrode. Thus, with a linear radiator of length I, a diameter of the lower electrode of 2 r v a ring-shaped mirror reflector subtending, from the base of the arc, the angles ^ and w 2 , and of the albedo of regular reflection a and the albedo of irregular reflection a', the light intensity distribution within is < (f> < (j> v I = //(^ 2 - Wl )cos^; (32) within (f> 1 < (/> < Wj is I = 7 (sin +fy K - ^) -- ^J cos ^; (33) within ^ < (j> < a> 2 is / = / (1 + a) sin (/> + \a (co 2 - ^) - atan^ -j lcos(/)|; (34) 220 RADIATION, LIGHT, AND ILLUMINATION. within to y - 7T . <2 1S Jsin (j>+\ a (tan a) 2 - tan w^) + a' (to 2 -u^ - ~ cos within and within I = I (sin $ tan a> 2 cos <), K to 2 < < n is / = 0. (35) (36) FIG. 89. The distribution curve of such an illuminant is plotted in Fig. 89 and recorded in Table V for the values ^= 60 deg. = ; co 2 = 85 deg. =-r', a =0.60; a'= 0.10, and I 1. Substituting the numerical values in the foregoing equations this gives ^ = 27 deg . (32) 7 = 0.044 7 cos , (33) 7 = 7 (sin - 0.456 cos <), (34) 7 = 7 (1.6 sin < - 1.495 cos <), (35) 7 = 7 (sin + 5.364 cos <), (36) 7 = 7 (sin - 11.43 cos ). FIG. 90. As comparison is given in Fig. 90 the distribution curve of the magnetite arc, which is designed of the type of Fig. 89 for the purpose of giving more nearly uniform illumination in street lighting. LIGHT FLUX AND DISTRIBUTION. 221 IV. DIFFRACTION, DIFFUSION, AND REFRACTION. 99. Many radiators are of too high a brilliancy to permit their use directly in the field of vision when reasonably good illumination is desired. A reduction of the brilliancy of the illuminant by increasing the size of the virtual radiator thus becomes necessary. This is accomplished by surrounding the radiator by a diffracting, diffusing, or prismatically refracting envelope. Diffraction is given by a frosted glass envelope, as a sand blasted or etched globe; diffusion by an opal or milk-glass globe. The nature of both phenomena is different to a consider- able extent, and a frosted globe and an opal globe thus are not equivalent in their action on the distribution of the light flux. This may be illustrated by Fig. 91. Let, in Fig. 91, 1A, R represent the light-giving radiator, for simplicity assumed as a point, and G represent a diffracting sheet, as a plate of ground glass. A beam of light, C, issuing from the radiator R is, in traversing the diffracting sheet G, scattered over an angle, that is, issues as a bundle of beams D } of approximately equal intensity in the middle and fading at the edges '. The direction of the scattered beam of light D, that is, its center line, is the same as the direction of the impinging beam C, irrespective of the angle made by the diffracting sheet with the direction of the beam. Different is the effect of diffusion, as by a sheet of opal glass, shown as G in Fig. 91, IB. Here the main beam of light G passes through, as C', without scattering or change of direction, but with very greatly reduced intensity; usually also with a change of color to dull red, due to the greater transparency of opal glass for long waves. Most of the light, however, is irregu- larly reflected in the opal glass, and the point or area at which the beam C strikes the sheet G becomes a secondary radiator and radiates the light with a distribution curve corresponding to the shape of (2, that is, with a maximum intensity at right angles to the plane of G, as illustrated in Fig. 91, 1 B. A point P thus receives from a radiator R, enclosed by a diffract- ing globe G, a pencil of light, as shown in Fig. 91, 2 A, and from the point P the radiator appears as a ball of light, shown densely shaded in 3 A, surrounded by a narrow zone of half light, 222 RADIATION, LIGHT, AND ILLUMINATION. shown lightly shaded, and in the interior of a non-luminous or faintly luminous envelope. If the radiator R is enclosed by a diffusing globe, Fig. 91, B2, the point P receives light from all points of the envelope G as FIG. 91. 3-B secondary radiator, and a ray of direct light from the radiator R. From the point P the entire globe G thus appears luminous, and through it shows faintly the radiating point R, as sketched in 3B. An incandescent-lamp filament in an opal globe thus is clearly LIGHT FLUX AND DISTRIBUTION. 223 but faintly visible, surrounded by a brightly luminous globe, while an incandescent filament in a frosted globe appears as a ball of light surrounded by a non-luminous or faintly luminous globe, but the outline of the filament is not visible. 