RADIATION, LIGHT AND ILLUMINATION -s g !? *rt OJ 0,8 bo RADIATION. LIGHT AND ILLUMINATION A SERIES OF ENGINEERING LECTURES DELIVERED AT UNION COLLEGE BV CHARLES PROTEUS STEINMETZ, A.M., PH.D. COMPILED AND EDITED BY JOSEPH LEROY HAYDEN THIRD EDITION FIFTH IMPRESSION McGRAW-HILL BOOK COMPANY, INC. NEW YORK: 370 SEVENTH AVENUE LONDON: 6 A 8 BOUVERIE ST., E. C. 4 1918 COPYRIGHT, 1909, 1918, BY THE McGRAW-HILL BOOK COMPANY, INC. PBINTED IN THE UNITED STATES OF AMERICA 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. ill 725190 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. PAGE LECTURE I. NATURE AND DIFFERENT FORMS OF RADIATION. 1. Radiation as energy. 1 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 Bo OILS 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 46. Transmitted light. 31 ^7. Opaque colors and transparent colors. 32 v!8. 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. 34 vii viii CONTENTS. PAOB 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. Power effect and specific high frequency effect. 57 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. A/. 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. ix 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. 238 Room Illumination by Incandescent Lamps. 106. Distribution curve of lamp. Calculation of resultant total intensity of direct light. 242 107. 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. PAGUI ^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 OP ILLUMINATING ENGINEERING. 123. Physical side of illuminating engineering. Physiological problems. 277 124. Physiological difference between diffused and directed light. 278 125. Indefiniteness 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 BADIATION, 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, usually 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 al cute ted from their observations by the law of gravita- tion, the' time at -Vhidfi the moon M should disappear from sight, N \ \ 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 17 J 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 195>OQ ^ Q( - > 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 v 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_MOES 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 agiin, 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 i 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 OAA sec., and as this is the time required by the light to travel 10 miles, this gives the velocity of light as 10 -s- - 18,800 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 ex- plain the radiations of radium, etc. Euler and others explained the light as a wave motion. Which of these explanations is correct can be experimentally decided in the following manner: Assuming light to be a bombardment of minute particles, if we combine 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 amplitude. If, however, we assume light is a wave motion, then two equal beams of light add to one of twice the amplitude only in case the waves are in phase, as A l and B l 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 z 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 6, 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 2 , etc. at which the distance FIG. 4. between the two glass plates is i wave length, or j, J, etc., the two component beams of a would differ by J, 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 \, 1, Ij, 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~* cm. (or about ? oooo in -) an( l since the speed is 8 = 3 X 10 l cm. the frequency S is / = = 500 X 10 12 , or .500 millions of millions of cycles per LW second, that is, inconceivably high compared with the frequencies with which we are familiar in alternating currents. If, as proven, light is a wave motion, there mast be some thing which is moving, a medium, and from the nature of the wave motion, its extremely high velocity, follow the properties of this medium: it has an extremely high elasticity and extremely low density, and it must penetrate all substances since no vacuum can be produced for this medium, because light passes through any vacuum. Hence it cannot be any known gas, but must be essen- tially different, and has been called the "ether." Whether the ether is a form of matter or not depends upon the definition of matter. If matter is defined as the (hypotheti- cal) carrier of energy (and all the information we have of matter is that it is the seat of energy), then the ether is matter, as it is a carrier of energy: the energy of radiation, during the time be- tween the moment when the wave leaves the radiator and the moment when it strikes a body and is absorbed, resides in the ether. 5. If light is a wave motion or vibration, it may be a longitudi- nal vibration, or a transversal vibration. Either the particles of the medium which transmit the vibrations may move in the direction in which the wave travels, as is the case with sound waves in air. If in Fig. 5 sound waves travel from the bell B in the direction BA , the air molecules m vibrate in the same direction, .4 to B. Or the vibration may be transversal ; that is, if the beam * As measures of the wave length of light, a number of metric unita have survived and are liable to lead to confusion: The micron, denoted by ( , equal to one thousandth of a millimeter. The ,,, equal to one millionth of a millimeter. The Angstrom unit, equal to one tenr-millionth of a millimeter. As seen, the basis of these units is the millimeter, which was temporarily used as a standard unit of length before the establishment of the present absolute system of units, the (C.G.S), which is based on centimeter length, gram mass, and second time measure. A radiation of the wave length of 60 microcentimeters thus can be expressed also as: 6000 Angstrom units, or 0.6 p, or 600 ft a. 8 RADIATION, LIGHT, AND ILLUMINATION. of light moves in Fig. 6 perpendicularly to the plane of the paper, the vibrating particles move in any one of the directions oa, ob, etc. in the plane of the paper, and thus perpendicular to the ray FIG. 5. of light. In the former case (a longitudinal vibration, as sound) there obviously can be no difference between the directions at right angles to the motion of the wave. In a transversal vibra- tion, however, the particles may move either irregularly in any of the infinite number of directions at right angles to the ray (Fig. 6) and thus no difference exists in the different directions perpendicular to the beam, or they may vibrate in one direction only, as the direction boa (Fig. 7). In the latter case, the wave is called " polarized" and has differ- ent characteristics in three direc- tions at right angles to each other: one direction is the direction of propagation, or of wave travel; the second is the direction of vibration ; and the third is the direction per- pendicular to progression and to vibration. For instance, the electric field of a conductor carrying alternating current is a polarized wave : the direction parallel to the conductor is the direction of energy flow; the direction concentric to the con- ductor is the direction of the electromagnetic component, and the direction radial to the conductor is the direction of the electrostatic component of the electric field. Therefore, if light rays can be polarized, that is, made to ex- hibit different properties in two directions at right angles to each other and to the direction of wave travel, this would prove the light wave to be a transversal vibration. This is actually the case. For instance, if a beam of light is reflected a number of times under a fairly sharp angle, as shown in Fig. 8, this beam becomes polarized; that is, for instance, the reflection from the mirror m , set like the mirrors m v m 2 . . . which produced the polarization, NATURE AND DIFFERENT FORMS OF RADIATION. 9 is greater, and the absorption less than from a mirror set at right angles thereto, as m '. Some crystals, as Iceland spar (calcium carbonate), show " double refraction," that is, dissolve a beam of light, a, enter- ing them, into two separate beams, b and c (Fig. 9) which are polarized at right angles to each other. In a second crystal, K 2 , beam b would then enter as a single beam, under the same angle as in the first crystal K v if K 2 were in the same position as K^ while if K 2 were turned at right angles to K v beam b would enter K 2 under the same angle as beam c in crystal K r 6. As seen, light and radiation in general are transversal wave FIG. 8. motions of very high speed, S = 3 X 10 10 cm. per sec. in a hypo- thetical medium, ether, which must be assumed to fill all space and penetrate all substances. Radiation is visible, as light, in a narrow range of frequencies only: between 400 X 10 12 and 770 X 10 12 cycles per sec. cor- responding to wave lengths from 76 X 10~~ 6 cm. to 39 X 10~ 6 cm.* All other radiations are invisible and thus have to be observed by other means. I have here a pair of rods of cast silicon (10 in. long, 0.22 in. in diameter, having a resistance of about 10 ohms each), connected * The visibility of radiation is greatest between the wave lengths 50 X 10"" to 60 X 10~ 8 and good between the wave lengths 41 X 10~ 8 to 76 X 10~ 8 , but extends more or less indistinctly over the range of wave lengths from 33 X 10~ 8 to 77 X 10-' and faintly even as far as 30 X lO" 9 to 100 X lO" 8 . 10 RADIATION, LIGHT, AND ILLUMINATION. in series with each other and with a rheostat of about 40 ohms resistance in a 120-volt circuit. When I establish a current through the rods, electric energy is converted into heat by the resistance of the rods. This heat energy is converted into and sent out as radiation, with the exception of the part carried off by heat conduction and convection. Reducing the resistance, I increase the heat, and thereby the radiation from the silicon reds. Still nothing is visible even in the dark; these radiations are of too low frequency, or great wave length, to be visible. By hold- ing my hand near the rods, I can feel the energy as heat, and show it to you by bringing the rods near to this Crookes' radiometer, FIG. 9. which is an instrument showing the energy of radiation. It con- sists (Fig. 10) of four aluminum vanes, mounted in a moderately high vacuum so that they can move very easily. One side of each vane is polished, the other blackened. The waves of radiation are reflected on the polished side of the vane; on the blackened side they are absorbed, produce heat, thus raise the temperature of the air near the vane ; the air expands and pushes the vanes ahead, that is, rotates the wheel. As you see, when I bring the heated rods near the radiometer, the wheel spins around at a rapid rate by the radiation from the rods, which to the eye are invisible. NATURE AND DIFFERENT FORMS OF RADIATION. 11 Increasing still further the energy input into the silicon rods, and thereby their temperature, the intensity of radiation increases, but at the same time radiations of higher and higher frequencies appear, and ultimately the rods become visible in the dark, giving a dark red light; that is, of all the radiations sent out by the rods, a small part is of sufficiently high frequency to be visible. Still further increasing the tempera- ture, the total radiation increases, but the waves of high frequency in- crease more rapidly than those of lower frequency; that is, the average frequency of radiation increases or the average wave length decreases and higher and higher frequencies appear, orange rays, yellow, green, blue, violet, and the color of the light thus gradually changes to bright red, orange, yellow. Now I change over from the silicon rods which are near the maximum tem- perature they can stand to a tung- sten lamp (a 40- watt 110-volt lamp, connected in series with a rheostat of 2000 ohms resistance in a 240- volt circuit). For comparison I also turn on an ordinary 16 c. p. carbon filament incandescent lamp, running at normal voltage and giving its usual yellow light. Gradually turn- ing out the resistance, the light of the tungsten lamp changes from orange to yellow, yellowish white and ultimately, with all the resistance cut out and the fila- ment running at more than double voltage, is practically white; that is, gives a radiation containing all the frequencies of visi- ble, light in nearly the same proportion as exist in sunlight. If we should go still further and very greatly increase the tem- perature, because of the more rapid increase of the higher fre- quencies (violet, blue, green) than the lower frequencies of light (red, orange and yellow) with increase in temperature, the light FIG. 10. 12 RADIATION, LIGHT, AND ILLUMINATION. should become bluish. However, we are close to the limit of temperature which even tungsten can stand, and to show you light of high frequency or short wave length I use a different apparatus in which a more direct conversion of electric energy into radiation takes place, the mercury arc lamp. Here the light is bluish green, containing only the highest frequencies of visible radiation, violet, blue and green, but practically none of the lower frequencies of visible radiation, red or orange. A _.240_V.OUr&_. 60 CYCLES FIG. 11. In the tungsten lamp at high brilliancy and more still in the mercury arc, radiations of higher frequencies appear, that is, shorter wave lengths than visible light, and these radiations are again invisible. As they are of frequencies beyond the violet rays of light, they are called " ultra-violet rays," while the radia- tions which we produced from the heated silicon rods at moderate temperatures were invisible because of too low frequency and are thus called "ultra-red rays," or " infra-red rays," as they are outside of and below the red end of the range of visible radiation. To produce powerful ultra-violet rays, I use a condenser dis- charge between iron terminals, a so-called ultra-violet arc lamp. Three iron spheres, / in Fig. 11, of about $ in. diameter, are mounted on an insulator B. The middle sphere is fixed, the NATURE AND DIFFERENT FORMS OF RADIATION. 13 outer ones adjustable and set for about T 3 g in. gap. This lamp is connected across a high voltage 0.2-mf. mica condenser C, which is connected to the high voltage terminal of a small step-up trans- former T giving about 15 ; 000 volts (200 watts, 110 -*- 13,200 volts). The low tension side of the transformer is connected to the 240-volt GO-cycle circuit through a rheostat 72 to limit the current. The transformer charges the condenser, and when the voltage of the condenser has risen sufficiently high it discharges through the spark gaps I by an oscillation of high frequency (about 500,000 cycles), then charges again from the transformer, discharges through the gap, etc. As several such condenser dis- charges occur during each half wave of alternating supply voltage the light given by the discharge appears continuous. You see, however, that this iron arc gives apparently very little light; most of the radiation is ultra-violet, that is, invisible to the eye. To make it visible, we use what may be called a frequency converter of radiation. I have here a lump of willemite (native zinc silicate), a dull greenish gray looking stone. I put it under the iron arc and it flashes up in a bright green glare by convert- ing the higher frequency of ultra-violet rays into the lower frequency of green light. This green light is not given by the iron arc, as a piece of white paper held under the arc shows only the faint illumination given by the small amount of visible radia- tion. I now move a thin sheet of glass, or of mica, between the iron arc and the lump of willemite, and you see the green light disappear as far as the glass casts a shadow. Thus glass or mica, while transparent t6 visible light, is opaque for the ultra-violet light of the iron arc. A thick piece of crystallized gypsum (sel- enite) put in the path of the ultra-violet light does not stop it, hence is transparent, as the lump of willemite continues to show the green light, or a piece of cast glass its blue light. I have here some pieces of willemite in a glass test tube. They appear dull and colorless in the ultra-violet light, as the glass is opaque for this light. I shift them over into a test tube of fused quartz, and you see them shine in the green glare. Quartz is trans- parent to ultra-violet light. When investigating ultra-violet light, quartz lenses and prisms must, therefore, be used. Still higher frequencies of ultra-violet light than those given by a condenser discharge between iron terminals are produced by a low temperature mercury arc. Obviously this arc must not be 14 RADIATION, LIGHT, AND ILLUMINATION. operated in a glass tube but in a quartz tube, as glass is opaque for these rays. These ultra-violet radiations carry us up to frequencies of about 3000 X 10 12 cycles per sec., or to wave lengths of about 10 X 10~ 6 cm. Then, however, follows a wide gap, between the highest frequencies of ultra-violet radiation and the frequencies of X-rays. In this gap, radiations of very interesting properties may some- times be found. At the extreme end of the scale we find the X-rays and the radiations of radio-active substances if indeed these radiations are wave motions, which has been questioned. Since at these extremely high frequencies reflection and refraction cease, but irregular dispersion occurs, the usual methods of measuring wave lengths and frequencies fail. The X-rays apparently cover quite a range of frequency and by using the atoms of a crystal as dif- fraction grating, their average wave length has been measured as 0.1 X 10" 6 cm., giving a frequency of 0.3 X 10 18 cycles per sec. In comparing vibrations of greatly differing frequencies, the most convenient measure is the octave, that is, the frequency scale of acoustics. One octave represents a doubling of the frequency ; ft octaves higher then means a frequency 2 W times as high, n octaves lower, a frequency (J) n as high. By this scale all the inter- vals are of the same character; one octave means the same relative increase, which ever may be the absolute frequency or wave length. As the perceptions of our senses vary in proportion to the per- centual change of the physical quantity causing the perception (Fechner's law), in the acoustic or logarithmic scale the steps are thus proportional to the change of sensual perception caused by them. The visible radiation covers somewhat less than one octave; ultra-violet radiations have been observed beyond this for about two more octaves. Nine octaves higher is the estimated frequency of X-rays. On the other side of the visible range, towards lower frequencies or longer waves, ultra-red rays, observations have been extended over more than eight octaves up to wave lengths as great as 0.03 cm. length, or frequencies of only 10 12 cycles per sec. The ultra- red rays given by the heated silicon rods of our experiment do not extend to such low frequencies, but such very low frequencies NATURE AND DIFFERENT FORMS OF RADIATION. 15 have been observed in the radiations of bodies of very low tem- perature, as liquid air, or in the moon's rays. 7. Very much longer waves, however, are the electric waves. They are used in wireless telegraphy, etc. I here connect (Fig. 12) FIG. 12. the condenser C of the apparatus which I used for operating the ultra-violet arc, to a spark gap G v of which the one side is con- nected to ground B v the other side to a vertical aluminum rod A v about 8 feet long. The charge and discharge of the aluminum rod A l by the oscillating condenser current, send out an electric wave of about 50 feet length. This wave passes through you, and when striking the aluminum rod A 2 back of you, induces therein an electric charge. A 2 is separated from ground B 2 by a narrow spark gap G 2 between graphite terminals, and the arrival of the electric wave at A 2 causes a small spark to jump across the gap G 2 , which closes the circuit of the tungsten lamp L, thereby lighting it as long as the wave train continues. 16 RADIATION, LIGHT, AND ILLUMINATION. The electric waves used in wireless telegraphy range in wave lengths from 100 feet or less to 10,000 feet or more, corresponding to 10 7 to 10 5 cycles per sec. or less. Still very much longer waves are the fields of alternating cur- rent circuits: the magnetic and electrostatic field of an alterna- ting current progresses as a wave of radiation from the conductor, But as the wave length is very great, due to the low frequency, 3 X 10 10 a 60-cycle alternating current gives a wave length of = 500 X 10* cm. or 3100 miles the distance to which the field of the circuit extends is an insignificant fraction only of the wave length, and the wave propagation of the field thus is usually not considered. Electric waves of higher frequencies than used in wireless telegraphy are the Herzian waves, produced by electric oscilla- tors, that is, a moderately long straight conductor cut in the middle by a gap and terminated by spherical condensers, as shown in Fig. 13. On these waves the velocity of propagation ENERGY-SUPPLY- * o ^^ o FIG. 13. has been measured by Herz by producing standing waves by combination of main wave and reflected wave. Still much higher frequencies are the oscillations between the cylinders of multi-gap lightning arresters, and the limit of fre- quency of electric waves would probably be given by the oscilla- ting discharge of two small spheres against each other when separated by a narrow gap. It probably is at about 5 X 10 10 cycles, or 0.6 cm. wave length. The blank space between the shortest electric wave and the longest ultra-red light wave thus has become fairly narrow - from 0.6 to 0.03 cm., or only about four octaves. 8. In the following tables, the different known forms of radia- tion are arranged by their frequency and wave length, and are given also in octaves, choosing as zero point the middle c of the piano, or a frequency of 128 cycles per sec. NATURE AND DIFFERENT FORMS OF RADIATION. 17 SPECTRUM OF RADIATION. Zero point chosen at c = 128 cycles per second. Speed of radiation S = 3 X 10 cm. Cycles. Wave Length in Air (or Vacuum). Octave No. of Octaves. Alternating current * field: 15 20,000 km. = 12,500 mi. -3 09 25 12,000 km. = 7, 500 mi. -2.36 3.15 60 5,000 km. = 3, 100 mi. -1.09 133 2,250 kin. = 1,400 mi. + 0.06. High frequency cur- \ rents, surges and oscillations, arcing V grounds, lightning (9.57) 31.64 phenomena, etc. J Wireless telegraph ( 105 3 km. = 10,000 ft. 9.63 ) 6rt9 waves : { 10 7 30m. = 100ft. 16.25 I . OZ Herzian waves: 10 7 10 30 in. = 100 ft. 30 cm. = 1 ft. 16.25 ) 22.90 J 12.3 Limit of electric waves : 5X10 10 0.6 cm. = 0.25 in. 28.55 ) First gap : [4.25] Ultra-red rays : 10 12 4xl0 14 30,000x10-" = 0.03 cm. 76xlO- cm. 32 80 41.48 8.68 Visible light rays : | 4X10 4 7.7X10" 70xlO- cm. 39xlO- cm. 41.48 I 42.45 \ 0.97 11.6 Ultra-violet rays: 7.7X10' 4 30X10* 39 x 10~* cm. 10 x 10-* cm. 42.45 j 44.40 j 1.95 Second gap: [7.0] X-rays (estimated) : 0.3X10' 8 0.1 x 10-' cm. 51.4 Sound Waves: Total : 57.7 octaves Lowest audible sound : 15 66 ft. in air -3.1 Highest audible sound : 16000 .75 in. in air 4-7.0 Total : 10.1 octaves These radiations are plotted graphically in Fig. 14, with the octave as abscissae. As seen, the total range of frequencies of radiation is enormous, covering nearly 60 octaves, while the range of sound waves is only about nine octaves, from 15 to 8000 cycles. There are two blank spaces in the range of radiation, one be- tween electric and light waves, and a second and longer one between light and X-rays. It is interesting to note that the range of electric waves is far greater than that of light waves. Only a very narrow range of radiation, less than one octave out of a total of 60, is visible. It is shown shaded in Fig. 14. This 18 RADIATION, LIGHT, AND ILLUMINATION. exhibits the great difficulty of the problem of efficient light pro- duction: it means producing as large a part of the total radiation as possible within this very narrow range of visibility. Regarding the range of frequencies covered by it, the eye thus is much less sensitive than the ear, which hears over ten octaves as sound waves. While the visible radiations are the most important ones, as light, the total range of radiation is of interest to the electrical engineer. The ultra-red rays are those radiations which we try to avoid as far as possible when producing light, as they consume power SOUND WAVES FIG. 14. and so lower the efficiency; the ultra-violet rays are of importance in medicine as germ killers. They are more or less destructive to life, appear together with the visible radiation, and where they are of appreciable amount, as in the arc, protection against them becomes desirable. The X-rays have become of importance in medicine, etc., as they penetrate otherwise opaque bodies and thus allow seeing things inside of other bodies. The total range of electric waves, between the frequencies of alternating currents and the limits of electric waves, has been of importance to the electrical engineer as harmful and destructive phenomena in electric circuits, which are to be guarded against, and only in recent years, with the development of wireless telegraphy, some such electric waves have found a useful com- mercial application. The main object of their study which is the study of transient electric phenomena, is still, however, to guard against their appearance in electric circuits and discharge them harmlessly when they appear. Considering the great difference which already exists between alternating currents of low frequency, 25 or 15 cycles, and of high NATURE AND DIFFERENT FORMS OF RADIATION. 19 frequency, 133 cycles, and realizing that the total range of waves, which may appear in electric circuits, is many hundred times greater than the difference between high and low frequency alter- nating currents, it can be realized that the differences in the character of electric waves are enormous between the low frequency surges of near machine frequency and the high frequency oscilla- tions of a multi-gap lightning arrester, near the upper limits of electric wave frequencies, and the problem of protecting circuits against them thus is vastly more difficult than appears at first sight and the conclusions drawn from experimental investigations of electric waves may be very misleading when applied to waves many octaves different from those used in the experiment. This explains the apparently contradictory evidence of many experi- mental investigations on the protection of electric circuits. LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the following, mainly the light waves, that is, the second or high frequency range of radiation, will be discussed. The elec- tric waves are usually of importance only in their relation to the radiator or oscillator which produces them, or to the receiver on which they impinge, and thus are treated in connection with the radiator or receiver, that is, the electric conductor, in the theory of transient electric phenomena and oscillations.