100. The distribution of light flux thus essentially depends on the shape of the diffusing envelope, but does not much depend on the shape of the diffracting envelope; that is, a diffracting envelope leaves the distribution curve of the radiator essentially unchanged, and merely smooths it out by averaging the light flux over a narrow range of angles, while a diffusing envelope entirely changes the distribution curve by substituting the diffusing globe as secondary radiator, and leaves only for a small part of the light - that of the direct beam C' the intensity distribution of the primary radiator unchanged. Thus, for a straight vertical cylindrical envelope surrounding a radiator giving the distribution curve shown in Fig. 92, curve I, FIG. 92. the distribution curve is changed by diffraction (frosted en- velope), to that shown in Fig. 92, curve II, but changed to that shown by Fig. 92, curve III, by diffusion (opal envelope). The latter consists of a curve due to the transmitted light and of the same shape as I, and a curve due to the diffused light, or light coming from the envelope as secondary radiator. The latter is the distribution curve of a vertical cylindrical radiator, as dis- cussed under heading I, class (5). The shape of a diffusing envelope thus is of essential importance 224 RADIATION, LIGHT, AND ILLUMINATION. for the distribution of the light intensity, while the shape of the diffracting envelope is of less importance. TABLE VI. f. v Clear globe. v Frosted globe. V Opal globe. n 5 U in 5 1U 20 6 8 11 2*5 7 12 m9 30 9 18 17 35 15 26 40 34 35 25 45 49.6 43 50 50.6 47.5 32 55 49.6 48 60 47.5 46 34.5 fi7 43 42 U 1 70 37 37 35 75 29 32 80 20 26 34 85 15 21 90 13.5 17 32 95 13 14 100 12.5 13 30.5 110 12 12 29.5 120 11 11 27 130 9 9 24 140 6 7 20 150 2 15 160 10 It is obvious that frosted glass does not perfectly represent diffraction, but some diffusion occurs, especially if the frosting is due to etching, less if due to sand-blasting. Opal glass also does not give perfect diffusion, but, in the secondary radiation issuing from it, the direction of the horizontal or impinging beam slightly preponderates. 101. Regular or prismatic refraction also affords a means of decreasing the brilliancy by increasing the size of the virtual illummant, and at the same time permits the control of the LIGHT FLUX AND DISTRIBUTION. 225 intensity distribution. It probably is the most efficient way, as involving the least percentage of loss of light flux by absorp- tion. For instance, by surrounding the radiator R by a cylindrical lens, as shown diagrammatically in Fig. 93, the rays of light may ^ FIG. 93. be directed into the horizontal (or any other desired) direction, and the entire lens then appears luminous, as virtual radiator. Usually in this case, instead of a complete lens, individual sec- tions thereof are used, as prisms, as shown in Fig. 94, and this FIG. 94. method of light control thus called "prismatic refraction," or, where the light does not pass through, but is reflected and turned back from the back of the prism, "prismatic reflection." Such prismatically reflecting or refracting envelopes and shades have found an extensive use. LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the required illumi- nation depends on the purpose for which it is used: a general illumination of low and approximately uniform intensity for street lighting; a general illumination of uniform high intensity in meeting rooms, etc.; a local illumination of fairly high intensity at the reading-table, work bench, etc. ; or combinations thereof, as, in domestic lighting, a general illumination of moderate inten- sity, combined with a local illumination of high intensity. Even the local illumination, however, within the illuminated area usually should be as uniform as possible, and the study of the requirements for producing uniformity of illumination either throughout or over a limited area thus is one of the main prob- lems of illuminating engineering. The total intensity of illumination, i, at any point in space is proportional to the light intensity, 7, of the beam reaching this point, and inversely proportional to the square of the distance I of the point from the effective center of the light source : If the beam of light makes the angle with the vertical direction, the illumination, i, is thus in the direction , the horizontal illumination, that is, the illumination of a horizontal plane (as the surface of a table), is , 7cos< , i h = i cos = 226 LIGHT INTENSITY AND ILLUMINATION. 227 and the vertical illumination, that is, the illumination of a vertical plane (as the sides of a room), is 7 sin i v = i sin < = !- , (3) If, then, in Fig. 95, L is a light source at a distance l v above a horizontal plane P, then, for a point A at the horizontal dis- FIG. 95. tance l h from the lamp, L (that is, the distance l h from the point B of the plane P, vertically below the lamp L), we have: , L v and the distance of the point A from the light is cos hence, the total illumination at point A is . 7 cos 2 () . the horizontal illumination is l 7 cos and the vertical illumination is . 7 cos 2 sin (4) (5) (6) (7) (8) where 7 is the intensity of the light source in the direc- tion . Inversely, to produce a uniform total illumination, i , on the 228 RADIATION, LIGHT, AND ILLUMINATION. horizontal plane P, the intensity of the light source must vary with the angle according to the equation (6) : 7" 1 2 (9) or, if we denote by 7 the vertical, or downward, intensity of the light source, A, - V, 2 ; (10) hence, 7 = ^- (11) gives the intensity distribution of the light source required to produce uniform total illumination i on a horizontal plane be- neath the light. In the same manner follows from (7) and (8) : To produce uniform horizontal illumination i hQ on a plane P beneath the light source L, the intensity curve of the light source is given by cos 3 and, to produce uniform vertical illumination i VQ of objects in the plane P beneath the light source L, 7 - /0 (13) cos"

= 90 deg. TABLE I. (Figs. 95 and 96.) UNIFORM DISTRIBUTION ILLUMINATION CURVES. f. COS (p. Total. 1 Horizontal. 1 Vertical. 1 degrees. cos 2 cos 3 sin ^ cos 2 1 1 1 00 5 996 1.01 1.015 11.60 10 985 1.03 1.045 5.90 15 966 .07 1.11 4.30 20 940 .13 1.20 3.30 25 906 .22 1.35 2.88 30 866 .33 1.54 2.66 35 819 .49 1.82 2.59 40 766 .70 2.22 2.64 45 707 2.00 2.83 2.83 50 643 2.43 3.73 3.17 55 574 3.03 5.27 3.70 60 500 4.00 8.00 4.60 65 423 5.59 13.20 6.16 70 342 8.35 24.4 8.90 75 259 15.10 58.3 15.60 80 174 33.00 190.0 32.50 85 087 132.00 152.0 133.00 90 00 00 00 103. Therefore, in the problem, as it is usually met, of pro- ducing uniform intensity i over a limited area, subtending angle 2 aj beneath the light source, the intensity of the light source 230 RADIATION, LIGHT, AND ILLUMINATION. FIG. 96. FIG. 97, LIGHT INTENSITY AND ILLUMINATION. 231 should follow (11) for < < a>. Beyond < = a>, the intensity may rapidly decrease to zero as would be most economical, if no light is required beyond the area subtended by angle 2 co. This, for instance, is the case with the concentrated lighting of a table, etc. However, the intensity beyond (f> = to may follow a different curve, to satisfy some other requirements, for instance, to produce uniform illumination in a vertical plane. Thus in domestic lighting, for the general uniform illumination of a room by a single illuminant, the intensity curve would follow equation (11) up to the angle a> if 2 w is the angle subtended by the floor of the room from the light source and for $ > cu the intensity curve would follow the equation, / = -4-r, (14) sin 2 which gives uniform illumination in the vertical plane, that is, of the walls of the room. In Fig. 98 are shown intensity curves of a light source giving uniform illumination in the horizontal plane beneath the lamp, from to CD, and the same uniform illumination in the vertical plane from $ = a> to = 90 deg., as diagrammatically shown in Fig. 97; that is, uniform illumination of the floor of a room and (approximately) its walls, by a lamp located in the center of the ceiling, where cu is the (average) angle between the vertical and the direction from the lamp to the edge of the floor: I for co = 30 deg.; or diameter of floor -f- height of walls = 2 2 tan 30 deg. = ==1.15. II for co = 45 deg.; or diameter of floor -j- height of walls = 2 tan 45 deg. = 2. III for aj = 60 deg.; or diameter of floor -H height of walls = 2 tan 60 deg. = 2 V3 = 3.46. IV for a) = 75 deg.; or diameter of floor -f- height of walls = 2 tan 75 deg. = 7.46. These curves are drawn for the same total flux of light in the lower hemisphere, namely, 250 mean hemispherical candle power; 232 RADIATION, LIGHT, AND ILLUMINATION. or, 1570 lumens. The vertical or downward intensities 7 are in this case: I: aj = 30 deg.; 7 = 428 cp. II: cu = 45 deg.; 7 = 195 cp. Ill: w = 60 deg.; 7 = 95 cp. IV: aj = 75 deg.; 7 = 41.5 cp. The values are recorded in Table II, in column I, for equal downward candle power 7 , and in column a, for equal light flux, corresponding to 1 mean hemispherical candle power. TABLE II. (Figs. 97 to 99.) INTENSITY CURVES. Uniform illumination from vertical = to = degrees from verti- cal, and (a) Uniform illumination (on vertical plane) from = w to horizontal = 90 deg. (6) No illumination beyond = w. 7 for unity illumination at = 0. a and 6 for mean hemispherical candle power 1, or 2 TT lumens. . ca = 30 deg. w = 45 deg. a> = 60 deg. to = 75 deg. /0< a. 6. V a. b. V a. b. I - a. 6. 