* The radiation may be of a single frequency, that is, a single wave; or a mixture of different frequencies, that is, a mixture of different and frequently of an infinite number of waves. Electric radiation usually is of a single frequency, that is, of the frequency or wave length determined by the constants of the electric circuit which produces the radiation, mainly the induct- ance L and the capacity C. They may, however, have different wave shapes, that is, comprise, in addition to the fundamental wave, higher harmonics or multiples thereof, just as the sound waves which represent the same tone with different musical instruments are of the same frequency but of different wave shapes, that is, contain different higher harmonics. Light radiations usually are a mixture of a number of waves of different frequencies, and very commonly a mixture of an infinite number of frequencies, as is, for instance, the case with the * "Theory and Calculation of Transient Electric Phenomena and Oscilla- tions. " RELATION OF BODIES TO RADIATION. 21 radiation of an incandescent body as a lamp filament, which contains all the frequencies from long ultra-red waves over visible light waves to ultra-violet waves. In the action of vibrations on our senses there is a characteristic difference between the perception of sound waves by the ear and that of light waves by the eye: the ear is analytic, that is, can separate the individual waves in a mixture of different sound waves, as an accord on the piano, and distinguish the individual components of the mixed sound which reaches the ear. Thus we can hear and distinguish an individual voice amongst a mass of other noises. The eye, however, perceives only the resultant of all the visible radiations which reach it, but cannot separate their components, and very different mixtures of radiations thus make the same impression upon the eye: thus, for instance, numerous mixtures of blue and yellow light appear alike to the eye and the same as green light, that is, appear green, while physically, it is obvious that mixtures of blue and yellow light are essentially different from green light. It is interesting to imagine how nature would look to us if the eye were analytic, that is, could separate the different component radiations, and if it could perceive waves over as great a range of frequency as the ear, about ten octaves instead of less than one octave as is now the case. The information given to us by the sense of sight would be infinitely increased, and we would see many differences and changes which now escape us. 10. However, while the eye cannot distinguish the different component radiations but sees only their resultant, the specific effects of the component radiations, as the physiologically harm- ful action of an ultra-violet component of light, still remain, even if the eye does not see the components, and in the study of radia- tion for the purpose of its engineering use for illumination it is therefore necessary to analyze the mixed radiation given by a source as a lamp, by resolving it into its component waves. This is done by using some feature of the radiation which varies with the frequency. Such is the case with the velocity of propagation. The velocity of light in empty space is 3 X 10 l cm. per sec. It is practically the same in air and other gases. In denser bodies, however, as water, glass, etc., the velocity of light is less and, as will be seen, is different for different frequencies. 22 RADIATION, LIGHT, AND ILLUMINATION. Assume then, in Fig. 15, a beam of light B striking under an angle the boundary between two media, as air A and water W, the vibration of the ether particles in the beam of light is at right angles to the direction of propagation BC, and successively the waves thus reach a l b l ,a 2 b 2 . . . As soon, however, as the back edge of the beam reaches the boundary at D its speed changes w S 2 FIG. 15. \ by entering the medium W decreases in the present instance. Let then /S t = speed of propagation in medium A, S 2 = speed of propagation in medium W. Then, while the center of the beam moves the distance EC, the back edge, in the denser medium, S moves only the distance DI = -^ EC, and the wave front of the ^! back half of the beam thus changes to CI while that of the front half of the beam, which is still in the medium A, remains GC. Then, while the front edge of the beam moves from G to H, the center and the whole back half of the beam moves in the denser a medium TF, only the distance CK = -^ GH, and the wave front \ of the beam, in the medium W, now is HL. That is, due to the difference in velocity in the two media A and W, the wave front of the beam, and thereby its direction of propagation, is changed RELATION OF BODIES TO RADIATION. 23 when traversing the boundary between the two media, and the beam EC continues its motion in the direction CM. Let then a^ = angle of incidence, that is, the angle between the incident beam BC and the perpendicular CN on the boundary, and a 2 = angle of refraction, that is, the angle between the out- going or refracted beam CM and the perpendicular CP on the boundary. It is then : FDH = a t and LHD = a 2 ; hence, FH = DH sin a, and DL = DH sin a 2 . (1) The front edge of the beam moves the distance FH in medium A, while the back edge moves the distance DL in medium W; that is, FH -v- DL = S, + S 2 ; (2) hence, substituting (1) into (2), gives: That is, the ratio of the sines of the angle of incidence and the angle of refraction equals the ratio of the speed of propagation in the two media, hence the ratio of the sines of these two angles is constant. This is the law of refraction, and this ratio of sines is called the refractive index between the two media A and W. As the refractive index of one medium W, then, is understood its re- fractive index against empty space or against air : sin a S where S is the velocity of light in empty space = 3 X 10 10 , and S l the velocity in the medium, of which ^ is called the refractive index. From equation (4) it follows, that, if d l-2 is the refractive index between medium 1 and medium 2, o 2 _ 3 , the refractive index between medium 2 and medium 3, <^_ 3 = o 2 _ 3 -*- S 1 _ 2 = refractive index of medium 1 and medium 3; that is, the refractive index between any two media is derived as the ratio of their refractive indices against a third medium, as, for instance, against air. 24 RADIATION, LIGHT, AND ILLUMINATION. 11. Incidentally, it is interesting to consider the corresponding relations in electric waves. In an electric circuit, the speed of propagation of an electric wave is, when neglecting the energy losses in and by the con- ductor: S = -_L=, (5) VLC where L is the inductance, C the capacity of the conductor per unit length (the length measured in the same measure as the speed S). The inductance L is proportional to the permeability /*, and the capacity C proportional to the dielectric constant, or specific capacity K of the medium surrounding the conductor, that is, the medium through which the electric wave propagates; that is, > A VfJLK where A is a proportionality constant. The ratio of the speed of propagation of an electric wave in two media 1 and 2 thus is : (7) for empty space, jn = 1 and K = 1 ; hence, s , _ S~ = V/ (8) ***! where S l is the speed of propagation in the medium of constants /^ and jc r Comparing equation (8) with (4) it follows : M = V; (9) that is, the square of the refractive index d equals the product of permeability jj. and dielectric constant K. Since for most media the permeability // = 1, for all except the magnetic materials RELATION OF BODIES TO RADIATION. 25 This relation between the constant of the electric circuit K and the constant of optics d was one of the first evidences of the identity of the medium in which the electric field exists with the medium which carries the light waves. It is, however, only approximately correct, as the refractive index d varies with the frequency and is derived for the extremely high frequencies of light radiation, while K refers to stationary conditions. A better agreement is thus reached when using as d the refractive index extrapolated for infinite wave lengths. 12. It is found that the different component frequencies of a beam of radiation are deflected differently when passing from one medium into another, and the higher frequencies are deflected FIG. 16. more than the lower frequencies, thus showing that the velocity of propagation decreases with an increase of frequency, that is, a decrease of wave length. This gives a means of resolving a mixed radiation into its com- ponent waves, that is, into a spectrum, by refraction. A narrow beam of light B (Fig. 16) is passed through a prism P of transparent material, and the component frequencies then appear on the screen A (or are seen by the eye) side by side, the red R below, the violet V above, in Fig. 16, and the green G in the middle. It is obvious that the material of the prism must be transparent to the radiation; thus, when studying ultra-violet radiation, to which glass is opaque, glass prisms cannot be used, but some material transparent to ultra-violet light such as a quartz or fluorite prism must be used. 26 RADIATION, LIGHT, AND ILLUMINATION. The beam of light also can be resolved into its components by a diffraction grating, in which case the lower frequencies are deflected more than the higher frequencies; that is, the red more than the violet. These two forms, the refracting spectroscope and the diffract- ing spectroscope, now enable us to resolve a beam of mixed radia- tion into its components and thus study its spectrum. 13. I show you here a number of typical spectra : (1). The spectra of an incandescent lamp and an alcohol lamp with Welsbach mantel. These are continuous spectra, that is, show all the radiations from red over orange, yellow, green, blue, indigo to violet, uniformly shading into each other. (2a). The spectrum of the mercury lamp. This is a line spectrum, that is, shows only a finite number of bright lines on black background. It contains five bright lines ; greenish yellow, bright green, indigo and two violet, one faint dark green line, and 1 1 1 1 1 RED ORANGE YELLOW 1 GREEN BLUE INDIGO VIOLET FIG. 17. a number of very faint red and orange lines, of which three are indicated dotted in Fig. 17. (26). The spectrum of an arc between titanium carbide elec- trodes. This also is a line spectrum, but unlike the mercury spectrum, which has only six bright lines, the titanium spectrum contains many thousands of bright lines, so that with the low power of the spectroscope which you have, the lines blurr into each other and we see only the most prominent or brightest lines on a uniformly luminous background, which latter requires a more powerful spectroscope to resolve into lines. (3) . The band spectrum. This shows a number of bright bands, frequently gradually fading out at their edge and separated by dark spaces. It thus differs from the continuous spectrum (1) in being discontinuous, that is, missing certain ranges of frequency, and differs from the line spectrum (2) in that the band spectrum has a number or range of frequencies in each band, where the line ! RELATION OF BODIES TO RADIATION. 27 spectrum has only one single frequency in each line. Such band spectra are usually characteristic of luminescent compounds or of gases and vapors at high pressure, while elementary gases or vapors give line spectra. Absorption and fluorescence also give band spectra, and I thus show you a band spectrum by opera- ting a mercury lamp in a tube of uranium glass, behind a trans- parent screen colored by rhodamine (an aniline dye which fluoresces red). As you see, the spectrum shows a broad red band, due to the reddish screen, and a greenish yellow band due to the uranium glass, while the normal mercury lines are de- creased in intensity. (4). If you now look with the spectroscope at the Welsbach mantel through the mercury arc stream, you see the continuous spectrum of the mantel and superimposed upon it the line spec- trum of the mercury lamp. The light giving mercury vapor thus is transparent for the light of the Welsbach mantel back of it, and lets it pass through, with the exception of those particular fre- quencies which it gives itself; that is, a luminous gas absorbs those frequencies of radiation which it produces, but is trans- parent for all other frequencies. This is easily understood: an atom on which a vibration impinges will be set in motion by it and thus absorb the energy of the impinging vibration if it is able to vibrate with the frequency of the impinging vibration; that is, to resonate with it, but will not be affected by any other frequency to which it cannot respond, and thus is transparent to all frequen- cies of vibration, except to those to which it can respond; that is, which it produces when vibrating. When looking at a continuous spectrum through a luminous gas or vapor, two cases thus may occur : either the spectrum lines of the gas are brighter than the continuous spectrum, as in the present case, and then appear as bright lines on a bright back- ground, or the continuous spectrum is brighter than the lines of the gas spectrum in front of it and the lines of the gas spectrum appear less bright than the background, that is, appear as dark lines on a bright background. Such a spectrum is called a reversed spectrum, or absorption spectrum. It shows the lines of the gas or vapor spectrum, by contrast, dark on the brighter back- ground of the continuous spectrum. The sun and many fixed stars present such a reversed spectrum : the sun's spectrum shows the spectrum lines of all the elements 28 RADIATION, LIGHT, AND ILLUMINATION. which are in the sun's atmosphere as dark lines on the continuous spectrum given by the inner core of the sun. Whether the line spectrum of a gas or vapor is reversed by the continuous spectrum of a solid or liquid back of it or not depends upon the relative intensity, and thus, to some extent, on the rela- tive temperature. Some fixed stars show bright lines on a Jess luminous background, due possibly to a higher temperature and greater thickness of their atmosphere, and sometimes bright lines and dark lines occur simultaneously, or dark lines may change to bright lines at such places at which, by some activity, as a tem- perature rise, their brilliancy is greatly increased. 18. Combinations of the different types of spectra: continuous spectrum, line spectrum, band spectrum, reversed spectrum, frequently occur, as we have seen bands and lines together in the modified mercury spectrum, and in this case, by turning on an incandescent lamp, we can still add a continuous spectrum due to the light of the incandescent lamp reflected from the walls of the room. So also in the continuous spectrum of incandescent bodies, bright bands or dark bands occasionally appear, that is, regions in the spectrum of greater or lesser intensity, as will be discussed in the paragraphs on colored radiation and selective radiation. RELATION OF BODIES TO RADIATION. 29 14. When a beam of radiation impinges upon a body it is resolved into three parts: one part is reflected, that is, does not enter the body at all, but is thrown back. The second part is absorbed in the body, that is, converted into another form of energy (which other form of energy usually is heat, but may be chemical energy, some other frequency of radiation, etc.) and the third part is transmitted, that is, passes through the body, and out of it, if the body is not too thick. No body reflects, or absorbs, or transmits all the radiations, but even the most per- fectly reflecting body absorbs and transmits some radiation, the most transparent body reflects and absorbs some radiation, etc. Reflection may be either regular reflection, or irregular reflec- tion. In the former case (Fig. 18) the beam of light is reflected under the same angle under which it impinges upon the body, and the body thus acts as a mirror, that is, gives a virtual image FIG. 19. back of it as shown in dotted line in Fig. 18. In the latter case (Fig. 19) the light is reflected irregularly in all directions. A body which reflects all the frequencies of radiation uniformly, that is, in which the percentage of the impinging radiation, which is reflected, is the same for all frequencies of radiation, is called a colorless body,a,ud a body which reflects a higher percentage of the radiation of some frequency than of other frequencies, is called a colored body, and its color is the color of radiation, that is, the frequency or frequencies which it reflects more than other frequencies. A colorless body which reflects all the radiation impinging upon it is called a white body. Most nearly white bodies are silver, magnesia, chalk, etc. A body which reflects none of the radiation impinging upon it, but absorbs all, is called a block body. The 30 RADIATION, LIGHT, AND ILLUMINATION. most nearly black bodies are lampblack, charcoal, etc. A body which reflects a constant part of the impinging radiation, that is, the same part or percentage for all frequencies, is called a grey body, and the ratio of the reflected light to the total impinging light is called its whiteness or albedo. A perfectly white body thus has albedo 1, a perfectly black body albedo 0, and a body which reflects one-quarter and absorbs the other three-quarters of the radiation of any wave length impinging upon it, would be said to have albedo 0.25. Black, white and grey thus are not considered as colors in physics. As examples of colorless bodies I show you here : Regular reflection: polished silver, white; polished iron, grey. Irregular reflection: powdered magnesia, white; lampblack, black; powdered zinc, barium sulphide, grey. As example of colored bodies I show you : Regular reflection: polished copper, red; polished gold or brass, yellow. Irregular reflection: mercury sulphide (cinnabar), red; potas- sium bichromate, orange; magnesium chromate, yellow; copper acetate-arsenite (paris green), green; copper oxide hydrate precipitated by ammonia, blue ; ultra-marine, indigo ; magnesium permanganate mixed with magnesia, violet. 15. Of the radiation which enters a body, that part which is absorbed is usually converted into heat. Thus a black body, when exposed to radiation, becomes hotter than a white body, which reflects, or a transparent body, which transmits, most of the radiation. Thus the globe of a colored incandescent lamp, which absorbs more of the radiation than a transparent globe, becomes hotter than a clear glass globe. When scattering dirt on the snow it can be made to melt down far more rapidly in the spring, under the rays of the sun, than when remaining clean, etc. Some bodies convert the absorbed radiation into chemical energy, into other frequencies of radiation, etc. Bodies which convert the absorbed radiation, or rather a part thereof, into radiation of different, as far as known always lower, frequencies, are called fluorescent bodies. Thus the solu- tion of rhodamine in alcohol, which 1 show you here, fluoresces red. It transmits red light, but absorbs green, blue and violet light, and converts a part thereof into red light. This is best RELATION OF BODIES TO RADIATION. 31 illustrated by exhibiting it in a source of light which contains no red rays, as the mercury lamp. You see in the rays of the mer- cury lamp the rhodamine solution looks bright red, the red light seems to come from the inside of it, and especially through a red glass the solution looks like a red hot incandescent body. Here then, as no red light reaches the solution, the red light given by it must be produced by frequency conversion from other radiation. The spectroscope shows especially the bright green mercury line weakened. The phenomena of conversion of absorbed light into other forms of energy will be more fully discussed in the following paragraphs. 16. By the transmitted light, that is, the radiation which passes through them, bodies are again divided into colorless bodies; that is, such bodies which transmit the same percentage of radiation for every wave length or frequency, and colored bodies; that is, bodies which transmit a larger percentage of radiation of some frequencies than of others, and as the trans- parent color of a body, then, is understood the color, that is, the frequency, of that radiation of which the greatest percentage is transmitted. Thus a red glass is one which transmits a higher percentage of red radiation than of any other radiation. A body, then, is called transparent, if it transmits all the radia- tion, and opaque, if it transmits no radiation, but absorbs or reflects all. If only a part of the radiation is transmitted, but in such manner that it is the same part for all frequencies, the body is called grey; or imperfectly transparent, if the part which is not transmitted is absorbed in the body; and translucent, if the part which is not transmitted is irregularly reflected inside of the body. The most perfectly transparent bodies, for visible light, are glass, water, quartz, etc. ; the most opaque are the metals, and perfectly, or almost perfectly opaque are the magnetic metals, perhaps due to the very low speed of propagation in these metals, which would result from the high value of the permeability jj. by equation (8) paragraph 11. As example of colorless bodies I show -you here a glass tube filled with water, transparent; a tube filled with nigrosine solu- tion in alcohol, opaque and black; a very diluted solution of nigrosine with traces of other aniline dye for color correction, in 32 RADIATION, LIGHT, AND ILLUMINATION. alcohol, as grey, and a tube filled with an emulsion of water with a solution of chloroform in white paraffin oil, which latter solu- tion has the same specific gravity as water, translucent. Samples of transparent colored bodies are: carmine solution, red; potassium bichromate solution, orange; potassium chroma te solution, yellow; nickel sulphate solution, green; copper nitrate solution, blue; diluted potassium permanganate solution, or diluted solution of iodine in chloroform, violet. As seen, the terms " colorless" and "colored" have two dif- ferent meanings when applied to the reflected radiation and when applied to the transmitted radiation, and the color of a body in reflected light may be different, and frequently is differ- ent, from its color in transmitted light, and some bodies may be colorless in reflected light, but colored in transmitted light, and inversely. In materials of low absorption, the transmitted and the reflected colors must be approximately complementary; thus the transmitted color of the atmosphere is orange, the reflected color blue. 17. Colors are, therefore, distinguished into opaque colors and transparent colors. The opaque colors are those shown by the light reflected from the body, the transparent colors those shown by the light transmitted through the body. In reflected light, the transparent colors, therefore, show only when covering a white, that is reflecting, surface, and then, because the light reflected from the white background of the transparent coloring body traverses this body twice, before and after reflection, and, therefore, depend in their brilliancy on the background. The difference between opaque and transparent colors, the former reflecting from the surface, the latter reflecting from back of the colored substance, is seen by comparing the appearance of the two classes of colors shown in 14 and in 16. In its general use, the terms colorless, white, black, transparent, opaque, refer only to the visible radiation, that is, to the frequen- cies within that octave which the eye perceives as light. More broadly, however, these terms may in physics be applied to the total range of radiation, and then many substances which are colorless for visible light, would be considered as strongly colored, that is, show for different frequencies great differences in the per- centage of radiation which they reflect or transmit. Thus we have seen that glass, which is transparent for visible light, is RELATION OF BODIES TO RADIATION. 