5 10 .00 .01 1.03 1.71 1.72 1.76 3.73 3.76 3.83 1.00 1.01 1.03 0.78 0.79 0.80 1.57 1.58 1.62 1.00 1.01 1.03 0.38 0.385 0.39 0.67 0.67 0.685 1.00 1.01 1.03 0.166 0.168 0.172 0.222 0.224 0.229 15 20 25 .07 .13 .17 1.83 1.93 2.00 3.98 4.20 4.35 1.07 1.13 1.22 0.83 0.88 0.95 1.68 1.77 1.99 1.07 1.13 1.22 0.41 0.43 0.465 0.71 0.75 0.81 1.07 1.13 1.22 0.178 0.188 0.203 0.237 0.251 0.271 30 35 40 1.20 1.01 0.81 2.05 1.73 1.38 4.47 3.57 2.24 1.33 1.49 1.70 1.03 1.16 1.32 2.08 2.33 2.66 1.33 1.49 1.70 0.51 0.57 0.65 0.89 0.99 1.13 1.33 1.49 1.70 0.221 0.248 0.283 0.295 0.331 0.377 45 50 55 0.67 0.57 0.50 1.14 0.98 0.85 0.57 1.80 1.70 1.49 1.40 1.32 1.16 2.85 2.50 1.10 2.00 2.43 3.03 0.76 0.93 1.16 1.34 1.62 2.02 2.00 2.43 3.03 0.333 0.405 0.504 0.445 0.540 0.672 60 65 70 0.44 0.41 0.38 0.75 0.70 0.65 1.33 1.22 1.13 1.03 0.95 0.88 0.31 3.60 3.51 3.39 1.37 1.34 1.29 2.40 2.00 0.80 4.00 5.59 8.35 0.665 0.930 1.39 0.887 1.24 1.86 75 80 85 0.36 0.34 0.34 0.61 0.58 0.58 1.07 1.03 1.01 0.83 0.80 0.79 3.21 3.09 3.03 1.22 1.18 1.16 0.20 12.80 12.40 12.10 2.13 2.07 2.02 2.85 2.11 0.67 90 0.33 0.57 1.00 0.78 3.00 1.14 12.00 2.00 0.11 LIGHT INTENSITY AND ILLUMINATION. 233 These curves in Fig. 98 consist of a middle branch, giving uni- form floor illumination, and two side branches, giving uniform side illumination, and are rounded off where the branches join. FIG. 98. Fig. 99 gives the intensity curves for the same angles, w = 30, 45, 60, and 75 deg., for uniform illumination only in the hori- FIG. 99. zontal plane beneath the lamp, but no illumination beyond this; for < > a>, the light flux rapidly decreases. The curves in Fig. 99 are also plotted for equal total light flux, of 150 mean hemispherical candle power, or 940 lumens. The 234 RADIATION, LIGHT, AND ILLUMINATION. curve, 0, giving (approximately) uniform illumination within an angle of 20 deg., or for a> = 10 deg., is added to the set; this curve, however, is plotted for one-tenth the light flux of the other curves, 94 lumens, or 15 mean hemispherical candle power. The vertical or downward intensities 7 are in this case, for equal light flux of 940 lumens : I: 'a> = 30 deg.; 7 = 500 cp. II: a) = 45 deg.; 7 = 235 cp. Ill: co = 60 deg.; 7 = 100 cp. IV: aj = 75 deg.; 7 = 25 cp. 0: aj = 10 deg.; 7 = 7000 cp. Fig. 99 best illustrates the misleading nature of the polar dia- gram of light intensities. It is hard to realize from the appearance of Fig. 99 that curves I, II, III and IV represent the same light flux, and curve one-tenth the light flux, that is, little more than half the light flux of a 16-cp. lamp. Curve 0, however, illustrates that enormous light intensities can be produced with very little light flux, if the light flux is concentrated into a sufficiently narrow beam. This explains the enormous light intensities given by search-light beams: for oj = 1 deg., or a concentration of the light flux into an angle of 2 deg. which is about the angle of divergency of the beam of a good search light we would get 7 = 700,000 cp. in the beam, with 15 mean hemispherical, or 7.5 mean spherical, candle power light source; and a light source of 9000 mean spherical candle power a 160-ampere 60- volt arc would thus, when concen- trated into a search-light beam of 2 deg., have an intensity in the beam of 7 = 210 million candle power, when allowing 75 per cent loss of light flux, that is, assuming that only 25 per cent of the light flux is concentrated in the beam. The numerical values of Fig. 99 are given as b in Table II, for equal light flux corresponding to 1 mean spherical candle power. B. STREET ILLUMINATION BY ARCS. 104. To produce uniform illumination in a plane beneath the illuminant, a certain intensity distribution curve is required, as discussed in A ; for other problems of illumination, correspond- ingly different intensity curves would be needed to give the desired illumination. LIGHT INTENSITY AND ILLUMINATION. 