33 entirely opaque for some ultra-violet light and also opaque for ultra-red light of low frequency, so in this broader sense would have to be called colored] the color of clear glass, however, is that of the visible spectrum; or, for instance, iodine solution, which is opaque for visible light, is transparent for ultra-red light, that is, its color is ultra-red, etc. In this broader sense, referring to the total range and not merely to the visible range, glass, water, mica, etc., are not color- less transparent but colored, and quartz is probably the most transparent and colorless body. 18. The color of the body, thus, is represented by that fre- quency or those frequencies of radiation of which a higher per- centage are reflected or transmitted than of the other frequencies of radiation. This color, therefore, is a characteristic property of the body and independent of the character of the light and of its physiological effect on the eye, and can thus be called the actual or objective color of the body. If we consider diffused daylight as white, then the body appears to the eye in its objective or actual color when compared with a white body, that is, a body uniformly reflecting all radiation in the diffused daylight. Under other conditions, as, for instance, in artificial illumination, bodies do not always appear to the eye in their objective colors, but may show a very different color depending on the character of the source of light. For instance, I have here a plate of colored glass : looking through it at the mercury lamp you see the glass has an olive green color ; but when I turn on an incandescent lamp you see that it is ordinary red glass. Its objective color is red, its subjective color in the mercury light is green. Looking through this glass in daylight it appears red as it transmits more red light than other colors of light, and the transmitted light thus contains a higher per- centage of red rays than diffused daylight. The rays of the mercury lamp, however, contain very little red light and very much green light, and while by this red glass a much higher percentage of the red light from the mercury lamp is trans- mitted than of its green light, this higher percentage of trans- mitted red light is very much less than the lower percentage of the transmitted green light, and, therefore, in the transmitted light, green still preponderates more than in the diffused day- light, that is, the glass appears green. For instance, if in the 34 RADIATION, LIGHT, AND ILLUMINATION. mercury lamp the ratio of red light to green light is only one hundredth of what it is in daylight, and the red glass transmits ten times as high a percentage of red as of green light, then in the light of the mercury lamp transmitted through this red glass the ratio of red light to green light is still only one-tenth of what it is in daylight, and the glass thus appears green. We have to distinguish between the actual or objective color of a body, which is a constant of the body, and its apparent or sub- jective color, which depends upon the light in which we view the body, and therefore may be very different for different illumi- nants, and bodies which have the same colors in one illuminant may have entirely different colors in another illuminant and inversely. It is, however, the subjective color of the body cor- responding to the particular illuminant used which we see, and which is, therefore, of importance in illuminating engineering, and the study of the subjective colors, therefore, is of foremost importance, and the success or failure of an illumination depends on the production of the desired subjective colors. 19. Broadly, an illuminant discriminates for the color in which it is deficient and the color in which it is rich. The color in which the illuminant is deficient as red in the mercury lamp, blue and violet in the incandescent lamp appears black; the color in which the illuminant is abnormally rich as yellow in the incandescent lamp, green in the mercury lamp appears as white; that is, both colors disappear, more or less; as colors, be- come colorless. Thus in the yellow incandescent lamp, opaque yellow appears the same as white, opaque blue and violet appear more or less as black ; transparent yellow appears colorless, trans- parent blue and violet appear colorless and from light transparent grey to opaque black. In the green mercury lamp, opaque green and white appear the same, opaque red appears as black; trans- parent green appears colorless, and transparent red appears colorless, from clear transparent to grey, to opaque black, de- pending upon its intensity. It is interesting to see the difference between opaque and transparent colors in this respect : as opaque colors the deficient color turns black, the excess color white; but as transparent colors both become colorless and more or less transparent. Thus, in the mercury lamp, red and green as transparent colors both vanish, or rather, very greatly decrease in their prominence. RELATION OF BODIES TO RADIATION. 35 As the eye perceives only the resultant of radiation, very dif- ferent combinations of radiation may give the same impression to the eye, but when blotting out certain radiations, as red and green, in the mercury lamp, these different combinations of radia- tion may not give the same resultant any more, that is, become of different colors, and inversely, different colors, which differ only by such component radiations as are blotted out by an illuminant, become equal in this illuminant. For instance, a mixture of red and blue, as a diluted potassium permanganate solution, appears violet in daylight. In the mercury light it appears blue, as the red is blotted out, and in the light of the incandescent lamp it appears red, as the blue is blotted out. I show you here, in the light of an incandescent lamp, two pieces of black velvet. I turn off the incandescent lamp and turn on the mercury lamp, and you see the one piece is blue, and the other black. Now I show you two pieces of brownish black cloth in the mercury light. Changing to the incandescent lamp you see that the one is a bright crimson, and the other still practi- cally black. In both cases the color deficient in the illuminant appeared as black. This tube of copper chloride crystals appears bright green in the incandescent lamp. In the mercury light it is a dirty white. The excess color, green, is blotted out. These crystals of didymium nitrate, which are a light pink in daylight, are dark pink in the incandescent light. In the mercury light they are blue: the color is a mixture of red and blue, and the one is blotted out in the mercury light and the other in the incandescent light. These two tubes, one containing a concentrated solution of manganese chloride, the other a solution of didymium nitrate, are both a dark pink in the incandescent light. In the mercury light the first becomes a faint pink, the second becomes grass green. These tubes, one containing a solution of didymium nitrate, the other a diluted solution of nickel sulphate, appear both light green in the mercury light. In the incandescent lamp the former is dark pink, the latter dark green. [Didymium, which formerly Was considered as an element, has been resolved into two ele- ments, praseodymium, which gives green salts, and neodymium, which gives pink salts. It is interesting to see that this separa- 36 RADIATION, LIGHT, AND ILLUMINATION. lion is carried out photometrically by the light: the mercury lamp showing only the green color of the praseodymium, the incandescent lamp the pink color of neodymium]. I have here a number of tubes, which seen in the light of the incandescent lamp contain red solutions of nearly the same shade. Changing to the mercury lamp you see that they exhibit almost any color. As the red disappeared in the mercury lamp the other component colors, which did not show in the incandes- cent lamp as they were very much less in intensity than the red, now predominate : potassium permanganate solution turns blue, carmine blue ; potassium bichromate, greenish brown ; coralline, (an aniline dye), olive green, etc., etc. Again, a number of tubes, which in the mercury light appear of the same or nearly the same blue color, turn to very different colors when seen in the incandescent lamp, due to the appearance of red and green, which were not seen with the mercury light. A solution of rhodamine, however, which looks a dull red in the light of the incandescent lamp, turns a glowing crimson in the mercury lamp, due to its red fluorescence. This diluted solution of rhodamine and methyl green (aniline dyes), which is grey in the light of the incandescent lamp, turns brownish red in the mercury lamp, the green is blotted out, while the rhodamine shows its red fluorescence. Thus, you see, the already very difficult prob- lem of judging the subjective colors of bodies under different illu- minants is still greatly increased by phenomena as fluorescence. To conclude then : we have to distinguish between colorless and colored bodies, between opaque colors and transparent colors, between color, as referred to the visible range of radiation only, or to the total range, including ultra-red and ultra-violet, and especially we have to realize the distinction between objective or actual color, and between subjective or apparent color, when dealing with problems of illuminating engineering. LECTURE III. PHYSIOLOGICAL EFFECTS OF RADIATION. Visibility. 20. The most important physiological effect is the visibility of the narrow range of radiation, of less than one octave, between wave length 76 X 1Q- 6 and 39 X 1Q- 6 . The range of intensity of illumination, over which the eye can see with practically equal comfort, is enormous: the average intensity of illumination at noon of a sunny day is nearly one million times greater than the illumination given by the full moon, and still we can see fairly well in either case; that is, the human eye can adapt itself to enormous differences in the intensity of illumination, and that so perfectly that it is difficult to realize the differences in intensity without measuring them. The photo- graphic camera realizes it. An exposure taken in T J ff second with T V opening of the diaphragm in full sunlight usually gives a better photograph than an exposure of 10 minutes at full opening, in the light of the full moon. The ratio of time of exposure in the two cases, however, is about 1 to 1,000,000, thus showing the difference in the intensity of illumination. Also, the disk of the moon, when seen in daylight, has about the same intensity as the sky somewhat more than the cloudless sky, less than white reflecting clouds. As the surface of the moon's disk, of one-half degree diameter, is about TTys/^ff the surface of the sky, it thus follows that the daylight reflected from the sky is about 100,000 times more intense than the light of the full moon. The organ by which we perceive the radiation, the human eye (Fig. 20), contains all the elements of a modern photographic camera an achromatic lense: the lense L, of high refractive power, enclosed between the two transparent liquids A and B which correct the color dispersion, that is, give the achromatic property; a diaphragm: the iris 7, which allows the increase or decrease of the opening P, the pupil ; a shutter : the eyelids and 37 38 RADIATION, LIGHT, AND ILLUMINATION the sensitive plate or retina R. The nerves of vision end at the back of the retina, and in the center of the retina is a spot F, the " sensitive spot " or " fova," at which the retina is very thin, and the nerve ends specially plentiful. At this spot we thus see sharpest and clearest, and it is this spot we use for seeing by turning the eye so as to fix on it the image of the subject we desire to see, while the image on the rest of the retina is used merely for orientation. The adaptability to the enormous range of intensity of illumination, which as seen we meet in nature, is secured: (1). By changing the opening and thereby the amount of light admitted to the eye, by contracting or opening the pupil P. This action is automatic. In low intensity of illumination the pupil thus is wide open and contracts at higher intensities. As this automatic action takes an appreciable, though short time, a flash light photograph shows the pupil of the eye fully open and thereby gives a staring impression to the faces which is avoided by keep- ing a photographically inactive light, as a candle, burning outside of the field of the camera when preparing for a flash light photo- graph. (2). By the fatigue of the optic nerves, exposed to high inten- sity of illumination, the nerves becomes less sensitive, while at low intensity they rest and thus become more sensitive, and the differences of sensation are hereby made very much less than corresponds to the differences of intensity of radiation. There- fore, when entering a brightly illuminated room from the dark- ness we are blinded in the first moment, until the eye gets accustomed to the light, that is, the nerves become fatigued and so reduce the sensation of light. Inversely, when stepping from a bright room into the darkness we first see almost nothing until the eye gets accustomed to the darkness, that is, the nerves of vision are rested and their sensitivity thus increased so as to per- ceive the much lower intensity of illumination. (3). By the logarithmic law of sensation. The impression made on our senses, eye, ear, etc., that is, the sensation, is not propor- tional to the energy which produces the sensation, that is, the PHYSIOLOGICAL EFFECTS OF RADIATION. 39 Intensity of the light, the sound, etc., but is approximately proportional to its logarithm and the sensation, therefore, changes very much less than the intensity of light, etc., which causes the sensation. Thus a change of intensity from 1 to 1000 is 1000 times as great a change of intensity as from 1 to 2, but the change of sensation in the first case, log 1000 = 3, is only about 10 times as great as the change in the latter case, log 2 = 0.301. This logarithmic law of sensation (Fechner's Law), while usu- ally not clearly formulated, is fully familiar to everybody, is con- tinuously used in life, and has been used from practical experience since by-gone ages. It means that the same relative or percent- age change in intensity of light, sound, etc., gives the same change of sensation, or in other words, doubling the intensity gives the same change in sensation, whether it is a change of intensity from one candle power to two candle power, or from 10 to 20, or from 1000 to 2000 candle power. It is obvious that the change of sensation is not proportional to the change of intensity; a change of intensity of light by one candle power gives a very marked change of sensation, if it is a change from one to two candle power, but is unnoticeable, if it is a change from 100 to 101 candle power. The change of sensation thus is not proportional to the absolute change of intensity one candle power in either case but to j the relative or percentage change of intensity, and as this is 100 per cent in the first, 1 per cent in the latter case, the change of sensation is marked in the first, unnoticeable in the latter case. This law of sensation we continuously rely upon in practice. For instance, when designing an electrical distribution system for lighting, we consider that the variation of voltage by 1 per cent is permissible as it gives a change of candle power of about 5 per cent, and 5 per cent variation is not seriously noticeable to the eye. Now this 5 per cent change of candle power may be a change from 1 to 0.95, or by ^ candle power, or it may be a change from 1000 to 950, or by 50 candle power, and both changes we assume, and are justified herein from practical experience, to give the same change of sensation, that is, to be near the limits of permissi- bility. This law of sensation (Fechner's Law) means : If i = intensity of illumination, as physical quantity, that is, 40 RADIATION, LIGHT, AND ILLUMINATION. in meter-candles or in watts radiation of specified wave length, the physiological effect given thereby is : L = A log V %> where A is a proportionality constant (depending on the physio- logical measure of L) and i Q 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 about 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 w 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 minimum near the middle of the spectrum and increases 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 kilo-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 0.02 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- YELLOW GRPEN 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 5 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 veiy 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 unnoticeable, 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 I-:! 50? 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~ e 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. 1.65 45.0 1.70 50.0 1.75 1.80 55.0 60.0 65.0 \ \ 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 l w = 61 X 10~ 8 ; 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). 1 Q = 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 m is the wave length at maximum sensitivity and H is the sensitivity at this wave length, that is, the maximum sensi- tivity and k a is a constant which is approximately 120 for low, LOG = - 8 8 - i + 1 4 > 4 3 57 k s = 0. )01 0. 01 1 1 1 /^> H) 100 ^s ME' \ ER-Ci NDLE '/ ';\ \ / / *n H=H, e-*' (>- 1)' ^X ?c * / l / FIG. 25. 62 for high intensities and changes in approximately the same range of intensities in which l^ 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, dtc.)'. 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 ultra-reel in the radiation of the incandescent bodies used for illuminants 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. In Fig. 26, let the curve A represent 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 FIG. 26. lamp carbon filament would be somewhat like C. Hence, the physiological 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' f 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. Eg' 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 (7; 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 trying 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 probably 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 possibly is of chemical nature, a destruction by chemical dissociation. This effect increases in severity the fur- ther we reach into the ultra-violet, and seems to become 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 Jess 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 in 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 Tfierapeutic 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, some twenty 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 63 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 cgnsuming 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 black or grey body varies with the fourth power of its absolute temperature, that is, If A = surface area, 7\ = 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 - TV), (1) where for a black body, as the carbon filament with P r given in watts per square cm., k is probably between 5 x 10~ 12 and 6 x lO" 12 ; (2) T 2 is usually atmospheric temperature or about 300 degrees abs. If T v does not differ much from T 2 , 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, - TJ (TV + T, 2 T 2 + T,T 2 2 + T 2 *); 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 A^ so as to include the heat conduction and convection: in stationary air k^ reaches values as high as k v = 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 v T 2 4 becomes negli- gible compared with Tf and equation (1) can, for high tempera- tures, thus be approximated by: Pr - kAT*; (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: 47-5- T -V 1 * 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. 1400 -130 -120 -110 ; 1 1 2 1 4 1 S-PE U ! 1 2 OH 6 2 8 3 3 Z 3 4j !i -r r^* 4 e ^^* ^^" ^ ' ^-- " ^^^ ^ *^ ^ ,--- ^ ^ ^- < "^* i X S* x^ ^ f r -80 : p / x ^x ^ " / ^ X s ' c-140- h t / / x i / X * Pr~~ *\Q 25-C -(T )-=2 '-T, )8a ) 3 / / / / / / f - 2 .0 I .0 6 .0 5 .1 ) .1 2 .1 I .1 6 .1 i 3. \ 8 .3 3 .3 2 .3 I .3 > .3 8 A .4 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 sV 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 as 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. If 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. Most bodies give approximately the same temperature radia- tion, that is, follow the temperature law (1), differing only by the numerical value of the constant &; 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 l w and temperature T l by normal temperature radiation is : b P (l w ) = Cl Al w % l " T , (Wien's law); or, ( A )_! P (U = Cl Al w i V - 1 } (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: f* OO Jo thus, for a = 5; P = cAT 4 ; or, Stefan's law, as discussed above. The maximum energy rate at temperature T occurs at the wave length l w = lm given by : dP (U = 0, dl w which gives : =-- = 0.284; or, lm = 50 X 10~ 6 thus gives : 2poui&** or small spheres or wires, with increasing voltage the disruptive strength of the gas is exceeded at those places where thn . field; mterisity 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 1 the luminous disks increases with decrease of the gas pressure. ' Two ^ets 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 dis- tances of 10 cm. and over very closely 4000 volts effective alternat- ing per cm. (10,000 volts per inch) are required (corresponding to a breakdown gradient of 30,000 volts per cm. in a uniform field) . With i I I i ^ i / 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. or less. The voltage consumed at the terminals seems to decrease with 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, and especially neon, 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 disruptive conduction, that is, Geissler tube lighting, is still limited (Moore tube) . So far only nitrogen gives a fairly good efficiency ; it reaches apparently values between the tungsten lamp and the tanta- lum lamp, or, a specific consumption of two watts per mean spherical candle power. The color of the nitrogen spectrum is a reddish 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 requires a tube length of 2000/2 = 1000 cm. = 10 m. or 33 feet, 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 the terminals, requires a tube length of 8000/2 = 40 m. or 133 feet. Thus the Geissler tube as an illuminant is essentially a large unit of light, requiring high voltage (which obviously may be produced by a transformer at the tube) and having a very great size. It gives, however, low intrinsic brilliancy and splendid diffusion of LUMINESCENCE. 105 the light. Neon gives a still much higher efficiency, though a red light, and as a noble gas is only very slowly absorbed, but is a very rare gas. Continuous Conduction. 47. In continuous conduction, or arc conduction, the conductor is a stream of electrode vapor, which bridges the gap between the electrodes or terminals. While in the spark, or the Geissler discharge, the conductor is the gas which fills the space between the terminals, in the electric arc the current makes its own conductor, by evaporation of the electrode material, and maintains this conductor by maintain- ing a supply of conducting vapor. The color and the spectrum of the arc, thus, are those of the electrode material, and not of the gas which fills the space in which the arc is produced, and the nature of the gas in the space thus has no direct effect on the arc. Its pressure obviously has an effect, as the vapor pres- sure of the conducting arc stream is that of surrounding space, thus increases with increasing gas pressure, and the arc vapor then contracts, the arc gets thinner, while with decrease of the gas pressure in the space surrounding the arc the vapor pressure of the arc stream also decreases, thus the vapor expands, and the arc stream becomes larger in section and correspondingly less luminous. As the arc conductor is a vapor stream of electrode material, this vapor stream must first be produced, that is, energy must first be expended before arc conduction can take place. An arc, that is, continuous conduction, therefore, does not start spon- taneously between the arc terminals if sufficient voltage is sup- plied at the terminals to maintain the arc, but the arc has first to be started, that is, the conducting vapor bridge produced by the expenditure of energy. If, therefore, in the arc the current ceases even momentarily, the conduction ceases by the disappearance of the vapor stream and does not start again spontaneously, but the arc has to be started by producing a vapor stream. With alternating voltage supply the arc, thus, would go out at the zero of current and have to be started again at every half wave. In general, the arc, thus, is a direct current phenomenon. 106 RADIATION, LIGHT, AND ILLUMINATION. Some of the means of starting arc conduction are : (1.) By bringing the terminals into contact with each other and thereby closing the circuit, that is, establishing the current, and then slowly separating them. In the moment of separation the contact point is heated, vapor produced at it, and during the separation of the terminals, a vapor stream is left behind as conducting bridge. Obviously, if the terminals are separated very rapidly, and the voltage is not much higher than required to maintain the arc, not enough vapor may be produced to con- duct the current, and the arc does not start. (2.) By raising the voltage between the terminals so high that a static spark passes between them, that is, disruptive conduction occurs. The energy of this static spark, if sufficiently large, that is, if the high voltage is maintained sufficiently long, then pro- duces the vapor stream and starts the arc, that is, the arc follows the spark. If the duration of the high voltage is very short, the energy of the spark may not be sufficient to start the arc. Thus high frequency discharges between live terminals frequently are not followed by an arc, and the lower the voltage between the terminals is, the more powerful a static spark is required to start an arc. (3.) By supplying the conducting vapor stream from another arc, that is, by an auxiliary arc. If the vapor stream of this auxiliary arc issues from the same terminal as the vapor stream of the main arc which is to be started, only the normal operating voltage is required in starting the latter arc, while a higher volt- age is required, if the vapor is supplied by an entirely separate arc. (4.) By raising the space between the terminals to a very high temperature, as by bridging the terminals by a carbon filament, and by the passage of current raising this filament to very high temperature. 48. The sharp distinction between the arc, in which the cur- rent makes its own conductor by a vapor stream issuing from the terminals, and the Geissler discharge, in which the current uses the gas which fills the space as conductor, is best illustrated by using in either case the same material, mercury, as conductor. I have here a vacuum tube, shown to scale in Fig. 33, about 2.5 cm. diameter, with three mercury terminals. The tube has four mercury terminals, of which, however, I use only three. The LUMINESCENCE. 107 gas which fills the space between the terminals is mercury vapor.* 1 now connect, as shown diagrammatically in Fig. 34, terminals 2 and 3 to the high potential coil of a step-up transformer the low potential circuit contains a reactance to limit the current and you see the striated Geissler discharge through mercury FIG. 33. vapor appear between terminals 2 and 3, giving the green light 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 * A trace of hydrogen is left in the tube, to lower the alternating voltage required for its ODeration 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, 2=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 componente 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 was 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 thus is 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 conductor 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 terminal?, 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 lead to the upper terminal B. I close the reversing switch S so as to make A negative, and B and C 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 C, 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 A B remains, but no current goes to C, although more 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 C, 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 FIG. 39. current during one half-wave only, but no current at all dur- ing the other. I show you this experimentally, using 110 volts alternating between A and C. 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 late 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 -ft 110 VJOLT8 60 CYCLES FIG. 40. terminals. The cause is obvious: to maintain an alternating 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 (3700 deg. cent.). The voltage re- quired to maintain a 13-mm. alternating arc must therefore be 116 RADIATION, LIGHT, AND ILLUMINATION. at 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.) 5(0 N 1090 1500 M CONDUCTION 2500 3000 8500 Q -3.0 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 " rectifying 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 by 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 peculiarity 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, and increase in intensity with m ~ *- ^ J YELLOW * BLUE VIOLET increasing vapor pressure. To ^T^ GR 1 EN 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 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 was 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 are 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 with 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 metal, 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 300 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 flickering 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, but the efficiency is lowered, and the lamp made more complicated. 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, calcium or mercury 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-candle 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 an .incandescent 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 6;* 6 thus may be called the luminosity index of the hydrocarbon. HYDROCARBONS. Name. State. Formula. Hydro- gen Index (a). Lumi- nosity Index (ft). Paraffines: Methane. Gas. CH 4 4 Ethane . ... . . do... C^HL 3.0 0.25 Propane . .do.. 2.67 0.333 Butane . . .do.... Q 3 jj 8 2.5 0.375 Pentane Liquid. Q 4 jj 10 2.4 0.40 Gasolene do CH 2 33 417 Kerosene do C 6 H* 2 2 45 Mineral oil do P 10 TT 22 2 14 464 Vaseline. Solid. 14 3 approx. 2 1 0.475 Paraffine . . .do... C^R 42 2.08 0.479 Olefines: Ethylene Gas. C 2 H, 2 0.50 Acetylenes: Acetylene Gas. C 2 H, 1 0.75 Benzols: Benzol Liquid 1 75 Naphthalene . . Solid. C^ TT 8 80 Anthracene ..do.... C 14 H 10 0.71 0.821 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 Q , 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 paraffine 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 = 0.50, 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 O 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 hydrocarbons, 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 200 190 180 170 160 / / / j / / / / / / / / 140 130 120 110 100 90 80 70 60 50 '40 30 20 10 / / / / x / / / X s / J / X > / jf / ^ X / 3 // / s / / / / i ^ ,x ^ / / X % i& x / / / / x X // '/ x X // '/s X* I ^ LEf GTH \ 26 5 z 1 & o 3. 5 CM 5 IN. FIG. 45. arc length, L, we get for 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- \ \ ^200 180 160- -10- 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, /, or rather to the arc length plus a small quantity, Z x = 0.125 (for the magne- tite arc): e l = k^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, e, in Fig. 46, the con- stant part, e Q = 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 , as the voltage consumed in the arc stream. The curves of arc-stream voltage, ei, as function of the current, i, in Fig. 46, can with good approximation be expressed by k cubic hyperbolas : e^i = k 2 2 ; or, e i = -~- 3 and since we find for Vi constant value of current: e l = k^ (I -f 0.12), as function of arc length and current, i, the voltage of the arc stream is ex- pressed by: \'t and the total arc voltage by : Vl where e , k and / 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 i, it follows that the voltage, e , consumed at the arc terminals is constant. The power consumed in the arc stream : p l = e^, 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 Z, or rather the arc length / increased 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 l consumed in the arc stream thus is proportional to the square root of the current, i, and to (I + y ; thatis ' p^kVid + lJ; and since = e which is equation (1), and herefrom, since e = e Q + e v 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 = 48.5 for magnetite (123 in inch measure) = 51 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 e ^ 3Q+ 48.5 (Z + 0.125). Vi 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 /, as done for the magnetite arc in Fig. 45, when using only the observations for arc length of 0.25 in. and over, we get fairly satisfactory straight lines, which intersect at the point, giving e Q = 36 volts, but ^ = - 0.8 cm. = - 0.33 in.; that is, a value much greater than for any other arc. For short arc vo 120- 110,1 100 LENGT -1.25 0.5 25 1 375 c* 1'5 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 c 7 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 IF 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 7 ' 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, t , where a small variation of voltage causes a large variation of current, the operation of the arc is unsatisfactory, that is, the FIG. 48. 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 i . At the stability limit i , the resultant characteristic III in Fig. 48 is horizontal, that is, the slope of the resistance curve e' II, r = - > is equal but opposite to the slope of the arc char- i de acteristic I. ; that is, at the stability limit, di and, substituting equation (2) in (4), gives 2 ii or ' fe and the total voltage consumed by the arc of current i and length I and such a series resistance r as just to reach stability is E = e + ir, v (L "| ^l/ *v \v "T" v-t ) = e that is, * = +! .- ; (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, e i = 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 v dissi- pated, by radiation, etc., may be assumed as proportional to the length I of the tube, and to the current i: p l = ej, = kli, (7) this gives e l = kl, or independent of the current; and = o + e v = * + kl- (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 : e = 13 volts ; k = -j- ld hence, - ,, e = 13 + - <, 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 itd 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 n. 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 <> the sum multiplied by -, where d, the angular distance under t which observations are taken, is given in radians, that is, 10 deg. gives d = n. This usually is done graphically. 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 plane of the filament; and a minimum in the two meridians at right angles to the former, giving a horizontal or equatorial distribution FIG. 60. of 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 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" 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 TT lumens (since the area at unit distance from a point is the surface of a sphere, or 4 TT). The unit of light intensity, or one candle power, thus gives, with a radiator of uniform light-flux distribution, 4 TT lumens of light flux, and inversely, a radiator which gives 4 TT 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 TT 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 TT, 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 = 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 m circumference, while the intensity in any other direction $ covers a zone of 2 m sin circumference; that is, an area which is the smaller, the nearer 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 I, II, III, IV in Fig. 99 give the same total light flux, and curve gives only one tenth the light flux. To the eye, however, the curve I gives the impression of a far more powerful illuminant than the curve IV, and curve appears practically equal to, if not larger than IV, while in reality it represents only one tenth the light output of IV. 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 (f> (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 and angle 0,that is, a zone of radius (Fig. 62) r = sin; thus surface d A = 2 TT sin = IdA = 2x1 sin (j)d(/)' } hence, the total light flux : 4> = 2 TT I V I sin (f>d(f>. FIG. 62. (1) (2) The light flux in the space from the downward direction (f> = to the angle (/> = fa against the vertical or symmetry axis, then is 3>* 1 = 2 TT f*' I sin dfa (3) /0 and the light flux in a zone between the angles fa and fa is (4) /. DISTRIBUTION CURVES OF RADIATION. (I) Point, or Sphere, of Uniform Brilliancy. In this case, the intensity distribution is uniform, and thus, if I = intensity of light, in candles, 4> = 4 id = 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 I, 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 ' B (7) 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- FIG. 63. tically downward, for < - 0. In any other direction, under angle against the vertical (Fig. 63), the intensity is I = 7 cos , (8) and is zero for = 90 deg. The light flux issuing from the radiator below angle $ is, by (3): hence, by (8) 4> * = 2 TT I 7 sin (f)d; */0 $0=2 7r7 i sin < cos y o -I'- cos -/{!- cos (9) LIGHT FLUX AND DISTRIBUTION. 191 and the total light flux, from < = to < = 90 deg. = , thus is : or, 4> /.-- (ID The brilliancy of the source of light is the total light flux divided by the luminous area; or, B *' -A' and, if r = radius of the luminous circle, A = nr\ and -; (12) or, / = r*B; (13) that is, the same as in class (1). Comparing (10) 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. 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 aj below the horizontal : 0< < <\-u\ 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 < -, however, the intensity is 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 - + aj < $ does the light cease. If r 2 = radius of carbon, the radius of the luminous segment is sin w ' the height of the segment is h = r\ (1 cos <*}) r 2 (1 cos aj) 194 RADIATION, LIGHT, AND ILLUMINATION, hence tne surface of the segment, or the luminous area, is A 2 = 2 rJiTr 2 r 2 ?r (1 cos aj) 2r 2 2 7r X 2 sin 2 ~ A ' 2 2 4 sm 2 - cos 2 - !^ (14) 2 cos 2 - Thus, if the luminous area is the same as in the plane circle class (2), it must be: , to COS r 2 = rcos; (15) and, if the brilliancy B is the same, the maximum intensity for = Ois =r*B 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 w below to w 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 cu = 30 deg. as 2, and a rounded circular radiator of angle co = 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 to the radiator, or in horizontal direction, < = 90 deg., when choosing the radiator as vertical axis. At angle , the intensity is, Fig. 68, / = / sin<, (17) and is zero for (j> = and (f> = 180 deg., or in the vertical. 196 RADIATION, LIGHT, AND ILLUMINATION. The light flux within angle $ from the vertical is, by (4), <|/ = 27r C I s *^o f# = 7r/ / (1 - ^ and the total light flux for < = K is * = *'/; (19) or, inversely: ^ (2Q) and the radiating surface is A = nwl, (21) where Z is the length; w the diameter of radiator. The bril- liancy, therefore, is or 00 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 3>, gives the angle (f>, which bisects the light flux : sin 2 (/) TT *- =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 : Uniform. Circle. Cylinder. Light flux , at equal maximun intensity 7 4 TT/ O TT/ O n 2 I 4 1 7r=3.14 Maximum intensity 7 , at equal < 4> < light flux $ 4* TT * a 1 4 i = 1.27 n As seen, at the same maximum intensity, the cylinder givea 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 x = 3.14 times the flux of light. In Fig. 64 the three distribution curves are shown for the sarm 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. FlG - 69 - The projection of the radiator in this direction of maximum intensity, = 0, has the length: 2 nr\ and if, by (24): TT = maximum linear intensity, 198 RADIATION, LIGHT, AND ILLUMINATION. where it is, B = brilliancy, /.- ' = 2rwB. (25) This is in the direction in which the projection of the radiator is a circle of radius r, and thus circumference 2 nr. In any other direction , the projection of the radiator is an ellipse, with r and r cos < as half axes, as seen from Fig. 69. If I = the circumference of this ellipse, the intensity in the direction (f> bears to the maximum intensity 7 the same ratio as the circumference of the ellipse to that of the circle; that is, The circumference of an ellipse with the half axes a and c is I = (a + c) TT (1 + q), (27) \ 4- -LII \-L-^L-(- -\ _L I * V . I <^m \~ . I ~ ... C) where I/a - c\ 2 4\a + c The ratio of the circumference of the ellipse to its maximum diameter, y = , is given in Table I, and plotted in Fig. 70, T with the ratio of the half axes, that is, cos <, as abscissas, and, in Fig. 71, with angle as abscissas. TABLE I. -CIRCUMFERENCE OF ELLIPSE. c - = COS ^. a I *. I If if 1.0 1.571= - 1.571 = - 0.9 1.495 10 1.560 0.8 1.418 20 1.525 0.7 1.345 30 1.470 0.6 1.278 40 1.390 0.5 1.210 45 1.350 0.4 1.150 50 1.305 0.3 1.110 60 1.220 0.2 1.055 70 1.120 0.1 1,025 80 1.045 1.000 90 1.000 LIGHT FLUX AND DISTRIBUTION. 199 \ H 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 s s ^ X S X ^ ^ ^^ C( s?> = min imum D . jrnet vof Ellii s\a [ 1 2 Js 4 0\5 6 7 8 9 m, ->, 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 O.i 0.3 0.2 0.1 "N \ \ \ ^ ^S V^ 1 ) I Ar 3 glej D 4 Dee ees D 50 A ) 7 ) t ) 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 2 vertical, and a minimum 7 X = 7 7T in the horizontal. Theoretically, exactly in the horizontal, = 90 deg., the in- tensity should be - 1 , as one half a 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. Fia. 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 : I, = 4 r/; {sin ( + 10) + sin ( - 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, /, = "f> (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. .Fie. 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 <, is added to the intensity 7 r This projection is, by Fig. 73, c = r (1 + cos <), (30) and thus 7 3 = c7 ' = r/ ' (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 r7 ' 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 = 7 t + 7 3 , Curve 2 of Fig. 74 ; and in the equator, / = / o + i v 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. Circular line. Single-loop filament. Plane. Rounded by Meridian of Equator. 30 deg. 60 deg. Max. intensity. Min. intensity. 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 7.00 6.88 6.57 6.05 5.35 4.50 3.50 2.39 1.21 6.50 6.40 6.12 5.63 4.98 4.19 3.25 2.31 1.47 0.75 0.39 0.09 5.25 5.18 4.94 4.56 4.07 3.55 3.01 2.44 1.90 1.37 1.00 0.07 0.04 0.02 005 3.14 3.12 3.05 2.94 2.78 2.61 2.44 2.24 2.09 2.00 1.70 1.73 2.47 3.19 3.84 4.41 4.88 5.23 5.44 5.51 1.70 1.68 2.35 2.97 3.53 4.02 4.41 4.70 4.88 4.94 5.51 5.50 5.46 5.41 5.33 5.24 5.16 5.06 4.98 4.94 . 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^B^. 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 = I tan (2) If now the projected circle 2 overlaps with the radiator circle Op 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 (f> thus reduced from that of the complete radiator surface, ^r 2 , to that of the radiator surface minus the shaded part S, that is, 7rr z S, or in the proportion r 2 7r - 8 S r TT (3) 204 RADIATION, LIGHT, AND ILLUMINATION. and the intensity of the remaining light flux, in the direction 0, thusis 7 = / gcos0. (4) If the distance, a, between the circles and 2 is greater than the sum of radii, I tan cf> > r + r v 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 0! given by r _l_ r tan 0, = - -. (5) I In the direction in which is smaller than the angle, > 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 Ti>r, and if this is the case, a circular area below the radiator receives no light. If r l = r, the intensity becomes zero only in the direction 0=0; and if r t < 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 t : S = D + D r Let 2 ID = angle subtending segment D and 2 w l = angle subtending segment D v and denoting the width of the segments thus w -= AC, w l = ~B, and the total width of the shaded area is p = AB 2 = w + w r (7) From Fig. 76, a = 00 2 = OA + ~Bf) 2 - AB 2 = r + r t - p; or, p = r + r, a; hence, by (2), p = r + r l tan . (8) LIGHT FLUX AND DISTRIBUTION. In A OJEO, sin w, r sin co r, ' 205 and hence, r . sin w l = - sin cos Furthermore, D = Sector = r 2 w - r 2 sin 2 sin 2 a sin 2 and, by (3), (9) (10) (11) (12) (13) (14) (15) (16) For different values of w the values of aj w 1 p D D l 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 7. 94. In Table III are given 0>9 the values of p and q for the ratio of radii : 3 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ^ N % ^ \ ^ \ \ \x V m \ \' \I V I\ \ \ \ X sn P- ^ o 1 2 3 0, i 5 6 7 8 k FIG. Z8. - = 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 5-i. r r .l = r = 0.7. I. II. III. IV. n 1 000 1 000 1 000 1 962 964 968 2 gg5 895 910 3 785 810 0.835 4 675 715 0.748 0.5 0.6 65 0.560 0.435 0.615 0.500 0.660 0.575 532 0.660 0.569 0.520 0.7 71 0.308 0.380 0.502 0.500 0.477 0.8 85 0.183 0.255 0.500 0.386 0.340 9 070 127 500 95 028 063 1 o o 500 If - < 1, the curve III represents the effective light-giving area only up to the values of p, where 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 electrode. From the value p f , which corresponds to w t = r v the area S then increases by 2^ (p-p)} hence, if 8'= shaded area for p = PJ for any value of p > p v and ^1--. (17) ;rr 2 ?rr 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 t at distance / [corresponding to a diameter of positive carbon 2 r, of negative carbon 2 r v and an arc length Z], are given in Figs. 79 to 82, and the numerical values given in Table IV. 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 I curves for = 1, and the arc lengths, r-= 0.25; 0.5; 1.0; 2.0, r 2r 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 *-2; -=2,asL 1 7 = 0.7; 1-0.5, asm. As seen from Fig. 82, a larger shade at greater distance, l y 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 V///A V////A FIG. 81. FIG. 82. LIGHT FLUX AND DISTRIBUTION. 209 1. If II I g 02 3 10 CO CO t^ 00 00 0404040 i"- ^ o o Ol ^ CO OO O4 O fH T-H Q O-HC^ CO-^IO t^OOO4O ^* CO CM O O O N ^ CO 00 O ^ T< CO C*5 CO CO C< ^H O O C<-iC5O t^ o o o o c^ COCO^ ^^^ ^*^CO CMi-nOO ooo o - -H ^H^-I coo>t>. -H o us oo o o o * -l O t^ CO CO "- O4 OO^H /~\ O O O I-H I-H O O O IOO*O OlOO iO ^i ^i 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)), FIG. 83. 7 sin <, has to be multiplied, is 1 - cot (20) LIGHT FLUX AND DISTRIBUTION. 211 sn and the light intensity in the direction thus is 7 = qI sin < = 7 (1 j- cot (f)} si = 7 (sin - -y 1 cos For values of < less than t , where tan ^ = , (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 w where 0/ and / is given by r l - w tan 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 , 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 CD and 90 deg., which is given by r t cot (180 - <) q = = tan w cot <; (2) hence, the light flux intensity which is intercepted by the reflec- tor is A = (A sm = 7 tan co cos <, (3) and the light intensity issuing into space from the main radiator in this angle, ^ < < < (180 - to), is 7 = (1 - q) i' sin = 7 (sin (/) tan co cos ). (4) Therefore the light flux intercepted by the reflector within the angle = to < = co (or rather, < = 180 deg. to $ = 180 - a}) is ^ f T C - > , r / sin 2 co $; = 2 */ J^ sin 2 dj> = xI (aj - -^ within the angle $ = co to = - is d(f> = 2 nI Q tan co I cos sin cf> d I + cos 2 2 = a^ l = nI aaj, (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 ^ 7 " = - 2 = 7 ooi, (7) and herefrom follows the intensity of radiation of the secondary radiator in any direction (f>, r = 7 " cos = 7 aco cos (j>. (8) The total intensity of radiation of main radiator and reflector or secondary radiator combined, in the lower hemisphere, or for < (/> < |, is 7 = /' + 7" = / o ( s in + aaj cos <); (9) and in the upper hemisphere light flux issues only under the angle - < < x - co, and is 2i I = /' = / (sin (j) tan w cos <). (10) FIG. 86. For oj = 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 I = 7 (sin < + 0.92 cos <), and in (10) gives / = 7 (sin < - 3.73 cos <). TABLE V. Regular: a = 0.6. Irregular reflection. Regular reflection. a = 0.7. Irregular: a' = 0.1. w l - 60 deg. 6. a = 0.7. w = 75 deg. w t - 60 deg. a> 2 = 85 deg. w 2 = 85 deg. 1 l ' 3.68 0.18 10 4.32 0.70 0.17 20 4.83 1.47 0.16 27 16 30 5.19 2.00 0.42 35 0.80 40 5.39 2.57 1.19 45 1 54 50 5.44 3.06 1.89 55 2 23 60 5.46 3.46 2.55 65 4.11 3.27 70 5.02 4.74 3.97 75 4.82 5.32 4.62 80 4.58 5.86 5.26 85 4.30 6.34 5.86 87 5 5 18 4 93 90 4.00 4.00 4.00 92 5 2 00 2 00 95 2.68 100 1.34 105 B. Regular Reflection. 97. With regular reflection by a polished reflector or mirror as used, for instance, in some forms of luminous arcs, the reflector is represented by a second radiator, which has the same shape as the main radiator and is its image with regard to the plane of the reflector. If a is the albedo of the radiator and 7 the maximum 216 RADIATION, LIGHT, AND ILLUMINATION. intensity of the main radiator, the maximum intensity of the virtual or secondary radiator is a/ . The reflector then cuts out of the light flux of the radiator that part intercepted by it, and adds to the light flux that part of the (virtual) light flux of the secondary radiator which passes through the plane of the reflector. As example may be considered the intensity distribution of a vertical luminous arc of length Z, supplied with a circular ring- shaped mirror reflector concentric with and in the plane of the top of the arc. Let w t be the angle subtended by the inner, co 2 the angle subtended by the outer edge of the reflector, from FIG. 87. the base of the arc, as diagrammatically illustrated in Fig. 87; then the intensity of the light flux of the main radiator for is and for is where, by (2), hence, and is zero for 7 = 7 sin , sn q z = tan w 2 cot (ID (12) (13) (14) // = 7 (sin (j> tan w 2 cos ), > n w 2 . All the light flux issuing from the main radiator between the upper vertical and the angle o^ (0 < < < o^) /' = 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 a> l and - from the upper vertical, the part \cu l < < I, = qJ sm (16) is wasted by passing through the hole in the reflector. Since, by (13), q l = tan ^ cot , (17) it is : 7j = 7 tan o^ cos $, (18) 7T for w l < (f> < - All the light flux issuing between the upper vertical and the angle w 2 , 7'=7 sin<, (19) is received by the reflector, with the exception of that part which passes through the hole in the reflector. Of the light flux issuing between angle co 2 and - from the upper 2i vertical, the part I 2 =q 2 i sm = 7 tan a> 2 cos , f or w 2 << (20) 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 ->4> > w 2 from the upper vertical, 2i /"= a (I 2 7J = a7 (tan $ >aj l from the upper vertical, /'" = a (I' - 7J = a7 (sin < - tan ^ cos <) ; (22) and for ^ > $ > 0, /"" = a (I' - 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 0< < -"i is 7=7 sin<; (24) for for for 7=7' + l' = 7 { (1 + a ) sin < - a tan ^ cos <) } ; (25 7 = /'+ 7"= 7 {sin < + a (tan co 2 - tan wj cos } ; (26) < / = // = 7 (sin < tan w 2 cos ), (27) and for > 7T W 2 is 7 = 0. 17* For ^= 60 = \, w 2 = 85= r, and albedo a= 0.7, the in- o 3o 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 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 0). 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 o^ to a> 2 , by (6), is fc.-Tr/oO'fa, -o^, (28) where of is the albedo of irregular reflection. This light flux gives in the lower hemisphere the maximum intensity for < = as 7 " = /X (o, 2 - a>J, (29) and thus the intensity of the irregularly reflected light in the direction < is 7 2 = 7 " cos j> = 7 a' (w 2 - coj 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 $ < v where tan ^ = y as discussed under heading II, class (2), equations (21), (22), where r l is the radius of the lower electrode. Thus, with a linear radiator of length /, 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 aj 2 , and of the albedo of regular reflection a and the albedo of irregular reflection a', the light intensity distribution within the angle < < < ^ is / = I a (aj 2 - ^)cos0; (32) within (f> l < (/) < Wj is / = / (sin <+[' (oj 2 - ^) - ^J cos 0); (33) within a) l < + \a (w 2 - uj - a tan ^ - ^1 cos 01; (34) 220 RADIATION, LIGHT, AND ILLUMINATION. within w, < d> < - is 7 |sin 0+ a (tan a) 2 tan co^ + of (co 2 co^) j cos (f>y, within and within - a> 2 is I = 7 (sin < - tan o> 2 cos 0), TT - w 2 < $ < n is 7 = 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 0)^= GOdeg. = ^; a> 2 = 85 deg. ^r', o= 0.60; a'= 0.10, and -^= 1. (/ Substituting the numerical values in the foregoing equations this gives 0i = 27 degi (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, 1 A, 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, (7, 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 (7, 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 C 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 G, 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 * See photographic illustration on front page. 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. *. 'o- Clear globe. V Frosted globe. 