235 It is not feasible to produce economically any desired distribu- tion curve of a given illuminant. Therefore, the problem of illuminating engineering is to determine, from the purpose for which the illumination is used, the required distribution of illu- mination, and herefrom derive the intensity curve of the illumi- nant which would give this illumination. Then from the existing industrial illuminants, or rather from those which are available for the particular purpose, that is selected whose intensity dis- tribution curve approaches nearest to the requirements, and from the actual intensity curve of this illuminant the illumination which it would give is calculated, so as to determine how near it fulfils the requirements. The intensity curve of the illuminant, required to give the desired illumination, depends on the location of the illuminant and the number of illuminants used. Thus if, with a chosen location and number of light sources, no industrial illuminant can be found which approaches the desired intensity curve sufficiently to give a fair approach to the desired illumination, a different location, or different number of light sources would have to be tried. Here, as in all engineering designs which involve a large number of independent variables, judgment based on experience must guide the selection. If so, practically always some industrially available illuminant can be found which sufficiently approaches the intensity curve required by the desired illumination. As example may be discussed the problem of street lighting. This problem is : with a minimum expenditure of light flux- that is, at minimum cost to produce over the entire street a sufficient illumination. This illumination may be fairly low, and must be low, for economic reasons, where many miles of streets in sparsely settled districts have to be illuminated. This requires as nearly uniform illumination as possible, since the minimum illumination must be sufficient to see by, and any excess above this represents not only a waste of light flux, but, if the excess is great, it reduces the effectiveness of the illumina- tion at the places, where the intensity is lower, by the glare of the spots of high illumination. Uniformity of street illumination thus is of special importance where the illumination must for economic reasons be low; while in the centers of large cities, or in densely populated districts, 236 RADIATION, LIGHT, AND ILLUMINATION. as European cities, the relatively small mileage of streets per thousand inhabitants economically permits the use of far greater light fluxes, and then uniformity, while still desirable, becomes less essential. TABLE III (Figs 100 and 101.) Intensity: 100 m. sph. cp. Illumination: 200 m. sph. cp.; / = 20. a. 6. c. a. 6. c. 1 D. C. D. C. D. C. D. C. c enclosed enclosed Magnetite Distance. enclosed enclosed Magnetite carbon carbon arc. carbon carbon arc. arc. arc. Clear arc. arc. . Clear Clear inner Opal inner globe. Clear inner Opal inner globe. globe. globe. globe. globe. 4>. 7. 7. 7. x = - i. i. t. h 30 45 59 15 22.5 29.5X10~ 3 10 42 50 63 0.2 22 24.5 30.5 20 92 70 69 0.4 46 33.0 31.0 30 182 107 79 0.6 73 42.5 31.0 40 247 150 102 0.8 73 44.5 30.5 45 270 1.0 67 40.5 29.5 50 257 171 136 1.2 53 35.5 28.0 60 210 181 177 1.4 39 30.5 26.0 70 147 182 226 1.6 30.5 25.5 23.5 75 122 181 243 1.8 24.5 21.5 21.5 80 97 160 250 2.0 19.0 18.0 19.0 85 75 118 249 2.5 11.5 13.0 15.0 90 65 89 197 3.0 7.0 9.5 12.0 100 57 82 47 3.5 5.0 7.0 9.5 110 57 77 16 4.0 3.5 5.5 7.5 120 60 68 5.0 2.0 3.2 4.8 130 35 62 6.0 1.2 2.0 3.4 140 3 56 7.0 1.0 1.4 2.5 150 17 8.0 0.8 1 .0 2.0 9.0 0.5 0.8 1.7 10.0 0.4 0.6 1 1 15.0 0.2 0.3 0.5 20.0 0. 1 0. 1 0.3 25^0 0.1 Q.I 0^2 The arc, as the most economical illuminant, is mostly used for street lighting. Fig. 100 gives the average intensity curves LIGHT INTENSITY AND ILLUMINATION. 237 of three typical arcs for equal light flux of 200 mean spherical candle power: FIG. 100. I. The direct-current enclosed carbon arc, with clear inner globe: a curve of the character discussed in Fig. 82. II. The direct-current enclosed carbon arc, with opal inner globe: a 0:20 III 1,60 1,00 0.4 0,2 08 0,4 06 08 10 12 It 16 18 20 22 24 26 28 FIG. 101. curve of the character discussed in Fig. 92. III. The magnetite arc or luminous arc, with clear globe: a curve of the character discussed in Fig. 89. The numerical values are recorded in Table III, per 100 mean spherical candle power. 238 RADIATION, LIGHT, AND ILLUMINATION. Herefrom then follows, by equations (6) and (4), the (total) intensity, i, in a horizontal plane beneath the lamp, at the horizontal distance l h from the lamp, where l v is the height of the lamp above this plane (the street). These values of illumination, i, are plotted, with x = - as ab- LV scissas, in Fig. 101 and recorded in Table III for l v = 20, and lamps of 200 mean spherical candle power. 