'o- Opal globe. o 5 10 5 20 6 8 11 25 7 12 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 67 43 42 70 37 37 35 75 29 32 1 O 80 20 26 34 85 15 21 90 13.5 17 32 OK 13 14 . i h = i cos = jj - 9 (2) 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 (j> i v = i sin (f> = (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 di&* 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 h tan hence, the total illumination at point A is 7 cos 2 . ^ = rr > the horizontal illumination is 7 cos and the vertical illumination is 7 cos 2 (f> sin (f> (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 t , on the 228 RADIATION, LIGHT, AND ILLUMINATION. horizontal plane P, the intensity of the light source must vary with the angle (f> according to the equation (6) : i 1 2 /--HrJJ (9) COS 2 or, if we denote by 7 the vertical, or downward, intensity of the light source, / - \ hence, 7 = cos 2 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 1= ^h' (12) 3 and, to produce uniform vertical illumination i. VQ of objects in the plane P beneath the light source L, /= , f. - (13) cos 2 sin (/) Where the objects in the plane P which are to be illuminated may have different shapes as on a dining-table, work bench, etc., uniformity of the total illumination, i, is desirable; where all the objects which shall be illuminated are horizontal as the sur'ace of a drafting-board constancy of the horizontal illumination i h is desirable, while where vertical objects are to be illuminated as, for instance, to read labels on bottles con- stancy of the vertical illumination i v is desirable. By " horizontal illumination" i h is here understood the illumi- nation of a horizontal plane, which is due to the vertical compo- nent of the total light flux, while the "vertical illumination 77 i v is the illumination of a vertical plane, due to the horizontal component of the light flux. LIGHT INTENSITY AND ILLUMINATION. 229 In Fig. 96, the intensity curves of the light source required to give uniform total illumination i (11) in a horizontal plane are plotted as curves I, II and III; the intensity distribution for uniform horizontal illumination i ho (12) is plotted as curve IV, and the intensity distribution for uniform vertical illumina- tion i VQ (13) in the horizontal plane beneath the light source is plotted as curve V. For convenience, curves IV and V are shown in the upper half of the diagram. The numerical values for l v = 1 are recorded in Table I. With increasing angle , the required intensity increases very rapidly, and, as is obvious, becomes infinite for $ '= 90 deg. TABLE I. (Figs. 95 and 96.) UNIFORM DISTRIBUTION ILLUMINATION CURVES. *. cos . Total. 1 Horizontal. Vertical. 1 decrees. cos 2 < cos 3 sin tf> cos 2 1 ! 00 5 996 .01 1.015 11.60 10 985 .03 1.045 5.90 15 966 .07 1.11 4.30 20 940 .13 1^0 3.30 25 906 1.22 - 1.35 2.88 30 866 1.33 1.54 2.66 35 819 1.49 1.82 2.59 40 766 1.70 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 oo 103. Therefore, in the problem, as it is usually met, of pro- ducing uniform intensity i over a limited area, subtending angle 2 cu 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 < < co. Beyond < = co, 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 = co 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 co if 2 co is the angle subtended by the floor of the room from the light source and for > co the intensity curve would follow the equation, / = s1^? . (14) 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 co, and the same uniform illumination in the vertical plane from = co 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 co 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 * height of walls = 2 2 tan 30 deg. = -^=1.15. \/3 II for co = 45 deg.; or diameter of floor -r- height of walls = 2 tan 45 deg. = 2. III for co = 60 deg.; or diameter of floor -f- height of walls = 2 tan 60 deg. = 2 \/3 = 3.46. IV for co = 75 deg. ; or diameter of floor -5- 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: co = 30deg.; 7 = 428 cp. II: aj = 45deg.; 7 = 195 cp. Ill: w = 60 deg.; 7 = 95 cp. IV: co = 75deg.; 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 = w degrees from verti- cal, and (a) Uniform illumination (on vertical plane) from = w to horizontal *= 90 deg. (6) No illumination beyond = . to = 30 deg. w = 45 deg. w = 60 deg. w = 75 deg. V .00 .01 .03 a. 6. V a. 6. V a. b. V a. 6. 5 10 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 l.OC 1.01 .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 .07 .13 .22 0.41 0.43 0.465 0.71 0.75 0.81 .07 .13 .22 0.178 0.188 0.203 0.237 0.251 0.271 30 35 40 .20 .01 0.81 2.05 1.73 1.38 4.47 3.57 2.24 1.33 1.49 1.70 .03 .16 .32 2.08 2.33 2.66 .33 .49 .70 0.51 0.57 0.65 0.89 0.99 1.13 .33 .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 .40 .32 .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, co = 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 < > w, 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 co = 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: aj = 30 deg.; 7 = 500 cp. II: w = 45 deg.; 7 = 235 cp. Ill: w = 60 deg.; 7 = 100 cp. IV: a) = 75 deg.; 7 = 25 cp. 0: co =. 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 a) = 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.; l v = 20. a. 6. c. a. b. c. "3 c D. C. D. C. D. C. D. 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 j x- - i. i. i. h 30 45 59 15 22.5 29.5X10- 2 10 42 50 63 02 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 1 0.3 25^0 0.1 0.1 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 \ 04 0,2 Q 0,8 0,4 08 1,0 1,2 1,4 1,6 l[8 gjO 8,2 84 86 28 30 32 3J4 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 Z Ao , 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 /- r\ * "~~ "\ 2 * 3 ' 4J \^*^/ where i v i 2 , i 3 , i* 4 are the illumination due to the lamps 1, 2, 3, 4, respectively. Let and Y = x; I'V (16) then the directions under which point A receives light are given by: tan < t = x, tan 2 = p x, tan 3 = p + x, tan < 4 = 2 p x, (17) LIGHT INTENSITY AND ILLUMINATION. 239 and l v 2 cos 2 &' 1 7 2 2 cos cos (18) where 7 P 7 2 , 7 3 , 7 4 are the intensities of the light source in the respective directions v (f> 2 , 3 , < 4 . 100 120 140 FIGS. 103, 104. ISO 200 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 hg = 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 = to = v and with gradually decreasing intensity from = 0J to at < = < 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 (f> = 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 = (f> 2 then is only by the FIG. 108. that reflected 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 / = 1, by equation (6), and the horizontal illumination i hj 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.). 244 RADIATION, LIGHT, AND ILLUMINATION. TABLE V. (Figs. 107 to 109.) *. /. lh lv tan $. i = I ft- 7 lh X = T V i = 7 ih = 7 COS 3 0! (Upper hemisphere). COS 2 < cos 3 ^ cos-> i'. 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 2KO 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 6.577 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 \ o.ofc 0.29 0.53 0.84 1.00 1.12 1.23 1.47 .66 .77 .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 o.h 0.29 0.42 O.S6 0.80 1.13 1.43 1.66 1.91 2.0 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 1.6 1.5 1.35 1.0 1.2 0.68 "i'.bs 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 FIG. 110. 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 cj 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 hv l he , l hd . These component illuminations are plotted in Figs. 112 to 115; as A a , A b , A c , A d 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, = 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&. 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 13 200 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 29 40 43 28 23 43 and also receives some reflected light from the walls. Thus, if ! = total light flux received by the ceiling, and 2 = total light flux received by the walls, the light flux received by the ceiling is * t = L, + 6 2 a 2 4> 2 , (21) where & 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 : (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 a> 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 0.2 1.0 0.8 Aa 0.4 0.2 Ba&d Bb&c 8 12 IS FIGS. 112, 113. Aft 8 12 10 20 21 Bakd light flux received by the walls as directed light, from each lamp, is I ^900 1 ^900 - I / sin d& H I 7 sin d& = 83 lumens ; (23) or, a total of L = 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 + 6^, (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 0.4 0.2 C6 Cd Cc 1.0 0.8 0.9 D 0.4 12 10 0.2 Dlkd Dc \ 24 FIGS. 114, 115. And the light reflected from the walls thus is : *,' = a 2 3> 2 = o 2 (L 2 + 6,0,^). (26) It thus remains to calculate the numerical values of 6, and b r 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. 75, for circular radiator and circular shades, by replacing the quadratic shade and radia- tor by circular shades of the same area, rV = 24 2 , and r = 13.5, at the same distance / = 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 b 2 - b v (27) equations (21) and (25) become: .^ = 4+6^, (28) a.-L.+ fr^; (29) hence, 2 2 1 + (30) and the light reflected from the ceiling is L. -f b.a 2 L 2 * 2 2 GL = a, 1 1 + the light reflected from the walls is = a 1 + (30) hence, substituting the numerical values : = 0, up to from = 40 deg. to = 70 deg., and is 75 lumens per lamp; or, a total of directed light in the test plane of 4 X 75 = 300 lumens. The diffused light in the test plane is 576 X 0.25 = 144 lumens, and the total light in the test plane thus is 444 lumens; while the total light issuing from the four lamps is 4 X 163 = 652 lumens, giving an 444 efficiency of illumination of = 0.68; or, 68 per cent: the 444 average horizontal illumination in the test plane is i h = - 576 770; while the average total illumination, from Fig. 117, is about i m = 870. The difference is due to the varying direction in which the directed light traverses the test plane. Measurement of the illumination of a room by illuminometer, to give correct values, thus must take in consideration the different directions in which the light traverses every point; by measuring the light flux intercepted by a horizontal sur- face, the result represents only the horizontal illumination, and not the total illumination at the point measured, and therefore frequently does not represent the illuminating value of the light. D. HORIZONTAL TABLE ILLUMINATION BY INCAN- DESCENT LAMPS. 109. Assuming a table, of 5 ft. by 13 ft., to be illuminated so as to give as nearly as possible uniform horizontal illumina- tion i h . With a light source of the distribution curve, Fig. 107, but of four times the intensity, and using two such lamps, they would be located vertically above the table, at a distance from each other which would be chosen so that, midways between the lamps, the illumination is approximately the same as verti- cally beneath the lamps. In the same manner as discussed in C, the illumination is calculated in characteristic lines, indicated as A, B, C in Fig. 118, using, however, the curve i^ of Fig. 109. About the most uniform horizontal illumination then is given by locating the lamps 5 ft. above the table, 8 ft. from each 254 RADIATION, LIGHT, AND ILLUMINATION. other and 2.5 ft. from the edge of the table, as shown in Fig. 118. The illuminations in the lines A, B, and (7, and their components are plotted in Figs. 119, 120, 121, and recorded in Table VII. ' ? 1 _ e 2.5--^ < ^ 4 9 > 2{5 2|5 6 FIG. 118. TABLE VIII. (Figs. 118 to 121.) HORIZONTAL ILLUMI- NATION OF TABLE. X. A a - Ab. A. B a . B b . B. Ca'b. C. -2.5 -2.0 -1.5 2.96 3.20 3.36 0.24 0.27 0.32 3.20 3.47 3.68 2.96 3.20 3.36 0.38 0.46 0.48 3.34 3.66 3.84 .55 .66 .79 3.10 3.32 3.58 1.0 0.5 3.41 3.37 3.36 0.37 0.43 0.50 3.78 3.80 3.86 3.41 3.37 3.36 0.48 0.50 0.50 3.89 3.87 3.86 .89 .96 .97 3.78 3.92 3.94 + 0.5 1.0 1.5 3.37 3.41 3.36 0.57 0.67 0.81 3.94 4.08 4.17 3.37 3.41 3.36 0.50 0.48 0.48 3.87 3.89 3.84 .96 .89 .79 3.92 3.78 3.58 2.0 2.5 3.0 3.2 2.96 2.63 0.96 1.15 1.37 4.16 4.11 4.00 3.20 2.96 0.46 0.38 3.66 3.34 .66 .55 3.32 3.10 3 5 2 28 1 66 3 94 + 4.0 1 96 1 96 3 92 LIGHT INTENSITY AND ILLUMINATION. 255 From the curves as given in Figs. 119 to 121 may then be plotted the equi-luminous curves at the table surface, as done in Fig. 117 of the preceding paragraph. In this case, which represents concentrated illumination, diffusion is not considered, but the light is all directed light. A Art A6 ,x-^ . ^^s* ^ "X / ^ ^^"^ 11 ^^, *> ^v 'X \ / N s \ / \ s / / A ^ / \ \^ ^ x' ^s \ *^*~ ^'S^ ^ 2 4 6 8 10 12 FIG. 119. 4.0 3.0 2.0 1.0 -*- 3.0 3.0 2.0 2.0 1.0 1.0 / x / \ ^ ^ --> \ FIG. 120. FIG. 121. LECTURE XII. ILLUMINATION AND ILLUMINATING ENGINEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the light flux in space, that is, the light flux density in space and more particularly at the illuminated objects; the illumination, that is, the light flux density reflected from the illuminated objects, and the effect produced thereby on the human eye. In the latter, we have left the field of physics and entered the realm of physiology, which is not as amenable to exact experimental determination, and where our knowledge thus is far more limited than in physical science. This then constitutes one of the main difficulties of the art of illuminating engineering: that it embraces the field of two dif- ferent sciences physics and physiology. The light flux entering the eye is varied in its physical quantity by the reaction of the eye on light flux density in contracting or expanding the pupil. The effect of the light flux which enters the eye is varied by the fatigue, which depends on intensity and also on color. Distinction is due to differences in the light flux density from the illuminated objects, that is, differences of illumination, which may be differences in quality, that is, in color, or differences in intensity, that is, in brightness, and as such includes the effect of shadows as causing differences in intensity at the edge of objects. The physical quantities with which we have to deal in illumi- nating engineering thus are : The intensity of the light source or the illuminant, and its brilliancy, that is, the flux density at the surface of the illuminant; The flux of light, that is, the total visible radiation issuing from the illuminant; 256 ILLUMINATION AND ILLUMINATING ENGINEERING. 257 The light flux density, that is, the distribution of the light flux in space, and The illumination, that is, the light flux density issuing from the illuminated objects. The intensity of a light source is measured in candles. The unit of light intensity, or the candle, is a quantity not directly related to the absolute system of units, but reproduced from specifica- tions or by comparison with maintained standards, and for white light is probably between 0.04 and 0.02 watt. Intensity has a meaning only for a point source of light; that is, an illumi- nant in which the flux of light issues from a point or such a small area that, at the distance considered, it can be considered as a point. " Intensity of light" thus is a physical quantity of the same nature as " intensity of magnet pole," which latter also presupposes that the total magnetic flux issues from a point, and thus is applicable only when dealing with such distances from the source of the light flux or magnetic flux, that the flux can be assumed as issuing from a point. Frequently the inten- sity of a light source is different in different directions, and then either the distribution curve of the light intensity is required for characterizing the illuminant, or the average of the intensities in all directions in space is used, and is called the "mean spherical intensity." The unit of light intensity, or the candle, is the intensity which produces unit flux density at unit distance from the light source, and thus produces a total flux of light equal to 4 n units (the surface of the sphere at unit distance from the light source). The unit of light flux is called the lumen, and one candle of light intensity thus produces 4 n lumens of light flux (just as a magnet pole of unit intensity produces 4 x lines of magnetic force). The light flux is the essential quantity which characterizes the usefulness of an illuminant, and it is the raw material from which all illuminating engineering starts. Any source of light can be measured in units of light flux or lumens the diffused daylight entering the windows of a room, or the visible radia- tion of the mercury lamp or a Moore tube as well as that of a point source by adding all the flux densities intercepted by any surface enclosing the source of light. In a point source of light, the intensity, in candles, is the total 258 RADIATION, LIGHT, AND ILLUMINATION. flux of light, in lumens, divided by 4 n. In any illuminant which is not a point source, we cannot speak of an intensity, except at such distances at which the source of light can be assumed as a point; and in interior illumination this is rarely the case. Since, however, the candle power, as measure of the intensity of light, has become the most familiar quantity in characterizing illuminants, very commonly even sources of light which are not point sources as a Moore tube or the diffused daylight are expressed in "equivalent candle power," and when thus speaking of the candle power of a mercury lamp, or of the diffused daylight from the windows, we mean the candle power of a point source of light, which would give the same total flux of light as the mercury lamp, or the daylight from the windows, etc. The " equivalent candle power/' or frequently merely called "mean spherical candle power/' thus is the total light flux divided by 4 TT, hence in reality is not a unit of intensity, but a unit of light flux. This explains the apparent contradiction between the claims that sources of light, as the mercury lamp or the Moore tube, can- not be expressed in candle powers, while at the same time their specific consumptions are given in candle power per watt : mean- ing equivalent candle power, which refers to the total flux of light, and thus is a definite and measurable physical quantity. While it is not probable that the custom of rating illuminants in candles, regardless of their shape, will quickly disappear, and no objection exists against it, provided that it is understood to mean the equivalent candle power, it is preferable to use the cor- rect unit of light flux, and express the output of a source of light in lumens, adding where necessary the equivalent candle power in parenthesis. Obviously, the use of the candle power in any particular direction horizontal, or terminal, or maximum can- dle power has a meaning only in characterizing the distribution of the light flux, as applicable for a particular purpose, as street lighting, but, when used for rating the illuminant by its light flux output, is an intentional or unintentional deception. Incandes- cent lamps have been rated, and to some extent still are, in hori- zontal candle power, but in this case the horizontal candle power has ceased to mean the actual horizontal candle power, but is the horizontal candle power which with a certain standard dis- tribution of light flux would correspond to the light flux of the ILLUMINATION AND ILLUMINATING ENGINEERING. 259 lamp, and thus also is merely a practical measure of the light flux, retained by convenience: one horizontal candle power rep- resents 0.78 mean spherical or equivalent candle power of the standard distribution curve, and thus 4 TT X 0.78 lumen. In general, intensity, or candle power, thus is an angular measure, useful in characterizing the distribution of the light flux, but not the total light flux. 111. Light-flux density is the light flux per unit area traversed by it, thus is measured in lumens per square meter (or square foot), just as the magnetic density is measured in lines of mag- netic force per square centimeter. In illumination, as unit of length, usually the meter is employed, and not the centimeter, as in the absolute system of units, and 10 2 thus is the reduction factor to absolute units. Frequently also the foot is used as practical unit of length. For a point source of light the light flux density is the inten- sity of the light source, in candles (in the direction towards the point of observation, if the distribution is not uniform in all directions), divided by the square of the distance, in meters, or feet, and the light flux density thus is frequently expressed in meter-candles, or foot-candles. Thus at 10 feet distance from a 16 candle power lamp, the light flux density is 0.16 foot-candle, or 0.16 lumen per square foot. Very commonly, therefore, the light flux density produced by sources of light which are not points, is also expressed in meter-candles or foot-candles which numerically is the same value, that is, the same quantity, as lumens per square meter or square foot, but physically would refer to the equivalent candle power of the light source. Illumination is the light flux density reflected from the illu- minated object, and as flux density thus is measured also in lumens per square meter or square foot, or in meter-candles or foot-candles. Brilliancy is the light flux density at the surface of the illumi- nant, and as flux density thus could also be measured in lumens per square meter or square foot, but, as this would usually give enormous values, brilliancy of the light source generally is meas- ured in lumens per square centimeter, or per square millimeter. It is a quantitj' which is of high importance mainly in its physio- logical effect. Light intensity, brilliancy and light flux thus are character- 260 RADIATION, LIGHT, AND ILLUMINATION. istics of the illuminant, while flux density is a function of the space traversed by the light flux, but not of the source of light: with the same source of light, in the space from the surface of the illuminant to infinite distance, all light flux densities exist between the maximum at the surface of the illuminant (its brilliancy) and zero. Brilliancy thus is the maximum of the light-flux density. While intensity and brilliancy depend upon the shape of the illuminant, light flux is independent thereof. Illumination is a quantity which depends not only on the source of light, that is, light flux and flux density, but also on the illumi- nated objects and their nature, and thus is the light flux density as modified by the illuminated objects. Very commonly, how- ever, the term " illumination'' is used to denote "light flux density," irrespective of the illuminated objects. 112. The light flux thus is the raw material with which illuminating engineering starts, and the first problem then is to distribute the light flux through space so as to give at all points the light flux density required for satisfactory illumi- nation. Some problems, as the lighting of a meeting place, school- room, etc., require a uniform or general, and fairly high intensity of illumination, while in street lighting a uniform but fairly low intensity of illumination is desirable. In other cases, mainly a local or concentrated illumination is needed. Usually, however, a combination of a local or concentrated illumination, of fairly high intensity, with a general illumination of lower intensity, is required: the former at those places where we desire to distinguish details, as where work is being done, at the reading- table, work bench, dining-table etc., while the general illumina- tion is merely for orientation in the space, and thus may be of lower intensity, and for reasons of economy, and also physio- logical reasons, should be of lower intensity. We thus have to distinguish between local or concentrated, and general or uniform, illumination, and a combination of both, and have to distribute the light flux in accordance there- with, that is, produce a high flux density at the points or areas requiring high concentrated illumination, a low and uniform flux density throughout the remaining space. This can be done by choosing a light source of the proper distribution curve, as, for instance, in street illumination a lamp ILLUMINATION AND ILLUMINATING ENGINEERING. 261 giving most of the light flux between the horizontal and 20 deg. below the horizontal; in many cases of indoor illumination a light source giving most of the light between the vertical and an angle of from 30 to 60 deg. from the vertical depending on the diameter of the area of concentrated illumination and the height of the illuminant above it. It can also be done by modifying or directing the light flux of the illuminant by reflec- tion or diffraction and diffusion, either from walls and ceilings of the illuminated area, or by attachments to the illuminant, as reflectors, diffusing globes, diffracting shades, etc. Further- more, the required flux distribution can be secured by the use of a number of illuminants, and with a larger area this usually is necessary. Frequently the desired flux distribution is pro- duced by using an illuminant giving more light flux than neces- sary, and destroying the excess of flux in those directions where it is not wanted, by absorption. Obviously this arrangement is uneconomical and thus bad illuminating engineering; the desired flux distribution should be secured economically, that is, without unnecessary waste of light flux by absorption, and this usually can be done by a combination of a number of light sources of suitable distribution curves. The most economical method of securing the desired distribution curve obviously is to choose a light source coming as near to it as possible, and then modifying it by reflection or diffraction. 113. Thus far, the problem is one of physics, and the result, that is, the objective illumination, can be measured by photometer or luminometer, and thus checked. The duty of the illuminat- ing engineer, however, does not end here, but with the same objective illumination, that is, the same distribution of light flux throughout the entire illuminated area, as measured by photometer, the illumination may be very satisfactory, or it may be entirely unsatisfactory, depending on whether the physio- logical requirements are satisfied or are violated ; and very often we find illuminations which seem entirely unsatisfactory, tiring, or uncomfortable, but when judged by the density and the distribution of the light flux, should be satisfactory. Even numerous commercial illuminants, designed to give suitable distribution curves, fail to do justice to their light flux and its distribution, by violating fundamental physiological require- ments. 262 RADIATION, LIGHT, AND ILLUMINATION. The physiological problems of illumination, that is, the effects entering between the objective distribution of light flux in space, and the subjective effects produced on the human eye, thus are the most important with which the illuminating engineer has to deal, and the first feature which must be recognized is that the objective illumination, as measured by the photometer, is no criterion of the subjective illumination, that is, the physiological effect produced by it, as regard to clearness, comfort and satis- faction, and it is the subjective illumination by which the success of an illuminating engineering problem is judged. The most important physiological effects are : (a) The contraction of the pupil. The pupil of the eye auto- matically reacts, by contraction, on high brilliancy at or near the sensitive spot, that is, the point of the retina, on which we focus the image of the object at which we look, and to a some- what lesser extent on high brilliancy anywhere else in the field of vision. If, therefore, points or areas of high brilliancy are in the field of vision, especially if near to objects at which we look, the pupil contracts the more the higher the brilliancy, and thereby reduces the amount of light flux which enters the eye, that is, produces the same result as if the objective illumination had been correspondingly reduced, intensified by the uncomfortable effect of seeing high brilliancy. The exist- ence of points of high brilliancy in the field of vision thus results in a great waste of light flux, and additional discomfort, and, for satisfactory illumination, points of high brilliancy thus must be kept out of the field of vision. Light sources of high brilliancy must be arranged so that they cannot directly be seen, but the illumination accomplished by the light reflected from ceilings, etc., or from reflectors attached to the illuminant: indirect light- ing; or at least the light sources should be located where we are rarely liable to look at them, that is, with moderate-sized rooms, at or near the ceilings. Or light sources of moderate intrinsic brilliancy should be used, as the Moore tube, the mercury lamp, the Welsbach mantel. Or, with illuminants of high brilliancy, as the electric arc, the incandescent lamp (especially the tungsten filament), etc., the brilliancy of the illuminant must be reduced by enclosing it with a diffusing or diffracting globe or shade, as an opal or frosted or holophane globe, etc. ILLUMINATION AND ILLUMINATING ENGINEERING. 263 No illumination, however, can be satisfactory in which the eye at any time can be exposed to the direct rays from a tungsten filament or an arc. While the methods of removing the high brilliancy of the illuminant usually involve a considerable loss of light flux, by absorption at the refracting surface, in the frosted or opal globe, etc., and the objective illumination thus is de- creased, if the methods of reducing the brilliancy are anywhere reasonably arranged, the light flux entering the eye, and thus the subjective illumination, is increased, and often very greatly. Thus while frosting an incandescent lamp decreases its light flux by about 15 per cent, in spite thereof usually more light flux enters the eye from the frosted lamp than from a clear glass lamp at the same distance. It is, therefore, inefficient to use illuminants of high brilliancy in the field of vision, and in addition makes the illumination uncomfortable and thereby unsatisfactory. Physiologically the brilliancy of the light source thus is one of the most important quantities. 114. (b) Fatigue. When exposed to fairly high light flux den- sity, that is, high illumination, the nerves of the eye decrease in sensitivity, by fatigue, and inversely, in lower illumination or in darkness, increase in sensitivity. This reaction, or adjust- ment of the sensitivity of the nerves of vision to different intensi- ties of illumination, enables us to see equally well in illuminations varying in intensity by more than 10,000 to 1 (as daylight and artificial light). Thus, when entering a well-illuminated room from the darkness, it first appears glaring, until gradually the impression fades down to normal. Inversely, coming from a well-lighted room into a space of much lower illumination, it first appears practically dark, until gradually the eye adjusts itself, that is, the nerves of vision increase in sensitivity by their rest, and then we again see fairly well. Fatigue and contraction of the pupil thus are similar in their action, in that they reduce the physiological effect for high intensities. The contraction of the pupil, however, is almost instantaneous, and is a protective action against excessive bril- liancies in the field of vision, while the fatigue is a gradual adjustment to the average intensity of illumination, within the operating range of the human eye. By exposure for a considerable period to the fairly high illumi- 264 RADIATION, LIGHT, AND ILLUMINATION. nation required when working by artificial light, the sensitivity of the eye decreases, the illumination appears less bright, and thus a higher illumination is required than would be sufficient in the absence of fatigue, and the continuous use and absence of rest cause the sensation of strain, that is, irritation or an uncomfortable feeling, as especially noticeable when working or reading for a considerable length of time in rooms having a high uniform intensity of illumination, as meeting-rooms, some libraries, etc. If, however, the eye can rest even momentarily, by a change to lower intensity of illumination, fatigue is decreased, never becomes as complete and uncomfortable, and the concen- trated illumination of the working-table appears brighter than it would without the possibility of rest. A room having a uniform intensity of illumination thus appears glaring and uncomfortable, and for satisfactory illumination it is necessary not only to provide a sufficiently high intensity at the place where needed, but it is just as necessary to keep the intensity of illumination as low as permissible, wherever it is not needed, so as to afford to the eye rest from the fatigue. In some cases, as meeting-halls, schoolrooms, this may not be possible, but a uniform high intensity required, to be able to work or read anywhere in the room. Where, however, it is not necessary, it is not merely uneconomical to provide a uniform high intensity of illumination, but it is an illuminating engineer- ing defect, and a high intensity should be provided, as concen- trated illumination, only at those places where required, as at the reading-tables of the library, but the general illumination should be of lower intensity. While we rarely realize the cause, we feel the superiority of the combination of high concentrated and lower general illumination, by speaking of such illumination as home-like, restful, etc. Especially in places where considerable work has to be done by artificial illumination, as -in libraries, factories, etc., to get satisfactory results, it is important to consider this effect of fatigue, and to properly combine a moder- ately low general illumination with a local higher intensity of illumination at the places of work. The latter can usually be given by a light source having a downward distribution, located sufficiently high above the place of work. The average standing or reading lamp, however, generally is not sufficiently high to accomplish the result. Obviously, in such local illumination, ILLUMINATION AND ILLUMINATING ENGINEERING. 265 the brilliancy of the illumination must be kept low, as discussed above. Of considerable importance regarding fatigue is the quality, that is, the color, of the light : fatigue at high intensities occurs far more with yellow and orange rays than with white light, and very little with green and bluish-green light. Thus, in arti- ficial illumination, in which practically always the yellow and orange rays greatly preponderate, the question of fatigue is fai more important than with the bluish-white diffused daylight, and the irritating effects of fatigue thus are mostly felt with artificial illumination. 115. (c) Differences. Objects are seen and distinguished by differences in quality, that is, color, and in intensity, that is, brightness, of the light reflected by them. If there were no differences in color or in intensity throughout the field of vision, we would see light but would not distinguish objects. Therefore, in good illumination, the differences in color and in intensity should be sufficiently high to see clearly by them, but still limited so as not to preponderate to such extent as to distract the atten- tion from smaller differences. The differences in intensity, to give distinction, should be high, but at the same time are limited by the phenomena of fatigue and of the contraction of the pupil: the minimum intensity must still be sufficiently high to see clearly, and the maximum intensity not so high as to cause fatigue and contraction of the pupil, much beyond that corresponding to the average intensity, otherwise the vision becomes indistinct and unsatisfactory, and uncomfortable by too much contrast; that is, the intensity differences must give a sufficient, but not an excessive, contrast, if the illumination is to be satisfactory. Differences in quality, that is, in color, are to a limited extent only under the control of the illuminating engineer. In some cases the illuminating engineer can control or advise regarding the color of objects, as the walls, ceilings, etc. In most cases, however, the absolute color of the illuminated objects is not within the control of the illuminating engineer: for instance, in street lighting, the color of the street surface, its surroundings, as vegetation, houses, etc., are fixed and cannot be changed for effects of illumination. So also in most cases of indoor illumina- tion. To some extent, however, the subjective color can be con- 266 RADIATION, LIGHT, AND ILLUMINATION. trolled by the choice of the proper shade of light, and thereby slight color differences increased and made more distinct, or decreased and thus obliterated. For instance, the color resulting from age and dirt is usually the color of carbon and of iron, yellowish brown or reddish brown, that is, colors at the long wave end of the spectrum. Spots and blemishes due to dirt or age, thus are made more distinct by using an illuminant defi- cient in the long waves of light, as the mercury lamp, while in- versely they are decreased by using a reddish-yellow illuminant, as the incandescent lamp or the candle. Thus the white arc lamp and still more so the bluish-green mercury lamp shows blemishes and slight color differences of age and dirt harsh and exaggerated, while the yellow light softens them and makes them disappear; and while, for a ballroom, the yellow light is thus preferred, and the mercury arc or even the ordinary white carbon arc would give a harsh and disagreeable effect, inversely the yellow light would be unsuitable where such slight differences should be distinguished. It is therefore essential for the illuminating engineer to choose as far as it is feasible the proper color of light, and an otherwise good illumination may be spoiled by using too white or too yellow a light. The main distinction of objects, however, is due to differences in intensity or brightness, and, for producing these, the shadows are of foremost assistance, and indeed the differences of inten- sity, by which we see objects, are to a large extent those due shadows. The study of the shadow thus is one of the most important subjects of illuminating engineering. If we have no shadows, but a perfectly diffused illumination, even if the intensity of illumination is sufficient, the illumination is unsatis- factory, as we lose the assistance of the shadows in distinguishing objects, and therefore find seeing more difficult, the illumination restless and uncomfortable. The use of shadows for illumination requires that we must have directed light, that is, light coming from one or a number of sources, and thus causing shadows, and not merely diffused illumination, that is, light coming from all directions and thus causing no shadows. While, however, in general perfectly dif- fused illumination is unsatisfactory, an illumination having only directed light is also unsatisfactory. If the light is all directed, as from a single arc, the shadows are absolutely black, we can- ILLUMINATION AND ILLUMINATING ENGINEERING. 267 not see anything in them, and, in attempting to see the objects in the shadows, the illumination becomes tiring to the eyes, irritating and restless. For satisfactory illumination, it therefore is necessary to have sufficient directed light to mark the edge of the objects by their shadow, and thereby improve distinction, but at the same time sufficient diffused light to see clearly in the shad- ows; that is, a proper proportion of directed and diffused light is necessary. In cases in which all the objects assume practically the same color, as in flour mills or foundries, a diffused illumination without shadows would make the illumination so bad as to be practically useless. In other cases, as a drafting-room, where all the objects requiring distinction are in one plane, as the drafting board, and the distinction is exclusively by differences of color and intensity, but not by shadows, a perfectly diffused illumination is required, and shadows would be objectionable and misleading, and this is one of the cases where directed light is objectionable. While with a single light source all the light issuing from it is directed light, by using a number of illuminants, the overlap of their light fluxes causes more or less light to reach objects from all directions, and thereby gives the effect of diffused light, except at those places where the shadows cast by the different light sources coincide, and by proper positions of sufficient numbers of light sources this can be avoided. The use of a number of light sources thus offers a means of increasing the proportion of diffused to directed light. 116. It is not sufficient, however, to have merely a combination of diffused and directed light in the proper proportion, but the direction of the latter also is of importance. In some simple cases this is obvious, as, in writing, the directed light should be from in front on the left side above the table, so as not to cast the shadow on the work. The purpose of the shadow in illumination is to mark the edge of the object, and its height by the length of the shadow. The shadow, therefore, should not extend too far from the object to which it is related, other- wise it loses its close relation to it and becomes misleading and thereby interferes with good illumination. Thus the directed light should come from above, that is, in a direction making a considerable angle with the horizontal, so as to limit the length 268 RADIATION, LIGHT, AND ILLUMINATION. of the shadow without, however, being vertical, as the latter would largely obliterate shadows. Perhaps an angle of 45 to 60 degrees with the horizontal would be most satisfactory. The practically horizontal shadows cast in the usual form of street lighting therefore are not satisfactory for best illumi- nation. The number of shadows is of less importance. While in nature objects have one shadow only, cast by the sun, indoors we are familiar with seeing several shadows due to the diffused day- light from several windows. Of high importance, however, is the shape of the illuminant, in so far as it determines the outer edge of the shadow. The purpose of the shadow is to give an intensity difference at the edge of the object, and thereby make it easier to see the object. The shadow, however, has another edge, its outer end, and that we should not see, as no object ends there, or at least it must be such that it cannot be mistaken for the edge of an object. The problem thus is not merely to provide sufficient directed light to cast a shadow, but the shadow should be such that only one side, at the edge of the object, is sharply defined, while the other edge of the shadow, which ter- minates on the flat surrounding surface, should gradually fade or blur. If we have to look closely to determine that the outer edge of the shadow is not the edge of another object, the strain of distinguishing between the edge of an object and the edge of a shadow makes the illumination uncomfortable and thus unsatisfactory. In the shadows cast by a single arc in a clear glass globe, this difficulty of distinguishing between the edge of a shadow and the edge of an object is especially marked, and, combined with the invisibility of objects in the shadow, makes such shadows appear on first sight like ditches or obstructions. In the use of shadows in illuminating engineering it thus is necessary to have the outer edge of the shadows blur or gradually fade, and this requires that the source of directed light be not a point, but a sufficiently large area to scatter the light at the outer edge of the shadow, preferably even more than is the case with the shadows cast by the sun. This requires enclosing the illuminant by a fairly large opal globe or other similar device ; that is, have the light issue from a fairly large luminous area. It must be recognized that the proper treatment of the shadows ILLUMINATION AND ILLUMINATING ENGINEERING. 269 is one of the most important problems determining the success or failure of an illumination. 117. Color sensitivity. The maximum of sensitivity of the eye shifts with decreasing illumination from yellow to bluish green, and where a low intensity of illumination is used, as in street lighting, a source of light which is rich in the shorter waves, that is, a white light, is superior in its physiological illuminating value to a yellow light of the same or even higher light flux, while inversely at high values of illumina- tion, as for decorative purposes, the yellow light is more effective. Therefore it is a mistake to choose a yellow light source for illumination of very low intensity, or a white or bluish-green light for illumination attempting high intensity effects. Thus, for the average street lighting of American cities, the white arc is superior to the yellow flame arc, but, to produce a glare of light, the latter would be superior. While there are further physiological effects which are of im- portance in illuminating engineering, the above four may illus- trate the long step which exists between the distribution of the light flux as measurable by the photometer, and the success or failure of the illumination represented by it. The requirements of satisfactory illumination can thus be grouped in two main classes, referring respectively to economy and to comfort, and the characteristics are: (1) General or uniform, and local or concentrated illumination, and combination of both. This is of importance for economy : to avoid the production of unnecessary light flux; and comfort: to reduce the effect of fatigue. (2) Diffused and directed illumination, and combinations of both, and the theory of the shadow. This is of importance for the comfort of illumination, in securing clearest distinction. (3) Quality or color of light, of importance in economy, to suit the color to the intensity of illumination, and to comfort, in increasing or softening differences in color shades. (4) Massed and distributed illumination, as controlling the distribution of the light flux, and thereby the economy and also the diffusion. (5) Direct illumination and indirect illumination, shaded, diffracted, diffused, or reflected light, in its relation to the bril- 270 RADIATION, LIGHT, AND ILLUMINATION. liancy of the light source, and thereby the effect of the contraction of the pupil, on economy and comfort. Some of the common mistakes made in illumination are: (1) Unsatisfactory proportion of general and of concentrated light. (2) Exposure of high brilliancies in the field of vision, as naked filaments. (3) Unsuitable proportion of diffused and directed light. (4) Improper direction of directed light and thereby improper length of shadows. (5) Sharp edges of shadows. In order to illustrate the preceding principles, some typical cases may be considered : (a) Domestic lighting. 118. Domestic lighting usually requires a combination of a concentrated illumination of fairly high intensity locally at the work-table, dining-table, etc., and a general illumination of low intensity, to secure comfort and economy. Occasionally, as in halls, etc., the local lighting is absent and only general illumina- tion required, while for instance in a sick room the general illumi- nation is absent and only local illumination required. In this illumination the proportion between directed and dif- fused light should be such as to give the proper effect of shadows. The problem of domestic illumination thus is to produce a defi- nite distribution of light flux density, with a definite proportion between diffused and directed light. If we deviate from the proper proportion on one side, the room appears cold and uncom- fortable; if we deviate in the other direction, it appears dark and gloomy. The light issuing directly from a single illuminant is directed light; the light issuing from a number of illuminants is diffused in proportion to the number of sources by the overlap of the light fluxes of the illuminants. The light reflected from walls and ceilings is diffused light. The proportion between the light reflected from walls and ceilings, or the indirect light, and the direct light from the illuminants, varies with the reflecting power of walls and ceilings, that is, their brightness or darkness. The proportion between directed and diffused light thus can be changed, and the diffused light increased by increasing the num- ber of illuminants, and also by increasing the brightness of walls ILLUMINATION AND ILLUMINATING ENGINEERING. 271 and ceilings. With a given brightness of walls and ceilings, the desired distribution of the light flux a local high and general low intensity can be produced by a single illuminant having the proper distribution curve of light flux. In this case, however, usually we get too much directed, and not enough diffused, light. The same distribution of light flux can be produced by a number of illuminants properly located : nearer together for the local than for the general illumination. In the latter case we get more diffused and less directed light, and thus by choosing the number of light sources it is possible, with any given brightness of walls and ceilings, to get the desired distribution of light flux and at the same time the proper proportion of directed and diffused light. With a different brightness of walls and ceilings, the dis- tribution curve of a single light source, required to give the desired light flux distribution, is correspondingly changed, and, the lighter the walls and ceilings, the more light is reflected, giving a diffused general illumination, and thus less direct light from the illuminant is required for the general illumination. With in- creasing reflecting power of walls and ceilings, the proportion of diffused light increases, and the number of light sources which are required to give the proper proportion between directed and diffused light is decreased, and inversely it is increased with increasing darkness of walls and ceiling. Therefore, in a room with light walls, a smaller number of light sources is required for good illumination than in a room with dark walls, assuming the same intensity of local and of general illumination. 119. The problem of domestic illumination: to get a certain distribution of illumination, with a definite proportion between directed and diffused light, thus leaves one independent variable the brightness of walls and ceilings. This is necessary, as the problem of domestic illumination is twofold: to get the proper illumination by means of the daylight, and also to get it for artificial illumination. During daytime, the windows are the source of light, the directed light issues from the windows, the diffused light from the walls and ceilings and by the overlap of the light from several windows. The proper distribution between local and general illumination during daytime, and at the same time the proportion of directed and diffused light, thus deter- mines the number of windows and the brightness of walls and ceilings, in the manner as discussed before. 272 RADIATION, LIGHT, AND ILLUMINATION. As the reflecting power of walls and ceilings is fixed by day- light considerations, it cannot be chosen, or at least only to a limited extent, by considerations of artificial illumination, but, as found above, this is not necessary, since by a combination of a suitable number of light sources of proper distribution curves the problem of artificial illumination may be solved. To some extent, due to the quality of artificial light and daylight, the walls can give a different reflecting power for the one than for the other. As artificial light is deficient in blue and green, a bluish or greenish shade of walls and ceilings gives them a greater reflect- ing power for daylight than for artificial light which usually is desirable and inversely with a reddish-yellow shade. (b) Street Lighting. 