105. With lamps placed at equal distances 4 o , and equal FIG. 102. heights l v , as shown diagrammatically in Fig. 102, the illumina- tion of any point A of the street surface is due to the light flux of a number of lamps, and not only to the two lamps 1 and 2, between which the point A is situated. As, however, the illumi- nation rapidly decreases with the distance from the lamp, it is sufficient to consider only the four lamps nearest to the point A. The illumination of a point A of the street surface, at a horizon- tal distance l h from a lamp, 1, then is: i = ^ + i 2 + ,; + ^ (15) where i v i v i s , i 4 are the illumination due to the lamps 1, 2, 3, 4, respectively. I j Let -r = P and ^==x; (16) k lv then the directions under which point A receives light are given by: tan fa = x, tan fa = p x, tan fa = p + x, tan fa = 2 p x } (17) LIGHT INTENSITY AND ILLUMINATION. 239 and 1 l v 2 cos 2 / V cos cos /4 cos (18) where I v I 2 , 7 3 , I 4 are the intensities of the light source in the respective directions v 2 , 100 120 110 FIGS. 103, 104. Herefrom are calculated the illumination, i, plotted in Figs. 103 and 104 and recorded in Table IV for l v = 20 ft. ; p = 5, hence l ho = 100 ft., Fig. 103, and p = 10, hence l ho = 200 ft., Fig. 104, for equal light flux of 200 mean spherical candle power per lamp. As seen, with the same light flux per lamp, the distribution curve III of Fig. 100 gives the highest and the curve I the lowest intensity at the minimum point midways between the lamps, while inversely I gives the highest and III the lowest intensity near the lamp; that is, I, the carbon arc with clear inner globe, gives the least uniform, and III, the luminous arc, the most uni- 240 RADIATION, LIGHT, AND ILLUMINATION. form, illumination, while the carbon arc with opal inner globe, II, stands intermediate. TABLE IV. (Figs. 101 to 106.) STREET ILLUMINATION. tan 4 = X. Equal light flux per lamp. Equal illumination at minimum. p = 10. p= 5. p = 10. p= 5. a. 6. c. a. &. c. a. b. c. a. 6. c. 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 5.0 15.8 22.8 46.8 74 74 68 54 40 32 26 20 12.7 8.2 6.3 4.9 4.2 23.7 25.7 34.7 44 46 42 37 32 27 23 19.5 14.6 11.3 9 8 6.7 31.7 32.7 33.5 33.5 33 32 30.5 29 26.5 24.5 22 18 15 13 11.5 10.2 20 27 51 78 78 72.5 59 45 37 32 29 25 29 31 40 50 52 48 43 38.5 35 32.5 30 29 41.5 42.5 43 43 43 42.5 41.5 40.5 39 37.5 36 34.5 38 54 111 176 176 162 128 95 76 62 48 30 20 15 12 10 35 38 52 66 69 63 55 48 40 34 29 22 17 13.5 12 10 31 32 32.7 32.7 32.3 31.4 30 28.4 26 24 22 18 15 13 11 10 8 11 20 31 31 29 24 18 15 13 11.6 10 10 11 14 17 18 17 15 13 12 11 10.4 10 12. 1~ 2 12.3 12.5 12.5 12.5 12.3 12.1 11.8 11.3 11 10.5 10 Ratio of minimum intensities. Ratio of total light fluxes. 1 1.60 2.43 1 1.16 1.38 5.95 2.43 3.75 1.53 2.45 1.00 4.0( 1.3* ) 3.45 2.90 1 1.19 1.00 Ratio of maximum to min. ilium. 17.6 6.9 3.3 3.1 1.8 1.25 The ratio of maximum to minimum illumination is : p = 10 p = 5 I. Carbon arc with clear globe: 17.6 3.1 II. Carbon arc with opal globe: 6.9 1.8 III. Luminous, or magnetite, arc : 3.3 1.25 LIGHT INTENSITY AND ILLUMINATION. 241 As seen, lower values of p, that is, either shorter distances between the lamps, or greater elevation of the lamps above the street surface, give a more uniform illumination, so that, for p = 5, III gives only 25 per cent intensity variation, while, for p = 10, I gives a very unsatisfactory illumination, alternating darkness and blinding glare. 0=2- iO 100 140 160 r\ i FIGS. 105, 106. In Figs. 105 and 106 are plotted, and recorded in Table III, the illuminations for equal minimum intensity midways between the lamps, and for equal distances l ho = 200 ft., between the lamps, for p = 5, or l v = 40 ft. height above the street level, Fig. 105. p = 10, or 1 = 20 ft. height above the street level, Fig. 106. To produce this minimum intensity of 0.1 candle feet, with 200 feet distance between the lamps, would require the following mean spherical candle powers : I. Carbon arc with clear globe: 1190 II. Carbon arc with opal globe: 750 III. Magnetite arc: 490 , or 4=40 ft. 800 690 580 242 RADIATION, LIGHT, AND ILLUMINATION. It is interesting to note the great difference in the light flux, required to produce the same minimum illumination, for the three distribution curves. The carbon arc gains in efficiency and in uniformity of illumi- nation by increasing the elevation from 20 to 40 ft., while the magnetite arc loses in efficiency due to the greater distance from the illuminated surfaces but makes up for this by the gain in uniformity of illumination. C. ROOM ILLUMINATION BY INCANDESCENT LAMPS. 106. Let Fig. 107 represent the intensity distribution of an incandescent lamp with reflector, suitably designed for approxi- mately uniform illumination in a horizontal plane below the lamp. Such a distribution curve can, for instance, be produced FIG. 107. by a spiral filament F (Fig. 108) located eccentric in a spher- ical globe G, of which the upper part is clear glass and covered by a closely attached mirror reflector R, while the lower part is frosted, as shown diagrammatically in Fig. 105. With this arrangement, half of the light flux issues directly, with approximately uniform intensity in the lower hemisphere, from = to = (f> l} and with gradually decreasing intensity from $ = 2 . The other half of the light flux is LIGHT INTENSITY AND ILLUMINATION. 248 reflected from the mirror, and, due to the eccentric location of the filament, the reflected rays are collected into an angle of about 45 deg. from the vertical, and cross each other, thereby producing the intensity maximum at 4> = 30 deg. The intrinsic brilliancy is sufficiently reduced, and the distribution curve smoothed out, by the frosting of the globe as far as not cov- ered by the reflector. The light in the upper hemisphere beyond = (j> 2 then is only that reflected by the frosting. The numerical val- ues of intensity of Fig. 107 are recorded in Table V. The mean spherical candle power of the lamp is 12.93, or 163 lumens ; the mean can- dle power in the lower hemisphere is 20.20, or 127 lumens, and the mean candle power in the upper hemi- sphere is 5.66, or 36 lumens. Table V gives the distribution of illumination i in a horizontal plane beneath and above the lamp, for different horizontal distances l h and the vertical distance l v = 1, by equation (6), and the horizontal illumination i h , by equation (7), as discussed in A. These are plotted in Fig. 109, for the lower hemisphere in the lower, for the upper hemisphere in the upper, curve. Assuming now that a room of 24 ft. by 24 ft. and 10 ft. high is to be illuminated by four such lamps, located 6 inches below the ceiling in such a manner as to give as nearly as possible uniform illumination in a plane 2.5 ft. above the floor (the height of table, etc.). FIG. 108. 244 RADIATION, LIGHT, AND ILLUMINATION. TABLE V. (Figs. 107 to 109.) #. 7. lh lv tan c. i = I COS 2 < **~ / Ik X = T V i I cosV fc*- / cos 3 ^ (Upper hemisphere). cos 3 tf, i f . i'h- 10 20 30 40 50 60 65 70 75 80 85 90 95 100 105 110 115 120 130 140 150 160 170 180 21.0 22.2 24.5 26.3 25.5 22.5 20.0 19.0 18.0 17.0 16.0 15.0 13.0 11.0 9.5 8.0 7.0 5.5 4.5 3.0 2.5 2.2 2.0 2.0 2.0 0.176 0.364 0.577 0.839 1.192 1.732 2.144 2.745 3.732 5.671 11.43 00 11.43 5.671 3.732 2.745 2.144 1.732 1.192 0.839 0.577 0.364 0.176 21.0 21.5 21.7 19.8 15.0 9.3 5.0 3.4 2.15 1.13 0.49 0.11 0.08 0.29 0.53 0.84 1.00 1.12 1.23 1.47 1.66 1.77 1.94 2.0 21.0 21.3 20.4 17.0 11.5 6.0 2.5 1.44 0.74 0.29 0.08 0.01 0.01 0.08 0.14 0.29 0.42 0.56 0.80 1.13 1.43 1.66 1.91 2.0 o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 21.0 21.25 21.55 21.8 21.6 20.8 19.4 17.7 15.8 13.9 12.2 10.6 9.2 5.1 7.2 6.45 5.8 5.2 4.7 4.2 3.9 2.55 1.8 1.33 1.0 0.8 0.67 0.45 0.33 0.25 0.20 0.17 21.0 21.1 21.3 21.0 20.0 18.5 16.5 14.3 12.3 10.4 8.6 7.2 6.0 5.1 4.2 3.55 3.1 2.65 2.25 1.95 1.7 1.0 0.6 0.37 0.25 0.18 0.13 0.10 0.08 0.05 2.0 2.0 *i'.i 1.5 1.35 1.0 1.2 0.68 Y.08 0.9 0.77 0.63 0.5 0.43 0.38 0.28 0.20 0.17 0.14 0.12 'b'.48 0.35 0.27 0.20 0.13 0.10 0.08 0.06 As the illumination in the space between the lamps is due to several lamps and thus is higher than that at the same horizon- tal distance outside of a lamp, for approximate uniformity of illumination, the distance between the lamps must be con- siderably greater than twice their distance from the side walls LIGHT INTENSITY AND ILLUMINATION. 245 0*6 08 II 246 RADIATION, LIGHT, AND ILLUMINATION. of the room. Locating thus the lamps, as shown diagrammati- cally in Fig. 110, at 5 ft. from the side walls and 14 ft. from each other, the (total) illumination in the lines A, B, C, D in the test plane 2.5 ft. above the floor is calculated. As this plane is 7 ft. beneath the lamps, first the illumination curve in a plane 7 ft. beneath the lamp is derived from that in Fig. 109, by dividing the ordinates by 7 2 = 49, and multiplying the abscissas by 7. It is given in Fig. 111. FIG. 111. The illumination, i, at any point, P, then is derived by adding the illumination i a , i b , i c , i d of the four lamps a, 6, c, d, taken from curve in Fig. Ill for the horizontal distances of point P from the lamps : l hg , l hb , l hc , l hd . These component illuminations are plotted in Figs. 112 to 115; as A , A b , A c , Ad in Fig. 112; as B a , B b in Fig. 113, etc., and their numerical values, in thousandths of candle feet, recorded in Table VI. In Fig. 116 are shown the four curves of the resultant direct illumination, superim- posed upon each other. 