120. The problem of street illumination is to produce a uni- form low intensity. For reasons of economy, the intensity must be low, at least in American cities, in which the mileage of streets, for the same population, usually is many times greater than in European cities, and, at the same time, the same type of illumi- nant is usually required for the entire area of the city. The low intensity of illumination requires the quality of light which has the highest physiological effect at low densities, that is, white light, and excludes the yellow light as physiologically inefficient for low intensities. Still better would be the bluish green of the mercury lamp, but is not much liked, due to its color. Quite satisfactory also is the greenish yellow of the Welsbach mantel for these low intensities. The American practice of preferring the white light of the carbon or magnetite arc thus is correct and in agreement with the principles of illumination, and the yellow -flame arc can come into consideration even if it were not handicapped by the necessity of frequent trimming only in those specific cases where a high intensity of illumination is used, as would be only in the centers of some large cities. Uniformity of illumination is specially important in street light- ing, where the observer moves along the street, and, due to the low intensity, the decrease of subjective illumination by fatigue is especially objectionable. For a street illuminant, a distribu- tion curve is required which gives a maximum intensity some- what below the horizontal, no light in the upper hemisphere, and very little downward light. Street lamps therefore should be judged and compared by the illumination given midways be- ILLUMINATION AND ILLUMINATING ENGINEERING. 273 tween adjacent lamps, or at the point of minimum intensity, or, in other words, by the intensity in a direction approximately 10 deg. below the horizontal. This also is in agreement with American practice. However, it is very important that the downward intensity be very low, and in this respect it is not always realized that the light thrown downward is not merely a waste of light flux, but is harmful in producing a glaring spot at or near the lamp and, by the fatigue caused by it, reducing the effective illumination at the minimum point between the lamps. Most objectionable in this respect is the open direct current car- bon arc and those types of lamps giving a downward distribution, but even with the enclosed arc lamp the distribution of light on the street surface is still far from uniform, and the intensity too high near the lamp, and in this respect improvements are desirable. 121. The greatest defects of the present street illumination, which frequently makes it inferior in subjective illumination even to the far lower illumination given by the full moon, are the absence of diffused light, and especially the improper direction and termination of the shadows, and also the high brilliancy of the illuminant. The light of the usual street lamp is practically all directed light, issuing in a nearly horizontal direction from a point source. Thus the shadows are far longer than permissible, and terminate sharply and without blur; objects in the shadows are practically invisible, and the end of the shadow looks like the edge of an object, thus producing a misleading effect, which results in unsatisfactory illumination. To give a somewhat better direction to the light requires considerable increase of the height of the lamp above the street surface. This also would essentially decrease the intensity of illumination below and near the lamp, without appreciably affecting the intensity at the minimum point, and thus would give a more uniform and thereby better illumination. No valid reason usually exists against greatly increasing the height of the lamps, except that of the greater cheapness of short lamp posts, which is hardly justifiable. It is, however, more difficult to give a proper blur to the ends of shadows, so as to distinguish them from edges of objects. This would require an increase of the surface of the illuminant, by opal or frosted globe, etc. Enclosing the arc by an opal globe, however, scatters the light more uniformly in all directions, and 274 RADIATION, LIGHT, AND ILLUMINATION. thereby spoils the distribution curve, and interferes with the required uniformity of illumination: with an opal globe, the intensity in the downward direction does not differ very much from that in the horizontal, while with lamps 20 feet above the street level, and at distances of 200 feet from each other, the downward intensity for uniform illumination should be not much more than one-twenty-fifth of that under an angle of sin < = 20 - = 0.2; or 12 deg. below the horizontal. Very much better is 100 the effect of a frosted or sand-blasted globe. The best way of maintaining a proper distribution curve and at the same time diffusing the light, so as to reduce its brilliancy and blur the shadows, appears the use of prismatic diffraction, on the principle of the Fresnel lenses of lighthouses (holophane). Obviously, where the lamps are close together, as in the center of large cities, their light fluxes overlap and thereby give a better diffusion, and, at the same time, the midway point between lamps is under a greater angle against the horizontal ; thus a more downward dis- tribution of the light flux permissible. For the largest part of American street lighting, however, this does not apply. 122. In the early days of using arc lamps for American city lighting, lighting towers were frequently used, and such tower lighting has still survived in some cities. One or a number of arc lamps are installed on a high tower and were supposed from there, like artificial suns, to spread their light over an entire city district. This method of city lighting was found unsatisfactory, as it did not give enough light. It is unsatisfactory, however, not in principle, but because it was too ambitious a scheme. If, in street illumination, we double the distance between the lamps, each unit must have four times the light flux to get the same minimum flux density, as the distance is doubled, and the flux density decreases with the square of the distance. At twice the distance between the lamps, each lamp thus must have four times the light flux, and each mile of street thus requires twice the power. Reducing the distance between lamps to one- half reduces the power to one-half with the same minimum illumination. In street lighting it is therefore of advantage to use as many units of illuminants as possible, and bring them together as close as possible, and correspondingly lower their ILLUMINATION AND ILLUMINATING ENGINEERING. 275 intensity, up to the point where the increasing cost of taking care of the larger number of units and increasing cost of poles and connections compensates for the decreasing cost of energy. There is a minimum which probably is fairly near our present practice. When, however, you come to square and exposition lighting, you find that the distance between the illuminants has no effect on the efficiency. Let us assume that we double the distances between the lamps which light up a large area. Then each lamp requires four times the light flux to get the same minimum flux density between the lamps, but at twice the distance between the lamps each lamp illuminates four times the area, and the total power per square mile of lighting a large area, like an exposition, thus is independent of the number of lamps used, and, whether you place them close together or far apart, you require the same total flux of light, and if you keep the same proportions of height from the ground and distance between lamps, you also get the same variation between maximum and minimum intensity. But, supposing the lamps to be placed further apart, the maximum or minimum points also are further apart, and you get a more satisfactory illumination by having a less rapid intensity variation. That points to the conclusion that, for exposition lighting, the most efficient way would be to use a relatively moderate number of high-power sources of light on high towers at distances from each other of the same magnitude as the height of the towers. We would get a greater uniformity and better physiological effect by having the illumi- nants further apart, and they would require the same total light flux, and therefore the same power, as if you bring the lamps close to the ground, and place them very close to each other. The tower lighting therefore is the ideal form for lighting a large area. W 7 hen the arc was first introduced, it was so much superior to any other illuminant known before, that people vastly over- rated it. They thought that they could light the whole city by it, and in trying to do so these towers would have been the proper way, but very soon it was found that even with the effi- ciency of the arc, to light not only the streets, but the whole area of the city, would require an entirely impracticable amount of light flux. It thus was too ambitious a scheme for city lighting, but it should be done in exposition work. City illumi- 276 RADIATION, LIGHT, AND ILLUMINATION. nation thus has come down from this first ambition to light the whole city to an attempt to light only the streets. For the latter purpose, however, lighting towers are inefficient, since much of the light flux is wasted on those places which we no longer attempt to light. In exposition lighting, however, the most effective general illumination would be given by white arcs on high towers, leaving the concentrated or decorative illumination to the incandescent lamp and flame arc, of yellow color. LECTURE XIII. PHYSIOLOGICAL PROBLEMS OF ILLUMINATING ENGINEERING. 123. The design of an illumination requires the solution of physiological as well as physical problems. Physical considera- tions, for instance, are the distribution of light -flux intensity throughout the illuminated space, as related to size, location and number of light sources, while the relation, to the satisfac- tory character of the illumination, of the direction of the light, its subdivision and diffusion, etc., are physiological questions. Very little, however, is known on the latter, and the entire field of the physiological effects of the physical methods of illumination is still largely unexplored. As result thereof, illuminating engineering is not yet an exact science, as is, for instance, apparatus design, but much further physiological investigation is needed to determine the requirements and conditions of satisfactory illumination. The physical side of illuminating engineering: to produce a definite light flux density throughout the illuminated space, is an engineering problem, which can be solved with any desired degree of exactness, usually in a number of different ways. The solution of the physical problem of light distribution, however, does not yet complete the problem of illuminating engineering, does not yet assure a satisfactory illumination, but with the same distribution of light flux density throughout the illuminated surface, the illumination may be anything between entirely unsatisfactory and highly successful, depending on the ful- fillment or failure to fulfill numerous physiological requirements. Some of these are well understood and such that they can be taken into consideration in the physical design of the illumina- tion, and thus no excuse exists to fail in their fulfillment, though it is frequently done. Such, for instance, is the requirement of low intrinsic brilliancy in the field of vision, of the color of the light, etc. Other physiological requirements are still very little 277 278 RADIATION, LIGHT, AND ILLUMINATION. understood or entirely unknown, while on others not sufficient quantitative data are available for exact engineering calculation. Thus, for instance, the usual suburban street illumination, with arcs spaced at considerable distances from each other and located on fairly low posts, is very much inferior to the illumina- tion given by moonlight, even when allowing for the difference in intensity. Here the reason of the unsatisfactory character of the former illumination is mainly the almost horizontal direc- tion of the light flux. A perfectly vertical direction of the light flux again is unsatisfactory in many cases, and the most satis- factory results are given by a direction of the light flux which makes a considerable angle with the horizontal as well as the vertical direction. Thus, when dealing with directed light, the direction angle is of essential physiological importance. We have very little exact knowledge to guide in the determination of the proper angle in which to direct the light flux; it is known that in general approximately horizontal and approximately vertical direction of the light flux are objectionable, and an in- termediary angle gives best results. However, the horizontal direction usually is objectionable by excessive contrasts, the vertical direction by flatness in the appearance of the illuminated objects, and, depending on the nature of the objects, sometimes the one, sometimes the other feature may be more objectionable. Hence, the best angle of incidence of the light depends on the nature, that is, the shape and location, of the illuminated objects, on the purpose of the illumination, etc., and thus is not con- stant, but is a function of the problem, which is still largely unknown. 124. Not represented by the physical distribution curve of illumination, but very marked in their physiological effect is the difference between directed light and diffused light. In most problems of illumination, either entirely directed light or entirely diffused light is unsatisfactory, and a combination of directed light and diffused light is required, as discussed in the preceding pages. No exact knowledge, however, exists on the proportion in which directed light and diffused light should be combined for satisfactory illumination, nor how this proportion varies with the nature, color, etc., of surrounding objects, with the purpose of the illumination, etc. That it varies is well known, as for some purposes, as a draughting room, entirely diffused light PHYSIOLOGICAL PROBLEMS. 279 seems best suited, while for other purposes mainly directed light seems more satisfactory. Furthermore, the relations between directed and diffused light have in the illuminating engineering practice been obscured to some extent by the relation between high and low intrinsic bril- liancy and between direct and indirect lighting. Thus, to eliminate the objectionable feature of high intrinsic brilliancy of the illuminant, direct lighting by light sources of high brilliancy, which was largely directed lighting, has been replaced by indirect lighting, by reflection from ceilings, etc., which is diffused light- ing. Where such change has resulted in a great improvement of the illumination, it frequently has been attributed to the change from directed to diffused lighting, while in reality the improve- ment may have been due to the elimination of high brilliancy light sources from the field of vision, and engineers thereby led to the mistaken conclusion that perfectly diffused lighting is the preferable form. Again, in other instances such a change from direct to indirect lighting has not resulted in the expected im- provement, but the indirect lighting been found physiologically unsatisfactory, and the conclusion drawn that the elimination of high brilliancy from the field of vision has not been beneficial, while in reality the dissatisfaction with the indirect light was due to the excess of diffused light and absence of directed light, and this improper proportion between directed and diffused light more than lost the advantage gained by eliminating the light sources of high brilliancy from the field of vision. In this case the proper arrangement would have been to reduce the brilliancy of the light sources, by diffusing or diffracting globes, to a suffi- ciently low value, but leave them in such position as to give the necessary directed light. Thus, in illuminating engineering, as in other sciences, it is very easy to draw erroneous conclusions from experience by attributing the results to a wrong cause. Any change in the arrangement usually involves other changes: as in the above instance, the change from high to low brilliancy commonly causes a change from directed to diffused light; by attributing the results to a wrong cause, serious mistakes thus may be made in basing further work on the results. 125. In discussing diffused light, we must realize that the meaning of " diffused light" is to some extent indefinite. To 280 RADIATION, LIGHT, AND ILLUMINATION. define diffused light as light which traverses the space in all direc- tions and thus casts no shadow, is not correct, since even diffused daylight casts shadows. For instance, if in Fig. 122 P is the sur- FIG. 122. face of the ground and A a flat circular shade at distance I above the ground, the intensity distribution of the light in plane P is as shown in Fig. 122 for Z = 0.2 A, thus showing a fairly dark shadow beneath the center of A, but a shadow which blurs so very gradually that with most objects it is not marked. The light from a single point source is perfectly directed light; it traverses every point of space in one single direction only, as shown as A in Fig. 123. If we now enclose the point source in an opal globe, which then becomes the radiator, as discussed before, as diagrammatically shown as B in Fig. 123, the light flux traverses each point not in a single direction but in all directions within a narrow angle a, which is the angle subtended by the radiator L from the point P. With increasing size of the illuminant, and thus increasing angle a, (7, Fig. 123, the pencil of rays, which traverses point P, gradually spreads, until, when a becomes 180 deg., we get perfectly diffused light, similar to daylight. Hence, with a gradual change of the diameter of the illum- inant, from a = to a = 180 deg., the light gradually changes from directed to diffused light. Thus, no sharp dividing line FIG. 123. PHYSIOLOGICAL PROBLEMS. 281 can be drawn between directed light, and diffused light, but the directed light from a light source of considerable diameter (that is, a diameter which is not neglible compared with the dis- tance of the illuminated objects from the light) already has to some extent the character of diffused light. Diffused light thus may be denned as light given by a radiator which subtends a spherical angle equal to a considerable part of the sphere. This makes the term "diffused light" a relative term. Near to a radiator of considerable size, the light given by this radiator thus is largely diffused light, while at considerable distance it is practically directed light, or, in other words, the light given by light sources of considerable size is directed light only at such distances from the radiator at which the law of inverse squares holds; but approaching the radiator so far that this law of inverse squares (flux density inverse proportional to the square of the distance) does not hold, the light approaches somewhat the character of diffused light. The physiological effects, however, during a gradual change from a = 0, or directed light, to a = 180 deg. , or diffused light, apparently do not change uniformly, but new effects appear and others disappear. 126. The main objection to directed light from a single source results from the absence of light in the shadows. Using, how- ever, two or more illuminants, that is, combining directed light of several widely different directions, the shadow cast by one illuminant is illuminated by the other illuminants, and thus an effect produced very similar to diffusion. Thus with two light sources, at a point at which both light sources give the same illumination, the intensity in the shadow cast by one illuminant is still 50 per cent, that is, the illumination the same as if equal volumes of directed and of diffused light were combined, and to a considerable extent the physiological effect is the same. It is not completely so, however. In the illumination by equal volumes of diffused light and directed light from a single source, each object casts a single shadow, in which the illumination is reduced to half. When producing an equivalent diffusion by two light sources, an object casts two shadows, in which the illumination is reduced to half (if the two light sources give equal illumination), but, where the shadows overlap, a perfectly black and lightless shadow is produced. The more the two 282 RADIATION, LIGHT, AND ILLUMINATION. half shadows overlap to a complete shadow, the less the combina- tion of the two light sources is equivalent to diffusion. At the same time, occasionally the existence of two or more half shadows and of their compound shadows may assist distinction, and thereby be advantageous. In short, there is a vast and largely unexplored field in the physiology of illumination, which the illuminating engineer will have to study and investi- gate. While one point source of light gives directed light, two sources at distances from each other give an effect equivalent to diffusion, and three or more sources still more so, until in the theoretical case of an infinite number of point sources distributed through space or, practically, a very large number of distrib- buted illuminants we get perfect diffusion. With a change from a single to a very large number of illuminants, the illumi- nation thus changes from directed to diffused, and thus, for a moderate number of illuminants, is intermediate between directed and diffused, but nevertheless this intermediate state is physiologically of entirely different character from that given by a single illuminant of very large diameter, that is large angle a, as discussed above. 127. We thus have true diffused light, as daylight, the equiva- lent diffusion given by the combination of several light sources, which depends on their relative location, and the equivalent diffusion given by a large relative diameter of the light source. The latter again varies with the shape of the light source, and in extreme cases, as a linear straight radiator, as a Geissler tube (Moore tube), we may get an illumination which, at any point of space, is practically diffused in one direction, and practically directed in a direction at right angle to the former. In such cases we again get different physiological phenomena. For instance, a straight rod, held parallel to the radiator, casts a sharp black shadow directed light while, when held at right angles to the radiator, it casts no shadow diffused light. With objects of more irregular shape, it can be seen that the shape and appearance of the shadows give a rather interesting problem, and the physiological impression made by such illumination thus is different again, from that of ordinary directed or diffused light or their combination. In general, wherever two or more illuminants are used, the PHYSIOLOGICAL PROBLEMS. 283 physiological effect depends on the relative position of the light sources to the illuminated objects, irrespective of the intensity of illumination. Thus, for instance, in the illumination shown in Fig. 117, on the same curve of equal illumination, the physiologi- cal effect is not constant, but varies from point to point. On the curve of 850 near the center of the room, an object casts four shadows of approximately equal intensity, in different direc- tions. The shadows are sufficiently marked to assist in seeing, and the illumination in the shadow is quite high ; thus the illumi- nation is very satisfactory. On the same curve 850, near the edge of the room, the four shadows fall in nearly the same direction, only one is marked, and by the overlap of the shadows a large compound shadow is formed, in which the illumination is very low, distinction difficult, and the illumination thus unsatisfactory. Thus with the same physical value of illumina- tion, on the same curve 850, the physiological effect in this case changes from a very satisfactory illumination at one place, to a quite unsatisfactory illumination at another place. Thus, in this instance, while the solution of the illuminating problem, given in Fig. 117, is physically perfect, that is, the illumination very uniform throughout the entire room, and the efficiency high, physiologically the illumination is satisfactory only in the middle of the room, but becomes more and more unsatisfac- tory the further we go outside of the square formed by the four light sources. Physiologically the illumination would probably be improved by locating the light sources in the four corners of the ceiling, or in the centers of the four sides of the ceiling. Physically, this arrangement of lamps in the corners of the room would greatly reduce the efficiency, thus require either more power, or lower the average illumination; the arrangement of the lamps at the sides would decrease the efficiency less, but would considerably impair the uniformity of illumination, giving a lower illumination near the corners of the room. Furthermore, in illuminating engineering, enters as an impor- tant and largely unknown factor, the effect on the physical and physiological illumination, of the objects in the illuminated space, and of the observer; that is, the light flux distribution and its physiological effect, as depending on the location of light sources and distribution of their light flux through the illuminated space, is not sufficient to solve the problem of 284 RADIATION, LIGHT, AND ILLUMINATION. illumination, but consideration must be given to the changes resulting from the use of the illumination. For instance, in the illumination shown in Fig. 117, and discussed above, the diffused light, 0.250, resulting from reflection from walls and ceiling, is quite considerable, and would be nearly sufficient for giving distinction in the compound shadow of all four illumi- nants, as it exists in a pronounced degree near the walls. Thus even there the illumination would be moderately fair. How- ever, when relying on this diffused illumination to see in the shadow of objects close to the walls, it may not be present, or largely reduced by the shadow of the observer, since, as seen above, diffused light also casts shadows, though the blur at the edges of these shadows is such as to make them very little noticeable. Thus, when approaching close to the walls to look at an object, we may find it shaded from the direct light and from most of the diffused light, thus giving unsatisfactory illumination. Locating the light sources in the corners or the centers of the sides of the room, we get pronounced shadows of the objects located against the walls of the room, and thereby again unsatisfactory illumination, although in this case, physio- logically, considering merely the room without the objects which may be located in it, the illumination would be satisfactory. Thus we may have to sacrifice uniformity of illumination still further, by arranging five light sources, four in the corners of centers of the sides of the room, and one, of larger light flux, in the center of the ceiling. Thus, occasionally, illuminations designed for uniform flux density are not satisfactory, even though the proportion of directed and of diffused light, and the direction of the directed light, is physiologically correct, because the changes resulting from the objects in the room, and the person of the user of the illumination, are not sufficiently considered. 