107. To this direct illumination is to be added the diffused illumination G resulting from reflection by ceiling and walls. Let: a t = 0.75 = albedo of ceiling; a 2 = 0.4 = albedo of walls; (19) while the floor may be assumed as giving no appreciable reflec- tion: a = 0. The diffused light, then, may be approximated as follows: The ceiling receives as direct light the light issuing in the upper hemisphere, or 36 lumens per lamp, thus a total of L x = 4 X 36 = 144 lumens, (20) LIGHT INTENSITY AND ILLUMINATION. TABLE VI. (Figs. 110 to 116.) 247 X. A a . Ab. A. B a and Bd- B. c a . c b . C. D a - D b and D c . D. 353 71 746 180 690 244 43 600 245 43 600 1 406 74 813 200 738 276 44 645 317 49 691 2 438 76 852 218 782 306 44 681 395 55 785 3 442 78 866 234 822 332 45 714 441 62 845 4 438 80 875 244 852 348 45 737 440 70 866 5 429 80 880 247 870 353 45 746 429 79 880 6 438 80 903 244 882 348 45 754 440 90 919 7 442 78 922 234 880 332 45 750 441 101 949 8 438 76 936 218 866 306 44 737 395 114 939 9 406 74 927 200 850 276 44 723 317 125 896 10 353 71 898 180 838 244 43 710 245 135 859 11 298 67 875 162 830 209 42 696 184 143 835 12 247 63 870 144 825 180 41 690 144 144 825 13 flOO 60 129 156 39 115 143 14 167 57 114 136 37 94 135 15 143 54 102 118 35 79 125 16 121 51 90 103 33 66 114 17 104 48 81 90 31 56 101 18 90 45 72 80 30 49 90 19 80 41 63 72 30 42 79 20 70 38 57 64 30 36 70 21 61 35 52 58 29 33 62 22 55 33 48 52 29 30 55 23 52 31 44 47 28 26 49 24 45 2P 40 43 28 23 43 and also receives some reflected light from the walls. Thus, if ^ = total light flux received by the ceiling, and 3> 2 = total light flux received by the walls, the light flux received by the ceiling is ^ = L, + b 2 a 2 3> 2 , (21) where b 2 is that fraction of the light flux issuing from the walls, which is received by the ceiling. And the light reflected from the ceiling thus is : $/= afr = a, (L, + b 2 a 2 $> 2 ). (22) The walls receive as direct light the light issuing from the lamps in the lower hemisphere, between the horizontal, = 90 248 RADIATION, LIGHT, AND ILLUMINATION. deg., and the direction, < = a) (Fig. 110), from the lamp to the lower edge of the walls. This angle co varies, and averages 30 deg. for that half of the circumference, PQR (Fig. 110), at which the walls are nearest, and 60 deg. for that half, RSTUP, for which the walls are farthest, from the lamp. Hence the 1.0 0.8 0.6 0.4 0.2 Act Ac 12 10 0.8 B 0.6 0.4 G 0,2 BaScd BbStc 6 *c B B G Bfc&c Bakd X x- ** -^ -^ -* ^ ->s X / \ -*- ^^ ^^** >J ^ _ ~~ _ - . , - - -, ~- .. 4 8 12 18 20 2* FIGS. 112, 113. light flux received by the walls as directed light, from each lamp, is - I I sin $ d$ + - T / sin $ d$ = 83 lumens; (23) Zt/ 30 ^^60 or, a total of L 2 = 4 X 83 = 332 lumens. (24) LIGHT INTENSITY AND ILLUMINATION. 249 In addition hereto, the walls receive some of the light flux reflected by the ceiling. The total light received by the walls thus is : $ 2 = L 2 + bpfr, (25) where b l is that fraction of the light flux issuing from the ceiling, which is received by the walls. 1.0 0.8 0.6 C G 0.2 Ca Cb Cd Cc 1.0 Cb 12 16 20 0.8 0.8 D O.i 0.2 Dbbd DC Da FIGS. 114, 115. And the light reflected from the walls thus is : *,' - a^ 2 = a 2 (L 2 + 6^*,). (26) It thus remains to calculate the numerical values of b l and b y Of the light reflected by the ceiling as secondary generator, /, a part is obstructed by the floor, a part received by the walls. 250 RADIATION, LIGHT, AND ILLUMINATION. The floor is a square plane, of the same size, 24 by 24 ft., as the radiator, that is, the ceiling, and at the distance 10. The light intercepted by the floor can thus approximately be calculated as discussed in Lecture X, II, 1, Fig. 82, for circular radiator and circular shades, by replacing the quadratic shade and radia- tor by circular shades of the same area, r 2 n = 24 2 , and r = 13.5, at the same distance I = 10, hence of the ratio : - = 0.74. Calculated as discussed in Lecture X, II, 1, the floor receives 55 per cent and the walls 45 per cent of the light reflected by the ceiling. Assuming, approximately, that the walls receive the same percentage of the light reflected from the ceiling, as the ceiling receives of the light reflected from the walls, or & 2 - &!, (27) equations (21) and (25) become: ^ = L,+ \a 2 $> 2 , (28) 2 = L 2 + 6^^; (29) hence, _L 2 + 2 1 + (30) and the light reflected from the ceiling is $/ = a^ = A * 2 2 ; the light reflected from the walls is