129. The cause of most of these difficulties in dealing with illuminating problems is that, physiologically, light is not a vector quantity; that is, light flux densities cannot be combined by the parallelogram law. Two magnetomotive forces A and B, Fig. 124, acting on the same point P, combine by the parallelogram law to a resultant C; that is, the combined action of A and B is identical with the action of a single m.m.f. C. Thus the m.m.f. existing at any PHYSIOLOGICAL PROBLEMS. 285 point P of space is perfectly characterized by two quantities only the resultant intensity, C, and its direction. If, however, in Fig. 125, A and B represent the two light flux densities produced at point P by two light sources L t and L 2 , their physiological and also their physical action may be entirely different from that of one light flux C derived by combining A and B by the parallelogram law. FIG. 124. In some respects the action of the two separate flux densities A and B is the same, or nearly the same, as that of a resultant flux density C; the illumination of an opaque plane a, located so that both light sources L^ and L 2 are on the same side of the plane, is the same. If, however, the illuminated plane is trans- parent or translucent, and also in regard to the effects of polariza- tion, reflection etc., the effect of the two separate flux densities A and B differs from that of a single resultant C. Entirely different is the effect if the light sources L t and L 2 are on dif- ferent sides of the plane. Thus, with a plane c located in the direction C, the resultant flux density C would give no illumina- tion, while in reality by A and B both sides of the plane are fairly well illuminated. Thus, with the plane in any direction within the angle aj between PL 2 and PA, it receives the same amount of light from A and B as it would receive from C; but in any direction within the angle r = it to, between PA and PB, it receives more light from A and B than it would receive 286 RADIATION, LIGHT, AND ILLUMINATION. from the resultant C, and receives infinitely more light in the direction c (that is, in this direction it receives no light from C). Within this angle T, both sides of the plane are illuminated by A and B, which obviously is never possible by a resultant vector C. In the illumination of a plane, the differences between the ac- tual illumination by A and B and the illumination which would result, if light were a vector quantity, by C, are only those of intensity of illumination. With an object of different shape, however, the phenomenon becomes far more complex. Thus the illumination of a sphere S by the resultant C would be as shown in Fig. 126, half the sphere dark, the other half light, and with a maximum intensity at c, shading off towards zero at the termi- nator mn. The actual illumination as shown in Fig. 127 gives a FIG. 126. FIG. 127. black segment of angle a>, while more than half the circumference of the sphere is illuminated. The maximum intensity is at the same place c, and of the same intensity as in Fig. 126 but the total light flux received by the sphere is far greater than would be received from the resultant C, and is the sum of the light fluxes received from the two light sources. Thus : In the illumination of a sphere the light flux densities are added, irrespective of their direction, and not vectorially com- bined. In the illumination of a plane, by light sources which all lie on the same side of the plane, the light flux densities are vectori- ally combined. PHYSIOLOGICAL PROBLEMS. 287 With other shapes of objects, the total received light flux may even be more than corresponds to the sum of the component flux densities. As in general illumination for distinguishing objects we have to deal with all possible shapes, it thus follows that for the gen- eral problem of illumination the resultant effect is most nearly related to the " total flux density" or " total illumination" as derived by adding, irrespective of their direction, all the light flux densities, as was done in the preceding lectures when dealing with light flux distribution. Only in special cases, as the illumi- nation of a draughting table, the flux density in one particular direction is of importance, and was used as the " horizontal illu- mination" in the instance represented by Figs. 119 to 121. 130. While the resultant effect, or the total illumination, is de- rived by adding the flux densities irrespective of their direction, in the physiological effect, that is, the appearance, the direction plays an essential part. Thus a sphere located as in Fig. 127 looks different than it looks in Fig. 126, even if it receives the same total light flux. Still more marked is this difference with more complex shapes of the illuminated objects. Thus a land- scape looks different with every different position of the sun in the sky, and different again in the diffused light of a cloudy day, irrespective of the intensity of the illumination. Under some conditions sharp contrasts appear, where under other illumina- tions the appearance is flat, and with the change of illumination contrasts disappear in some places, appear in others, etc.; that is, the appearance of a complex body very greatly varies with the character of the illumination, entirely independent of its intensity. With artificial illumination it then is the problem of the illuminating engineer to design the illumination so as to bring out contrasts where required by the purpose of the illumination, reduce them where too great or unnecessary, etc. If we consider the possible personal equations of the user of the illumination as depending on his physical nature, occupation or state, further- more the effect of the color of light and the marked physiological effect which even slight variations in the color shade produce, it can be seen that the success of illuminating engineering prob- lems still largely depends on the judgment of the designer, and this judgment is not yet guided by any extended exact experi- 288 RADIATION, LIGHT, AND ILLUMINATION. ence, thus rather uncertain. An enormous amount of work is still to be done mainly in the field of "engineering physiology," before the design of a system of illumination can approach the same exactness as for instance the design of long-distance trans- mission or other engineering work. INDEX. PAOB Absolute color in illumination 265 Absorption of excess of light flux 261 of light by body 28 spectrum 27 Acclimatization to radiation 59 Acetylene flame 130 standard 178 Acoustic scale of frequency 14 Actual or objective color 33 Adaptability range of eye 38 Albedo of ceiling 246 radiator 85 reflector 212, 215 walls 246 whiteness 30 Allotropic modifications of carbon 81 Alternating arc 114, 116, 125 Alternating current field, frequency and wave length 17 as polarized wave 8 Amyi acetate lamp 177 Analytic action of animal organism 65 Angle of directed light 278 Angstrom unit 7 Animal organism, analytic action 65 Apparent or subjective color 34 Arc characteristics 138 conduction 105 conductor 105, 110 electric 98 efficiency of light production 122 flame 110 Arcing ground, frequency and wave length 17 Arc lamps 151 photometry 182 rectifier 114 spectrum 105 stability curve 144 stream 105 street illumination 234 as unidirectional conductor 113 289 INDEX. PAGE Arc voltage curve 139 Area lighting 275 Armature reaction of arc machine 163 Artificial illumination, domestic lighting. . , 271 more harmful than daylight 54 Auxiliary arc starting main arc 112 Band spectrum 26 Base filament 81 Beam of searchlight, intensity 234 Biological phosphorescence 96 Black 32 body 29 radiation 84, 88 of hydrocarbon flame 134 Blood, opaque for ultra-violet light 58 transparent for long light waves 58 Blue light, specific effect 51 Blurring of the shadow in illumination 268 vision 54 Borides as refractory bodies 78 Bolometer measuring radiation power 166 Brightness of walls and ceiling in domestic lighting 270 Brilliancy and contraction of pupil 262 of light sources 256, 259 objectionable effect 263 of radiator 189, 221 Brush arc machine 163 Brush discharge 101 Bunsen photometer 170 Burns by radiation 48 Calcium arc, orange yellow 123 carbide arc 124 Calculation of room illumination 247 street illumination f 238 Candle 128 power 186 equivalent 258 standard of light 177 unit of light intensity < 257 Carbides as refractory bodies 78 Carbon, allotropic modifications 81 arc 140 distribution . . 203 efficiency 122 electrode as radiator 190, 193 INDEX. 291 PAGE Carbon, arc, incomplete rectification 117 lamp as incandescent radiator 76 not a typical arc 109 in street illumination 236, 240 bisulphide lamp 135 filament as radiator 195 as refractory element 77 vapor tension 79 Cathode of arc 108 Ceiling, albedo 246 Change carbons 82 Characteristics of the arc 137 Chemical action of light 63 on plants 64 luminescence 97 of flame 133 phosphorescence 95 rays 63 Chimney of luminous arc lamp 158 Chlorophyl 64 Circular cylinder as radiator 197 line as radiator 197 plane as radiator 190 shading circular radiator 203 shading linear radiator 210 radiator shaded by circular plane 203 Circulating flame lamp 126 Clutch of arc lamp 153 Cold light , 48 Color change of light of arc 118 differences in illumination 265 photometry 172 Colored 33 body 29, 31, 36 lights, comparison 42 radiation 85 radiator of magnesium flame 134 Color effect in illuminating engineering 269 street lighting 272 Colorless 32 body 29, 31, 36 Color of light and economy 269 fatigue 265 Combination of light fluxes by addition 285 Comfort and economy in domestic lighting 270 Comparison of arcs for street lighting 236 colored light 42 292 INDEX. PAGE Comparison of globes regarding light flux distribution 224 illumination curves 232 radiators 202 and shadows 209 reflectors 215 Concentrated illumination 260 or local illumination 269 Conduction, continuous 98, 105 disruptive 98 Constant current system of arc lighting 162 Constructive action of plant 65 Continuous conduction 98, 105 spectrum 26 Continuity of the arc at the cathode Ill Contraction of pupil 38, 262 Control of subjective color in illumination 265 Core of arc flame 1 10 Corona 101 Crater of the arc as radiator 191 Crookes' radiometer 10 Cylindrical radiator 195 Daylight illumination, domestic lighting 271 Defects of street lighting 273 Density of light flux 256, 259 Destructive effect of radiation 48, 57, 59 short ultra-violet light 52 Dielectric constant and refractive index 24 Differences of color in illumination 265 intensity in illumination 265 Differential arc lamp 156 Diffracting globe and light flux distribution 223 Diffraction grating 26 and light distribution 221 spectroscope 26 Diffused and directed light 267, 269 illumination 251, 266 in indoor lighting 246 light, definition 279 and directed light, proportions 278 shadow 280 Diffusing globe and light flux distribution 223 Diffusion, equivalent 281 and light distribution 221 by number of radiators 281 by size of radiator 280 Directed and diffused light , 267, 269 INDEX. 293 PAGE Directed light 266 angle of direction 278 Direct and indirect illumination 269 Discontinuity of the arc at the anode 112 Disease germs, action of light 61 Disinfecting action of light 60 Disruptive conduction 98 voltage 99 and gas pressure 100 Distinction between arc and Geissler discharge 106 of objects by shadow 267 Distributed and massed illumination 269 Distribution curve and design of incandescent lamp 243 of frosted globe 221 of light 180, 187, 256 of opal globe 221 in street lighting 272 Domestic lighting 226, 270 Double refraction 9 Downward candle power 184 Ear as analytic organ 21 Economies of flame arc lamp 212 Efficiency and arc length 146 of illuminant 186 light production by arc 118, 122 light production by incandescence. 74, 81 room illumination 253 Electric waves, engineering importance 18 frequency 15 Electro-conduction feeding arc 123 Electro-luminescence, efficiency 126 of gases and vapors 98 solids 95 Ellipse, circumference 198 Emulsions as translucent bodies 32 Enclosed arc efficiency 148 carbon arc 160 in street lighting 236 Energy of plant life derived from radiation 65 Engineering physiology 288 Equatorial distribution of light 181 Equiluminous curves 251 Equivalent candle power 258 diffusion 281 Etched glass globe, diffraction 221 Ether. . 7 294 INDEX. PAGE Ether as carrier of energy 7 form of matter 7 Euler's theory of radiation 4 Evaporation of carbon 79 Exposition lighting 275 Eye perceiving only the resultant 21 structure of 37 Fatigue and color of light 265 of the eye 263 optic nerve 38 Fechner's law 39 Feeding device of arc lamp 151 Filament, single loop, distribution curve 199 Fire-fly, light of 96 Fireworks 98 Fixed arc length of luminous arc 158 Flame arc distribution 212 Flame carbon arc 123, 160 distribution 212 Flames as illuminants 128 Flicker photometer 173 Flickering of the arc 110 Floating system of arc control 156 Fluorescence 66, 94 spectrum 27, 69 Fluorescent bodies . 30 Flux of light 256, 259 Frequency converter of radiation 13, 31 of radiation 7 and temperature 73 scale of acoustic 14 of ultra-violet radiation 14 Frosted globe 262 diffraction 221 Gas flame 128 pressure and disruptive voltage 100 Gasolene deposited carbon 81 flame. 128 Geissler discharge 98 tube efficiency > 104 glow 100 lighting 104 General illumination 260 or uniform illumination 269 German candle. . , 178 INDEX. 295 PAGE Germicidal action of light 60 Glass, opaque for ultra-violet light 13 as protection against ultra-violet light 55 Globes, comparison of light distribution 224 Glow of Geissler tube 100 Grey body 30 radiation 84, 93 Gypsum, transparent for ultra-violet light 13 Harmful effect of light on vegetation 56 radiation 48 violet and ultra-violet 52 Harmless radiation 48 Harmlessness of artificial illuminants 56 Harmonics of radiation 20 Heat evaporation feeding arc 123 Heat evaporation from positive terminal of arc 109 luminescence 91, 93, 96 at positive terminal of arc 109 radiation 1 rays 63 Hefner lamp 178 Helium 78 Hemispherical candle power 185 Hertzian waves, frequency and wave length 16, 17 High frequency currents, frequency and wave length 17 light, therapeutic action 61 Hollow circular surface as radiator 191 Holophane globe 262 Horizontal candle power of incandescent lamp 258 illumination 226, 287 of room 253 intensity 184 of light 182 table illumination 253 Hydrocarbon flames 128 Hydro-oxygen flame 136 Iceland spar 9 Illuminant 256 Illuminating engineering 256 Illumination ; . . 177, 179, 256, 259 Illumination curves 226, 229 of arcs for street lighting 236 comparison 232 of incandescent lamp 244 of table by incandescent lamps 254 296 INDEX. PAGE Illumination, horizontal 226 objective 261 problems 260 of streets by arcs 234 subjective 262 of table by incandescent lamp 253 total 226 uniform 226 vertical 227 Illuminometer in indoor illumination 253 Imperfectly transparent bodies 31 Incandescent lamp , 76 design and distribution curve 243 illumination 242 photometry 182 Indirect and direct illumination 269 lighting 262 Indoor illumination, calculation 247 by incandescent lamps 242 Inflammation of the eye by ultra-violet light 53 radiation 48 Infra-red rays 12 Integrating photometry 183 sphere and photometry 184 Intensity curves of arcs for street lighting 256 comparison 232 comparison of radiators 197 differences in illumination 265 of light 257 of light source 256, 259 Interference - 6 rings 6 Intermediary color in photometry 172 Intermediate carbon 83 International candle 178 Intrinsic brilliancy, see Brilliancy. Iridescence 6 Iron arc 119 giving ultra-violet light 13 Irregular reflection 28 and light distribution 212 Irritation by uniform intensity of illumination 264 Kerosene lamp 128 Kirchhoff's law of radiation 85 Lamps, arc 151 Light flux 177, 186, 256, 259 INDEX. 297 PAGE Light flux, combination by addition 285 comparison of radiators 197 density 177, 256, 259 distribution by frosted globe 223 distribution by opal globe 223 as germicide 60 intensity 177, 186 measurement 166 Lightning phenomena frequency and wave length 17 Light not a vector quantity 284 as physiological effect 168 production by incandescence 74 also see Radiation. sources, comparison 202, 209, 215 and enclosing globe, comparison 224 intensity 256, 259 as transversal vibration 8 Lighting, tower 274 Light unit 177 as wave motion 6 Lime light 136 Limits of electrical waves, frequency and wave length 17 frequency of electric waves 16 Linear radiator shaded by circular flame 210 Line spectrum 26 of arc 118 Local or concentrated illumination 269 illumination ! 226, 260 and uniform illumination ' 264 Logarithmic scale of frequency 14 law of sensation 38 Long burning carbon arc 160 Longitudinal vibration 7 Lumen 186 as unit of light flux 257 Luminescence 94 of arc 117 chemical 97 of flame 133 by heat 91 Luminometer 43, 174 chart 175 Luminous arc 123, 160 distribution 210, 215, 220 efficiency 149 lamp 157 radiator.. 195 298 INDEX. PAGE Luminous arc in street illumination ". 240 flame 129 Magnesium flame 134 Magnetite arc 123 constants 140 distribution 220 in street lighting 236, 240 Magnetite arc as typical arc 109 Massed and distributed illumination 269 Maximum candle power 184 visibility 46 Mean spherical intensity 180, 184, 257 Measurement of light and radiation 166 Mechanical equivalent of light 42 Mechanism of arc lamp 152 Melting points of elements 77 Mercury arc, constants 140, 145 greenish blue 123 higher frequency of ultra-violet light 13 rectification 117 rectifier 114 rectifier system 165 tube as radiator 195 Meridian curve of light 180, 188 Metal arcs and ultra-violet light 56 unsteadiness 125 Metallic carbon 81 Metals as most opaque bodies 31 Methane 128 Mica opaque for ultra-violet light 13 Micron 7 Micro-organisms, effect of light 61 Milk glass globe diffusion 221 Minimum visible amount of light 45 Mirror 28 reflector and light distribution 215 Misleading character of meridian curves of light 188 polar curves of light 187 Modifications of carbons 81 Negative carbon electrode shadow 203 spot of arc 107, 110, 125 terminal, also see Cathode. determining character of arc 108 Newton's theory of radiation 4 Normal temperature radiation 75, 84 INDEX. 299 PAGE Objects, effect on light distribution 283 Objective or actual color. 33 color in illumination 265 illumination 261 Observer, effect on light distribution 283 Octave as frequency scale 14 Oil lamp 128 Opal globe 262 diffusion 221 and nature of shadow 268 Opaque 32 body 31 colors 32, 36 Open arcs, efficiency 148 Open carbon arc 160 Oscillations, electrical, frequency and wave length 17 Osmium lamp 79 Overlap of light fluxes in illumination 267 Oxygen in flame 132 Ozone production by ultra-violet light 64 Paraffine candle 131 photometer 171 Parallelogram law and light flux 284 Pathogenic bacilli, effect of light 61 Pathological effects of radiation 57 Pentane lamp 178 Periodic system of elements and radiation efficiency 77 Permeability and refractive index 24 Personal equation of user in illuminating engineering 287 Physical phosphorescence 95 Physiological effect of sensation 40 in light measurement 167 measure of light 168, 186 problems of illumination 262 illuminating engineering 277 unit of light 177 Phosphorescence 66, 94 Photography 63 Photometry 169 Phototheraphy 61 Pigment in acclimatization 59 Plane illumination 286 as radiator 190 Plants, action of light 64 Point as radiator 189 Polar curves of light distribution > 187 300 INDEX. PAGE Polarized wave 8 Positive terminal of arc 109 also see Anode. Power burn 53 effect of radiation 57 Primary standard color 179 standards of light 177 Prismatic reflection and refraction 221, 224 Problems of illumination 260 Protection against ultra-violet light 55 Protective device of arc lamp 151 mechanism of the eye against radiation 50 Protoplasm, effect of radiation 57 Pulsations of arc voltage 159 Pupil contraction 262 Putrefactive bacilli, effect of light 60 Pyro-luminescence 96 Pyrometers, visual 90 Quality or color of light 269 Quartz as most transparent body 31 transparent for ultra-violet light 13 Radiant heat 1 Radiation efficiency , 86 as a form of energy 1 measurement 166 measured as power 166 power 72 also see Light. Radiators, comparison 202, 209 of light 187 separate from flame 135 Radio-active substances 14 Radio-fluorescence 95 Radio-luminescence 95 Radio-phosphorescence 95 Radio-therapy 61 Radium rays, harmful effects of 58 Range of frequencies of radiation 17 Reading distances measuring light 174 Rectification by arcs 114 Rectifying range of arc voltage 116 Red fluorescence 67 light, chemical action of 64 therapeutic effect 62 lines of mercury arc spectrum 120 INDEX. 301 Red mercury arc 121 Reduction factor of incandescent lamp 182 Reflected light from walls and ceiling, calculation 250 Reflection affecting light distribution 212 of light by body 28 regular, and light distribution 215 and shadow with radiator 219 Reflectors, comparison 215 as secondary radiators 212 as virtual radiators 215 Refraction law 23 and light distribution 221 spectroscope 25 Refractive index 23 and dielectric constant 24 and permeability 24 Regenerative flame lamp 126 Regular reflection 28, 215 and refraction 224 Regulator of arc machine 164 Reversed spectrum 27 Ring carbon 82 Room illumination, calculation 247 by incandescent lamp 242 Rounded circular surface as radiator 193 Sand blasted globe, diffraction 221 Saprophytic bacilli, effect of light 60 Searchlight beam, intensity 234 Secondary radiator and reflector 212, 216 Selective radiation 87 Sensitivity curve of the eye 43, 47 Sensitivity of the eye 263 and frequency 40 to ultra-violet light 54 maximum, of the eye : 46 Separate radiator of flame 135 Series arc lamp 157 system of arc lighting 162 Shadow 202 blurring of, in illumination 268 of diffused light 280 in illuminating engineering 266 of negative carbon 203 of negative terminal of arc * 148 number of 268 proper intensity in illumination 266 302 INDEX. PAGE Shadow photometer 171 in street lighting, defective 273 theory of 269 Shell of arc flame 110 Short burning carbon arc 160 Short ultra-violet light, destructive effect. 52 Spherical intensity 257 Signal lights, color 98 Silicides as refractory bodies 78 Single loop filament, distribution curve 199 Smokiness of flame 130 Smoky flame 129 Sound as longitudinal vibration 8 waves, frequency and wave length 17 Spark voltage 100 Specific effects of high frequency radiation 51 Spectrum of arc 118 and negative terminal 108 by diffraction 26 of flames 134 of luminescence 96 of radiation 17 by refraction 25 Sphere, illumination 287 as radiator , 189 Spherical intensity 180 reduction factor of incandescent lamp 182 Stability curve of the arc 142, 144 limit of arc 143 Stable branch of arc characteristic 142 Standard candle 170 Starting of arc 106 by auxiliary arc 112 device of arc lamp 151 Steadying device of arc lamp 151 reactance or resistance of arc lamp 151 Stephan's law 70, 75 Stimulating effect of radiation 57, 59 Straight line as radiator 195 Street illmination by arcs 234 comparison of arc lamps 240 Street lighting 226, 272 calculation 238 comparison of illuminants 236 defects 273 Striated Geissler discharge 101 Subjective or apparent color 34 INDEX. 303 PAGE Subjective color, control in illumination 265 illumination 262 Sulphur flame 135 Sunburn 59 Sun spectrum 27 Surges, electrical, frequency and wave length 17 Symptoms of ultra-violet burns 54 Synthetic action of plants 65 Table illumination 253 Tanning 59 Tantalum lamp 80 Temperature of arc stream 108 of carbon filament 79 and frequency of radiation 73 of maximum efficiency of light production 74 measurement by radiation law 89 radiation 70 of flame 128 law of 84 standard 178 Therapeutic use of light 61 effects of radiation 57 Thermo-couple measuring radiation power 166 Thermo-luminescence 95 Threshold value of visibility 45 Titanides as refractory bodies 78 Titanium arc, white 123 carbide arcs 117, 123 Total illumination 226, 287 of room 253 Tower lighting 274 Transfer of arc between anodes 112 Transient electric phenomena 18 Translucent body 31 Transmission of light by body 28 Transparent 32 body 31 color 31, 32, 36 Transversal vibration 7 Tungsten lamp 80 as refractory element 78 Also see Wolfram. Typical arc 109 Ultra-red rays 12 frequency and wave length 14, 17 304 INDEX. PAGE Ultra-violet arc lamp 12 burn 53 burn in wireless telegraphy 54 iron arc 119 lamp 135 light of arc 55 light and fluorescence 67 light harmful effect 62 therapeutic action 61 radiation, frequency 14 rays 12 frequency and wave length 17 Unidirectional conduction of electric arc 113 Uniform distribution illumination curve 229 or general illumination 269 illumination 226, 260 in street lighting 235 Uniformity in street lighting 272 Uniform and local illumination 264 total illumination 228 Unit of light 177 Unstable branch of arc characteristic 142 Unsteadiness of metal arcs 125 Vacuum arc 145 Vapor pressure of the arc 105 stream of the arc 105 tension of carbon 79 Vector quantities and light * 284 Velocity of electrical radiation 4 light 2 in a medium 23 Vertical illumination 227 Violet light, harmful effect 52 specific effect 52 Violie standard of light , 177 Virtual radiator 221 and reflector 216 Visible light, frequency and wave length 17 radiation 10 power measurement 168 range 14 and temperature 74 Visibility range of radiation 37 Visual pyrometers 90 Walls, albedo 246 Warm light 48 INDEX. 305 PAGE Waste of light flux by absorption 261 Water as transparent body 31 Wave length determination 6 of visible radiation 10 Welsbach mantle 92, 136 White 32 body 29 iron arc 119 Whiteness or albedo 30 Willemite fluorescence 13 Wireless telegraph waves, frequency and wave length 15, 17 ultra-violet burn 54 Wolfram as refractory element 77 also see Tungsten. X-ray frequency and wave length 14, 17 harmful effects of 58 specific action 56 Zinc arc, constants 140 rectification 117 THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. DAVIS \RY LOAN UG 27 USE OCT2M9S7 REC'D LD OCT231957 LD 21-50m-l,'33 725190 UNIVERSITY OF CALIFORNIA LIBRARY *